LIFE HISTORY ASPECTS and POPULATION DYNAMICS of a COMMERCIALLY EXPLOITED STINGRAY, Dasyatis Dipterura

LIFE HISTORY ASPECTS AND POPULATION DYNAMICS OF A COMMERCIALLY EXPLOITED STINGRAY, Dasyatis dipterura

A thesis submitted to the faculty of Moss Landing Marine Laboratories and San Francisco State University In partial fulfillment of The requirements for The degree

Master of Science In Marine Science

by

Wade Daniel Smith

San Francisco, California

May, 2005 Copyright by Wade Daniel Smith 2005 LIFE HISTORY ASPECTS AND POPULATION DYNAMICS OF A COMMERCIALLY EXPLOITED STINGRAY, Dasyatis dipterura

Wade Daniel Smith San Francisco State University 2005

The diamond stingray, Dasyatis dipterura (Jordan and Gilbert, 1880) inhabits shallow coastal waters from southern California to Chile, including the Galapagos and

Hawaiian Islands. The directed batoid fishery at Puerto Viejo in the Bahia Magdalena

Bay lagoon complex, Baja California Sur, Mexico was surveyed during the course of this study to assess species- and sex-specific catch composition during peak summer landings

(June, August). Rhinobatos pro ductus, D. dipterura, Narcine entemedor, and Gynmura marmorata were the four most commonly landed rays. Median disc width (DW) at maturity was determined to be 57.3 em for females and 46.5 em for males, respectively.

Growth characteristics were estimated by a detailed examination of banding patterns present in thin-sectioned vertebral centra. Age estimates were obtained from 304 fishery- derived specimens (169 female, 135 male). An annual nature of band deposition was confirmed through centrum edge and marginal increment analyses. Gompertz and von

Bertalanffy growth models were fit to the age-at-DW/weight data. Growth characteristics differed significantly between females and males. The maximum estimated age was 28 years for females and 16.5 years for males. Traditional three parameter von Bertalanffy growth models indicated relatively low growth rates: females (DWco = 92.4 em, k =

0.055, t0 = -7.61); males (DWco = 62.2 em, k= 0.10, t0 = -6.80). Demographic analyses were developed from the resulting maturity, longevity, and growth information to estimate population growth characteristics and potential responses to fishing pressure.

Monte Carlo simulation was incorporated to introduce demographic variability and uncertainty in age at maturity, fecundity, survivorship, and longevity. Ten models were developed from deterministic (4) and probabilistic (6) approaches based on maximum observed age (28 years), theoretical maximum age (63 years), and variable longevity (25-

39 years) under unexploited and exploited (F=0.05) conditions. Elasticity analyses detennined the relative contribution and impact of changes in fertility, juvenile, and adult survival to population growth rates (/c). Annual survivorship probabilities ranged between 0.71-0.94. Projections generated through the incorporation ofMonte Carlo simulations produced mean A. of 1.05-1.06 (5-6% increase) per year, net reproductive

rates per generation (R 0 ) of2.4-3.0, and generation times (A) from 14.4-15.2 years.

Introducing relatively low fishing mortality into population models produced a maximum

A. value under an optimal, static scenario of 1.09 and a minimum value of 1.01 annually using probabilistic models. Deterministic and probabilistic demographic analyses indicate that the Bahia Magdalena lagoon complex population of D. dipterura has a low intrinsic growth potential and possesses a limited resilience to fishing pressure.

I certify that the Abstract is a correct representation of the content of this thesis. " '

I Date ACKNOWLEDGMENTS

This study was made possible, in part, by funding provided from the General

Service Foundation, Homeland Foundation, Earl H. and Ethel M. Myers Oceanographic and Mruine Biological Trust, National Marine Fisheries Service via the National Shark

Research Consortium m1d Pacific Shark Research Center, P ADI Foundation, P ADI

Project AWARE, SFSU Student Project Fund, and the Packard Foundation Scholarship.

Additional support was received through the Sally Casanova Pre-Doctoral Program,

Martha Jolmston Memorial Scholarship, and the Kim Peppard Memmial Scholarship.

This study was conducted in accordance with and under the approval of the SFSU

Committee for the Protection ofHuman and Animal Subjects Protocol #01-038. Joe

Bizzano offered umnatched, unwavering support under demanding conditions in Baja.

His assistance through tropical stonns, car accidents, scorpion stings, food poisoning, blazing heat, ru1d countless sampling complications made this study possible to a large extent. I am deeply grateful for his professionalism and friendship. I sincerely thank my committee members for their help with this process; Dr. Gregor Cailliet, my friend and advisor, for his guidance and support throughout my extended and often complicated time at MLML, Dr. Ralph Larson for his editing and helpful comments, and Dr. Enric

Cmies for his invaluable technical input on demographic analyses. I hold enom1ous gratitude for Dr. Cailliet, who lent me his personal vehicle for use in the rather extreme conditions of Baja. Further orientation and field assistance was provided by Carolina

Downton-Hoffinan. Carlos Villavicencio-Garayzar and Everardo Mariano-Melendez

VI offered archived vertebral samples for use in the study. Jason Cope challenged me with many topics of inquiry and freely lent both quantitative and creative ideas throughout the course ofthis research. Mindy Hall proved to be an excellent intern. Dr. Dave Ebe1i ensured that there was considerable flexibility with my work schedule at the Pacific

Shark Research Center which allowed me the time to focus and make substantial progress over the past year in particular. With much appreciation, I acknowledge Aldo DeRose,

Joan Parker and the library staff, Dr. Keru1eth Coale, and Dmma Kline for their assistance, patience, and reliability. My father, Gary Smith, encouraged exploration and fostered within me a sense of wonder for the natural enviromnent from an early age. For that spark and his support, I will always be fmiunate and thankful. I also thank the rest of my family, Rosemary Smith (mother), Rose Murphy (sister), Sara Smith (sister), Helen

Sterba (grandmother), and June Bosarge (grandmother), for their encouragement, interest, and love. Debbie Feichtinger offered immeasurable support prior to and during my lengthy graduate career at MLML. My rock climbing, bad movie-watching, soccer and foosball playing companions and colleagues (Rhea Sanders, Jason Cope, Joe Bizzarro,

Andrew Thurber, Lisa KelT, Matt Levey, JeffField, Aaron Carlisle, Tonatiuh Trejo, Chris

Rinewalt, Dawn Taru1er, and John Haskins) worked hard to provide much needed distractions and balance in my life. The encouragement and fiiendship of many at Moss

Landing Marine Laboratories will always be remembered.

Vll TABLE OF CONTENTS

List ofTables ...... ·...... x

List of Figures ...... xiii

List of Appendices ...... xvii

GENERAL INTRODUCTION ...... 1 Literature cited ...... 8

CHAPTER 1 - Catch composition and the contribution of Dasyatis dipterura to an artisanal batoid fishery in the Bahia Magdalena lagoon complex, Baja California Sur, Mexico ...... 12 Introduction ...... 13 Study area ...... 16 Methods ...... 20 Results ...... 22 Discussion ...... 27 Literature cited ...... 3 7

CHAPTER 2 - Life history characte1istics of Dasyatis dipterura: Maturity, age, growth, and longevity ...... 53 Introduction ...... 54 Methods ...... 57 Field sampling...... 57 Matmity assessment...... 58 Age and Growth ...... 60 Results ...... 73 Maturity and reproductive observations ...... 73 Age, growth, and longevity...... 7 5 Discussion ...... 83

Vlll Maturity and reproduction...... 83 Age, growth, and longevity...... 93 Literature cited ...... 109

CHAPTER 3 -Population dynamics and potential responses to fisheries exploitation of Dasyatis dipterura in the Bahia Magdalena lagoon complex, B.C.S. Mexico ...... 143 Introduction ...... 144 Methods ...... 149 Demo graphic models ...... 149 Monte Carlo simulation ...... 156 Life history parameters ...... 157 Natural mortality scenarios ...... 161 Fishery exploitation scenarios ...... 162 Results ...... 164 Natural mortality and survivorship ...... 164 Demographic analysis ...... 165 Elasticity analysis...... 169 Fisheries impacts...... 170 Discussion ...... 172 Mortality and survivorship...... 172 Demo graphic analysis ...... 177 Elasticity analysis...... 182 Fisheries impacts and conservation implications ...... 184 Model limitations, potential improvements, conclusions ...... 187 Literature cited ...... 192

IX LIST OF TABLES

Table Page

CHAPTER 1

1. Elasmobranch landings recorded from Puerto Viejo during June 1998,

1999 and 2000 ...... 45

2. Elasmobranch landings recorded from Puerto Viejo during August 1998

and 1999 ...... 46

3. Total elasmobranch landings recorded from Puerto Viejo from June

1998-2000 and August 1998, 1999 ...... 47

CHAPTER2

1. Categories applied for assessing readability and clarity of vertebral

centra ...... 123

X CHAPTER 2 (continued)

2. Percent agreement (P A) between the final, consensus read and baud

count with the greatest assigned difference for each sample in relation to

size classes ...... 124

3. Summary of growth parameters and goodness-of-fit descriptors

estimated from size- and weight-based models of female and male

D. dipterura age data ...... 125

4. Longevity (co) estimates (years) for D. dipterura based on maximum

observed ages and three theoretical methods ...... 126

5. Comparison of maturity, age, and select growth (k, DWro) parameters

among myliobatifonn stingrays ...... 127

CHAPTER3

1. Natural mortality (M) estimates for Dasyatis dipterura based on eight

indirect methods using life history parameters or wet body weight...... 203

2. Intrinsic and finite population growth rates (r, lv), net reproductive

rate (Ra), population doubling time Ctx2), and rate of increase per

generation (rT) projected from deterministic and probabilistic life table

models for Dasyatis dipterura ...... 204

3. Estimates ofpopulation generation time ...... 205

XI CHAPTER 3 (continued)

4. Fertility, juvenile survivorship, and adult survivorship elasticities and

co1Tesponding elasticity ratios ...... 206

5. Estimates of longevity (m), fecundity (mx), annual population growth rates

(A.), net reproductive rates (Ra), and generation times (f-!1) of 16

elasmobranchs based on deterministic models using best-case or optimal

scenarios...... 207

6. Comparative elasmobranch demography based on probabilistic models

incorporating uncertainty and variability in vital rates ...... 208

Xll LIST OF FIGURES

Figure Page

CHAPTER 1

1. Location (A) and prominent features (B) of the Bahia Magdalena

lagoon complex...... 48 2. Size frequency distribution of female and male Dasyatis dipterura ...... 49

3. Linear relationship between body length and disc width for (A) female

and (B) male Dasyatis dipterura ...... 50

4. Power relationship of weight to disc width for (A) female and (B) male

Dasyatis dipterura ...... 51

5. Repmied batoid landings based on three general categories (A) and

monthly distribution of "Mantarraya" landings (B) from the Pacific

states of Mexico, 1997-2000 ...... 52

CHAPTER2

1. A representative sagittally thin-sectioned vertebral centrum as viewed

under transmitted light...... 128

Xlll CHAPTER 2 (continued)

2. Examples of centrum edge and marginal increment analysis

procedures ...... 129

3. Relationship between maturity status and disc width for female and

male D. dipterura ...... 130

4. Relationship of disc width to inner clasper length for D. dipterura ...... 131

5. Relationship between observed fecundity and maternal disc width (em)

in D. dipterura ...... 132

6. Size frequency histogram of D. dipterura from which vertebrae were

processed for ageing ...... 133

7. Relationship between mean centrum diameter and disc width for D.

dipterura...... · ...... 134

8. Bias plot for pairwise comparisons of final age estimates from centra

collected from anterior and posterior locations ...... 135

9. Individual Index of Relative Precision (D) values by sex and final

band count...... 136

10. Differences in sample band counts between each round ...... 137

XlV CHAPTER 2 (continued)

11. Monthly variation in centrum edge type and mean monthly marginal

increment ratios ...... 138

12. Mean monthly marginal increment ratios (MIR) by size class ...... 139

13. Two and three parameter von Bertalanffy growth functions fit to (A)

femaleand (B) maledisc width at age data...... 140

14. Gompertz growth models based on size (DW) fit separately to

female and male disc width at age data...... 141

15. Weight based growth models for D. dipterura ...... 142

CHAPTER3

1. Examples of probability density functions developed for (A) age 0

survivorship, (B) longevity, (C) age at 50% maturity, and (D) fecundity

for use in Monte Carlo simulations ...... 209

2. Hypothetical stable age distribution (ex) ofDasyatis dipterura ...... 210

XV CHAPTER 3 (continued)

3. Hypothetical stable age distribution (ex) of Da:syatis dipterura based

on (A) deterministic and (B) probabilistic models incorporating the

presence and absence of fishing mortality (F=0.05) ...... 211

4. Age-specific reproductive values (vx) generated from best-case

deterministic (D) and probabilistic (P) demographic models ...... 212

5. Influence of longevity and age at maturity on population mean

annual population growth rates (A} ...... 213

6. Fertility (age 0 survivorship), juvenile and adult survivorship elasticity

values summed across relevant age classes ...... 214

7. Influence of longevity and age at maturity on mean fertility, juvenile

survivorship, and adult survivorship elasticity values ...... 215

xvi LIST OF APPENDICES

Appendix Page

1. Sources and equations used to calculate the eight indirect

estimates of instantaneous natural mortality ...... 216

2. Minimum and maximum survivorship estimates incorporated into

probability distributions for natural and fishing mortality scenarios

based on the longevity (CD) of 28 years ...... 219

3. Minimum and maximum survivorship estimates incorporated into

probability distributions for natural and fishing mortality scenarios

based on the longevity (CD) of 63 years ...... 220

XVll General Introduction

1 2

Rays (Batoidea) are the most speciose elasmobranchs and include some of the most derived members of this group (Compagno, 1990). The stingrays

(Myliobatiformes) comprise one of the largest elasmobranch orders and include approximately 160 known species, accounting for about 36% of all batoids (Compagno,

1990, 1999). A highly efficient aplacental mode of viviparity has evolved among

Myliobatiformes and most biological studies of species within this order have examined aspects of development and reproduction (Wood-Mason and Alcock, 1891; Wourms,

1977; Hamlett et al., 1996). Embryonic Myliobatiformes are initially nourished via yolk sacs. However, as the yolk stores are depleted, long, flattened villous extensions, termed trophonemata, develop from the uterine lining (Wounns, 1977; Hamlett and Koob, 1999).

These specialized villi secrete a viscous protein/lipid-rich fluid (uterine milk or histotroph) that is ingested or absorbed by developing embryos. The efficiency of nutrient transfer in this mam1er is greater than that of the yolk sac placenta (Wounns,

1977; Hamlett et al., 1985). Comparatively little is known of the ecology and life history of Myliobatifonnes beyond their specialized reproductive biology despite the diversity and prevalence of this group.

The Dasyatidae is the largest of the nine families that compose the

Myliobatifonnes. Dasyatid stingrays are common benthic inhabitants of inshore tropical and subtropical waters but have also successfully expanded into continental slope (to at least 480 m), euryhaline, pelagic, and freshwater environments (Compagno, 1990; Last 3

and Compagno, 1999). The success of dasyatid stingrays in warm water marine environments is illustrated by Bigelow and Schroeder's (1953) description oftheir abundance: " .. .in suitable localities ... they occur in such great plenty that it may seem as though the bottom were paved with them".

Four dasyatid stingrays are reported from the eastern Pacific: Dasyatis dipterura,

D. longa, D. (Pteroplatytrygon) violacea, and Himantura pacifica, although the validity of this species has been questioned (Beebe and Teevan, 1941; Nishida and Nakaya, 1990;

McEachran and Notarbartolo-di-Sciara, 1995). Biological information on eastern Pacific dasyatids is extremely limited and primarily restricted to opp01iunistic fishery observations (Villavicencio-Garayzar et al., 1994; Acero and Frank, 1995; Villavicencio­

Garayzar, 1995) and details of exploratory fishery surveys (Beebe and Teevan, 1941;

Mathews and Druck-Gonzalez, 1975; Flores et al., 1995). Within the genus Dasyatis, the cosmopolitan pelagic species D. violacea is readily distinguished from D. dipterura and

D. longa, but, the latter two species are difficult to differentiate. Additionally, nomenclatural confusion sunounding the status of D. brevis versus D. dipterura has further inhibited species-specific identification among landings (Mathews and Druck­

Gonzalez, 1975; Flores et al., 1995) and occasionally led researchers to inconectly conclude that these are separate species.

Field guides and systematic studies of Pacific dasyatids have primarily followed the nomenclature of Garman (1913) (e.g.; Beebe and Tee-Van, 1941; Nishida and 4

Nakaya, 1990; Rosenberger, 2001 ). Confusion surrounding the appropriate designation

of D. dipterura has arisen because the species was described by different authors during

the same year. Jordan and Gilbert (1880) designated the stingray as Dasybatus

dipterurus based on four small specimens from San Diego Bay, California in a

publication that appeared in May of that year. Garman's (1880) description of the same

species collected from Payta, Peru was assigned as Trygon brevis in an October

publication. Jordan and Gilbert (1896) later corrected and modified the generic and

specific names as Dasyatis dipterura (Jordan and Evennann, 1896). Curiously, Gannan

(1913) miscited the year and volume of the Jordan and Gilbert publication and reported

his own record as having precedence. Whether Garman's synonymy was an oversight or

deliberate obfuscation, it is ironic because he was otherwise purportedly insistent in adopting the earliest available work for nomenclature and synonymy. Garman's (1913) tome, The Plagiostomia, became an invaluable, comprehensive reference and subsequent investigators adopted the erroneous assigmnent of D. brevis as valid, apparently without examining the original descriptions. Nishida and Nakaya (1990), for example, offer support to Garman's synonymy of D. dipterura with D. brevis and a second synonymization of the north central Pacific species D. hawaiensis (Jenkins, 1903) with

D. brevis. However, because the Califomian and Peruvian specimens do not appear to be different species and the Jordan and Gilbert (1880) record was published first, D. brevis

(Garman, 1880) should be regarded as a junior synonym of D. dipterura. Additionally, if 5

a valid synonymy, the stingray originally described as D. hawaiensis should be

synonymized with D. dipterura as well.

Although it is possible for benthic nearshore marine species to cross a

biogeographic impediment such as the East Pacific BatTier and colonize the north central

Pacific, it is uncommon for organisms, including elasmobranchs, to do so (Briggs, 1961;

Lessios et al., 1998). The range expansion of D. dipterura into the Hawaiian archipelago, if valid, is noteworthy and may indicate the potential for extensive movements and utilization of the water column by this species. Improved species descriptions and fmiher clarification of the taxonomic validity and systematics of Pacific dasyatids are necessary.

It is highly probable that undescribed and mis-attributed stingray species occur in the central and eastern Pacific.

Dasyatis dipterura is abundant in the shallow, inshore waters of western Mexico.

In the Gulf of California, it was found to be the second most abundant benthic species

(26% of total catch weight) taken in exploratory trawl surveys (Flores et al., 1995).

Similar surveys conducted in the Bahia Magdalena lagoon complex also indicate relatively high densities of D. dipterura and revealed distinct seasonal changes in species abundance (Mathews and Druck-Gonzalez, 1975). Dasyatis dipterura has recently been identified as a primary component of artisanal elasmobranch fisheries in the Gulf of

Califomia (Ocampo-Torres, 2001; Marquez-Farias, 2002) and Bahia Magdalena lagoon complex (Villavicencio-Garayzar, 1995). Despite its abundance, nearshore accessibility, 6

and potential for contribution to local fisheries, biological infom1ation on D. dipterura in

Mexico and throughout its range remains scarce.

Elasmobranchs typically exhibit life history characteristics that include relatively

slow growth, late age of maturity, low birth rates, long gestation periods, and decreased

natural mmiality rates over their relatively long life spans (Holden, 1974; Hoenig and

Gruber, 1990; Musick, 1999). These life history strategies have resulted in highly

successful competitive advantages and an evolutionary flexibility but conversely render

the group especially vulnerable to fisheries exploitation (Holden, 1974; Pratt and Casey,

1990; Stevens et al., 2000). If D. dipterura also exhibits the long life span, slow growth, and late age of maturity associated with many other elasmobranchs, depletion or collapse of targeted populations is possible. An improved understanding of the biology and population dynamics of D. dipterura is crucial for fonnulating effective, sustainable management strategies for the population.

The primary objectives of this thesis research were to: assess the contribution of

D. dipterura to the artisanal batoid fishery at Puerto Viejo, Baja California Sur, Mexico; determine fundamental life history aspects (including maturity, fecundity, growth, and longevity) of D. dipterura from the Bahia Magdalena lagoon complex; describe population growth characteristics based on these newly established biological parameters; and assess the impact and population responses of simulated increases in mmiality due to fisheries exploitation. Results are presented in three separate chapters that correspond to 7

fisheries and morphometric relationships, life history characteristics, and population dynamics. This thesis provides the first record of growth, longevity, natural mortality rates, and demographic parameters of the widely distributed, commercially impmiant stingray, D. dipterura. 8

Literature Cited

Acero, A.P. and Franke, R. 1995. Nuevas registros de peces cartilaginosos del Parque Nacional Natural Gorgona (Pacifico Colombiano), II. Rayas y descripcion de una nueva especie. Biblioteca Jose Jeronimo Triana 11: 9-21.

Beebe, W. and Tee-Van, J. 1941. Fishes of the tropical eastem Pacific. [From Cedros Island, Lower Califomia, South to the Galapagos Islands and northem Peru]. Part 3. Rays, mantas, and chimaeras. Zoologica 26(3): 245-280.

Bigelow, H.B. and Schroeder, W.C. 1953. Fishes of the Westem North Atlantic. Sawfishes, guitarfishes, skates, rays, and chimaera ids. No. 1, Part 2. Memoir of the Sears Foundation for Marine Research, Yale University Press. 588 pp.

Briggs, J.C. 1961. The East Pacific Barrier and the distribution of marine shore fishes. Evolution 15: 545-554.

Campagna, L.J. V. 1990. Altemative life-history styles of cartilaginous fishes in time and space. Environmental Biology of Fishes 28: 33-75.

Campagna, L.J.V. 1999. Checklist ofliving elasmobranchs. In Sharks, Skates, and Rays: The Biology ofElasmobranch Fishes (W.C. Hamlett, ed.), p. 471-498. Jolms Hopkins University Press, Baltimore, MD.

Flores, J.O., Rodriguez, M., Shimizu, M., and Machii, T. 1995. Evaluation of demersal fishery resources of the Gulf of Califomia using Mexican shrimp trawlers. Joumal ofthe National Fisheries University 44 (1): 9-19.

Gannan, S. 1880. New species ofselachians in the museum collection. Bulletin ofthe Museum of Comparative Zoology at Harvard College 6(11): 167-172.

Garman, S. 1913. The Plagiostoma (Sharks, Skates and Rays). Memoirs of the Museum ofComparitive Zoology. Harvard Collection, Volume 36. Cambridge, MA. 515 p., pls. 1-75.

Hamlett, W.C. and Koob, T.J. 1999. Female reproductive system. In Sharks, Skates, and Rays: The Biology ofElasmobranch Fishes (W.C. Hamlett, ed.), p. 398-443. Johns Hopkins University Press, Baltimore, MD. 9

Hamlett, W.C., Musick, J.A., Eulitt, A.M., Jarrell, R.L., and Kelly, M.A. 1996. Ultrastructure of uterine trophonemata, accommodation for utero lactation, and gas exchange in the southem stingray, Dasyatis americana. Canadian Joumal of Zoology 74: 1417-1430.

Hamlett, W.C., Wounns, J.P., and Smith, J.W. 1985. Stingray placental analogues: structure oftrophonemata in Rhinoptera bonasus. Joumal of Submicroscopic Cytology 17: 541-550.

Hoenig, J.M. and Gruber, S.H. 1990. Life-history pattems in the elasmobranchs: implications for fisheries management. NOAA Teclmical Report NMFS 90: 828- 903.

Holden, M.J. 1974. Problems in the rational exploitation of elasmobranch populations and some suggested solutions. In Sea Fisheries Research (J.A. Gulland, ed.), p. 117-138. Elek Scientific, London, England.

Jenkins, O.P. 1903. Report on collections of fishes made in the Hawaiian Islands, with descriptions of new species. Bulletin ofthe U.S. Fish and Wildlife Commission 22:417-511, pls. 1-4.

Jordan, D.S. and Gilbe1i, C.H. 1880. Notes on a collection of fishes from San Diego, Califomia. Proceedings ofthe United States National Museum 3(106): 23-34.

Jordan, D.S. and Evennmm, B.W. 1896. The Fishes ofNorth and Middle America. Pati 1. Bulletin of the National Museum 47. 953 p.

Last, P.R. and Campagna, L.J.V. 1999. Dasyatidae. In The Living Marine Resources of the Westem Central Pacific, Volume 3 (K.E. Carpenter and V.H. Niem, eds.), p. 1479-1480. Food and Agriculture Organization ofthe United Nations, Rome, Italy.

Lessios, H.A., Kessing, B.D., and Robe1ison, D.R. 1998. Massive gene flow across the world's most potent marine biogeographic barrier. Proceedings of the Royal Society of London B 265: 583-588.

Marquez-Farias, F.J. 2002. The artisanal ray fishery in the Gulf of Califomia: development, fisheries research, and management issues. IUCN/SSC Shark Specialist Group. Shark News 14: 1-5. 10

Mathews, C.P. and Druck-Gonzalez, J. 1975. Potencial pesquero y estudios de Bahia Magdalena III. Las existencias de rayas con especial interes a las ya aprovechadas. Ciencias Marinas 2(1): 67-72.

McEachran, J.D. and Notarbartolo-di-Sciara, G. 1995. Peces Batoideos. In Guia FAO para la identificacion de especies para los fines de la pesca centro oriental. Volumen II. Vertebrados- Parte 1 (W. Fischer, F. Krupp, W. Schneider, C. Sommer, K.E. Carpenter and V.H. Niem, eds.), p. 745-792. Food and Agriculture Organization, Rome, Italy.

Musick, J.A. 1999. Ecology and conservation of long-lived marine animals. In Life in the slow lane: ecology and conservation oflong-lived marine animals, (J. Musick, ed.), p. 1-10. American Fisheries Society Symposium 23, Bethesda, Marlyand.

Nishida, K. and Nakaya, K. 1990. Taxonomy ofthe genus Dasyatis (Elasmobranchii, Dasyatididae) from the north Pacific. NOAA Technical Report NMFS 90: 327- 346.

Ocampo-Torres, A. I. 2001. Descripci6n y amilisis de la pesca artisanal de elasmobranquios de Sinaloa, Mexico. M.S. thesis, Centro de Investigacion Cientifica y de Educaci6n Superior de Ensenada, B.C., Mexico. 117 p.

Pratt, H.L., Jr. and Casey, J.G. 1990. Shark reproductive strategies as a limiting factor in directed fisheries, with a review of Holden's method of estimating growth parameters. In Elasmobranchs as Living Resources: Advances in the Biology, Ecology, Systematics, and the Status ofthe Fisheries (H.L. Pratt, S.H. Gruber, and T. Taniuchi, eds.), p. 97-109. NOAA Technical Report NMFS 90.

Rosenberger, L.J. 2001. Phylogenetic relationships within the stingray genus Dasyatis (Chondrichthyes: Dasyatidae). Copeia 2001(3): 615-627.

Stevens, J.D., Bonfil, R., Dulvy, N.K., and Walker, P.A. 2000. The effects of fishing on sharks, rays, and chimaeras (chondrichthyans), and the implications for marine ecosystems. ICES Journal ofMarine Science 57: 476-494.

Villavicencio-Garayzar, C.J. 1995. Distribuci6n temporal y condici6n reproductive de las rayas (Pisces: Batoidei), capturadas commercialmente en Bahia Almejas, B.C.S., Mexico. Revista de Investigaci6n Cientifica 6(1-2): 1-12. 11

Villavicencio-Garayzar, C.J., Downton-Hoffmann, C.C., and Mariano-Melendez, E. 1994. Tamafio y reproducci6n de Dasyatis longus (Pisces: Dasyatidae ), en Bahia Almejas, Baja California Sur, Mexico. Revista Biologia Tropical 42 (112): 375-377.

Wood-Mason, J. and Alcock, A. 1891. On the uterine villiform papillae of Pteroplatea micrura, and their relation to the embryo. Proceedings of the Royal Society of London 49: 359-367.

Wourms, J.P. 1977. Reproduction and development in chondrichthyan fishes. American Zoologist 17: 379-410. CHAPTER!

Catch composition and the contribution of Dasyatis dipterura to an artisanal batoid

fishery in the Bahia Magdalena lagoon complex, Baja California Sur, Mexico

12 13

Introduction

The utilization of marine resources has increased dramatically in recent years, tripling over the past four decades (Csirke, 1997; FAO, 2004). As a result, many traditional fish stocks have experienced worldwide declines, resulting in the establislm1ent of fisheries for previously unexploited species. Elasmobranch fisheries have typically been smaller and have provided more inconsistent yields than other fisheries, but are expanding in size and importance (Pratt and Casey, 1990; Csirke, 1997).

Currently, elasmobranch populations are experiencing their highest rate of reduction through fishing activities than any other time in history (Bonfil, 1994; V mmuccini, 1999).

Holden (1973, 1974) cautioned that this group offered limited opportunities for long-term exploitation and summarized the rapid rise and collapse of several historic shark fisheries. However, the vulnerability ofbatoids (i.e., skates and rays) to fishing pressure was not fully recognized until Brander (1981) documented the localized extirpation of a once common skate, Dipturus batis, as a result of bycatch overfishing. Slow growth, long life spans, late ages of maturity, low birth rates, and extended gestation periods are life history characteristics that are commonly exhibited among elasmobranchs. These attributes restrict fisheries productivity and population resilience (Holden, 197 4; Hoenig and Gruber, 1990; Stevens et al., 2000). Over-exploitation of elasmobranchs, therefore, often leads to severe and rapid depletion of these populations, endangering their resource and ecological value over broad regions. 14

Assessments and reviews of elasmobranch fisheries have focused almost exclusively on sharks (e.g., Pratt and Casey, 1990; Walker, 1998; Stevens et al., 2000).

However, batoids are more speciose (Compagno, 1999) and comprise a greater component of reported global elasmobranch landings than do sharks (Weber and

Fordham, 1997). Although recent publications have drawn increased attention to the contribution and sensitivity of batoids to both directed and bycatch fisheries, these studies and reviews have primarily related to skate populations from northern latitudes (Casey and Myers, 1998; Walker and Hislop, 1998; Dulvy et al., 2000). The contribution of other batoids (e.g., Dasyatidae, Gymnuridae, Myliobatidae, Rhinobatidae, Rhinopteridae) to global fisheries is poorly documented and rarely discussed, despite their abundance within the near-shore tropical and subtropical marine environments that support much of the world's elasmobranch fisheries.

Mexican elasmobranch fisheries rapidly expanded during the mid-1970's, yielding an estimated average of 30,000 tons annually through the late 1990's (Bonfil,

1994; Vannuccini, 1999). Catches have since declined, but Mexico's elasmobranch fishery remains impmiant and currently ranks as the second largest in the Americas (F.

Marquez-Farias, pers. comm.). Although the majority ofthe research on Mexcian fisheries has been conducted in the Caribbean and Gulf of Mexico the majority of shark and ray landings are believed to be taken from Mexico's Pacific coast (Applegate, 1993;

Bonfil, 1994). Small-scale, coastal m1isanal fisheries account for approximately 80% of the nation's elasmobranch landings (Castillo-Geniz et al., 1998). Concem over increased 15

shark and ray catches prompted a moratorium on the issuance of elasmobranch fishing

permits in 1993, but no other regulations have been implemented.

Previous reviews of Mexican elasmobranch fisheries reported that large sharks

dominated catches in Mexican waters from 1977-1991 while rays represented only 4.2%

of the total tonnage landed (Applegate et al., 1993; Bonfil, 1994). However, preliminary

results of an international, collaborative two year survey of artisanal elasmobranch

fisheries of the Gulf of California do not support this trend. Batoids, notably Dasyatidae,

Gymnuridae, Mobulidae, Narcinidae, Rhinobatidae, and Rhinopteridae, were found to numerically dominate landings at many sites throughout the Gulf of California (Marquez­

Farias, 2002). This apparent contradiction suggests that the available catch records were biased against batoids, that a significant expansion of a directed fishery for rays has occurred, or that a combination of the two is responsible for the difference.

The Bahia Magdalena lagoon complex supports an important elasmobranch fishery on the Pacific coast ofMexico (Ramirez-Rodriguez, 1987). On the basis of exploratory trawl surveys fisheries for batoids were encouraged in this region (Mathews and Druck-Gonzalez, 1975; Guardado-France, 1976). During the past two decades, multi-species batoid fisheries have expanded within the lagoon complex (Villavicencio­

Garayzar, 1995). The diamond stingray, Dasyatis dipterura, is considered to be a primary component of these landings.

Dasyatis dipterura has been reported from British Columbia, Canada to Chile, including the Galapagos and Hawaiian Islands (Hart, 1973; Nishida and Nakaya, 1990; 16

Lamilla et al., 1995). However, the northern-most record of occurrence remains unconfirmed. Dasyatis dipterura is most commonly associated with shallow, inshore waters from southern California to Peru (Eschmeyer et al., 1983). Depth of occmTence in the eastern Pacific ranges from intertidal to at least 32m while records from the

Hawaiian archipelago, if valid, indicate a shift toward greater depths of 10-150 m (Druk­

Gonzalez, 1978; Chave and Mundy, 1994). Within the Bahia Magdalena lagoon complex, biomass estimates of the population indicate that this stingray is one of the primary elements of the soft-bottom demersal fish assemblage (Gutienez-Sanchez,

1997).

Villavicencio-Garayzar (1995) docmnented the catch composition of a directed batoid fishery in the Bahia Magdalena lagoon complex (Puerto Viejo) for a total of 17 days over a one year period. The objective of this investigation was to repeat surveys at

Puerto Viejo and examine species and sex catch composition of landings during the peak summer fishery. Additional fishing camps and ports throughout the lagoon complex were surveyed with the aim of obtaining more detailed biological and morphological data for the poorly known, commercially exploited stingray, D. dipterura.

Study Area

The Bahia Magdalena lagoon complex (~24.46-24.47° N, -111.73° W) is situated in a region of dynamic biological and physical transition and complexity on the Pacific coast of the Baja California peninsula (Figure 1). Temperate and tropical species 17

converge within this confluence between the San Diego Province of the temperate

California Region and the Cortez (or Panamic; Hubbs, 1960; Brusca, 1980) Province of the tropical East Pacific Region (Briggs, 197 4; Hastings 2000). Eelgrass (Zostera marina), for example, reaches its southern limit and exhibits its highest regional flowering effort at the Bahia Magdalena lagoon complex (Cabello-Pasini et al., 2003;

Santamaria-Gallegos et al., 2003). Mangroves also replace salt marshes as the dominant littoral vegetation in this region (Brusca, 1980; Ibarra-Obando et al., 2001). Black

(Avicennia germinans), red (Rhizophora mangle), and white (Laguncularia racemosa), mangroves occur in Bahia Almejas, where they fonn consolidated, littoral forests.

Additionally, a wide variety of marine fauna (Castro-Aguirre and Torres-Orozco, 1993;

Felix-Pico and Garcia-Dominguez, 1993) occupy this region as either eurythennal resident species or seasonal transients.

The Bahia Magdalena lagoon complex is one of the largest embayments in

Mexico and the most important fishing port in the state of Baja California Sur (Ramirez­

Rodriguez, 1987; Cruz-Aguero et al., 1994). It is bounded by a series of islands and sand bars that parallel the coast and divide it into three well-defined regions: 1) a northwest zone of canals and mangrove-lined channels, referred to as the Zona de Canales (~299

2 2 km ); 2) a central zone, consisting of Bahia Magdalena (~696 km ); and 3) a southeast

2 zone, composed ofBahia Almejas (~414 km ) (Alvarez-Borrego et al., 1975; Figure 1).

The interior canals and cham1els that constitute the vast majority of this region are nanow

(0.2-2 km) and shallow (3.5 m mean depth, 17.8 m maximum depth). In contrast, Bahia 18

Magdalena and Bahia Almejas are expansive lagoons that are connected by a shallow, 2.5 km wide cham1el (Alvarez-Borrego et al., 1975; Contreras-Espinosa, 1993). The deepest isobaths 2:38 m) are associated with Canal Rehusa in Bahia Magdalena, but depths of 10-

20 mare common throughout the central and northwest regions. The vast majority of

Bahia Almejas is <10m (maximum 27m) and much of the northern and southeastern regions are exposed daily at low tide (Alvarez-Borrego et al., 1975; Obeso-Nieblas et al.,

1999). A more tropical fauna generally persists in the warm, shallower waters of Bahia

Almejas, providing notable diversity within the lagoon complex itself (Hubbs, 1960).

Water temperatures within the Bahia Magdalena lagoon complex are wanner than the adjacent Pacific Oceans during all months of the year, with the slightest differences

(<0.7° C) occurring between October and January and the greatest (2.6-3.7° C) between

March and August (Lluch-Belda et al., 2000). The average sea surface temperature of

Bahia Almejas is 23.1±2.6 °C. Temperatures remain relatively consistent (20.3-21.5° C) between December and May, increase in June (22.3° C) and remain high (>25) from July to October, peaking in August (27.7° C). June and November typically represent transitional months for sea surface temperatures. In general, elevated temperatures are · located in the interior portions of the lagoon complex and cooler waters are found near the open sea connections. Monthly average temperature is, however, highly unifonn throughout Bahia Almejas. During El Nifio conditions, temperatures within the embayment can reach> 31 o C with anomalies >6° C. 19

Salinities within the lagoon complex remain higher than that of the Pacific throughout the year because of low precipitation, negligible freshwater input, and high evaporation rates (Alvarez-Borrego et al., 1975). Shallower regions ofthe complex tend to be higher in salinity and the western portion of Bahia Magdalena reflects more oceanic conditions. In Bahia Almejas, surface salinity values are relatively uniform throughout the year, ranging from lows of 34.0%o in the west-central region, to highs of 35.1 %o in the northeast. Dissolved oxygen content is typically 5.0 ml/1 or greater (> 100% saturated) with little spatial or temporal variation. Local pH values range from 8.0-8.5.

Upwelling occurs in portions of the central and southeastern zones throughout much of the year, resulting in high productivity (Nienhuis and Guerrero, 1985).

Microphytoplankton densities are greatest from November to May and subsequently decrease during the late spring through early fall (Jtme-October). Two peaks of phytoplankton abundance, corresponding to the autumn and spring, occur annually

(Garate-Lizarraga and Siqueiros-Beltrones, 1998). The density and composition of phytoplankton differs between Bahia Almejas and Bahia Magdalena during the autumn­ spring peaks. Dramatic decreases in the density and shifts in the distribution and structure of these populations have been reported in response to El Nifio events, thereby reducing productivity within the system during wann water periods. 20

Methods

Artisanal fishery landings from the Bahia Magdalena lagoon complex were

sampled during 1998-2001 as part of a larger project to obtain morphological data and the

biological material necessary to assess the life history characteristics of D. dipterura.

Sampling was primarily conducted during the summer months of June and August, but

additional surveys were completed during October (2001) and December (1999) as well.

The number of dasyatid rays landed by each artisanal fishing vessel was recorded,

specimens were sexed, and measured to the nearest centimeter. Disc width (DW), measured between the broadest points of the pectoral fin, and body length (BL ),

measured from the snout tip to the posterior margin of the longest extended pelvic fin,

were recorded from each specimen whenever possible. Total length was not measured

because of irregular, highly variable tail lengths that are associated with stingrays.

Clasper length of each male was measured to the nearest millimeter from the posterior end of the cloacal slit to the i1mer tip of the longest clasper with the specimen lying with the ventral surface upward and the clasper supported to eliminate sag (Snelson et al.,

1988). Weight was determined to the nearest 0.1 kg using a spring scale for all undressed individuals :S 25 kg.

A detailed survey of the elasmobranch catch composition at the primary study site ofPuerto Viejo (24° 28.34' N, 111° 37.12' W) was completed during June 1998-2000 and

August 1998-1999 (Figure 1). Gear type, soak time, and species-specific landings were recorded for each active fishing vessel. Elasmobranchs were identified to the lowest 21

possible taxon, sexed, and enumerated. Measurements ofDW, BL, clasper length, and weight were obtained from D. dipterura. Gravid females and the presence of seminal fluid among males were noted for all elasmobranchs. Specimens were specified as neonates if unhealed umbilical scars were noted.

Measurement and weight data for D. dipterura were combined from all sampling locations to develop predictive morphometric relationships. Body length and weight to

DW were fit to linear and power regression models in SigmaPlot (SPSS, Chicago, IL).

Sex-specific differences between these features were examined using analysis of covariance (ANCOVA) (Zar, 1996). Weight data were log+ 1 transformed and fit to a linear weight-DW regression to enable ANCOVA. Mean and median DW of female and male D. dipterura recorded from Puerto Viejo were calculated for June, August, and combined monthly landings.

The proportion of females to males was calculated for the most commonly landed species in the Puerto Viejo fishery. Significant departure from a 1:1 relationship was tested using l goodness of fit tests (a=O.Ol) for species that totaled :?:25 individuals within June or August landings (Zar, 1996). Power of the resulting x2 tests were assessed following Cohen (1988) as:

where w is the effect size, P li is the proportion observed from sampled population, and

Po; is the frequency assumed by the null hypothesis (i.e. 0.5). 22

Elasmobranch catch composition of Puerto Viejo was compared between months

(June and August), years, and summarized based on overall combined landings. The

percent contribution of each species to these landings was detennined. Catch per unit

effort (CPUE) was calculated based on the lowest possible taxon identified and defined

as the number of individuals per vessel per trip.

Results

Batoids were commonly landed among direct and indirect fisheries throughout the

Bahia Magdalena lagoon complex. Fishermen typically employed bottom-set mono- and

multi-filament gillnets of 12.7-33.0 em stretch mesh to target a suite ofray species or

oppmiunistically capture a mixed assemblage of demersal elasmobranchs and teleosts.

However, mesh sizes as narrow as 7.6 em stretch were observed to effectively capture large (>60 em DW) D. dipterura, D. Zanga, and Myliobatis californica. Rays were also taken to a lesser extent by longline, but most of this effort was based from Isla

Magdalena and Isla Santa Maria and occmTed in the Pacific Ocean. Fishermen from a single cooperative based out ofPueiio San Carlos used large beach seines during the summer months to directly target rays. Gillnets were set for 12-24 hours and fishing was generally conducted by 2-3 men aboard 5.5-7.0 m long, open-hulled, fiberglass vessels, locally tenned "pangas". Although batoids were landed during all months surveyed, directed fishing effort and landings were highest during the summer months. Fishery surveys were conducted over a total of 69 days. 23

The size range and frequency of D. dipterura recorded from the fishery at Puerto

Viejo was representative of landings observed throughout the Bahia Magdalena lagoon complex. A total of 601 specimens was measured from the summer fishery at Puerto

Viejo (Figure 2). The smallest female and male specimens measured 25.8 em DW (n=2).

The largest female and male D. dipterura landed were 83 and 60 em DW, respectively.

Females averaged 50.9 em DW and the mean size of males was 47.8 em DW in the fishery.

A strong linear relationship between body length (em) and DW (em) was detected for female and male D. dipterura (Figure 3, A and B). Significant differences in this relationship were detected between females (n=176) and males (n=432) (ANCOVA,

F=6.935, P=0.009). Regressions were therefore developed separately for each sex. The conesponding linear regressions are described by the following equations:

Female: Body length (em)= 1.0513 * DW (em)- 2.5776 (r2=0.99)

Male: Body length (em)= 1.0839 * DW (em)- 3.7717 (r2=0.96)

Female D. dipterura attained greater weights and DWs than their male counterpmis. Wet weight of females greater than 72 em DW frequently exceeded 25 kg.

A significantly different relationship between body weight and DW was also identified between females (n=177) and males (n=433) (ANCOVA, F=85.879, P

A and B). Power regressions indicated strong, curvilinear relationships between weight and DW for both sexes as described by the following equations:

3 1598 2 Female: Weight (kg)= 0.00002 * DW (cm) · (r =0.98) 24

3 1953 2 Male: Weight (kg)= 0.00001 * DW (cm) · (r =0.89)

Dasyatis dipterura was the fourth most abundant elasmobranch of the 1985 individuals identified from June landings at Puerto Viejo (Table 1). The 165 recorded D. dipterura represented 8.31% of the June total. Rhinabatas praductus was the most commonly recorded elasmobranch from the June fishery in all years except 2000, accounting for 50.58% ofthe total recorded June catch (n=1004). Gymnura marmarata

(n=196) and Narcine entemedar (n=494) ranked as the second and third most abundant species. Other batoids including D. Zanga, MyZiabatis caZifarnica, M Zangirastris,

Rhinaptera steindachneri, Urabatis chilensis, Zapteryx exasperata, and Urat1ygan spp. were landed but less frequently taken among the June fishery. Gravid females with late­ ten11 embryos included D. Zanga, R. praductus, and R. steindachneri. Juvenile and neonate sharks, including Carcharhinus faZcifarmis, C. Zeucas, C. abscurus, Jsurus axyrinchus, Sphyrna Zewini, and S. zygaena were also taken in the fishery in small numbers. A single gravid Carcharhinus parasus (166 em TL) containing near-term embryos was recorded in June 2000. Sharks represented <2% of the June elasmobranch landings. Fishen11en retained the entire elasmobranch catch, therefore no discard of elasmobranchs occurred at sea.

In contrast to the catch composition of G. marmarata, N. entemedar, and R. praductus, the sex ratio of D. dipterura did not differ significantly from a 1:1 relationship among June landings (x2=0.25, P=0.88) (Table 1). The overwhelming majority of R. praductus were mature females (x2=526.26, P<0.0001), many of which were gravid. 25

Females also accounted for a greater proportion of G. marmorata Cl=98.45, P

However, power analyses of the l tests indicated that the possibility of make a type II 13 error was high for D. dipterura (Power=3) and G. marmorata (Power=2) from June 1998 and for D. dipterura from June 1999 (Power=2) and overall analyses (Power=6) given the number of individuals sampled. Several June 1999 surveys of artisanal catches conducted in Puerto San Carlos, Puerto Chale, and Puerto Datil revealed that male R. productus were almost exclusively landed in Bahia Magdalena while females comprised the majority of R. productus taken within Bahia Almejas during the same period (Figure

1).

Overall species-specific June CPUE values ranged from 0.02-21.83 individuals per vessel trip (Table 1). CPUE exceeded 1.0 for five species; D. dipterura, G. marmorata, N. entemedor, R. productus, and Z. exasperata. CPUE of D. dipterura was greatest from June 2000 (10.25) and averaged 3.59 for all June landings. The highest

CPUE was observed during June 1999 in which an estimated 33.71 R. productus were landed per vessel trip. CPUE of G. marmorata, N. entemedor, and R. productus was lower in 1998 than calculated for 1999 and 2000. The total June CPUE was 43.15 elasmobranchs per vessel trip.

Dasyatis dipterura was the primary elasmobranch landed during the August fishery at Puerto Viejo (Table 2). A total of 870 D. dipterura was recorded among 2052 individuals observed over 35 days in 1998 and 1999. The relative contribution of D. 26

dipterura to August landings was similar between years. Gymnura marmorata (n=436),

R. productus (n=271), and N. entemedor (n=249) were also commonly captured. These four batoids accounted for 89% of the total August catch composition. Rhinobatos productus was landed more frequently in 1999 (n=249) than 1998 (n=22). Additional batoid species including D. Zanga, M californica, M longirostris, Raja velezi,

Rhinoptera steindachneri, Z. exasperata, and Raja spp. were taken in the fishery. Gravid

D. dipterura, G. marmorata, N. entemedor were observed to be carrying late-tenn embryos in August. Only a single juvenile carcharhinid, C. falciform is, was noted from the fishery. However, catches of S. lewini were greater during August than June. Adult female, neonate, and juvenile S. lewini were landed while only juvenile S. zygaena were observed during August. Neonates comprised the majority of AugustS. lewini landings.

The proportion of landed females differed significantly from that of males among the August fishery for the four most frequently landed species (Table 2). Males dominated D. dipterura (x2=136.76, P<0.0001) and R. productus (x2=98.82, P<0.0001) catches while female G. marmorata Cl=102.53, P<0.0001) andN. entemedor Cl=42.77,

P<0.0001) were landed in significantly greater proportions than males. Power analyses of the x2 tests indicated that the possibility of committing a type II l3 error based on analyses of R. productus from August 1998 was high (Power=3).

Overall species-specific August CPUE values were less than those calculated for

June and ranged from 0.01-9.46 (Table 2). CPUE exceeded 1.0 for four species; D. dipterura (9.46), G. marmorata (4.74), R. productus (2.95), and N. entemedor (2.71). 27

The highest August CPUE of 13.31 calculated for D. dipterura from 1999. August

CPUE was greater during 1999 than 1998. Total August CPUE was 22.3 elasmobranchs

per vessel trip.

The artisanal batoid fishery in Bahia Almejas was dominated by four species (R. productus, D. dipterura, N. entemedor, and G. marmorata) during June and August

(Table 3). Three additional species, R. steindachneri, S. lewini, and Z. exasperata,

generated approximately 6.7% ofthe overall landings. More than 19 elasmobranch

species were identified from the fishery. Distinct, significant trends were identified

among the sex composition of the most frequently landed species. Males comprised the

majority of D. dipterura (x2=119.40, P<0.0001) catches while female G. marmorata

(x2=116.60, P<0.0001), N. entemedor (x2=73.82, P<0.0001), and R. productus

Cl=225.00, P<0.0001) were primarily taken in the fishery.

Discussion

Of the 46 elasmobranch species documented from the Bahia Magdalena lagoon

complex (Castro-Aguirre and Torres-Orozco, 1993; Cruz-Agi.iero et al., 1994; Galvan­

Magana et al., 2000), 19 were identified from the artisanal fishery at Puerto Viejo. Five

additional unidentified specimens included carcharhinid (Carcharhinus spp.),

smoothhound (Mustelus spp.), skate (Raja spp.) and round ray (Urot1ygon spp.) species,

elevating the total to a minimum of 22 elasmobranchs observed from the fishery. Two

of these species, C. falciformis and R. velezi, were previously unrep01ied from the lagoon 28

complex. Rhinobatos productus, D. dipterura, N entemedor, and G. marmorata were the primary constituents of June and August landings. These four rays were also reported to be the most prevalent within summer catches at Puetio Viejo from a 1990-91 survey

(Villavicencio-Garayzar, 1995).

Batoids were oppmiunistically targeted by fishermen throughout the Bahia

Magdalena lagoon complex. However, very few fishermen were exclusively dedicated to this fishery throughout the year. Rhinobatos productus was targeted by groups of fishennen from Puerto Chale, Puerto Datil, and Lorna Amarilla during May and June. A single vessel operating out of Lorna Amarilla targeted G. marmorata throughout the year.

Rhinobatos productus, D. dipterura, N entemedor, and G. marmorata were recorded among landings from Puerto San Carlos and Puetio Adolfo Lopez Mateo, but sampling in these more developed locations was complicated by the large number of active vessels, variety of target species, and multiple points oflanding.

The maximum DWs reported for D. dipterura (female=99 em DW; male=113 em

DW) from the Bahia Magdalena lagoon complex by Mathews and Druck-Gonza.Iez

(1975) and Druk-Gonza.Iez (1978) exceeded those observed in this study. However, these authors did not acknowledge the occurrence of D. longa within the region and openly expressed ambiguity in their identifications. Female myliobatifonn rays typically attain larger sizes than their male counterparts (e.g., Smith and Merriner, 1986; Mmiin and

Cailliet, 1988). It is therefore likely that the large males identified as D. dipterura were actually representatives of the larger species, D. longa. 29

Minimum sizes of D. dipterura within the lagoon complex were documented as

12 em DW for females and 15 em DW for males by Mathews and Druck-Gonzalez

(1975). These sizes are less than the minimum size at birth of 17 em DW estimated by

Mariano-Melendez (1997) and may have been measured from expelled embryos or have been based on misidentified round rays, possibly Urotrygon rogersi. These size data were not subsequently reported by Druk-Gonzalez (1978) in his study that included the previous 1975 survey data. Instead, a minimum size of23 em DW was reported. It would be appropriate to conservatively interpret the data presented by Mathews and

Druck-Gonzalez (1975) and Druk-Gonzalez (1978) as incorporating more than a single species of stingray. The size ranges of both females and males observed in this study correspond well with those observed by Villavicencio-Garayzar (1995) during the 1990-

91 Puerto Viejo fishery.

Striking species-specific differences in the proportion of females to males were evident within the catch composition at Puerto Viejo. Shifts among these sex ratios were detected between June and August surveys. Segregation by sex, size, or habitat is a common characteristic of elasmobranch behavior (e.g., Steven, 1933; Springer, 1967;

Klimley, 1987). Male D. dipterura, for example, have been previously documented to be more common than females within Bahia Almejas than Bahia Magdalena throughout the year (Druk-Gonzalez, 1978). The overwhelming majority of R. productus sampled during June consisted of gravid females. Female G. marmorata and N. entemedor were significantly more abundant that males throughout the summer landings. By August, the 30

majority of the landings consisted of gravid female, reproductively active male, and juvenile D. dipterura, G. marmorata, and, to a lesser extent, R. steindachneri.

Reproductive studies by Villavicencio-Garayzar (1993a, b, 1995, 1996) from this location lend further support to these observations and trends. The artisanal fishery within Bahia Almejas appears to be coupled with the reproductive cycles, nursery utilization, and sex-specific movement patterns of resident and transient elasmobranchs.

The dominance of D. dipterura among August landings conforms to documented patterns of species abundance and biomass within the Bahia Magdalena lagoon complex

(Druk-Gonzalez, 1978; Gutierrez-Sanchez, 1997). Although D. dipterura is reported to occur within the lagoon complex throughout the year, it exhibits marked seasonal fluctuations in abundance. Population densities peak during August and decrease throughout the fall to a minimum between November and January, increasing again by

March (Druk-Gonzalez, 1978; Gutierrez-Sanchez, 1997). A strong pattern of seasonal abundance of D. dipterura has been also been repmied from Estero de Punta Banda along the northern Baja California Pacific coast (Beltran-Felix et al., 1986). The an·ival and peak abundance of adult D. dipterura occurs in May and decreases by August with the species being apparently absent from the embayment during the fall and winter (Beltran­

Felix et al., 1986). Seasonal movements of dasyatids have generally been strongly linked to water temperature and migrations from coastal embayments into deeper offshore waters are typical during winter months (Schwmiz and Dahlberg, 1978; Snelson and 31

Williams, 1981; Struhsaker, 1969). It is probable that D. dipterura also migrate into

deeper waters outside of the lagoon complex during the winter.

Although rarely discussed or considered in the primary literature, artisanal

fisheries are frequently directed toward myliobatifonn rays, particularly dasyatids. These

fisheries have been considered very important in Indonesia, Thailand, Singapore, and

Malaysia (Last and Compagno, 1999). Multi-species ray fisheries have perhaps been best

documented from India (e.g., James, 1973; Devadoss, 1978; Devadoss et al., 1989; Raje,

2003) where Dasyatis spp. and Himantura spp. have historically provided important

yields. Devadoss et al. (1989) noted that the majority oflndian elasmobranch landings

from 1961-1985 consisted of rays, largely D. uanrek, D. sephen, and D. alcockii.

Dasyatids are also a common component of trawl fisheries off the Kenyan coast

(Ochumba, 1988). Japanese catch records indicate that more than 35,000 kg of D. akajei

were landed from a single prefecture over a nine month period during 1949-1950

(Yokota, 1951 ). However, no additional landing details or documentation of

myliobatifonn fishery trends have been published from this region. It is likely that these

rays constitute important, yet poorly reported, directed artisanal and incidental industrial

fisheries in subtropical and tropical marine enviromnents.

Mexican catch records typically lack species-specific designation of

elasmobranchs. Batoids were either unrecognized (listed as "otras especies") or

collectively designated as "mantarraya" prior to 1997 (Bon:fil, 1994; Vannuccini, 1999).

Current records ofbatoid landings consist of several general categories that classify

-- 32

multiple species into three basic groups ("gavilan"; typically Myliobatis spp. but may include R. steindachneri, "guitana"; Rhinobatos spp. and Zapteryx exasperata, and

"mantarraya"; generally Dasyatis spp.) and relegate other rays to the broad category of

"otras especies". Species such as Mobula spp. and G. marmorata may be inconsistently categorized as "mantanaya". This lack of species-specific infom1ation inhibits the identification oftrends or changes in the composition of landings and restricts the application of sustainable management strategies.

As noted by Bonfil (1994), batoids have historically represented a relatively minor proportion of Mexico's repmied elasmobranch landings. Reported atmuallandings from Mexico's Pacific states indicate average catches of 425, 6932, and 10,349 kg for

"gavilan", "guitana", "mantarraya", respectively during 1997-2000 (Secretaria de Media

Ambiente, Recursos Naturales y Pesca, unpublished data) (Figure 5A). Landings of

"mantanaya" were highest in 1997 and the maximum reported landings of "guitarra" occuned in 1998.

Contrasted with official monthly catch statistics, estimated June and August catch weights of D. dipterura from Puerto Viejo reveal striking discrepancies between reported and observed "mantanaya" landings during 1998 and 1999 (Figure 5B). June landings of

D. dipterura directly recorded from Puerto Viejo during the course of this study represent

21% of the total June 1998 reported "mantarraya" landings and exceeded reported June

1999 landings by 20 kg for all Mexican Pacific states. August 1998 D. dipterura catches from Puetio Viejo total 80% of the official recorded landings of the entire Mexican 33

Pacific. The catch weight of D. dipterura that I recorded only from Puerto Viejo in

August 1999 exceeded federal catch records for the same month by more than 4700 kg.

The Puerto Viejo D. dipterura catch records based on a combined 33 days of sampling presented in this study from June and August 1999 surpass the total landings of

"mantarraya" docwnented from the Mexican Pacific for that year (Secretaria de Medio

Ambiente, Recursos Naturales y Pesca, unpublished data). Given that the designated category "mantarraya" may include more than one species, that my estimates of June and

August D. dipterura catches from a single camp (Puerto Viejo) are based on fewer than

21 days sampled within each month, and that a maximwn of three artisanal vessels operate daily from this location, it is evident that available catch data grossly underestimate artisanal dasyatid landings and, likely, batoid landings in general.

Although D. dipterura is a common component of we stem Mexico's artisanal elasmobranch fishery (Villavicencio-Garayzar, 1995; Ocampo-Torres, 2001; Marquez­

Farias, 2002), the extent of incidental landings of this species among trawl fisheries is unknown. Exploratory fishery surveys within the Gulf of Califomia and Bahia

Magdalena Bay lagoon complex indicate that D. dipterura constitute a large proportion of available biomass within soft-bottom, demersal communities (Flores et al., 1995;

Gutierrez-Sanchez, 1997). Dasyatis dipterura produced 26% ofthe total catch weight of fishery-independent trawl survey catches within the Gulf of California (Flores et al.,

1995). Bycatch associated with shrimp fisheries is notoriously high and shrimp trawl operations from the Gulf of California are reported to discard 9. 7 kg of biomass for every 34

kg oflanded target species (Alverson et al., 1994). It is likely that typical soft-bottom demersal species such as D. dipterura are a common component of bycatch within these fisheries. Where detailed bycatch composition data are available, myliobatifonn rays have been found to be principal constituents. Analyses of shrimp fisheries off Brazil indicated that CPUE of rays is almost three times greater than that of targeted shrimp

(Menni and Stehmann, 2000). Mortality of rays upon capture may be high, ranging from

53-56% within Australian shrimp trawl fisheries (Stobutzki et al., 2002). Subsequent survivorship of discarded individuals that endure initial capture may be quite low and represent an important source of incidental fishing mortality for many batoids. Analyses of long-term datasets have revealed sharp reductions in the abundance of demersal batoids, notably D. pastinaca, as a direct result ofbycatch overfishing (Philippmi, 1998;

Quero, 1998). Large, long-lived species have been demonstrated to be most impacted by trawl fisheries.

The history of the miisanal fishery in Bahia Almejas suggests the serial depletion of several elasmobranchs. Established in 1960, Puerto Viejo is the oldest fishing camp in

Bahia Almejas. Fishing at this location was initially conducted year-round and targeted primarily large sharks and rays using longlines. By 1994, however, declining shark catches prompted an exclusive emphasis on demersal batoids. Year-round use ofthe encampment ceased and fishing activity at this site was restricted from April-October, coinciding with peak seasonal abundance of the targeted species. By the late 1990s, directed batoid fishing effort was focused largely toward R. productus. The extent of 35

batoid fisheries in other locations was undocumented prior to this study. Landings of

demersal rays at Puerto Viejo began to decline and the season was further restricted,

operating primarily from May to August. In 2003, catches became too low to warrant

continued fishing effort and Puerto Viejo was abandoned. Salazar-Hermoso and

Villavicencio-Garayzar (1999) considered fishing effmi to have a relatively insignificant

affect on local population abtmdance of R. productus based on sampling conducted in the

early 1990s. However, protracted or increased effmi directed mainly at gravid females

has clearly resulted in depletion of R. productus and other targeted elasmobranch

populations in Bahia Almejas. It is recommended that elasmobranchs in this embayment

be afforded protection through seasonal closures and gear restrictions.

Dasyatis dipterura and most elasmobranch fisheries and bycatch are unmanaged throughout Mexico. However, legislation is currently being developed to establish a national elasmobranch fishery management plan. Species-specific monitoring of shark

catches, delineation of nursery grounds, and recognition of special areas of congregation have been identified as critical, but undeveloped measures for effective shark management in Mexico (Applegate et al., 1993). This information remains largely unavailable for Mexican shark populations and is equally deficient but essential for the

management of expanding batoid fisheries. Surveys of catch composition, such as those presented in this study, provide a practical approach to simultaneously addressing these critical directives. Details of relative abundance, sex ratios, and reproductive status can readily be obtained through these assessments. Once principal species are recognized 36

from landings, biological studies can be developed and directed toward species commercial importance to provide additional infonnation necessary for formulating successful management strategies. However, because ofthe established vulnerability of elasmobranchs to fishing pressure, implementation of fishery regulations should not be further delayed. 37

LITERATURE CITED

Alvarez-Borrego, B.S., Galindo-Bect, A. and Chee-Barragan, A. 1975. Caracteristicas hidroquimicas de Bahia Magdalena, B.C.S. Ciencias Marinas 2(2): 94-110.

Alverson, D.L., Freeberg, M.H., Murawski, S.A., and Pope, J.G. 1994. A global assessment of fisheries bycatch and discards. F AO Fisheries Teclmical Paper 339. Rome, Italy. 233 p.

Applegate, S.P., Espinosa, L., and Sotelo, F. 1993. An overview ofMexican shark fisheries, with suggestions for shark conservation in Mexico. In Conservation Biology of Sharks (S. Branstetter, ed.), p. 31-37. NOAA Technical ReportNMFS 115.

Beltran-Felix, J.L, Gregory-Hammann, M.G., Chagoya-Guzman A. and Alvarez-Borego, S. 1986. Ictiofauna del estero de Punta Banda, Ensenada, Baja Califomia, Mexico, antes de una operacion de dragado. Ciencias Marinas 12(1): 79-92.

Bonfil, R. 1994. Overview of world elasmobranch fisheries. F AO Fisheries Technical Paper 341. Rome, Italy. 119 p.

Brander, K. 1981. Disappearance of common skate Raja batis from the Irish Sea. Nature 5801: 48-49.

Briggs, J.C. 1974. Marine Zoogeography. McGraw-Hill, New York, New York. 475 p.

Brusca, R. C. 1980. Common intertidal invertebrates of the Gulf of California. The University of Arizona Press, Tuscan, AZ. 513 p.

Cabello-Pasini, A., Muniz-Salazar, R., and Ward, D.H. 2003. Photosynthesis and biochemical characteristics of eelgrass along the Pacific coast of Baja California, Mexico. GulfMexico Science 21(1): 100.

Casey, J.M. and Myers, R.A. 1998. Near extinction of a large, widely distributed fish. Science 28: 690-692.

Castillo-Geniz, J.L., Marquez-Farias, J.F., Rodriquez de la Cruz, M.C., Cmies, E., and Cid del Prado, A. 1998. The Mexican artisanal shark fishery in the Gulf of Mexico: towards a regulated fishery. Marine and Freshwater Research 49: 611- 620. 38

Castro-Aguirre, J.L. and Torres-Orozco, R.T. 1993. Consideraciones acerca del origen de la ictiofauna de Bahia Magdalena-Almejas, un sistema lagunar de la costa occidental de Baja California Sur, Mexico. Annales de la Escuela Nacional de Ciencias Biologicas, Mexico 3 8: 67-73.

Chave, E.H. and Mundy, B.C. 1994. Deep-sea benthic fish of the Hawaiian archipelago, Cross Seamount, and Jolmston Atoll. Pacific Science 48(4): 367-409.

Cohen, J. 1988. Statistical Power Analysis for the Behavioral Sciences. 2nd edition. Lawrence Erlbaum Associates, Hillsdale, New Jersey. 567 p.

Compagno, L.J.V. 1999. Checklist ofliving elasmobranchs. In Sharks, Skates, and Rays: The Biology ofElasmobranch Fishes (W.C. Hamlett, ed.), p. 471-498. Jolms Hopkins University Press, Baltimore, MD.

Contreras-Espinosa, F. 1993. Ecosistemas costeros Mexicanos, 415 p. Universidad Aut6noma Metropolitana Unidad Iztapalapa, Iztapalapa, Mexico.

Cruz-Aguero, J. de la, Galvan-Magana, F., Abitia-Cardenas, L.A., Rodriguez-Romero, J., and Gutierrez-Sanchez, F.J. 1994. Lista sistematica de los peces marinas de Bahia Magdalena, Baja California Sur (Mexico). Ciencias Marinas 20(1): 17-31.

Csirke, J. 1997. Review ofthe state of world fishery resources: marine fisheries. Food and Agriculture Organization of the United Nations Marine Resources Service, Fishery Resources Division. Fisheries Circular Number 910. 173 p.

Devadoss, P. 1978. A preliminary study on the batoid fishery ofCuddalore with a note on the biology. Indian Journal of Fisheries 25(1-2): 180-187.

Devadoss, P., Kuthalingam, M.D.K., and Thiagarajan, R. 1989. The present status and future prospects of elasmobranch fishery in India. Bulletin of the Central Marine Fisheries Research Institute 44(23): 188-199.

Druk-Gonzalez, J. 1978. Algunas observaci:ones biol6gico pesqueras en la raya diamante (Dasyatis spp.) y raya nariz redonda (Myliobatis californica) en Bahia Magdalena y Bahia Almejas, Baja California Sur, Mexico. B.S. thesis, Universidad Aut6noma de Baja California, Ensenada, Mexico. 70 p.

Dulvy, N.K., Metcalfe, J.D., Flanville, J., Pawson, M.G., and Reynolds, J.D. 2000. Fishery stability, local extinctions, and shifts in community structure in skates. Conservation Biology 14(1): 283-293. 39

Eschmeyer, W.N., Herald, E.S. and Hammatm, H. 1983. A field guide to Pacific coast fishes of North America. Houghton Mifflin Co., Boston, MA. 336 p.

FAO. 2004. The state of world fisheries and aquaculture. Food and Agriculture Organization ofthe United Nations, Fisheries Department. Rome, Italy. 153 p.

Felix-Pica, E.F., Salaices-Polanco, H.A., Alvarez, F.M., and Alvarez, A. 1986. Infonne final: ecologia de la fauna macrobent6nica litoral de las costas de Baja California Sur. In Bioversidad Marina y Costera de Mexico (S.I Salazar-Vallejo y N.E. Gonzalez, eds.), p. 389-410. Comision Nacional de Biodiversidad y CIRQ, Mexico.

Flores, J.O., Rodriguez, M., Shimizu, M., and Machii, T. 1995. Evaluation of demersal fishery resources of the Gulf of California using Mexican shrimp trawlers. Journal of the National Fisheries University 44 (1): 9-19.

Galvan-Magana, F., Gutienez-Sanchez, F., Abitia-Cardenas, L.A., and Rodriguez­ Romero, J. 2000. The distribution and affinities ofthe shore fishes ofthe Baja California Sur lagoons. In Aquatic ecosystems of Mexico: status and scope (M. Munawar, S.G. Lawrence, I.F. Munawar, and D.F. Malley, eds.), p. 383-398. Backhuys Publishers, Leiden, The Netherlands.

Garate-Lizarranga, and Siqueriros-Beltrones, D.A. 1998. Time variation in phytoplankton assemblages in a subtropical lagoon system after the 1982-1983 1 "El Nifio" event (1984 to 1986) . Pacific Science 52(1): 79-97.

Guardado-France, V.M. 1976. Estudios ecol6gicos de elasmobranquios en la zona de Bahia Magdalena, B.C.S. B.S. thesis, Universidad Aut6noma deBaja California, Ensenada, Mexico. 135 p.

Gutierrez-Sanchez, F.J. 1997. Ecologica de peces de fondos blandos del complejo lagunar Bahia Magdalena, B.C.S., Mexico. M.S. thesis, Centro Interdisciplinario de Ciencias Marinas, Instituto Politecnico Nacional, La Paz, Mexico. 84 p.

Hart, J .L. 1973. Pacific Fishes of Canada. Fisheries Research Board of Canada Bulletin 180. 740 p.

Hastings, P.A. 2000. Biogeography of the Tropical Eastern Pacific: distribution and phylogeny of chaenopsid fishes. Journal of the Linnean Society London Zoology 128: 319-335. 40

Hoenig, J.M. and Gruber, S.H. 1990. Life-history patterns in the elasmobranchs: implications for fisheries management. In Elasmobranchs as Living Resources: Advances in the Biology, Ecology, Systematics, and the Status ofthe Fisheries (H.L. Pratt, S.H. Gruber, and T. Taniuchi, eds.), p. 828-903. NOAA Technical Report NMFS 90.

Holden, M.J. 1973. Are long-tenn sustainable fisheries for elasmobranchs possible? Rapports et Proces-verbaux des Reunions, Conseil International pour L'Exploration de laMer 164: 360-367.

Holden, M.J. 1977. Elasmobranchs. In Fish Population Dynamics (J.A. Gulland, ed.), p. 187-214. John Wiley and Sons, New York, NY.

Hubbs, C. 1960. The marine vertebrates ofthe outer coast. Symposium: the biogeography of Baja California and adjacent seas. Systematic Zoology 9(3-4): 134-147.

Ibarra-Obando, S.E., Camacho-Ibar, V.F., Carriquiry, J.D., and Smith, S.V. 2001. Upwelling and lagoonal ecosystems of the dry Pacific coast of Baja California. In Ecological studies. Vol. 144: Coastal and marine ecosystems ofLatin America, (U. Seeliger, and B. Kjerfve, eds.) p. 315-330. Springer-Verlag, Berlin, Germany.

James, P.S.B.R. 1973. Sharks, rays, and skates as a potential fishery resource off the east coast of India. Proceedings of the symposium on living resources of the seas around India, Central Marine Fisheries Research Institute special publication: 483-494.

Klimley, A.P. 1987. The detenninants of sexual segregation in the scalloped hammerhead shark, Sphyrna lewini. Environmental Biology ofFishes 18(1): 27- 40.

Lamilla, J., Pequefio, and Kong, I. 1995. Dasyatis brevis (Garman, 1880) segunda especie de Dasyatidae registrada para Chile (Chondrichtyes, Myliobatiformes) Esudios Oceanol6gicos 14: 23-27.

Last, P.R. and Compagno, L.J.V. 1999. Dasyatidae. In The Living Marine Resources of the Western Central Pacific, Volume 3 (K.E. Carpenter and V.H. Niem, eds.), p. 1479-1480. Food and Agriculture Organization of the United Nations, Rome, Italy. 41

Lluch-Belda, D., Hernandez-Rivas, M.E., Saldierna-Martinez, R., and Guerrero­ Caballero, R. 2000. Variabilidad de la temperatura superficial del mar en Bahia Magdalena, B.C.S. Oceanides 15(1): 1-23.

Mariano-Melendez, E. 1997. Biologia reproductiva de la raya lodera Dasyatis brevis (Garman, 1880), en Bahia Almejas, B.C.S., Mexico. B.S. thesis, Universidad Aut6noma de Baja California Sur, La Paz, B.C.S., Mexico. 46 p.

Marquez-Farias, F.J. 2002. The artisanal ray fishery in the Gulf of California: development, fisheries research, and management issues. IUCN/SSC Shark Specialist Group. Shark News 14: 1-5.

Martin, L.K. and Cailliet, G.M. 1988. Aspects of the reproduction of the bat ray, Myliobatis californica, in central California. Copeia 1988(3): 754-762.

Mathews, C.P. and Druck-Gonzalez, J. 1975. Potencial pesquero y estudios de Bahia Magdalena III. Las existencias de rayas con especial interes a las ya aprovechadas. Ciencias Marinas 2(1): 67-72.

Me1mi, R.C. and Stehmann, M.F.W. 2000. Distribution, environment and biology of batoid fishes off Argentina, Uruguay, and Brazil. A review. Revista del Museo Argentinio de Ciencias Naturales 2(1): 69-109.

Nienhuis, H. and Guerrero-Caballero, R. 1985. A quantitative analysis ofthe annual phytoplankton cycle ofthe Magdalena lagoon complex (Mexico). Journal of Plankton Research 7(4): 427-444.

Nishida, K. and Nakaya, K. 1990. Taxonomy ofthe genus Dasyatis (Elasmobranchii, Dasyatididae) from the north Pacific. NOAA Technical Report NMFS 90: 327- 346.

Obseso-Nieblas, M., Gavifio-Rodriguez, J.H., and Jimenez-Illescas, A.R. 1999. Modelaci6n de la marea en el sistema lagunar Bahia Magdalena-Almejas, B.C.S., Mexico. Oceanides 14(2): 79-88.

Ocampo-Torres, A. I. 2001. Descripci6n y analisis de la pesca artisanal de elasmobranquios de Sinaloa, Mexico. M.S. thesis, Centro de Investigacion Cientifica y de Educaci6n Superior de Ensenada, B.C., Mexico. 117 p. 42

Ochumba, P.B.O. 1988. The distribution of skates and rays along the Kenyan coast. Journal of the East Africa Natural History Society and National Museum 78(192): 25-51.

Philippart, C.J.M. 1998. Long-tern1 impact ofbottom fisheries on several by-catch species of demersal fish and benthic invertebrates in the south-eastern North Sea. ICES Journal ofMarine Science 55: 342-352.

Pratt, H.L., Jr. and Casey, J.G. 1990. Shark reproductive strategies as a limiting factor in directed fisheries, with a review of Holden's method of estimating growth parameters. In Elasmobranchs as Living Resources: Advances in the Biology, Ecology, Systematics, and the Status ofthe Fisheries (H.L. Pratt, S.H. Gruber, and T. Taniuchi, eds.), p. 97-109. NOAA Teclmical ReportNMFS 90.

Quero, J.C. 1998. Changes in the Euro-Atlantic fish species composition resulting from fishing and ocean warming. Italian Journal of Zoology 65: 494-499.

Raje, S.G. 2003. Some aspects ofbiology of four species of rays offMumbai water. Indian Journal of Fisheries 50(1): 89-96.

Ramierz-Rodriguez, E.M. 1987. Analisis perliminar de las pesquerias artesanales del area de Bahia Magdalena, B.C.S. durante 1982 y 1983. Memoires de la V Simposio de Biologia Marina, Universidad Aut6noma de Baja Califomia Sur, p. 149-154.

Salazar-Hern1oso, F. and Villavicencio-Garayzar, C. 1999. Abundancia relative de la guitarra Rhinobatos productus (Ayres, 1856) (Pisces: Rhinobatidae) en Bahia Almejas, Baja California Sur, de 1991 a 1995. Ciencias Marinas 25(3): 401-422.

Santamaria-Gallegos, N.A., Sanchez-Lizaso, J.L., Riosmena-Rodriguez, R. 2003. Life strategies of subtropical eelgrass Zostera marina L. populations in southern Baja California: its southern limit distribution along East Pacific. Gulf of Mexico Science 21(1): 130-131.

Schwartz, F.J. and Dahlberg, M.D. 1978. Biology and ecology ofthe Atlantic stingray, Dasyatis sabina (Pisces: Dasyatidae), in North Carolina and Georgia. Northeast Gulf Science 2(1): 1-23.

Smith, J.W. and Meniner, J.V. 1986. Observations on the reproductive biology ofthe cownose ray, Rhinoptera bonasus, in Chesapeake Bay. Fishery Bulletin 84(4): 871-877. 43

Snelson, Jr., F.F. and Williams, S.E. 1981. Notes on the occurrence, distribution, and biology of elasmobranch fishes in the Indian River Lagoon System, Florida. Estuaries 4(2): 110-120.

Snelson, F.F. Jr., Williams-Hooper, S.E. and Schmid, T.H .. 1988. Reproduction and ecology of the Atlantic stingray, Dasyatis sabina, in Florida coastal lagoons. Copeia, 3: 729-739.

Springer, S. 1967. Social organization of shark populations. In Sharks, Skates, and Rays (P.W. Gilbert, R.F. Mathewson, and D.P. Rail, eds.), p. 149-174. Jolms Hopkins University Press, Baltimore, MD.

Steven, G.A. 1933. Rays and skates ofDevon and Cornwall III. The proportions ofthe sexes in nature and in commercial landings, and their significance to the fishery. Journal of the Marine Biological Association of the United Kingdom 18: 611-625.

Stevens, J.D., Bonfil, R., Dulvy, N.K., and Walker, P.A. 2000. The effects of fishing on sharks, rays, and chimaeras (chondrichthyans), and the implications for marine ecosystems. ICES Journal ofMarine Science 57: 476-494.

Stobutzki, I. C., Miller, M.J., Heales, D.S., and Brewer, D.T. 2002. Sustainability of elasmobranchs caught as bycatch in a tropical prawn (shrimp) trawl fishery. Fishery Bulletin 100: 800-821.

Struhsaker, P. 1969. Observations on the biology and distribution ofthe thorny stingray, Dasyatis centroura (Pisces: Dasyatidae ). Bulletin of Marine Science 19(2): 456- 481.

Torres-Orozco, R.E. and Castro-Aguirre, J.L. 1992. Registros de peces tropicales en el complejo lagunar de Bahia Magdalena-Almejas, Baja California Sur, Mexico. Anales del Instituto de Biologia Universidad Naciona1 Aut6noma de Mexico, Serie Zoologia 63(2): 281-286.

Vannuccini, S. 1999. Shark utilization, marketing, and trade. FAO Fisheries Technical Paper 389. 470 p.

Villavicencio-Garayzar, C.J. 1993a. Observaciones sobre la biologia reproductive de Narcine brasiliensis (Olfers) (Pisces: Narcinidae), en Bahia Almejas, B.C.S. Mexico. Revista de Investigaciones Cientificas 4(1): 95-99. 44

Villavicencio-Garayzar, C.J. 1993b. Biologia reproductiva de Rhinobatos productus (Pisces: Rhinobatidae), en Bahia Almejas, Baja California Sur, Mexico. Revista de Biologia Tropical41(3): 777-782.

Villavicencio-Garayzar, C.J. 1995. Distribuci6n temporal y condici6n reproductiva de las rayas (Pisces: Batoidei), capturadas commercialmente en Bahia Almejas, B.C.S., Mexico. Revista de Investigaci6n Cientifica 6(1-2): 1-12.

Villavicencio-Garayzar, C.J. 1996. Tallas, proporci6n de sexos y reproducci6n de Myliobatis californica y M longirostris (Pisces: Myliobatidae) en Baja California Sur, Mexico. Revista de Biologia Tropical43(2): 291-295.

Walker, T.I. 1998. Can shark resources be harvested sustainably? A question revisited with a review of shark fisheries. Marine and Freshwater Research 49: 553-572.

Walker, P.A. and Hislop, J.R.G. 1998. Sensitive skates or resilient rays? Spatial and temporal shifts in ray species composition in the central and north-western North Sea between 1930 and the present day. ICES Joumal ofMarine Science 55: 392- 402.

Weber, M.L. and Fordham, S.V. 1997. Managing shark fisheries: opportunities for international conservation. TRAFFIC International and the Center for Marine Conservation, Washington D.C. 61 p.

Y okata, T. 1951. Studies on the stocks of sharks and rays. 11. Age composition of the ray, Dasybatus akajei (Muller et Henle), as observed in the catch by trawlers landed at Totoro, Miyazaki prefecture during a period September, 1949 to May, 1950. Bulletin ofthe Japanese Society of Scientific Fisheries 16(12): 188-189.

Zar, J.H. 1996. Biostatistical Analysis. 3rd ed. Prentice Hall, New Jersey. 662 p. r

Table 1. Elasmobranch landings recorded from Puerto Viejo during June 1998, 1999 and 2000. The numbers of sampling days and vessels surveyed during each year are indicated in parentheses. Female to male sex ratios are presented for the four most commonly landed batoids when sums are ~25 individuals. An* denotes a significant difference from a 1:1 sex ratio (P<0.0001). CPUE = number of individuals/vessel trip.

June 1998 (6 days, 18 vessel trips) June 1999 (12 days, 24 vessel trips) June 2000 (2 days, 4 vessel trips) June Total (19 days, 46 vessel trips) Lowest Possible Taxon n % F:M CPUE n % F:M CPUE n % F:M CPUE n % F:M CPUE Carcharhinusfalciformis 2 0.58 0.11 2 0.13 0.08 0 0.00 0 4 0.20 0.09 Carcharhinus leu cas 0 0.00 0.00 2 0.13 0.08 0.72 0.25 3 0.15 0.07 Carcharhinus lim batus 0.29 0.06 0 0.00 0.00 0 0.00 0 0.05 0.02 Carcharhinus obscurus I 0.29 0.06 0 0.00 0.00 0 0.00 0 0.05 0.02 Carcharhinus porosus 0 0.00 0.00 0 0.00 0.00 0.72 0.25 0.05 0.02 Carcharhinus spp. 0 0.00 0.00 0 0.00 0.00 0.72 0.25 0.05 0.02 Dasyatis dipterura 56 16.14 1.00:1.33 3.11 68 4.54 1.00:0.84 2.83 41 29.50 10.25 165 8.31 1.00:1.10 3.59 Dasyatis longa 2 0.58 0.11 7 0.47 0.29 4 2.88 I 13 0.65 0.28 Gymnura marmorata 30 8.65 1.00:0.58 1.67 112 7.47 1.00:0.12* 4.67 54 38.85 1.00:2.38* 13.5 196 9.87 1.00:0.50* 4.26 Isul'Us oxyrinchus 2 0.58 0.11 0 0.00 0.00 0 0.00 0 2 0.10 0.04 Mustelus spp. 0 0.00 0.00 I 0.07 0.04 0 0.00 0 0.05 0.02

Myliobatis californica 1 0.29 0.06 0~7 ~04 0 0.00 0 2 0.10 0.04 Myliobatis longirostris 0 0.00 0.00 0.07 0.04 0 0.00 0 I 0.05 0.02 Narcine entemedor 45 12.97 1.00:0.22* 2.50 427 28.49 1.00:0.02* 17.79 22 15.83 1.00:0.05 5.5 494 24.89 1.00:0.07* 10.74 Raja spp. 0 0.00 0.00 0 0.00 0.00 0 0.00 0 0 0.00 0.00 Raja velezi 0 0.00 0.00 0 0.00 0.00 0 0.00 0 0 0.00 0.00 Rhinobatos productus 190 54.76 1.00:0.03* 10.56 809 53.97 1.00:0.00* 33.71 5 3.60 1.25 1004 50.58 1.00:0.01 * 21.83 Rhinoptera steindachneri 2 0.58 0.11 0 0.00 0.00 4 2.88 I 6 0.30 0.13 Sphyrna lewini 2 0.58 0.11 0 0.00 0.00 0.72 0.25 3 0.15 0.07 Sphyrna zygaena 11 3.17 0.61 0 0.00 0.00 0.72 0.25 12 0.60 0.26 Urobatis chilensis 0 0.00 0.00 I 0.07 0.04 0 0.00 0 0.05 0.02 Urotrygon spp. 0.29 0.06 0 0.00 0.00 0 0.00 0 I 0.05 0.02 Zapteryx exasperata 0.29 0.06 68 4.54 2.83 4 2.88 73 3.68 1.59

Total 347 100.00 19.28 1499 100.00 62.46 139 100.00 34.75 1985 100.00 43.15 r

Table 2. Elasmobranch landings recorded from Puerto Viejo during August 1998 and 1999. The numbers of sampling days and vessels surveyed during each year are indicated in parentheses. Female to male sex ratios are presented for the four most commonly landed batoids when sums are 2:25 individuals. An* denotes a significant difference from a 1:1 sex ratio (P<0.0001). CPUE= number of individuals/vessel trip.

August 1998 (14 days, 41 vessel trips) August 1999 (21 days, 51 vessel trips) August Total (35 days, 92 vessel trips) Lowest Possible Taxon n % FM CPUE n % FM CPUE n % FM CPUE C archarhinus falciform is 0 0.00 0.00 1 0.06 0.02 1 0.05 0.01 Carcharhinus /eucas 0 0.00 0.00 0 0.00 0.00 0 0.00 0.00 Carcharhinus /imbatus 0 0.00 0.00 0 0.00 0.00 0 0.00 0.00 Carcharhinus obscurus 0 0.00 0.00 0 0.00 0.00 0 0.00 0.00 Carcharhinus porosus 0 0.00 0.00 0 0.00 0.00 0 0.00 0.00 Carcharhinus spp. 0 0.00 0.00 0 0.00 0.00 0 0.00 0.00 Dasyatis dipterura 191 42.92 1.00:4.08* 4.66 679 42.25 1.00:2.66* 13.31 870 42.40 1.00:3.03* 9.46 Dasyatis longa 4 0.90 0.10 4 0.25 0.08 8 0.39 0.09 Gymnura marmorata 18 4.04 0.44 418 26.01 1.00:0.26* 8.20 436 21.25 1.00:0.27* 4.74 lsurus oxyrinchus 0 0.00 0.00 0 0.00 0.00 0 0.00 0.00 Muste/us spp. 0 0.00 0.00 0 0.00 0.00 0 0.00 0.00 Myliobatis ca/ifornica 0 0.00 0.00 0.06 0.02 0.05 0.01 My/iobatis /ongirostris 0 0.00 0.00 22 1.37 0.43 22 1.07 0.24 Narcine entemedor 139 31.24 1.00:0.40* 3.39 110 6.85 1.00:0.34* 2.16 249 12.13 1.00:0.38* 2.71 Raja spp. 0 0.00 0.00 3 0.19 0.06 3 0.15 0.03 Raja ve/ezi 0 0.00 0.00 1 0.06 0.02 0.05 0.01 Rhinobatos product us 22 4.94 1.00:1.44 0.54 249 15.49 1.00:26.00* 4.88 271 13.21 1.00:6.78* 2.95 Rhinoptera steindachneri 71 15.96 1.73 37 2.30 0.73 108 5.26 1.17 Sphyrna /ewini 0 0.00 0.00 78 4.85 1.53 78 3.80 0.85 Sphyrna zygaena 0 0.00 0.00 3 0.19 0.06 3 0.15 0.03 Urobatis chi/ensis 0 0.00 0.00 0 0.00 0.00 0 0.00 0.00 Urotrygon spp. 0 0.00 0.00 0 0.00 0.00 0 0.00 0.00 Zapteryx exasperata 0 0.00 0.00 0.06 0.02 0.05 0.01.j:>.. 0\ Total 445 100.00 10.85 1607 100.00 31.51 2052 100.00 22.30 47

Table 3. Total elasmobranch landings recorded from Puerto Viejo from June 1998-2000 and August 1998, 1999listed from most to least common. Female to male sex ratios are presented for the four most commonly landed batoids. An * denotes a significant difference from a 1:1 sex ratio (P

Lowest Possible Taxon n % F:M CPUE Rl1inobatos productus 1275 31.58 1.00:0.29* 9.239 Dasyatis dipterura 1035 25.64 1.00:2.52* 7.500 Narcine entemedor 743 18.40 1.00:0.32* 5.384 Gymnura marmorata 632 15.66 1.00:0.35* 4.580 Rhinoptera steindachneri 114 2.82 0.826 Sphyrna lewini 81 2.01 0.587 Zapteryx exasperata 74 1.83 0.536 Myliobatis longirostris 23 0.57 0.167 Dasyatis Zanga 21 0.52 0.152 Sphyrna zygaena 15 0.37 0.109 Carcharhinus falciform is 5 0.12 0.036 Myliobatis californica 3 0.07 0.022 Raja spp. 3 0.07 0.022 Carcharhinus leucas 3 0.07 0.022 Carcharhinus spp. 2 0.05 0.014 Isurus oxyrinchus 2 0.05 0.014 Carcharhinus limbatus 1 0.02 0.007 Carcharhinus obscurus 1 0.02 0.007 Carcharhinus porosus 1 0.02 0.007 Mustelus spp. 1 0.02 0.007 Raja velezi 1 0.02 0.007 Urobatis chilensis 1 0.02 0.007 Urotrygon spp. 1 0.02 0.007

Total 4037 100.00 29.261 48

11 °20'

N

Zona de Canales

b u,0 N

10 0 10 20 Kilometers ~!~.-~-~~~-- Boca Flor B de Malva 112°20' 112°00' 111 °40'

Figure 1. Location (A) and prominent features (B) of the Bahia Magdalena lagoon complex, Baja California Sur, Mexico. Numbered symbols signify sampling locations, the primary study site is distinguished by a triangle. 1=Puerto Adolfo Lopez Mateo, 2=Pueiio San Carlos, 3=San Buteo, 4=Puerto Cancun, 5=El Cayuco, 6=Puerto Viejo, ?=Puerto Chale, 8=El Datil, 9=Loma Amarilla. -- 49

200 180 II Female DMale 160

'"0 140

Figure 2. Size frequency distribution of female (n=182) and male (n=419) Dasyatis dipterura recorded from the directed batoid fishery at Puerto Viejo. Data represent combined landings recorded during Jtme 1998-2000 and August 1998-1999. Disc width distributions are binned by 5 em intervals. Values within the figure indicate the number observed within each 5 em size class. Sums S14 are not individually listed within the histogram. 50

90 A 80

70 ,-... 6 u '--' 60 ...c:...... tlO >=: ~ >. 50 '"d 0 a:1 40

30

20

70 B

60

,-... 6 u '--' 50 ...c: t'o >=: ~ >. '"d 40 0 a:1

30

20+------.------.------.------.-----.------.------. 20 30 40 50 60 70 80 90 Disc width (em)

Figure 3. Linear relationship between body length and disc width for (A) female (n=l76; r2=0.99) and (B) male (n=432; r2=0.96) Dasyatis dipterura. 51

30 A 25 • • • 20

-----01) ~ '-' .:E 15 01) "iii ~ 10

5

0

14 B 12

10

-----01) ~ 8 '-' ..c...... 01) "iii 6 ~

4

2

0 20 30 40 50 60 70 80 90 Disc width (em)

Figure 4. Power relationship of weight to disc width for (A) female (n=l77; r2=0.98) and (B) male (n=433; r 2=0.89) Dasyatis dipterura. Note: scales of they-axes differ between females and males. 52

20000 rEI "Gavilan" A D "Guitarra" 16000 !Ill "Mantarraya" bilc Cll .sbl) 12000 "0 .§ "0 (!) t:! 0 8000 0.. (!) ~

4000

1997 1998 1999 2000 Year 6000 131997 B D 1998 5000 IIIIIIPV 1998 EZI1999 4000 B PV 1999 lllill2000

3000

2000

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month Figure 5. Repmied batoid landings based on three general categories (A) and monthly distribution of"Mantarraya" landings (B) from the Pacific states of Mexico, 1997-2000. Species designation within each of the three batoid categories are crude, but typically include Myliobatis spp. as "Gavilan", Rhinobatos spp. as "Guitarra", and Dasyatis spp. as "Mantarraya". Estimated landings in kg of Dasyatis dipterura from Puerio Viejo during June and August of 1998 (PV 1998) and 1999 (PV 1999) are contrasted with official catch statistics. Batoid landings are based on unpublished Secretaria de Medio Ambiente, Recursos Naturales y Pesca data. CHAPTER2

Life history characteristics of Dasyatis dipterura: Maturity, age, growth, and

longevity

53 54

Introduction

Studies of growth (increases in size or mass) comprise a fundamental component of biological research. A complex of genetic, environmental, and ecological processes interact to influence cellular and organismal growth characteristics with time. In tum, the dynamics of populations (changes in abundance) are inherently bound by these constraints and growth potentials. The growth properties of maximum size and age are, fmihennore, strongly correlated with bioenergetics and life history traits, including maturity, fecundity, and mortality (Blueweiss et al., 1978; Platt and Silvert, 1981;

Stearns, 1992). Thus, investigations of growth properties link cellular, metabolic, individual, and population-level processes.

Analyses of growth patterns and rates are a principal component of ichthyology and fisheries research. Fishes typically exhibit indetenninate growth, maturing prior to attaining maximum size (Weatherley 1972). Although fishes continue to grow throughout the course of their lives, somatic growth often decreases following maturation and attenuates toward an asymptote with increasing age (Ricker, 1979; Moreau, 1987).

Intraspecific plasticity within this generalized growth pattern may vary considerably and be strongly influenced by environmental conditions. The summation of individual size­ at-age data provides the basis for establishing mean population growth parameters and an understanding how species interact with their environment. As such, species-specific models of growth and associated life history characteristics are essential for assessing the 55

productivity and resilience of fish populations to commercial exploitation and other anthropogenic or environmental impacts (Hilborn and Walters, 1992; Haddon, 2001).

Age and growth estimation of elasmobranchs has predominantly been accomplished by examining and enumerating the differentially mineralized bands deposited within vertebral centra (Cailliet et al., 1986; Cailliet, 1990; Cailliet and

Goldman, 2004). Other well-calcified structures which may reveal similar growth patterns have also been applied in elasmobranch ageing studies; including dorsal spines, caudal thorns, and neural arches (Ketchen, 1975; Gallagher and Nolan, 1995; McFarlane et al., 2002). Interpretation and detection of bands in hard body parts is complicated by the presence of finer bands and irregular or discontinuous increments of varying widths within these structures (Cailliet et al., 1986; Cowley, 1997). Thus, criteria for increment and band recognition must be well defined to ensure reliability and repeatability of resulting age estimates. An annual pattern of band deposition has been commonly assumed to occur and increasingly validated among elasmobranchs (Cailliet and

Goldman, 2004). However, observed growth patterns have been found to be associated with lunar periodicity (Brown and Gruber, 1988) or to simply reflect somatic growth rather than explicit seasonal or annual growth patterns (Natanson and Cailliet, 1990).

Assessment of age based on banding patterns therefore requires confirmation of consistency in band interpretation and knowledge of the periodicity of band deposition.

Although much of the pioneering work on elasmobranch age, growth, and validation was conducted on batoids (e.g., Stevens, 1936; Ishiyama, 1951; Daiber, 1960; 56

Holden and Vince 1973), life history information on commercially exploited rays remains extremely limited. Of the approximately 92 known batoid species from the eastem

Pacific, age and growth characteristics have been detennined for only five (Babel, 1967;

Martin and Cailliet, 1988b; Zeiner and Wolf, 1993; Neer and Cailliet, 2001). Validation of the temporal nature of vertebral band deposition has not been accomplished in any of these studies, rendering the interpretation and application of the reported growth characteristics somewhat tenuous (Beamish and McFarlane, 1983; Campana, 2001).

Dasyatis dipterura is a broadly distributed eastem Pacific stingray that is known to attain disc widths of at least 97 em and weights to 51 kg (Feder et al., 1974). It comprises a primary component of the artisanal elasmobranch fisheries in westem

Mexico and is likely to be commonly taken as bycatch in trawl fisheries throughout the region (Flores et al., 1995; Villavicencio-Garayzar, 1995; Marquez-Farias, 2002). Life history infonnation published on D. dipterura is restricted to estimates of size at maturity

(Mathews and Druck-Gonzalez, 1975; Villavicencio-Garayzar, 1995). If D. dipterura also exhibits the long life span, slow growth, late age of maturity, and low fecundity described for many other elasmobranchs, depletion or collapse of the fished population is possible. These life history characteristics can constrain population growth rates and rebound potential and extend recovery periods following over-exploitation (Holden,

1973; Hoenig and Gruber, 1990; Musick, 1999; Stevens et al., 2000). An improved understanding of the biology and population dynamics of D. dipterura is crucial for fonnulating effective, sustainable management strategies for these populations. Thus, the 57

objectives of this research component were to detennine the fecundity, age and size at maturity, growth characteristics, and longevity of the commercially exploited stingray, D. dipterura from the Bahia Magdalena lagoon complex, B.C.S. Mexico.

Methods

Field Sampling

Dasyatis dipterura were collected from artisanal elasmobranch fishery landings throughout the Bahia Magdalena lagoon complex as described in the preceding chapter.

The majority of specimens were obtained from the directed batoid fishery of Puerto Viejo in the southern portion of the lagoon complex. All field work was conducted during

1998-2000 and included the months of June, August, October, and December. Basic biological infonnation (e.g., disc width, sex, weight) was obtained from all D. dipterura observed while sampling. As a result of equipment limitations in the field, weights (±0.1 kg) could only be obtained for specimens <25 kg. Vertebrae and maturity status were collected with an effort to obtain samples from representative size ranges and were not collected from every stingray. A minimum of five vertebra were excised from the region posterior to the cranium between the 5th and 15th vertebral elements. To provide a basis for comparison of banding consistency within centra, samples were additionally removed from distinct anterior and posterior regions of the vertebral column from a subset of specimens. Monospondylous vertebrae were collected in all cases, with anterior samples excised posterior to the cranium as previously described and posterior segments being 58

removed over the pelvic girdle. Vertebrae were individually labeled with an identification number and stored in 70% isopropyl alcohol until preparation for sectioning. An archived collection ofvertebral sections collected from the Puerto Viejo fishery during 1992 and 1998 was provided by the Laborotorio de los Elasmobranqios at the Universidad Auton6ma de Baja California Sur (UABCS) in La Paz, Mexico for use in this study. Vertebral sections were collected in a mmmer similar to that described above and included samples obtained during February, March, May, and June, 1992. These samples were also stored in 70% isopropyl alcohol until processed for ageing.

Maturity Assessment

The reproductive condition of male and female stingrays was assessed to estimate size/age at maturity and detennine fecundity. Individual specimens were assigned a maturity status ofO (immature) or 1 (mature) following measurement and macroscopic examination of reproductive tracts in the field. Criteria for maturity were modified after

Martin and Cailliet (1988b), Smith and Merriner (1986), and Snelson et al. (1988).

Females were considered to be mature ifvitellogenic ova> 1 em diameter were present in the lefi ovary, uteri were well developed, trophonemata were present, or if gravid. A single functional ovary is a common feature among myliobatiforms and I encountered no evidence that the right ovary was functional in this species as well (Bigelow and

Schroeder, 1953; Wounns, 1977; Lewis, 1982). Males were considered to be mature if the claspers were well calcified and easily rotated, clasper tips (rhipiodon) were calcified 59

and could be expanded; the vas deferens was highly coiled, and the testes were enlarged and lobed. The presence of seminal fluid, while noted, was not considered alone to be an indicator of maturity (Pratt, 1979). The extent of gonadal differentiation among immature specimens was recorded.

Median disc-width-at-maturity was estimated by fitting a logistic model to the binomial maturity data (0 =immature; 1 =mature) (Mollet et al., 2000). Maturity data were binned into 1 em DW size classes and males and females were analyzed separately.

The following form of the logistic equation was fitted using least squares non-linear regression and SigmaPlot graphical software (SPSS Inc., vers. 8.0, Chicago, IL):

y- 1 - (1 + e -(a+bx)) where Y = maturity status and x = disc width in centimeters. Median disc width at maturity (DW50) was calculated as -alb. Using ages detennined in this study, the range of age at maturity estimates was determined by relating DWso to observed size-at-age estimates.

As a secondary determinant of size-at-sexual-maturity among males, the relationship between inner clapper length and disc width was plotted and the maturity status of specimens indicated. Clasper length of each male was measured to the nearest millimeter from the posterior end of the cloacal slit to the inner tip of the longest clasper with the specimen lying with the ventral surface upward and the clasper supported to eliminate sag (Snelson et al., 1988). An abrupt change in the relationship of clasper 60

length to body size occurs at the onset of maturity in male myliobatifonns (Hess, 1959;

Babel, 1967; Struthsaker, 1969) and this con-elation was used as a supportive assessment of maturity for males.

When present, developing embryos were measured, sexed, vertebral segments were removed, and specimens were preserved for further examination in the laboratory.

The extent of pigmentation, development ofthe tail spine, presence of yolk sac, and content of the spiral valve were evaluated to provide a basic assessment of developmental stage (Babel, 1967; Lewis, 1982). The relationship between the number of observed embryos and maternal DW was plotted. Because few gravid females were landed in the fishery and expulsion of embryos upon capture was common, these data were combined with those ofMariano-Melendez (1997) that were also collected from the Puerto Viejo fishery during 1993-94.

Age and Growth

Vertebral centra were removed from each sample, separated, and cleaned ofthe remaining cmmective tissue and neural arches using a cartilage knife and scalpel in the laboratory. All samples were rinsed thoroughly in fresh water, air dried, placed in scintillation vials, identified only by a sample number, and stored dry. A cleaning method frequently used by other researchers (e.g., Smith and Me1Tiner, 1987; Mariin and

Cailliet, 1988b; Cowley, 1997) using low concentration sodium hypochlorite solutions to aid in the removal of connective tissue was found to be damaging to centra following 61

soaks often or more minutes during preliminary trials. The impact of bleach immersion was most notable on centrum edges. Careful, minimal, manual cleaning of vertebrae proved to be a more successful preparation technique.

A potential ageing structure must be present throughout the life span of an individual and increase proportionally to specimen size for it to be considered appropriate for age and growth analysis. The use of tail spines as an ageing structure was dismissed because they are shed periodically throughout the life of a stingray (Russell, 1955; Teaf,

1987). Vertebrae were therefore considered to be the best potential ageing structures for

D. dipterura. Using dial calipers, a mean diameter was calculated from individual centra based on two measurements (nearest 0.1 mm) to account for non-concentric growth of the structure. Measurements were taken at opposing right angles across whole centra. The relationship between disc width and vertebral centrum diameter was examined using least squares linear and quadratic regression analysis (Zar, 1996). Analysis of covariance

(ANCOV A) was applied to compare potential sex-specific differences between centrum diameter and disc width.

Numerous methods to enhance the visibility of growth bands deposited within vertebral centra of elasmobranchs have been developed with varying degrees of success among species (Cailliet et al., 1983; Cailliet and Goldman, 2004). The effectiveness ofx­ radiographs (Miller and Tucker, 1979; Martin, 1982), graphite microtopography

(Parsons, 1983, Neer and Cailliet 2001); alizarin red (LaMarca, 1966, Gruber and Stout,

1983) and crystal violet stains (Johnson, 1979; Schwartz, 1983) on growth band 62

enhancement of whole and thin-sectioned D. dipterura centra were evaluated during preliminary trials. Unstained, thin-sectioned centra best distinguished banding patterns among all ve1iebral size classes and this method was adopted for the preparation of all samples.

Cleaned, dry vertebrae were centered on wax coated tags (35x25 mm), embedded in polyester resin, and sectioned to incorporate the focus using paired diamond blades on a Buehler Isomet low-speed jeweler's saw. Resulting vertebral sections were approximately 0.4 mm thick. Thin-sections were affixed to glass slides with Cytoseal mounting medium and successively polished with 800- and 1200-grit wet sandpaper to create an even surface. All sections were viewed under transmitted light using a binocular microscope. Centrum faces were brushed with mineral oil prior to viewing to improve sample clarity and mask superficial surface irregularities.

Casselman (1983) stated that objective criteria for age and growth analysis should be established prior to the examination of age structures. However, due to extensive variability among vertebral banding patterns, birth mark fonnation, and the extent of calcification observed among elasmobranchs (e.g., Ridewood, 1921; Cailliet et al., 1983;

Natanson and Cailliet, 1990; McFarlane et al., 2002) a preliminary assessment for each species is required in order to establish objective ageing criteria. A basis for consistent interpretation of banding patterns within vertebral centra of D. dipterura was established during initial attempts to compare the benefits of selected band enhancement techniques.

Optically distinct alternating zones were readily distinguished within the centra of all 63

free-living specimens. Vertebrae of near-tenn embryos were examined and no pre-birth marks were evident within the structures. Based on these observations, the birth mark was defined as the first translucent (i.e., light or bright) zone encountered distal to the focus and was associated with an angle change in the intennedialia (Figure 1). This mark was considered to represent age 0. Banding patterns within the intennedialia frequently serve as a common and reliable continuous reference among thin-sectioned carcharhinifonn centra (e.g., Casey et al., 1985; Natanson et al., 1995). However, banding within the intermedialia of D. dipterura was irregular and indistinct. Notably, on the outer edges of larger centra in particular, curvature and narrowing of growth zones compact potentially distinguishable banding patterns, creating an inconsistent, unreliable reference point for age estimation. Distinct alternating opaque (i.e., dark) and translucent

(i.e., light) increments were evident within the corpus calcareum and age estimates were made by enumerating growth zones in this region.

Ambiguous terminology relating to the optical qualities and growth zones of ageing structures frequently creates confusion conveying these criteria and interpreting ageing results (Casselman, 1983 ). An "increment" in this study indicates any distinct, ' continious growth zone within the vertebral centra. This term applies to both opaque and translucent zones (Figure 1). A valid increment could be distinguished by its presence on both edges as well as opposing anns of the corpus calcareum, but may or may not be clearly visible and continuous within the inte1medialia. The width of opaque and translucent increments varied throughout a section and was not a sole determinant of 64

increment validity. Checks, or incomplete increments, were occasionally visible within

centra and these abrupt discontinuities could be identified from increments by examining

upper, lower, and opposing halves of each sample. The tenn "band" indicated a pair of

opaque and translucent increments adjacent to one another within a thin-sectioned

vertebral centrum. Age estimates were made by counting the number of completely

formed bands observed within each sample. Translucent increments were first identified

and served as the primary reference for band counts. If a translucent increment was

detennined to be fanning on the outer centrum edge, the age estimate was assigned as the

number of completely formed bands plus 0.5 (e.g., 2.5 years).

All ve1iebrae were prepared and examined by a single reader using the previously

described terminology and objective criteria for band definition. A single reader may

minimize the bias often introduced by multiple readers (Cailliet, 1990; Sminkey and

Musick, 1995). However, studies have indicated that experienced readers are more

precise and less biased than those with limited experience ageing elasmobranchs (Officer

et al., 1996; Simpfendorfer et al., 2000). To increase the experience level ofthe single reader involved in the study, ages were estimated from a total of 50 thin-sectioned centra

based on triplicate reads during the preliminary evaluation of band enhancement techniques. These initial age estimates were completed to increase familiarity with the ageing structure and benefits of enhancement techniques and were not included with the final counts. Subsequent age estimates were based on four independent counts of each

sample. Estimates were made without knowledge of the specimen's sex, size, date of 65

capture, or any previous counts and were separated by a minimum of two weeks between rounds. Ifthe final count did not agree with one of the first three, it was excluded from growth models. Following each reading, clarity and readability of the sample was assessed on a qualitative scale of 1-5 in a manner modified from Officer et. al (1996)

(Table 1). Band counts were derived only from samples receiving a clarity grade of 2-4.

Typically, all samples assigned a low grade of 1 or 2 were re-sectioned, read, and assigned a new clarity rating. If the lowest clarity grade (1) was again assigned, the sample was excluded from further analysis.

Reproducibility and precision of the age estimates detennined in this study was measured in several ways. A commonly applied index of the average deviation of each estimate from the means of all other readings was proposed by Beamish and Fournier

(1981 ). This index of average percent error (lAP E) is calculated as:

where N is the number of specimens aged, R is the number of times each is aged ( 4 ), Xi} is the ith age estimate of the jth specimen, and J0 is the average age calculated for that specimen. A set of band count estimations with a smaller lAPE is considered more precise. Chang (1982) presented two alternative measures of precision that were also employed in this study. The coefficient of variation (CV) was determined by dividing the standard deviation by the mean for each set of age estimates. These values were summed 66

and multiplied by 100 to express the measure as an overall percentage. Chang (1982) also recommended an index of precision (D) which assesses the percent enor contributed by each estimate to the average age class and is determined from CVas (CV 1-JR ). In addition to assessing the precision of age estimates, potential systematic bias of these counts among rounds was examined graphically using pair-wise age difference plots

(Campana et al., 1995).

Measures of precision such as JAPE and CVare dependent on subjective age estimates and assume that variability among reads derived from individuals can be averaged over all age groups. As a result, important considerations of precision among age estimates may be overlooked or over-summarized (Hoenig et al., 1995). Percentage agreement calculations were based on consensus counts and their corresponding maximum differences. Perfect agreement and agreement plus or minus 0.5, 1, 2, 3, and 4 years were summed overall and calculated for 5 em DW size classes following Cailliet and Goldman (2004).

Consistency of the banding pattern throughout the vertebral column was evaluated from 30 paired samples collected from anterior and posterior regions of the column.

Centra from both regions were aged non-consecutively and independently without knowledge of the centrum location. A paired-sample t-test was applied to examine the hypothesis that banding patterns were uniform within monospondylous vertebrae (Zar,

1996). 67

Based on the relationship between mean centrum diameter and disc width,

average disc width at birth (DW0 ) was estimated from measurements of centrum thin­ sections. Images of centra with high clarity grades were measured using Image Pro Plus image analysis software (Media Cybernetics, 1998). Straight-line radius measurements from the focus to the origin of the birthmark within the intermedialia were recorded,

distances converted into diameters, and a mean DW0 was estimated from linear and quadratic relationships of mean centrum diameter versus disc width.

The temporal periodicity of increment deposition within vertebral centra was assessed using centrum edge and marginal increment ratio (MIR) analyses as semi-direct methods ofvalidation (Hayashi, 1976; Tanaka and Mizue, 1979; Morales-Nin and

Panfili, 2002). Centrum edge analysis is the qualitative process of determining the outer most increment type based on optical qualities (opaque/translucent). However, useful information is most often overlooked using this approach and limited description of edge formation is produced. Prompted by the work of Anderson et al. (1992) and Vilizzi and

Walker (1999) on teleost growth, I modified the traditional criteria applied by Tanaka and

Mizue (1979) and Natanson and Cailliet (1990) to include four distinct edge classes based on optical qualities and the extent of increment deposition: narrow opaque (0 1), broad opaque (02), narrow translucent (T1), and broad translucent (T2). A nmrow increment is defined as having a width that is less than 50% of the previously fully­ formed like increment and broad increments on the centrum edge are distinguished as 68

having a width that is equal to or greater than half of the previous like increment width

(Figure 2).

Marginal increment and band widths were measured(± 0.0001 mm) along the

. corpus calcareum from centrum images of sufficient clarity using Image-Pro Plus image analysis software (Media Cybernetics, 1998). MIR was calculated following Conrath et al. (2002) as:

MIR=MWIPBW where MW is the margin width or width of the outer-most fonning band and PBWis the width of the penultimate band. Age 0 specimens were excluded from analysis as no completely fonned bands are present. Mean monthly MIRs were plotted for all samples.

Sample size and availability throughout the year was not sufficient to allow age-specific assessments of monthly mean MIRs, but plots based on general size classes were created.

Additionally, mean MIRs were pooled across all size- and age-classes and graphed to examine seasonal trends in marginal increment development. Potential differences among mean MIRs were compared between months of capture with a non-parametric

Kruskal-Wallis one-way analysis ofvariance by ranks (Simpfendorfer et al., 2000).

Dunn's (1964) comparison of group rank sums for unequal sample sizes was applied to detect which months accounted for any significant differences indicated by the Kruskal­

Wallis test (Zar, 1996).

Mean growth parameters for D. dipterura were calculated from individual disc width and weight-at-age estimates based on centrum band counts using the non-linear 69

Marquardt-Levenberg least squares method (Marquardt, 1963) and SigmaPlot graphical software program (SPSS Inc., 2002). Age estimates were fit to four growth functions to generate and assess multiple descriptions of this species' growth characteristics. The von

Bertalanffy growth function (VBGF; modified from von Be1ialanffy, 1938; as cited by

Beverton and Holt, 1957) is the most widely applied growth model in fish ecology and fisheries science and was calculated as:

where DW, is the mean disc width at age t, DWw is the theoretical average asymptotic disc width, k is the growth coefficient that describes the rate at which DWw is attained, tis

the estimated age, and t0 is the hypothetical age at 0 disc width. Throughout this study, this form of the VBGF is refened to as the traditional three parameter model. A modification of this growth function based on two flexible parameters was also calculated that anchors the model with a known or estimated size at birth (von Bertalanffy, 1960):

DW = DW - (DW - DW Xe(-k+t)) l O'J 00 0 where D Wo is the fixed size at birth and the remaining parameters are as previously defined. A weight based form of the VBGF was also applied after Fabens (1965) and

Ricker (1979):

where w1 and Woo represent weight at age and theoretical asymptotic weight rather than size and the other parameters are as described above. The fourth and final growth 70

function applied in this study was fitted using disc width as well as weight at age data. A form of the Gompertz equation (Winsor, 1932) following Ricker (1979) was calculated as:

where Wt and Woo are as defined for the weight based VBGF, k is a dimensionless parameter, g is the instantaneous growth rate, and tis the estimated age. The parameters

k*g equal the instantaneous growth rate when t = 0 and w =weight at birth (w 0 ). The inflection point of the curve is calculated as Wool e. Disc-width-at-age data were substituted for the weight variables to obtain size-at-age models based on the Gompe1iz growth function (Ricker, 1975). Weights oflarge females occasionally exceeded the 25 kg maximum that could be recorded using our spring scales and therefore could not be included in weight-based growth analyses.

A final three parameter VBGF model was generated using modified size-at-age data for females and males. Several outliers were removed from the original datasets and growth parameters were recalculated to provide comparison with other models. Outliers were removed in an attempt to correct potential sampling errors and only data points derived from archived specimens (and therefore samples which I can not directly attest to the measurement and proper labeling of) were deleted from analyses. Relationships between centrum diameter and disc-width-at-age were assessed to identify potential errors. 71

Growth characteristics of female and male stingrays were evaluated to detennine if these parameters were equivalent between the sexes. Growth models generated for the sexes were compared using Analysis ofResidual Sums of Squares (ARSS) (Chen et al.,

1992; Haddon, 2001 ). The sum of squared residuals (RSSi) was obtained from fitting disc width and weight at age data with pooled and separate sex models (i), the degrees of freedom (DF) associated with each model was recorded, and resultant RSS and DF were summed. An F statistic was calculated to test the hypothesis that the growth models generated for females and males are coincident as:

RSSP- l:RSSi 3*(K -1) F=----=='---'-- LRSSi N-3*K where RSSp is the sum of squared residuals fitted by pooled sex growth data, RSSs is the sum of the residual sum of squares from each growth model for each individual sample,

N is the total sample size, and K is the number of samples in the comparison. The calculated F was compared the critical F value to test the null hypothesis of coincident curves. Results of three parameter VBGFs were assessed using ARSS to establish a basis for growth model development. Additionally, ARSS was applied to the modified female and male three parameter VBGF models to establish if the removal of outliers resulted in significantly different growth curves.

Frequently, only a single model is considered in studies of age and growth even though alternate functions may provide a better description of these characteristics 72

(Moreau, 1987). Akaike's Information Criterion (AIC) (1973) was applied to rank growth models in terms of their ability to produce the most parsimonious explanation of observed size- and weight-at-age data. The model with the lowest relative AIC value was selected as the most optimal growth function. A fom1 of AIC modified for nonlinear least squares models was calculated as (Burnham and Anderson ,2002):

AIC = n*log(MLE)+2K where n is the sample size, MLE is the maximum likelihood estimator of model variance and is obtained by dividing the estimated residual sums of squares by n, and K is the

2 number of regression parameters plus one to include the residual variance ( a ). Model error was assumed to be nonnally distributed and variance was assumed to be constant within each model for this analysis. Differences (L1i) between the remaining models and the one which results in the minimum AIC value were calculated to aid in ranking and comparison of models (Burnham and Anderson, 2002). Additionally, traditional

2 2 goodness of fit measures - including the coefficient of detennination (r ), adjusted r

(Kvalseth, 1985), and standard error ofthe model estimate (SEE) (Cailliet et al., 1992)­ were also assessed and compared with the results of AIC.

The maximum estimated age may not provide an adequate measure of species longevity (CD) (Beukema, 1989). In addition to reporting the maximum observed age in this study, CD was estimated for females and males separately based three additional methods. The sizes at which 95% (5(ln2)/k) and 99% (7(ln2)/k) ofDWoo is attained were detennined as a measure of CD following Ricker (1979) and Fabens (1965), respectively. 73

Taylor's (1958) method of estimating life span as the time required to attain 95% ofLo

(or DWoo)was calculated as:

loge (1- 0.95) t + ----''---"----'------'-- 0 k where parameters for the Ricker, Fabens, and Taylor fommlas were derived from resultant three parameter VBGF parameters. Growth coefficients derived from the three parameter VBGF were used solely in these calculations to allow comparisons to previously published studies.

Results

Maturity and Reproductive Observations

Reproductive observations were based on the direct assessments of 126 female and 55 male D. dipterura. Females attained maturity at greater sizes than males (Figure

3). DW50 was 57.3 em for females and 46.5 em for males. All females greater than 58 em DW were assessed as mature. A female of 58 em DW was the largest immature specimen and the smallest mature female measured 57 em DW. All males greater than

50 em DW were found to be mature. The smallest observed mature male examined was

47 em DW and the largest immature male was 50 em DW.

The onset of maturation in males was initiated near 42 em DW as indicated by clasper development (Figure 4). Transition to maturity appeared to occur between 42 and

50 em DW. Subsequently, the growth of claspers in relation to disc width markedly 74

decreased. Clasper length averaged 24.9% ofDW within this transitional size range,

11.5% ofDW below 42 em, and 27.7% ofDW above 50 em. Seminal fluid was readily expelled from many mature males during August 1998 and 1999, but was not detected during June, October, or December.

Gravid females were infrequently encountered among the artisanal fishery landings at Puerto Viejo. Eight gravid females were observed during August 1999. An additional four females examined during this period possessed enlarged uteri that contained histotrophe and extended villi, suggesting that embryos had been recently expelled, likely as a result of capture. No gravid females were observed during August of

1998, but four specimens with characteristics equivalent to post-partum conditions were noted. Fecundity ranged from 1-3 embryos per female with the smallest gravid female

(64 em DW) containing a single embryo. However, larger females did not contain more embryos than smaller gravid females (Figure 5), but may instead produce larger embryos.

Embryos measured 12.9-19.2 em DW and consisted of 13 females and five males.

Embryos less than 17 em DW were lightly pigmented and possessed sheathed tail spines.

No yolk sacs were evident on embryos 18 em DW or greater and abdomens appeared swollen due to engorged spiral valves. Embryos greater than 18.4 em DW were pigmented in manner similar to adults and appeared to be near-term. 75

Age, Growth, and Longevity

Vertebral centra from 339 specimens (191 females, 148 males) were processed for

ageing (Figure 6). While surveying artisanal fishing camps in the Bahia Magdalena

lagoon complex, I collected vertebrae from a total of289 specimens during 1998-2000

but prepared samples in an attempt to represent the entire available size range without

overemphasizing dominant size classes. Only a fraction of the archived UABCS samples

could be included in the study because of inventory labeling errors and data

inconsistencies. Vertebral centra obtained from both sampling periods included

collections that were made during February, March, May, June, August, October, and

December.

Analyses of the relationship between DW and mean centrum diameter (MCD)

indicate a significant positive linear correlation for both female and male stingrays

(Figure 7). Because no significant difference in the DW (cm)-MCD (mm) relationship

was detected between female and male stingrays, these data were combined for

regressions (n=345) (ANCOV A, F=0.833, P=0.362). A quadratic regression produced a

marginally improved fit ofthe DW-MCD relationship. The linear and quadratic

regressions are described by the following equations:

Linear: DW = 9.0075 + 6.4505 * MCD (r2=0.92)

Quadratic: DW = -0.2368 + 9.3811 * MCD + -0.2152 * MCD2 (r2=0.93)

Birth marks were easily distinguished within the vertebral centra of D. dipterura.

A birth mark was measured and identified in all centra within 2.2 mm of the focus.

- 76

Centrum composition appeared uniform within near-term embryos and no discrete increments were present. Based on the measurements of 157 centrum images and the previous linear equation, mean DW at birth was estimated to be 21.3 em, approximately 2 em DW greater than the largest observed near-term embryo. However, a broad range of size at birth was indicated, ranging from 16-28 em DW. The smallest free-living specimens collected from the fishery were 25.8 em DW (n=2; one female, one male).

Band counts of paired samples collected from anterior and posterior regions of monospondylous vertebral centra indicate a consistent pattern of increment deposition throughout the vertebral column (Figure 8). Perfect agreement was achieved in 57%

(n=17) of the estimates and percent agreement ±0.5-1.0 was 73% (n=22). When counts differed between vertebral regions, estimates based on posterior centra were typically found to be less than that of anterior samples. Count discrepancies occuned primarily among specimens estimated to have 11 or more bands. No significant difference was detected between mean band counts from anterior and posterior vetiebral regions (paired­ sample t-test, to.05(2),29=2.045, t=0.68). Counts obtained from consecutive vertebrae within either anterior or posterior regions displayed much higher agreement. All size-at­ age estimates incorporated into growth models were based on estimates derived from anterior centra.

Clarity ratings assigned to samples during each round of age estimates indicated that the readability of banding patterns within D. dipterura vetiebrae is variable and not explicit. The majority of thin-sectioned centra received a clarity grade of 3 (84.4%, 77

n=286), indicating that two band counts could be interpreted from the sample. No centra were ranked as unambiguous and exceptional in clarity (grade 5). A total of 4.1% (n=14) was noted to be unambiguous with reduced clarity (grade 2), 10.0% (n=34) possessed banding pattems that resulted in two or more potential age estimates (grade 4), and 1.4%

(n=5) were discarded because of extremely poor clarity or damage.

Age estimates of D. dipterura were complicated by diverse pattems of increment deposition observed with the vertebral centra. Agreement could not be achieved among

10.4% (n=35) ofthe remaining vetiebrae aged in this study following four reads because of vague or irregular banding patterns. Irregular pattems observed within this species included discontinuous, joined, split, narrow, and crowded or clustered increments.

Widths of both opaque and translucent bands were highly variable in relation to each other and like increments. In general, deposition patterns differed notably following the first 4-6 bands.

Based on four independent reads, precision estimates were 9.85% (JAPE),

13.18% (CV), and 6.59% (D) overall. Repeatability of age estimates was slightly lower among females (IAPE=10.06%) than males (IAPE=9.59%). However, after reviewing final ages and notes associated with each ageing round, my impression is that the interpretation of banding patterns within large males was generally more challenging than among their female counterparts. The lowest relative ageing precision occurred among the youngest age classes (Figure 9A, B, C). Estimates of D produced maximum individual values greater than 35% among those with band counts of 1-1.5. Values of D 78

decreased with increasing ages, consistently remaining below 11% among all specimens by age 8.

An assessment of band count differences between the final and previous rounds indicated that differences tended to decrease following the first round of estimates

(Figure 10). The dispersion of differences between reads decreased slightly in subsequent rounds. Differences in band counts between rounds appeared to be randomly distributed, suggesting that linear, systematic bias of age estimates did not occur between or among rounds.

Percent agreement (100%) calculated from four rounds of age estimates was 8.6% when grouped by 5 em DW size classes (Table 2). Much of the disagreement associated with band counts arose from initial difficulties determining the edge type. The percent agreement that differed based only on disparity of edge type classification (±0.05) was

27.2%, thus cumulative agreement ±0-0.05 bands was 35.8%. Agreement within a maximum of± 1 band was achieved for 73.5% of the centra examined. In contrast to the individual values of D that indicated increasing precision with age, differences in percent agreement generally increased among larger size classes. However, repeatability of band counts was not high among any particular size class.

Seasonal trends in the type and extent of increment development were detected using centrum edge analysis (Figure 11 ). Centrum edge analysis was conducted on 205 thin-sectioned samples which were detennined to have unambiguous edge types. The propmiion and class of edge types varied among all months examined (February, March, 79

May, June, August, October, and December). Translucent increments were primarily observed during the winter and spring months. Narrow translucent edges were only observed in December, February, and March. The number of centra with broad translucent edges decreased from February to a minimum in Jtme. Translucent edges were most common during the late spring through late fall months. During August and

October, all samples were determined to have opaque edges. Broad opaque edges were the only type detected during the month of October. Monthly centrum edge characteristics suggest that a single complete band, comprised of one translucent and one opaque increment, is formed within vertebral centra each year.

Variation of mean MIRs was also seasonal, closely following the trends exhibited by centrum edge analysis (Figure 11). Mean MIRs were calculated from 139 D. dipterura collected during four non-consecutive years. Lowest monthly mean MIR values among pooled samples occurred in February, with a peak in December. Kruskall­

Wallis one-way analysis of variance on ranks indicated that mean MIR values varied significantly among months (H= 19.59, df= 6, P= 0.003). The mean MIRs of October and February (qo.os,7=3.038, Q=3.377) and December and February (qo.os,7=3.038,

Q=3.408) were identified as the source of the significant difference among months using

Dmm's multiple comparison of ranks. Maximum and minimum MIR values suggest that increment formation is initiated during or shortly after December and May. In conjunction with centrum edge analysis, analyses of mean MIRs confirm the annual deposition of a single band within the vertebrae of D. dipterura. 80

Trends in mean MIRs were examined graphically for three arbitrary size classes by month of capture (Figure 12). Large and medium size classes exhibited pattems of monthly MIRs similar to each other and that of the pooled assessment. Mean MIR values were lowest in February and increased throughout the year among medium and large sizes classes, but peaked in May within the smallest size class. Standard errors among mean MIRs were highest in May and December. This variability is consistent with the hypothesis that new increment formation occurs at or near these times. However, a distinct trend among mean monthly MIRs was not evident among the smallest (20-40 em

DW) size class.

In total, age estimates from 304 out of 344 D. dipterura vertebral samples were incorporated into size-based (i.e., DW) growth models. The largest female in the study measured 83 em DW and a maximum age based on consensus of counts of28 was obtained for a 76 em DW female. The largest male collected for this study was 60 em

DW and the maximum final band count recorded was 19 years. Both female and male samples included age 0 and 0.5 year old specimens. A variable range in size-at-age estimates was observed within both sexes. Growth characteristics were detennined to differ significantly between the sexes (ARSS, F=ll.73, P=

DW and weight-at-age data were therefore analyzed separately for all models.

Estimates ofDWoo resulting from three parameter VBGF models were greater than those obtained from the two parameter form for both females and males (Table 3,

Figure 13). The two parameter VBGF model produced estimates ofDWoo that were less 81

than the maximum sizes of both sexes that were included in these analyses. Although the three parameter VBGF form generated DWoo estimates that were greater than the maximum sizes ofthis study, the estimates were within the range of maximum sizes reported for the species. Growth coefficients (k) based on the traditional three parameter

VBGF were less than predicted by the two parameter model. The size at birth (DWo) calculations of the three parameter VBGF are notably greater than the estimates based on direct vertebral measurements (mean=21.3 em DW).

Female D. dipterura grow at slower rates and mature at later ages than males.

This sexually dimorphic growth pattern was revealed by both two and three parameter fonns ofthe VBGF and was further supported by ARSS (Table 3, Figure 13). However, growth rates of juvenile females and males were similar. Estimates of median age at maturity based on the three parameter VBGF and DW50 conesponded to ages of 8-11 years among females and 5-8 years among males.

Growth parameters estimated using size-based Gompertz models fell between those predicted by two and three parameter VBGFs (Table 3, Figure 14). Female and male DWoo predictions were very similar to, but slightly greater than the maximum sizes

included in this study. However, DW0 estimates are greater than those previously calculated using VBGFs and nearly 10 em greater than the probable mean DW at birth.

The magnitude of differences in k between the sexes was equivalent between Gompertz and VBGF three parameter models. Growth rates of juveniles (ca. 25-45 em DW) were similar between the three parameter VBGF and Gompertz models. 82

Weight-based Gompertz models predicted smaller weight-at-age estimates for females and males than were generated from the VBGF (Table, 3; Figure 15). The VBGF

predicted greater Woo values and W0 estimates more similar to weights obtained from the smallest free-living specimens than were generated using the Gompertz model (Table 3).

Estimates of W 0 based on both growth functions provided weight at birth values that are relatively more comparable to actual values than were generated using the equivalent size

at birth estimates (DW0 ) of other models. Both weight-based growth models predicted male Woo values that were less than the maximum observed (60 em DW, 11.4 kg).

Variability among individual weight-at-age data was observed for both sexes.

Growth parameters estimated using three parameter VBGFs from which outliers

were removed generated reduced estimates of D Woo and greater k and D W 0 values for both females and males than were obtained using the unmodified disc-width-at-age data

(Table 3). Standard errors associated with DWoo, k, and t0 were also decreased by using the modified data sets. Omission of data points did not result in significantly different

VBGF curves for females (ARSS, F=0.03, P=0.99) or males (ARSS, F=0.02, P=0.99).

Goodness-of-fit estimators included in this study provided conflicting evidence of the most appropriate description of growth for female and male D. dipterura (Table 3).

The broadly applied r2 statistic indicated that the three parameter VBGF and weight­ based Gompertz models best explained the growth data of females and males, respectively. Less commonly applied, but more appropriate for non-linear models, adjusted r 2 values supported these models for each sex as well. In contrast, consideration 83

of SEEs results in the conclusion that the Gompertz weight-based model is the most appropriate description of female growth and weight-based models in general provide the best fits of male growth data. Weight-based models produced the best approximating and most parsimonious fits of growth data according to SEE and AIC.

Based on AIC, female weight-at-age data were best fit by the VBGF and male weight-at-age data were best interpreted using the Gompertz weight-based model (Table

3). The modified VBGF provided the best fit of disc-width-at-age data for both females and males. However, Gompertz and VBGF models produced similarly parsimonious descriptions of size- and weight-based age data.

A wide range of CD estimates was calculated from tlu·ee parameter VBGF values determined for females and males (Table 4). All theoretical CD estimates produced values that are considerably greater than the maximum observed ages. Taylor's (1958) method of estimation generated the lowest maximum age estimates. Potential maximum ages approaching 90 years are predicted when CD is considered to represent 99% ofDWoo. All estimates indicated that females attain greater ages than males.

Discussion

Maturity and Reproduction

Aspects of the reproductive biology of D. dipterura from the Bahia Magdalena lagoon complex have been examined by several other researchers. Mathews and Dmck­

Gonzalez (1975) estimated that the onset of maturity among male D. dipterura occurred 84

at approximately 47-48 em DW and that the majority were mature by 51 em DW (n=106) based on clasper length-DW relationships. Female reproductive condition was not assessed by Mathews and Druck-Gonzalez (1975). Based on a 1992-1994 study of 1,223 female and 1,516 male specimens derived from the Puerto Viejo artisanal fishery,

Mariano-Melendez (1997) determined that size at 50% maturity was 65.5 em and 45.5 em DW for females and males, respectively. An abrupt increase in clasper length to DW was recorded among males 40-47.5 em DW.

Estimates ofDW5o in this study were 57.3 for females and 46.5 em for males.

The smallest mature specimens that I observed were a 57 em DW female and 47 em DW male. Maturation among females appeared to occur over a relatively narrow size range.

The apparent contradiction between predicted male DW50 having a value less than that of the smallest observed mature male in this study can be attributed to the relatively small sample size of males included in the logistic regression (n=55) and that median size at maturity is a theoretical estimate based on the available empirical data. However, both the estimate ofDW5o resulting from fitting the logistic equation to binomial maturity data and direct observations of male maturity based on clasper length from this study agree well with the estimates of male size at maturity repmied by Mathews and Druck­

Gonzalez (1975) and Mariano-Melendez (1997).

Female D. dipterura mature later and grow to larger sizes than males. Earliest observed and estimated median size at maturity for females was 10.0 em and 10.8 em

DW greater than observed for male D. dipterura, respectively. Such variation between 85

the sexes is common among dasyatid stingrays. Female size at maturity is repmied as 10 em greater for D. imbricatus (Devadoss, 1978), 30 em greater than that of males for D. longa (Villavicencio-Garayzar et al., 1994), 13 em greater for D. sayi (Snelson et al.,

1989), and 2 em greater for D. marmorata (Capape, 1995).

Sexual dimorphism and variation in size at maturity are differentially exhibited within the myliobatiforms. Females within the family Myliobatidae mature at larger sizes than males, but sexual dimorphism may be less prominent among the closely related urolophid stingrays than observed for dasyatids (Table 5). Babel (1967) and White et al.

(2002) noted that although females attain larger maximum sizes, maturation of both sexes occurs within the same size range. Additional information on the relationship between maturity and size of selected male and female myliobatiform stingrays is presented in

Table 5.

Although male size-at-maturity estimates reported in this investigation coiTespond well with those of previous studies, female DW50 and earliest size at maturity were considerably less than those determined by Mariano-Melendez (1997). In his study, females of 64 em DW or less were typically found to have poorly developed uteri

(Mariano-Melendez, 1997). Females 56-69 em DW were classified as maturing on the basis of a shift in ovocite and oviduct diameters in relation to DW. Although the criteria of Snelson et al. (1988) were applied in both studies for assessing maturity, I simplified the method in this study and classified female reproductive status as either immature or mature. Non-reproductively active females that had attained maturity for the first time 86

would have been categorized as mature in this study only. Mariano-Melendez (1997) did not apply a logistic regression and reported the average size at maturity based on methods that were not fully clarified. The smallest mature and largest immature females were not reported and limit additional comparison of our maturity data. Both Mariano-Melendez

(1997) and I observed gravid females of64 em DW.

The Phenomenon of Apparent Change in Growth Rate occurs as a result of the increased likelihood of slower growing individuals of a population experiencing a higher rate of fishing mortality than those that are relatively faster growing portion of the population (Ricker, 1969; Moulton et al., 1992). Differences in maturity or other life history characteristics may be reported for the same species depending on collection or sampling methodology. However, because specimens in both the present and Mariano­

Melendez (1997) studies were obtained from the same fishing camp, used similar gear and mesh types, and fished in similar locations, the potential for bias related to sampling artifacts such as the Phenomenon of Apparent Change in Growth Rate is low. It is likely that the observed differences in size at maturity have resulted from discrepancies in methods of maturity estimation, sample sizes, proportional differences in the size distribution of samples, and the temporal distribution of sample collection. Inter-ammal variability in the vulnerability of the fished population from increased fishing intensity within the lagoon complex, environmental conditions, or stingray behavior may also have contributed to the divergent estimates of female size at maturity between these studies

(Ricker, 1975). 87

Increased mortality from fishing pressure can serve as a selective force that results in shifts in population growth and reproductive characteristics (Holden, 1973; Sminkey and Musick, 1995; Rose et al., 2001 ). Because of density dependency and phenotypic plasticity, species may alter growth and reproduction as a result of fishing pressure over a short period (Steams, 1992; Rochet, 1998). Holden (1973) considered density-dependent influences of elasmobranch life histories in response to exploitation and suggested that inverse effects on litter size and growth. Populations at reduced densities may reach maturity at earlier sizes and/or increase reproductive output. A decrease of age at maturity and associated an increased growth rate was detected among Atlantic sharpnose sharks, Rhizopriondon terraenovae, following population reductions due to fishing pressure (Carlson and Baremore, 2003). An increase in juvenile sandbar shark,

Carcharhinus plumbeus, growth rate and size at maturity following population decline was reported by Sminkey and Musick (1995), but no change in the associated age at maturity was observed. Although density-dependent compensatory responses are difficult to conclusively demonstrate, the potential for fishing mortality to induce changes in life history parameters is well established (Roughgardren, 1971; Rochet, 1998; Rose et al., 2001).

The observed differences between female size at maturity for D. dipterura during the early versus late 1990's could indicate an inverse, density-dependent response to fishing pressure. Fishing activity throughout the Bahia Magdalena lagoon complex would reduce the abundance of D. dipterura as well as its potential predators and 88

competitors. Increased growth rates could result from decreased population densities and a concomitant decrease in the size at maturity would be evident. Although growth information prior to that produced by this study are not available, the possibility that a shift in female size at maturity (1992-94: 65.5 em DW; 1998-2000: 57.3 em DW) in response to fishing pressure is unlikely given the time span, but should not be completely dismissed. An analysis of potential density-dependent, compensatory mechanisms is outside of the scope of this study, but related hypotheses should be examined within the

Bahia Magdalena lagoon complex.

Mariano-Melendez (1997) concluded that reproduction in D. dipterura was annual and that pmturition occurred in August tln·ough early September following a 9.5-

10 month gestation period that included diapause. Although a detailed investigation of the reproductive cycle was not an objective of this study, the absence of gravid females collected during the month of August in the wann water year of 1998, suggests that the plasticity of parturition and the gestation period are occurring. Lewis (1982) reported that pmiurition of D. sabina in the northeastern Gulf of Mexico occurred 3-4 weeks earlier in the summer during 1977 than it had in 1976. Fetal and birth sizes were greater when pmiurition occurred earlier in the year. The occurrence and abundance of D. centroura on the southeastern U.S. coast is strongly associated with water temperature

(Hess, 1959; Struthsaker, 1969). It is likely that mature and gravid females arrived sooner and parturition occun-ed earlier in the summer of 1998 than in the cooler water year of 1999 in the Bahia Magdalena lagoon complex. If embryonic diapause and 89

arrested development are reproductive strategies employed by D. dipterura as has been suggested for other dasyatids (Snelson et al., 1989; Maruska et al., 1996), it may provide a mechanism to incorporate flexibility into parturition, thus, occurring somewhat earlier or later within a season dependent on environmental conditions.

Fecundity is notoriously difficult to estimate among myliobatifonn rays. Because of stress from capture and elevation of the specimen from the water, embryos of various stages are commonly aborted by myliobatiforms (Hamilton and Smith, 1941; Struthsaker,

1969; Snelson et al., 1988). Gravid D. dipterura were not an exception to this tendency.

When present, embryos were often expelled upon removal from the gillnet and mature females containing uterine histotrophe and long uterine villi associated with gestation were occasionally observed. I recorded a maximum of three embryos that were collected females of65, 66, and 72 em DW. Mariano-Melendez (1997) examined 24 gravid females that contained 2-4 embryos. Combining our data (32 females, 82 embryos), I calculated the average fecundity of D. dipterura as 2.72±0.73 SD and range as one to four offspring.

Low fecundity is characteristic of dasyatid stingrays. The similarly sized stingrays, D. chrysonota and D. sayi, give birth to 1-5 (mean 3.07) and 1-6 (mean 3.5), respectively (Cowley 1990; Snelson et al., 1989). The limited infonnation available on the eastem Pacific congener, D. longa, suggest a production of 1-4 young (Villavicencio­

Garayzar et al., 1994). Observed fecundity of D. dipterura closely approximates that of the smaller bodied stingray, D. sabina, which produces 1-4 (mean 2.6) offspring annually 90

(Snelson et al., 1988). However, considering the difficulty in accurately determining litter size, it is possible that maximum fecundity of D. dipterura is slightly underestimated and maximum brood size could be five to six.

A relationship of increasing fecundity with matemal size has often been described among sharks (e.g., Pratt, 1979; Loefer and Sedberry, 2002), but may not be common among myliobatiforms. Martin and Cailliet (1988) suggested that energetic costs of reproduction may be optimized by reducing the number of eggs produced but simultaneously allowing egg/embryos size to increase. They concluded that the number of offspring of the myliobatid ray, Myliobatis californica, increased with female size.

Because fecundity is largely space limited, an altemative trade off would be to produce larger, not necessarily more offspring. Myliobatiform rays may not have the luxury of producing both larger and greater numbers of offspring with increasing matemal size.

Comparatively larger offspring bi1ihed by the largest females of a population could be afforded the advantage of increased survivorship due to a larger size at birth (Steams,

1992).

Although I was only able to examine a small munber of gravid females (n=8), it does not appear that fecundity of D. dipterura increases with increasing maternal size

(Figure 5). Instead, it appears that larger females generally give birth to larger young.

This relationship has been suggested for several dasyatids, including D. centroura (Hess,

1959), D. imbricatus (Devadoss, 1978), D. sayi (Hess 1959), and D. sephen (Raje, 2003).

Cowley (1990) reported that no significant relationship was detected between uterine 91

fecundity and matemal size in D. chrysonata but did not examine the possible increase in

offspring size. Among two comparatively smaller stingrays, D. sabina and Urobatis

halleri, larger females have been found to produce larger broods (Babel, 1967, Lewis,

1982). However, this pattem was not supported for D. sabina from the Atlantic coast of

Florida (Snelson et al., 1988). The relationship between matemal size and fecundity or

offspring size among myliobatiforms requires additional investigation to clarify these

trends and their potential life history implications.

Wide ranges in size at birth have been reported among dasyatids. Estimates of

DW at birth based on measurements of centrum birth marks and the relationship between

DW and mean centrum diameter suggest that size at birth ranges from 16-28 em DW.

However, because of the limited number of small specimens available in this study, it is

likely that the linear and quadratic regressions ofDW-mean centrum diameter relationship overestimate the size at birth. Linear regression predicted greater mean sizes at birth than were obtained by a quadratic fit to the same data. The smallest free-living specimens collected in this study were 25.3 em DW. Mariano-Melendez (1997) collected free-living specimens of both sexes measuring 24 em DW and estimated size at birth to range from 17-19 em DW. I observed near-tenn embryos in excess of 19 em DW and

suggest that a more likely range of size at birth for D. dipterura is 18-23 em DW and that this range is likely skewed toward greater sizes at birth. A wide range ofrepmied DWs

at birth could be accounted for by larger females within the population giving birth to comparably larger offspring. Estimates of size at birth based on examination of embryos 92

and free-living specimens range from 34-37 em DW in D. centroura (Struthsaker, 1969;

Capape, 1993), 17.4-25.1 em DW in D. ch1ysonata (Cowley, 1990); 10.0-13.5 em DW in D. sabina (Lewis, 1982); and 15-17 em DW in D. sayi (Snelson et al., 1989).

Due, in part, to conservative reproductive strategies, elasmobranchs have frequently demonstrated rapid reduction in abundance and low resilience to fishing pressure (Holden, 1973; Pratt and Casey, 1990; Stevens et al., 2000). These conservative strategies include low fecundity, large sizes at birth, late maturity, and long gestation periods. Although myliobatifonn stingrays possess some of the shortest gestation periods known for elasmobranchs (Babel, 1967; Lewis, 1982), actual fertilization of ova may be delayed or embryonic development may be arrested for many months prior to actual gestation (Snelson et al., 1989; Maruska et al., 1996). The reproductive characteristics described for D. dipterura indicate a conservative reproductive strategy and high vulnerability to fisheries exploitation.

Based on the median female and male sizes at maturity estimated in this study, I conclude that the majority D. dipterura landed in the fishery at Puerto Viejo are immature (Chapter 1). The Bahia Magdalena lagoon complex may serve as an impmiant birthing and nursery area for this species. Thus, in addition to the conservative reproductive strategy employed by D. dipterura, the nature of a fishery directed on individuals that have not yet reproduced in locations that may serve as a critical pupping area may further decrease the resilience of this exploited population. 93

Age, Growth, and Longevity

The inherent variability of increment deposition within an ageing structure and subjectivity associated with interpreting banding patterns influence the accuracy and precision of age estimation and resulting growth models. The clarity and readability of banding patterns within the vetiebral centra of D. dipterura were complicated by irregular or discontinuous increments. Structural discontinuities, general low clarity of samples, and the limited initial experience of the author constrained repeatability of estimates and contributed to an overall JAPE of9.8%. However, this value is artificially inflated in comparison to other studies because band counts of D. dipterura were estimated to the nearest 0.5 years and thus incorporated a greater potential for error.

When precision estimates based on the number of completed bands (whole values) are considered in this study, overall JAPE decreases to 8.4%. An investigation of the age and growth of the lesser electric ray, Narcine entemedor, fi-om the Bahia Magdalena lagoon complex produced comparable levels of precision to those calculated in this study

(JAPE=10.4%; D=6.1; Villavicencio-Garayzar, 2000). Similar levels ofprecision have been reported for age estimates derived from thin-sectioned vertebrae among relatively long-lived elasmobranchs including; Carcharhinus plumbeus (Sminkey and Musick,

1995), Galeocerdo cuvier (Wintner and Dudley, 2000), and Lamna nasus (Natanson et al., 2002).

Assessments of percent agreement among age estimates facilitate valuable secondary evaluations of precision and dispersion of ageing en·or that may otherwise be 94

masked by the traditional measures of CV, D, and lAPE (Hoenig et al., 1995; Cailliet and

Goldman, 2004). Initial difficulty interpreting the edge type among the smallest age classes resulted in much greater relative imprecision within this group than detected among the largest size classes. The proportion of samples discarded because of low clarity or a lack of agreement among reads was similar to or less than those reported in studies of other batoids (Cowley, 1997; Martin and Cailliet, 1988b; Walmsley-Hart et al.,

1999). Despite the complexity of interpreting banding patterns, vertebrae proved to be useful ageing stmctures for D. dipterura. Centra were well calcified and their diameters increased in direct proportion to disc width (Figure 7).

Irregular or discontinuous increment patterns (checks) as well as the shape and composition of the ageing stmcture itself affect clarity and readability. Vertebral stmcture and the extent of calcification may vary considerably among elasmobranchs

(Ridewood, 1921; Officer et al., 1996). Exogenous factors, such as El Nifio or La Nifia events, may further affect the appearance of hard parts and increment deposition within them (Pearson, 1996; Meekan et al., 1999). These sources of error may be linked with interpretation error and simultaneously influence age and growth estimates in a random or biased manner (Campana, 2001 ).

The limited infonnation available for dasyatid stingrays suggests that the interpretation ofve1iebral banding pattems within this group may be relatively complex.

Sclm1id (1988) obtained reproducible counts from only 36 of 104 (65%) whole xylene stained D. sabina ve1iebrae. Ground sections of these centra provided improved 95

resolution, but 33% of the samples were discarded because of a lack of agreement among counts. The ability to consistently identify discrete bands was considered a primary factor for these discrepancies.

Cowley (1997) reported difficulty interpreting distinct bands due to the consistent presence of"false rings" within broad translucent increments of thin-sectioned D. chrysonata centra. False rings were identified on the subjective basis of width and may have lead to underestimation of ages if valid ammal growth zones were excluded. A similar pattern of narrow false ring deposition was reported by Goosen and Smale (1997) within smoothound sharks, Mustelus mustelus, from South African waters. Although narrow increments were observed within D. dipterura centra, the regular pattern of narrow, bunched false rings within broad, translucent increments as described by Cowley

(1990, 1997) were not observed. Unfortunately, the repeatability of band counts among these studies of dasyatid stingrays caru1ot be assessed because neither Cowley (1997) or

Schmid (1988) calculated measures of precision or bias associated with their age estimates.

Well-defined criteria for valid increment and band identification were established for this study prior to assigning any ages. Additionally, four age estimates were made for each sample in an attempt to reduce potential errors resulting from the ageing structure or reader subjectivity. However, the possible influence ofEl Nino or La Nina events on ecophysiological processes regulating growth within this population should not be ignored and may have resulted in check marks (false rings) that were incorrectly 96

interpreted as valid increments within vertebral centra. If so, a tendency for slight

underestimation of ages within this study is more probable than that of overestimation.

Vertebrae that had been stored in alcohol were frequently cloudy in appearance

and generally more difficult to read. Of the 92 samples used in this study that had been

collected and stored in alcohol since 1992, 24% of the samples (n=21) were discarded as a result of inconsistent reads. In contrast, only 5% (n=14) of the samples collected between 1998 and 2000 were discarded because of a lack of agreement. These latter samples were stored in alcohol for no longer than six months before being cleaned and stored dry in vials. Wintner and Cliff ( 1996) and Wintner et al. (2002) also noted a reduction in contrast between growth bands among vertebrae that had been stored in alcohol. A remarkably high percentage of unreadable vertebrae (21 %) were reported from an age and growth study of dusky sharks, Carcharhinus obscurus (Natanson et al.,

1995). Although these authors did not discuss possible reasons for such limited readability, it is noteworthy that some samples had been stored in ethanol since 1963.

Because long-tenn storage of elasmobranch vertebrae in alcohol may severely reduce sample clarity and precision of age estimates, ageing structures should be stored frozen or dry whenever possible.

The timing of birth mark fonnation among elasmobranchs is highly variable.

Vertebrae from the largest near term embryos collected in this study provided no evidence ofbi1ih mark development. In contrast, Cowley (1990) reported evidence of a birth mark forming on the outer centrum edge of a full-term D. ch1ysonata embryo. The 97

smallest free-living D. dipterura (25.8 em DW, age 0, n=2) captured in August of 1998 possessed opaque increments that were developing beyond fully formed translucent birth marks within their vertebral centra. Loefer and Sedberry (2003) noted that vertebral birth marks were actually formed subsequent to birth among Rhizoprionodon terraenovae from the southeastem United States. A similar pattem of deposition appears to occur among D. dipterura, however additional vertebrae from embryos and neonates are necessary to conclusively establish the timing of birth mark formation.

Significant differences among pooled monthly mean MIRs indicate that a single band is formed annually within the vertebrae of D. dipterura. October and December

MIRs differed from mean February values, demonstrating winter fonnation of new bands. This evidence for seasonal increment deposition validates the assumption that one band is equivalent to a year for models of age and growth of this species. Based on relative marginal increment analysis, Villavicencio-Garayazar (2000) suggested that a single growth band was formed annually within the vertebral centra of the lesser electric ray (Narcine entemedor) collected from the Bahia Magdalena lagoon complex during

1991 and 1992. Opaque and translucent increment formation withinN entemedor centra appeared to be initiated during May (as proposed in this study) and September-October, but these trends were not evaluated statistically. The pattem of increment deposition observed for D. dipterura agrees with the findings of Cowley (1990, 1997), who concluded that one distinct opaque and translucent increment was fonned annually in captive D. chtysonata. The results ofMIR analysis provide validation of increment 98

periodicity in D. dipterura but should not be interpreted as validation of the absolute ages or ageing method (Cailliet and Goldman, 2004; Campana, 2001).

Although commonly employed as a semi-direct validation method, marginal increment analysis has often been applied inappropriately and may be of low resolution

(Campana, 2001 ). Validation should be applied to all ages and marginal increment analyses should ideally be restricted to a single age class at a time (Beamish and

McFarlane, 1983; Campana, 2001 ). Variability of seasonal increment deposition patterns may be obscured by pooling age classes. An observed periodicity of increment deposition that is assumed as valid may not reflect the growth patterns among all age classes as a result of differences in relative growth rates, particularly among older classes.

Although an insufficient sample size restricted the assessment of age-specific MIR analysis, a size-based assessment of MIRs was evaluated for comparison to the pattern indicated from pooled MIRs (Figure 12). Such size-based analyses were not advocated by Campana (200 1), but may provide an improved method of analysis by examining

MIRs in tenns of empirical measurements rather than subjective age estimates. Although a complete size- or age-based MIR analysis was not examined, a broad range of age and size classes was included in the MIR analysis and a subsequent assessment of general size classes supported the trends observed from pooled data alone. Conclusions drawn from MIR analysis may be further biased by the inclusion of specimens from multiple or non-continuous years and the vagaries associated with identifying recently formed increments. Although significant differences were detected in mean MIRs among 99

months, conclusions regarding the timing and periodicity of band fonnation could be enhanced by including samples from all months and extending this analysis to specific age or s1ze groups.

Non-parametric statistical analyses were applied to mean monthly MIR data because of unequal sample sizes and heterogeneity ofvariances. Upon determining that a significant difference existed among the mean monthly values, Dunn's test of multiple comparisons on ranl<:s was applied to identify which month or months produced these significant differences in MIRs. This approach had not previously been applied in marginal increment analyses, but provides an objective, quantitative assessment for demonstrating the timing of increment formation.

The modified technique of centrum edge analysis presented in this study provided extremely valuable, corroborative evidence of mmual band formation in D. dipterura.

Edge analyses among elasmobranch ageing studies have primarily identified only the type of increment forming on the outer edge of the ageing structure on the basis of optical qualities (i.e., opaque or translucent increments) (e.g., Martin and Cailliet, 1988b, Yudin and Cailliet, 1990; Wintner et al., 2002). Consideration of the relative width ofboth opaque and translucent increments in relation to time of capture may provide details that would otherwise be undetected through MIR analysis alone. For example, although the

December MIR is the greatest mean value calculated in the study, it is also associated with the largest standard enor (Figure 11 ). Centrum edge analysis from December not only indicates that both opaque and translucent margins were present on the edges of 100

vertebrae collected from this month, but that the translucent bands were of the narrowest

type and had not been observed within the sampled population for several months. Thus,

it may be inferred that the standard error associated with the mean MIR from December

does not simply result from broad variation in marginal widths or edge types present in

the population, but that a shift in the depositional pattern of increment formation is

occurring at this time.

The classification of marginal edge types and extent of development corresponded

well with known seasonal sea surface temperature fluctuations in Bahia Almejas. Sea

surface temperatures recorded from the lagoon complex typically range from 20.3-21.5°

C between December and May, increase slightly during June (22.3° C), remain elevated

(>25° C) from July tlu·ough October, with peak temperatures occurring in August (27.7°

C) (Lluch-Belda et al., 2000). Although inter-mmual variability and large-scale oceanographic events may alter this thermal regime, June and November commonly represent seasonal transition periods in this region. The changes in centrum edge type detected during May and December in D. dipterura may reflect ecophysiological responses to enviromnental changes occurring during the aforementioned transition periods.

Details regarding the prevalence or periodicity of check marks could also be inferred using centrum edge analysis. Although a qualitative measure, the association of centrum edge type and relative width within each month provides a constructive supplementary account of increment deposition and periodicity that is not incorporated 101

by the traditional approach. Statistical evaluations of categorical centrum edge data may

be applied to enhance the rigor ofthe assessment (e.g., Vilizzi and Walker, 1999), but

were not developed in this study. Ideally, centrum edge analysis could be enhanced

through the use of year-, age-, and size-specific evaluations.

Single outliers were observed in the centrum edge analysis data from February

and May. Examples of broad translucent increments were recorded from each of these

months. These examples may reflect individual variability in growth rates or responses to environmental influences. It is also possible that the edge type of these samples may

have been misinterpreted because of sample damage. Among ageing studies using

otoliths, newly formed margins are often only recognized after attaining 20-40% of the previous like increment width (Vilizzi and Walker, 1999). Both ofthese samples were obtained from the archived collection of vertebrae at UABCS. The archived D. dipterura ve1iebral collection contained incorrectly placed vertebrae from other batoids and incompletely labeled material. It is perhaps most likely that these samples were improperly labeled or incorrectly grouped.

Although elasmobranchs are generally considered to possess slow growth rates, estimates of mean growth rates (k) encompass a broad range ofvalues (Musick, 1999;

Cailliet and Goldman, 2004). Branstetter (1990) delineated growth rates among sharks as

1 1 slow if k is detennined to be <0.1 year- and relatively fast if k >0.1 yea{ • Dasyatis dipterura are long-lived (up to 28 years), slow growing elasmobranchs. Growth rates of males and females are similar initially but diverge significantly as maturity is approached 102

between 8-11 years and 5-8 years among females and males, respectively. Differential growth rates and maximum sizes between females and males are commonly observed among myliobatifom1 stingrays (Martin and Cailliet, 1988b; Smith and Meniner, 1987;

White et al., 2002). The faster growth rate of males is associated with decreased longevity relative to females.

The growth trajectory of an individual may markedly differ from the predicted population average (Sainsbury, 1980; Pilling et al., 2002). Notable individual variability within size- and weight-at-age groups was observed among D. dipterura. As previously discussed, difficulties inherent in enumerating valid increments may contribute to the observed variability around fitted mean growth rates. Officer et al. (1996) reported considerable variation among size-at-age estimates based on the region of vertebrae that were examined. However, vertebrae used in this study were consistently collected from the same location. Analysis of band count variability between vertebral regions indicated that divergence of counts between anterior and posterior locations occuned primarily among larger individuals in this study.

Interannual variation of oceanographic conditions may differentially affect growth characteristics of specific cohmis. Because the Bahia Magdalena lagoon complex is located on the cusp of a biogeographic and oceanographic gradient, such extrinsic environmental influences may be particularly acute. Natural variation of individual growth characteristics was evident within the study population. The largest female stingray (81 em DW) was not detennined to be the oldest in the study. However, the 103

oldest individual aged (76 em DW) did possess the largest centrum diameter. Three parameter von Bertalanffy fits to age-at-mean-centrum diameter data were associated with considerable reductions in the variation of residuals about the regression plane

(SEE: female= 0.65; male= 0.45). Because a single band is formed annually within the vertebral centra of D. dipterura, individuals within an age-class may not be of the same disc width, but are more likely to possess centra of the same diameter. The potential for individual growth differences within this population tmderscore the value of incorporating uncertainty and stochasticity into projections of population growth parameters derived from mean growth rates.

The von Bertalanffy growth function is pervasive among biological assessments of growth in fishes. The function's extensive application, biologically interpretable parameters, and derivation :from bioenergetic principles of anabolism and catabolism help to propagate its' appeal (Ricker, 1979; Haddon, 2001). However, serious limitations and reservations have been identified with the growth function (Knight, 1968; Moreau, 1987;

Roff, 1980). Evidence of the model's limited ability to reflect early growth (Gamito,

1998; Moreau, 1987) was observed in this study. Many ofthe criticisms applied to the

VBGF are, however, relevant to many growth functions in general (e.g., assumption of asymptotic growth). Appropriate growth models should be selected on the statistical basis oftheir fit, indication ofbiological reality, and convenience (Moreau, 1987). If an investigator's objective is to express the growth characteristics of a species in quantitative 104

terms, it is imprudent and may be counter-productive to base this description on a single, exclusive model.

Size-based estimates of three parameter VBGFs produced the most biologically realistic and more practical growth parameters for D. dipterura. In contrast, weight­ based von Bertalanffy and Gompertz models generated the best statistical descriptions of growth for this species. The lower SEEs associated with Gompertz and von Bertalanffy fits of age-weight data alike demonstrate improved goodness of fit. The volumetric measure encompassed by body weight data may incorporate greater detail and thus provide enhanced resolution of growth characteristics. This potential may prove to be particularly beneficial for growth descriptions of dorso-ventrally flattened batoids.

However, the comparatively lower number of data points and lack of weight information available across the entire observed range of females reduced the explanatory value of weight-based models in this study.

The common, sole use of the three parameter VBGF belies that fact that it does not provide a universally appropriate description of organismal growth. Despite any perceived convenience gained through the ability to compare generated parameters to another study, a model that produces a poor fit to data is of little benefit and may fmihermore be misleading (Buckland et al., 1997; Hilborn and Mangel, 1997).

Evaluations of model fit should be a routine component of age and growth studies. When reported in age and growth studies, model goodness-of-fit has primarily been estimated

2 using the coefficient of variation, r . This measure represents the proportion of the total 105

variation in Y explained by the fitted regression (Zar, 1996). In this study, both r 2 and adjusted r2 provided potentially misleading information in tenns of model selection.

Examination of r 2 values obtained from the three parameter size-based VBGF and the weight-based Gompertz and VBGF indicate very similar descriptions of model fit.

However, errors associated with these models are notably different (Table 3). While r 2 may provide a useful description of fit when only a single model is considered, the measure may be insufficient for evaluating multiple models. Ratkowsky (1983) advocated "residual variance" (also referred to as residual mean square error, the square root of which is SEE) and Student's t as useful criterion for examining and comparing model perfom1ance but did not recommend r2 or adjusted r2 for this purpose.

Additionally, the use of AIC provides an extremely useful method of evaluating as well as directly ranking the benefits of individual growth models in tenns of the most parsimonious fit. The consideration of alternate goodness of fit measures such as AIC and SEE should be widely applied among age and growth studies.

Growth rates estimated for female D. dipterura using the traditional three parameter von Bertalanffy growth function are the lowest reported for any myliobatiform stingray (Table 5). Growth parameters derived from this study are comparable to those ofthe similarly sized stingray, D. chrysonata (Cowley, 1997). The published growth characteristics of D. pastinaca (Ismen, 2003) are problematic and cannot be directly evaluated in relation to this investigation or that of Cowley (1997). Ismen (2003) relied on reads of stained, whole vertebrae and developed much of the D. pastinaca growth 106

assessment using the inappropriate measure of total length as a basis for size of the species (tails ofwhiptail stingrays are easily damaged and may undergo ontogenetic changes, there is considerable, significant variation in total length as a result). Annual growth rates among the smaller bodied urolophid stingrays are more than double those of

D. dipterura (Table 5). The maximum recorded ages of D. dipterura represent the greatest longevities observed within the order. The species Myliobatis californica attains similar maximum ages and greater maximum disc widths but grows at a faster rate

(Martin and Cailliet, 1988b).

Oviparous batoids including Dipturus batis (k=0.057; DuBuit, 1972), D. pullopunctata (k=0.05; Walmsley-Hart et al., 1999), and Leucoraja ocellata (k=0.059;

Sulikowski et al., 2002) exhibit annual growth rates comparable to D. dipterura.

However, growth rates of most skates studied to date are in excess of 0.10 yea{1 (Cailliet and Goldman, 2004). Several large, long-lived sharks including Carcharhinus plumbeus

(k=0.059; Sminkey and Musick, 1995) and the infamous Carcharodon carcharias

(k=0.059; Cailliet et al., 1985) also display growth rates that are relatively similar to the diamond stingray.

A broad range of samples were incorporated in this study and included specimens that measured only 14 em DW less than the maximum reliably reported size (Feder et al.,

1974). However, complete asymptotes among female growth curves were not achieved and were minimally evident among fits of male growth. Estimates of DWw resulting from the three parameter size-based VBGF using both raw and modified datasets are 107

biologically reasonable and exceed the maximum size of both males and females included in this study. Age 0 D. dipterura were rarely encountered within artisanal fishery landings. The limited number of small specimens likely contributed to the

elevated predicted initial growth rates and values of DW0 • Improved descriptions of growth for this species may be obtained if additional of young of the year, in particular, and large specimens were available.

Theoretical estimates of longevity derived from k generated strikingly divergent values of the age at which 95% ofLoo is attained in D. dipterura. The estimates following

Ricker (1979) and Fabens (1965) produced longevities that are more than double the maximum age observed from vertebral counts. Longevities of more than 60 years seem improbable for D. dipterura and the estimate of 47 years following Taylor (1958) may provide the most reasonable prediction of longevity.

Comparisons and interpretations of growth coefficients between species are restricted by sample sizes, size ranges incorporated into the study, ageing methodology, validation of band periodicity, and model fitting techniques (Cailliet and Goldman,

2004). With this in mind, k may still provide a practical, albeit generalized, characterization of fundamental life history traits that may be linked to fecundity, longevity, and size or age at maturity (Adams, 1980; Steams, 1992). The growth characteristics detennined in this study indicate that D. dipterura is a relatively long­ lived, slow growing species. Musick (1999) reviewed life history characteristics of long­ lived marine species and concluded that those with k coefficients equal to or less than 108

0.10 year- 1 are extremely vulnerable to overexploitation. Due to the conservative growth and reproductive characteristics demonstrated by D. dipterura, it is evident that careful monitoring and precautionary management strategies should be employed where this species is harvested or incidentally landed. 109

LITERATURE CITED

Adams, P.B. 1980. Life history patterns in marine fishes and their consequences for fisheries management. Fishery Bulletin 78: 1-11.

Akaike, H. 1973. Information theory and an extension ofthe maximum likelihood principle. In Second International Symposium on Information Theory (B.N. Petrov and F. Csaki, eds.), p.-267-281. Akademiai Kiado, Budapest.

Anderson, J.R., Morison, A.K., and Ray, D. 1992. Age and growth of Murray cod, Maccullochella peeli (Percifonnes: Percichthyidae), in the Lower Murray-Darling Basin, using thin-sectioned otoliths. Australian Journal of Marine and Freshwater Research 43:983-1013.

Babel, J.S. 1967. Reproduction, life history, and ecology of the round stingray, Urolophus halleri Cooper. Depmiment ofFish and Game Fish Bulletin 137. 104 p.

Beamish, R.J. and Fournier, D.A. 1981. A method for comparing the precision of a set of age determinations. Canadian Journal of Fisheries and Aquatic Sciences 38: 982-983.

Beamish, R.J. and McFarlane, G.A. 1983. The forgotten requirement for age validation in fisheries biology. Transactions of the American Fisheries Society 112(6): 735- 743.

Beukema, J.J. 1989. Bias in estimates of maximum life span, with an example ofthe edible cockle, Cerastoderma edule. Netherlands Journal of Zoology 39(1-2): 79- 85.

Beverton, R.J.H. and Holt, S.J. 1957. On the dynamics of exploited fish populations. Fishery Investigations Series II. Volume XIX. Her Majesty's Stationery Office, London, England. 533 p.

Bigelow, I--LB. and Schroeder, W.C. 1953. Fishes of the Western North Atlantic. Sawfishes, guitarfishes, skates, rays, and chimaeroids. No. 1, Part 2. Memoir of the Sears Foundation for Marine Research, Yale University Press. 588 p.

Blueweiss, L., Fox, H., Kudzma, V., Nakashima, D., Peters, R. and Sams, S. 1978. Relationships between body size and some life history parameters. Oecologia 37: 257-272. 110

Branstetter, S. 1990. Early life-history implications of selected carcharhinoid and lamonid sharks of the northwest Atlantic. In Elasmobranchs as Living Resources: Advances in the Biology, Ecology, Systematics, and the Status ofthe Fisheries (H.L. Pratt, S.H. Gruber, and T. Taniuchi, eds.), p. 17-28. NOAA Technical Report NMFS 90.

Breder, C.M., Jr. and Krumholz, L.A. 1941. On the uterine young of Dasyatis sabinus (Le Sueur) and Dasyatis hastatus (De Kay). Zoologica: New York Zoological Society 26:49-53.

Brown, C.A. and Gruber, S.H. 1988. Age assessment ofthe lemon shark, Negaprion brevirostris, using tetracycline validated vertebral centra. Copeia 1988(3): 747- 753.

Buckland, S.T., Burnham, K.P., and Augustin, N.H. 1997. Model selection: an integral part of inference. Biometrics 53: 603-618.

Burnham, K.P. and Anderson, D.R. 2002. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. 2nd Edition. Springer-Verlag, New York, New York. 488 p.

Cailliet, G.M. 1990. Elasmobranch age determination and verification: An updated review. In Elasmobranchs as Living Resources: Advances in the Biology, Ecology, Systematics, and the Status of the Fisheries (H.L. Pratt, S.H. Gruber, and T. Taniuchi, eds.), p. 157-165. NOAA Technical Report NMFS 90.

Cailliet, G.M. and Goldman, K.J. 2004. Age determination and validation in chondrichthyan fishes. In Biology of Sharks and Their Relatives (J.C. Carrier, J.A. Musick, and M.R. Heithaus, eds.), p. 399-447. CRC Press, New York, New York.

Cailliet, G.M., Martin, L.K., Kusher, D., Wolf, P., and Welden, B.A. 1983. Techniques for enhancing vertebral bands in age estimation of California elasmobranchs. NOAA Teclmical Repmi NMFS 8: 179-188.

Cailliet, G.M., Natanson, L.J., Welden, B.A., and Ebert, D.A. 1985. Preliminary studies on the age and growth of the white shark, Carcharodon carcharias, using vertebral bands. Southern California Academy of Sciences Memoirs. 9: 49-60. 111

Cailliet, G.M., Mollet, H.F., Pittenger, G.G., Bedford, D., and Natanson, L.J. 1992. Growth and demography of the Pacific angel shark (Squatina californica), based upon tag returns off California. Australian Journal ofMarine and Freshwater Research 43: 1313-1330.

Cailliet, G.M., Radtke, R.L., and Welden, B.A. 1986. Elasmobranch age detennination and verification: a review. In Indo-Pacific Fish Biology: Proceedings of the Second International Conference on Indo-Pacific Fishes (T. Uyeno, R. Arai, T. Taniuchi, and K. Matsuura, eds.), p. 345-379. Ichthyological Society of Japan, Tokyo.

Campana, S.E. 2001. Accuracy, precision and quality control in age determination, including a review of the use and abuse of age validation methods. Journal of Fish Biology 59: 197-242.

Campana, S.E., Am1and, M.C., and McMillan, J.I. 1995. Graphical and statistical methods for determining the consistency of age determinations. Transactions of the American Fisheries Society 124: 131-138.

Capape, C. 1993. New data on the reproductive biology ofthe thorny stingray, Dasyatis centroura (Pisces: Dasyatidae) from offthe Tunisian coasts. Environmental Biology ofFishes 38: 73-80.

Capape, C. and Zaouali, J. 1995. Reproductive biology ofthe marbled stingray, Dasyatis marmorata (Steindachner, 1892) (Pisces: Dasyatidae) in Tunisian waters (Central Mediterranean). Journal of Aquaculture and Aquatic Sciences 7: 108- 119.

Carlson, J.K. and Baremore, I.E. 2003. Changes in biological parameters of Atlantic sharpnose shark Rhizoprionodon terraenovae in the Gulf of Mexico: evidence for density-dependent growth and maturity? Marine and Freshwater Research 54: 227-234.

Casey, J.G., Pratt, H.L., and Stillwell, C.E. 1985. Age and growth ofthe sand bar shark (Carcharhinus plumbeus) from the western North Atlantic. Canadian Journal of Fisheries and Aquatic Sciences 42: 963-975.

Casselman, J.M. 1983. Age and growth assessment offish from their calcified structures - teclmiques and tools. NOAA Technical Report NMFS 8: 179-188. 112

Chang, W. Y.B. 1982. A statistical method for evaluating the reproducibility of age determination. Canadian Journal of Fisheries and Aquatic Sciences 39: 1208- 1210.

Chen, Y., Jackson, D.A., and Harvey, H.H. 1992. A comparison ofvon Bertalanffy and polynomial functions in modelling fish growth data. Canadian Journal of Fisheries and Aquatic Sciences 49: 1228-1235.

Conrath, C.L., Gelsleichter, J.G., and J.A. Musick. 2002. Age and growth of the smooth dogfish (Mustelus canis) in the northwest Atlantic Ocean. Fishery Bulletin 100: 674-682.

Cowley, P.D. 1990. The taxonomy and life history ofthe blue stingray Dasyatis marmorata capensis (Batoidea: Dasyatidae) from southern Africa. M.S. thesis, Rhodes Unviersity, South Africa. 136 p.

Cowley, P.D. 1997. Age and growth of the blue stingray Dasyatis chrysonota ch1ysonota from the south-eastern cape coast of South Africa. South African Journal ofMarine Science 18: 31-38.

Daiber, F.C. 1960. A technique for age determination in the skate Raja eglanteria. Copeia 1960(3): 258-260.

Devadoss, P. 1978. Maturation and breeding habit of Dasyatis (Amphotistius) imbricatus (Schneider) at Porto Novo. Indian Journal of Fisheries 25(1&2): 29- 34.

Devadoss, P. 1998. Observations on the breeding and development in some batoid fishes. Indian Journal of Fisheries 45(3): 271-283.

DuBuit, M.H. 1972. Age et croissance de Raja batis et de Raja naevus en Mer Celtique. Journal du Conseil International pour L'exploration de laMer 37: 261-265.

Dunn, O.J. 1964. Multiple contrasts using ranks sums. Teclmometrics 6: 241-252.

Edwards, R.R.C. 1980. Aspects ofthe population dynamics and ecology ofthe white spotted stingaree, Urolophus paucimaculatus Dixon, in Pmi Phillip Bay, Victoria. Australian Journal of Marine and Freshwater Research 31: 459-467.

Fabens, A.J. 1965. Properties and fitting of the von Bertalanffy growth curve. Growth 29: 265-289. 113

Feder, H.M., Turner, C.H. and Limbaugh, C. 1974. Observations on fishes associated with kelp beds in southern California. California Fish and Game Fish Bulletin 160, 44 p.

Flores, J.O., Rodriguez, M., Shimizu, M., and Machii, T. 1995. Evaluation of demersal fishery resources of the Gulf of California using Mexican shrimp trawlers. Journal of the National Fisheries University 44 (1): 9-19.

Gallagher, M. and Nolan, C.P. 1999. A novel method for the estimation of age and growth in rajids using caudal thorns. Canadian Journal of Fisheries and Aquatic Sciences 56: 1590-1599.

Gamito, S. 1998. Growth models and their use in ecological modelling: an application to a fish population. Ecological Modelling 113: 83-94.

Goosen, A.J.J. and Smale, M.J. 1997. A preliminary study of age and growth of the smoothhound shark Mustelus mustelus (Triakidae). South African Journal of Marine Science 18: 85-91.

Gruber, S.H. and Stout, R.G. 1983. Biological materials for the study of age and growth in a marine tropical elasmobranch, the lemon shark, Negaprion brevirostris Poey. NOAA Technical ReportNMFS 8: 193-205.

Haddon, M. 2001. Modelling and Quantitative Methods in Fisheries. Chapman and Hall/CRC Press, Boca Raton, FL. 406 p.

Hamilton, W.J. Jr. and Smith, R.A. 1941. Notes on the sting-ray, Dasyatis say (Le Sueur). Copeia 1941(3): 175.

Hayashi, Y. 1976. Studies on the growth of the red tilefish in the East China Sea- I. A fundamental consideration for age determination from otoliths. Bulletin of the Japanese Society~ofScientific Fisheries 42(11): 1237-1242.

Hess, P.W. 1959. The biology oftwo stingrays, Dasyatis centroura Mitchill1815 and Dasyatis say Lesueur 1817, in Delaware Bay. M.S. thesis, University of Delaware, Delaware. 42 p.

Hilborn, R. and Mangel, M. 1997. The ecological detective: confronting models with data. Monographs in Population Biology 28, Princeton University Press, Princeton, NJ. 315 p. 114

Hilborn, R. and Walters, C.J. 1992. Quantitative Fisheries Stock Assessment: Choice, Dynamics, and Uncertainty. Chapman and Hall, New York, NY. 570 p.

Hoenig, J.M. and Gruber, S.H. 1990. Life-history patterns in the elasmobranchs: implications for fisheries management. In Elasmobranchs as Living Resources: Advances in the Biology, Ecology, Systematics, and the Status of the Fisheries (H.L. Pratt, S.H. Gruber, and T. Taniuchi, eds.), p. 828-903. NOAA Technical Report NMFS 90.

Hoenig, J.M., Morgan, M.J., and Brown, C.A. 1995. Analysing differences between two age determination methods by tests of symmetry. Canadian Joumal of Fisheries and Aquatic Sciences 52: 364-268.

Holden, M.J. 1973. Are long-term sustainable fisheries for elasmobranchs possible? Rapports et Proces-verbaux des Reunions, Conseil Intemational pour L'Exploration de laMer 164: 360-367.

Holden, M.J. and Vince, M.R. 1973. Age validation studies on the centra of Raja clavata using tetracycline. Joumal du Conseil Intemational pour L'exploration de laMer 35:13-17.

Hyndes, G.A., Loneragan, N.R., and Potter, I. C. 1992. Influence of sectioning otoliths on marginal increment trends and age and growth estimates for the flathead Platycephalus speculator. Fishery Bulletin 90: 276-284.

Ishiyama, R. 1951. Studies on the rays and skates belonging to the family Rajidae, found in Japan and adjacent regions. 2. On the age-determination of Japanese black-skate, Rajafusca Gannan (Preliminary report). Bulletin ofthe Japanese Society of Scientific Fisheries 16(12): 112-118.

Ismen, A. 2003. Age, growth, reproduction and food of common stingray (Dasyatis pastinaca L., 1758) in iskendenm Bay,m the eastem Mediterranean. Fisheries Research 60: 169-176.

Johnson, A. G. 1979. A simple method for staining the centra ofteleosts veriebrae. Nmiheastem Gulf Science 3:113-115.

Ketchen, K.S. 1975. Age and growth of dogfish (Squalus acanthias) in British Columbia waters. Joumal ofthe Fisheries Research Board of Canada 32: 13-59. 115

Knight, W. 1968. Asymptotic growth: an example of nonsense disguised as mathematics. Journal ofthe Fisheries Research Board of Canada 25(6): 1303- 1307.

Kusher, D.I., Smith, S.E., and Cailliet, G.M. 1992. Validated age and growth ofthe leopard shark, Triakis semifasciata, with comments on reproduction. Environmental Biology ofFishes 35: 187-203.

2 Kvalseth, T.O. 1985. Cautionary note about r . The American Statistician 39( 4): 279- 285.

LaMarca, M. J. 1966. A simple technique for demonstrating calcified annuli in the vertebrae of large elasmobranchs. Copeia 1966:351-352.

Lewis, T.C. 1982. The reproductive anatomy, seasonal cycles, and development ofthe Atlantic stingray, Dasyatis sabina (Lesueur) (Pisces, Dasyatidae) from the northeastern Gulf of Mexico. Ph.D. dissertation, The Florida State University, Florida. 206 p.

Lluch-Belda, D., Hermindez-Rivas, M.E., Saldierna-Martinez, R., and Guenero­ Caballero, R. 2000. Variabilidad de la temperatura superficial del mar en Bahia Magdalena, B.C.S. Oceanides. 15(1): 1-23.

Loefer, J.K. and Sedberry, G.R. 2002. Life history ofthe Atlantic sharpnose shark (Rhizoprionodon terraenovae) (Richardson, 1836) offthe southeastern United States. Fishery Bulletin 101: 75-88.

Mariano-Melendez, E. 1997. Biologia reproductiva de la raya lodera Dasyatis brevis (Garman, 1880), en Bahia Almejas, B.C.S., Mexico. B.S. thesis, Universidad Aut6noma de Baja California Sur, La Paz, B.C.S., Mexico. 46 p.

Martin, L.K. 1982. Growth and reproduction ofthe bat ray, Myliobatis californica Gill, in California. M.A. thesis, San Jose State University, California. 87 p.

Martin, L.K. and Cailliet, G.M. 1988a. Aspects of the reproduction ofthe bat ray, Myliobatis californica, in central California. Copeia 1988(3): 754-762.

Mmiin, L.K. and Cailliet, G.M. 1988b. Age and growth detern1ination ofthe bat ray, Myliobatis californica Gill, in central California. Copeia 1988(3): 762-773. 116

Marquardt, D.W. 1963. An algorithm for least squares estimation of parameters. Journal ofthe Society oflndustrial and Applied Mathematics 11:431-441.

Marquez-Farias, F.J. 2002. The artisanal ray fishery in the Gulf of California: development, fisheries research, and management issues. IUCN/SSC Shark Specialist Group. Shark News 14: 1-5.

Mathews, C.P. and J. Druck-Gonzalez. 1975. Potencial pesquero y estudios de Bahia Magdalena III. Las existencias de rayas con especial interes a las ya aprovechadas. Ciencias Marinas 2(1): 67-72.

Maruska, K.P., Cowie, E.G., and Tricas, T.C. 1996. Periodic gonadal activity and protracted mating in elasmobranch fishes. Joumal of Experimental Zoology 276: 219-232.

McFarlane, G.A., King, J.R., and Saunders, M.W. 2002. Preliminary study on the use of neural arches in the age detennination ofbluntnose sixgill sharks (Hexanchus griseus). Fishery Bulletin 100: 861-864.

Meekan, M.G., Wellington, G.M., and Axe, L. 1999. El Nifio-Southem Oscillation events produce checks in the otoliths of coral reef fishes in the Galapagos archipelago. Bulletin of Marine Science 64(2): 383-390.

Miller, J.M. and Tucker, J.W. 1979. X-radiography oflarval and juvenile fishes. Copeia 1979 (3): 535-538.

Mollet, H.F., Cliff, G., Pratt, H.L. Jr., and Stevens, J.D. 2000. Reproductive biology of the female shorfin mako, Isurus oxyrnichus Rafinesque, 1910, with comments on the embryonic development. Fishery Bulletin 98:299-318.

Mollet, H.F., Ezcurra, J.M., and O'Sullivan, J.B. 2002. Captive biology ofthe pelagic stingray, Dasyatis violacea (Bonaparte 1832). Marine and Freshwater Research 53: 531-541.

Morales-Nin, B. and Panfili, J. 2002. Semi-direct validation. In Manual offish sclerochronology (Panfili, J., Pontual, H. (de), Troadec, H., and Wright, P.J., eds.), p. 129-134. Ifremer-IRD coedition, Brest, France.

Moreau, J. 1987. Mathematical and biological expression of growth in fishes: recent trends and further developments. In Age and Growth ofFish (Summerfelt, R.C. and Hall, G.E., eds.), p. 81-113. Iowa State University Press, Ames, IA. 117

Moulton, P.L., Walker, T.I., and Saddlier, S.R. 1992. Age and growth studies of gummy shark, Mustelus antarcticus GUnther, and school shark, Galeorhinus galeus (Litmaeus), from southern Australian waters. Australian Journal of Marine and Freshwater Research 43: 1241-1267.

Musick, J.A. 1999. Ecology and conservation oflong-lived marine animals. American Fisheries Society Sympositm1 23: 1-10.

Natanson, L.J. and Cailliet, G.M. 1990. Vertebral growth zone deposition in Pacific angel sharks. Copeia 1990(4): 1133-1145.

Natanson, L.J., Casey, J.G., and Kohler, N.E. 1995. Age and growth for the dusky shark, Carcharhinus obscurus, in the western North Atlantic Ocean. Fishery Bulletin 93: 116-126.

Natanson, L.J., Mello, J.J., and Campana, S.E. 2002. Validated age and growth of the porbeagle shark (Lamna nasus) in the western North Atlantic Ocean. Fishery Bulletin 100: 266-278.

Neer, J.A. and G.M. Cailliet. 2001. Aspects of the life history of the Pacific electric ray, Torpedo californica (Ayres). Copeia 2001(3): 842-847.

Officer, R.A., Day, R.W., Clement, J.G., and Brown, L.P. 1997. Captive gummy sharks, Mustelus antarcticus, for hypermineralised bands in their vertebrae during winter. Canadian Joumal of Fisheries and Aquatic Sciences 54: 2677-2683.

Officer, R.A., Gason, A.S., Walker, T.I., and Clement, J.G. 1996. Sources ofvariation in counts of growth increments in vertebrae from gummy shark, Mustelus antarcticus, and school shark, Galeorhinus galeus: implications for age determination. Canadian Journal of Fisheries and Aquatic Sciences 53: 1765- 1777.

Parsons, G. R. 1983. An examination of the vertebral rings of the Atlantic sharpnose shark, Rhizopriodon terraenovae. Northeast Gulf Sci. 6:63-66.

Pearson, D.E. 1996. Timing ofhyaline-zone formation as related to sex, location, and year of capture in otoliths of the widow rockfish, Sebastes entomelas. Fishery Bulletin 94: 190-197. 118

Pilling, G.M., Kirkwodd, G.P., and Walker, S.G. 2002. An improved method for estimating individual growth variability in fish, and the correlation between von Bertalanffy growth parameters. Canadian Journal of Fisheries and Aquatic Sciences 59: 424-432.

Platt, T. and Silvert, W. 1981. Ecology, physiology, allometry, and dimensionality. Journal of Theoretical Biology 93(4): 855-860.

Porch, C.E., Wilson, C.A., and Nieland, D.L. 2002. A new growth model for red drum (Sciaenops ocellatus) that accommodates seasonal and ontogenic changes in growth rates. Fishery Bulletin 100:149-152.

Pratt, H.L. 1979. Reproduction in the blue shark, Prionace glauca. Fishery Bulletin 77(2): 445-470.

Pratt, H.L., Jr. and Casey, J.G. 1990. Shark reproductive strategies as a limiting factor in directed fisheries, with a review of Holden's method of estimating growth parameters. In Elasmobranchs as Living Resources: Advances in the Biology, Ecology, Systematics, and the Status of the Fisheries (H.L. Pratt, S.H. Gruber, and T. Taniuchi, eds.), p. 97-109. NOAA Teclmical Report NMFS 90.

Raje, S.G. 2003. Some aspects ofbiology of four species of rays offMumbai water. Indian Journal of Fisheries 50(1): 89-96.

Ratkowsky, D.A. 1983. Nonlinear regression modeling: a unified practical approach. Statistics: Textbooks and Monographs Volume 48, Marcel Dekker, Inc. New York, NY. 276 p.

Ricker, W.E. 1969. Effects of size selective mortality and sampling bias on estimates of growth, mortality, production, and yield. Journal of the Fisheries Research Board of Canada 26: 479-541.

Ricker, W.E. 1975. Computation and interpretation of biological statistics offish populations. Fisheries Research Board ofCanada, Bulletin 191. 382 p.

Ricker, W.E. 1979. Growth rates and models. In Fish Physiology, Volume VIII. (Hoar and Randall, eds.), p. 677-743. Academic Press, New York, NY.

Ridewood, W. G. 1921. On the calcification ofthe vertebral centra in sharks and rays. Philosophical Transactions ofthe Royal Society, Series B Biological Sciences 210:311-407. 119

Rochet, M.J. 1998. Sho1i-te1m effects of fishing on life history traits of fishes. ICES Journal ofMarine Science 55: 371-391.

Roff, D.A. 1980. A motion to retire the von Bertalanffy function. Canadian Journal of Fisheries and Aquatic Sciences 37: 127-129.

Roughgarden, J. 1971. Density-dependent natural selection. Ecology 52:453-468.

Rose, K.A., Cowan, J.H., Winemiller, K.O., Meyers, R.A., and Hilborn, R. 2001. Compensatory density dependence in fish populations: importance, controversy, understanding and prognosis. Fish and Fisheries 2: 293-327.

Russell, F.E. 1955. Multiple caudal spines in the round stingray, Urolophus halleri. California Fish and Game 41: 213-217.

Sainsbury, K.J. 1980. Effect of individual variability on the von Bertalanffy growth equation. Canadian Journal of Fisheries and Aquatic Sciences 37: 241-247.

Schmid, T.H. 1988. Age, growth, and movement patterns ofthe Atlantic stingray, Dasyatis sabina, in a Florida coastal lagoon system. M.S. thesis, University of Central Flo1ida, Florida. 85 p.

Schwartz, F. J. 1983. Shark aging methods and age estimates of scalloped hammerhead, Sphyrna lewini, and dusky, Carcharhinus obscurus, sharks based on vertebral ring counts. NOAA Teclmical Report NMFS 8: 167-174.

Schwmiz, F.J. and Dahlberg, M.D. 1978. Biology and ecology of the Atlantic stingray, Dasyatis sabina (Pisces: Dasyatidae), in North Carolina and Georgia. Nmiheast Gulf Science 2(1): 1-23.

Sebens, K.P. 1987. The ecology of indeterminate growth in animals. Annual Review of Ecology and Systematics 18: 371-407.

Simpfendorfer, C.A., Chidlow, J., McAuley, R., and Unsworth, P. 2000. Age and growth of the whiskery shark, Furgaleus rnacki, from southwestem Australia. Envirmm1ental Biology of Fishes 58: 335-343.

Sminkey, T.R. and Musick, J.A. 1995. Age and growth ofthe sandbar shark, Carcharhinus plumbeus, before and after population depletion. Copeia 1995(4): 871-883. 120

Smith, J.W. 1980. The life history of the cownose ray, Rhinoptera bonasus (Mitchell 1815), in lower Chesapeake Bay, with notes on the management ofthe species. M.A. thesis, College of William and Mary, Virginia. 150 p.

Smith, J.W. and Merriner, J.V. 1986. Observations on the reproductive biology ofthe cownose ray, Rhinoptera bonasus, in Chesapeake Bay. Fishery Bulletin 84(4): 871-877.

Smith, J.W. and Merriner, J.V. 1987. Age and growth, movements and distribution of the cownose ray, Rhinoptera bonasus, in Chesapeake Bay. Estuaries 10(2): 153- 164.

Snelson, F.F. Jr., Williams-Hooper, S.E. and Schmid, T.H.. 1988. Reproduction and ecology of the Atlantic stingray, Dasyatis sabina, in Florida coastal lagoons. Copeia, 3: 729-739.

Snelson, F.F. Jr., Williams-Hooper, W.E., and Schmid, T.H. 1989. Biology ofthe bluntnose stingray, Dasyatis sayi, in Florida coastal lagoons. Bulletin of Marine Science 45(1): 15-25.

Steams, S.C. 1992. The Evolution of Life Histories. Oxford University Press, New York, NY. 249 p.

Stevens, J.D., Bonfil, R., Dulvy, N.K., and Walker, P.A. 2000. The effects of fishing on sharks, rays, and chimaeras (chondrichthyans), and the implications for marine ecosystems. ICES Journal ofMarine Science 57: 476-494.

Struhsaker, P. 1969. Observations on the biology and distribution ofthe thorny stingray, Dasyatis centroura (Pisces: Dasyatidae). Bulletin ofMarine Science 19(2): 456- 481.

Sulikowski, J.A., Morin, M.D., Suk, S.H., and W.H. Howell. 2003. Age and growth estimates of the winter skate (Leucoraja ocellata) in the western Gulf of Maine. Fishery Bulletin 101:405-413.

Tanaka, S., Chen, C.-T., and Mizu, K. 1978. Studies on sharks. XVI. Age and growth of Eiraku shark, Galeorhinus japonicus (Muller et Henle). Bulletin of the Faculty of Fisheries, Nagasaki University 45: 19-28. 121

Taylor, C. C. 1958. Cod growth and temperature. Journal du Conseil International pour L'exploration de laMer 23:366-370.

Teaf, C.M. 1987. Seasonal occurrence of multiple caudal spines in the Atlantic stingray, Dasyatis sabina (Pisces: Dasyatidae). Copeia 1987(1): 224-227.

Vilizzi, L. and Walker, K.F. 1999. Age and growth of the common carp, Cyprinus cmpio, in the River Murray, Australia: validation, consistency of age interpretation, and growth models. Environmental Biology of Fishes 54: 77-106.

Villavicencio-Garayzar, C.J. 1995. Distribuci6n temporal y condici6n reproductive de las rayas (Pisces: Batoidei), capturadas commercialmente en Bahia Almejas, B.C.S., Mexico. Revista de Investigaci6n Cientifica 6(1-2): 1-12.

Villavicencio-Garayzar, C.J. 2000. Taxonomia, abundancia estacional, edad y crecimiento y biologia reproductive de Narcine entemedor Jordan y Starks (Chondrichthyes: Narcinidae), in Bahia Almejas, B.C.S., Mexico. PhD. dissertation, Universidad Autonoma de Nuevo Leon, Monterrey, Mexico. 131 p.

Villavicencio-Garayzar, C.J., Downton-Hoffmann, C.C., and Mariano-Melendez, E. 1994. Tamafio y reproducci6n de Dasyatis longus (Pisces: Dasyatidae), en Bahia Almejas, Baja California Sur, Mexico. Revista Biologia Tropical 42 (1/2): 375-377. von Bertalanffy, L. 1938. A quantitative theory of organic growth (inquiries on growth laws II). Human Biology 10(2): 181-213. von Bertalanffy, L. 1960. Principles and theory of growth. In Fundamental Aspects of Nonnal and Malignant Growth. (W.W. Nowinski, ed.), p. 137-259. Elsevier Publishing Company, New York, NY.

Walmsley-Hari, S.A., Sauer, W.H., and Buxton, C.D. 1999. The biology of the skates Raja wallacei and R. pullopunctata (Batoidea: Rajidae) on the Agulhas Bank, South Africa. South African Journal of Marine Science 21: 165-1 79.

Weatherley, A.H. 1972. Growth and ecology of fish populations. Academic Press, London, England. 293 p.

White, W.T., Hall, N.G., and Potter, I.C. 2002. Reproductive biology and growth during pre- and postnatal life of Trygonoptera peronata and T. mucosa (Batoidea: Urolophidae). Marine Biology 140: 699-712. 122

White, W.T., Platell, M.E., and Potter, I.C. 2001. Relationship between reproductive biology and age composition and growth in Urolophus lobatus (Batoidea: Urolophidae). Marine Biology 138: 135-147.

Winsor, C.P. 1932. The Gompertz curve as a growth curve. Proceedings of the National Academy of Sciences 18(1 ): 1-8.

Wintner, S.A. and Cliff, G. 1996. Age and growth detennination of the blacktip shark, Carcharhinus limbatus, from the east coast of South Africa. Fishery Bulletin 94: 135-144.

Wintner, S.A. and Dudley, S.F.J. 2000. Age and growth estimates for the tiger shark, Galeocerdo cuvier, from the east coast of South Africa. Marine and Freshwater Research 51:43-53.

Wintner, S.A., Dudley, S.F.J., Kistnasamy, N., and Everett, B. 2002. Age and growth of the Zambezi shark, Carcharhinas leucas, from the east coast of South Africa. Marine and Freshwater Research ~3: 557-566.

Wourms, J.P. 1977. Reproduction and development in chondrichthyan fishes. American Zoologist 17: 379-410.

Yudin, D.G. and G.M. Cailliet. 1990. Age and growth ofthe gray smoothhound, Mustelus californicus, and the brown smoothhound, M henlei, sharks from central California. Copeia 1990 (1): 191-204.

Zar, J.H. 1996. Biostatistical Analysis. 3rd ed. Prentice Hall, NJ. 662 p.

Zeiner, S.J. and P. Wolf. 1993. Growth characteristics and estimates of age at maturity of two species of skates (Raja binoculata and Raja rhina) from Monterey Bay, California. NOAA Technical Report NMFS 115: 87-99. 123

Table 1. Categories applied for assessing readability and clarity of vertebral centra.

Grade Criteria

1 Banding pattem vague; increments irregular or cloudy; limited confidence distinguishing band count; sample may be damaged 2 More than two band cotmts possible; indefinite banding pattem in one or more sample locations; best estimate recorded 3 Two band counts possible; recorded estimate is the most probable 4 Band count tmambigious but incrementls are not of exceptional clarity 5 Band count unambigious; all increments are distinct and readily distinguished Table 2. Percent agreement (P A) between the final, consensus read and band count with the greatest assigned difference for each sample in relation to size classes. Size classes are based on 5 em disc width (DW) groupings. The sample size of each P A calculation is indicated within parentheses. Percent agreements (P A) are presented for no difference among rounds (± 0) and± 0.5, one, two, three, and four or more estimated years. Overall and cumulative percent agreements are summarized for each category.

DW (em) # PA ± 0 (n) PA ± 0.5 (n) PA ± 1 (n) PA ± 2 (n) PA ± 3 (n) PA2:4(n) 25.1-30.0 4 0 100.0 (4) 0 0 0 0 30.1-35.0 18 16.7 (3) 55.6 (10) 27.8 (5) 0 0 0 35.1-40.0 40 20.0 (8) 57.5 (23) 22.5 (9) 0 0 0 40.1-45.0 39 12.8 (5) 30.8 (12) 46.2(18) 7.7 (3) 2.6 (1) 0 45.1-50.0 51 7.8 (4) 25.5 (13) 51.0 (26) 5.9 (3) 3.9 (2) 5.9 (3) 50.1-55.0 53 7.5 (4) 24.5 (13) 37.7 (20) 22.6 (12) 3.8 (2) 3.8 (2) 55.1-60.0 29 0 13.8 (4) 37.9 (11) 34.5 (1 0) 13.8 (4) 0 60.1-65.0 26 7.7 (2) 7.7 (2) 42.3 (11) 15.4 (4) 19.2 (5) 7.7 (2) 65.1-70.0 21 0 0 47.6 (10) 28.6 (6) 23.8 (5) 0 70.1-75.0 13 0 0 23.1 (3) 53.8 (7) 15.4 (2) 7.7 (1) 75.1-80.0 6 0 16.8 (1) 16.8 (1) 50.0 (3) 0 16.8 (1) 80.1-85.0 2 0 0 0 0 0 100.0(2)

n = 302 26 82 114 48 21 11 PA 8.6 27.2 37.7 15.9 7.0 3.6 Cum. PA 8.6 35.8 73.5 89.4 96.4 100.0

...... N +::- Table 3. Summary of growth parameters and goodness-of-fit descriptors estimated from size- and weight-based models of female and male D. dipterura age data. The abbreviation VB indicates that the model is a form of the von Bertalanffy growth function.

Size-Based Models Parameter 3 Parameter VB 2 Parameter VB 3 Par. VB (Modified Data) VB Weight

a Parameter indicates asymptotic disc width in em or weight in kg

b Instantaneous growth rate is signified by k in von BertalaniJY and gin Gompertz models

c Parameter is not comparable between von BertalanfJY- and Gompertz-type models

d Parameter indicates hypothetical disc width in em or weight in kg at birth 'Disc width at birth fixed based on the estimated meansize of21.3 em I relative AIC values calculated separately for female and male size- and weight-based growth models; values presented represent difference between the growth model and minimum

(optimal) AIC value 126

Table 4. Longevity (m) estimates (years) for D. dipterura based on maximum observed ages and three theoretical methods. Each method incorporates values obtained from the traditional three parameter von Bertalanffy growth function to determine m.

Female Male Method 0) 0)

Maximum 0 bserved 28 19

Ricker (95% DW oo) 63.5 33.6

Fabens (99% DWoo) 88.9 47.1

Taylor (95% DW oo) 47.3 22.3 Table 5. Comparison of maturity, age, and select growth (k, DWoo) parameters among myliobatiform stingrays. All growth data are based on fits of three parameter von Bertalanffy growth functions. DW5o =median disc width at maturity; 1st Mat.= earliest observed size at maturity; SS = sagital thin-section; NA = not applicable; NR = not reported; W =whole vertebrae; S = stained; VS =vertical half-section; 0 =oil-cleared; X= x-radiography.

Location of Sex Method n k DW~ DWso DW 50 /DW~ !"Mat. lst/DW~ Source

Dasyatis dipterura S Central Mexico Female ss 169 28 0.055 92.4 57.0 61.7% 57.0 61.7% This Study Male ss 135 19 0.103 62.2 46.8 75.3% 47.0 75.6%

Myliobatis californica SWUSA Female VS,O 104 23 0.100 158.7 88.1 55.5% NR Martin (1982); Male VS,X 60 6 0.229 100.4 NR NR Martin and Cailliet (1988)

Trygonoptera mucosa SW Australia Female ss 324 >17b 0.241 30.8 25.3 82.1% 22.0c 71.4% White et al. (2002) Male ss 400 >lib 0.493 26.1 22.2 85.0% 19.0c 72.7%

U rolophus lobatus SW Australia Female ss 388 15 0.369 24.9 20.1 80.8% NR White et al. (200 I) Male ss 448 13 0.514 21.1 16.3 77.4% NR

a Ism en (2003) used total length (TL) to model size at age instead of DW, growth parameters are included for relative comparison

b Maximum ages not reported, estimates are inferred from figures and do not exceed 20 years

c Estimates offirst maturity are based on pooled size classes, 19.0- 19.9 em and 22.0- 22.9 em disc width 128

cc

IM

cc

2

Figure 1. A representative sagittally thin-sectioned vertebral centrum as viewed under transmitted light. Only half of the centrum is depicted in this image. Abbreviations are as follows: F =focus, located in the center of the notochordal remnant; BM =the birth mark is indicated by an anow and is associated with a change in angle of the growth stmcture and the first visible light (translucent) increment; I= increments, both dm:k (opaque) m1d trm1slucent increments are indicated; CC = corpus calcareum; IM = intermedialia. In addition to the bi1ihmark, four complete increments (2 bands) are present with a fifth opaque increment forming on the centrum edge. The specimen was assigned a band count of2 as indicated by the anows on the lower right p01iion ofthe Image. A B c

1 mm '

Figure 2. Examples of centrum edge and marginal increment analysis procedures. (A) Broad, translucent increment forming on outer centrum edge (T2); (B) narrow opaque increment forming on centrum edge (01); and (C) regions identified for measurement and calculation of the marginal increment ratio; MW =margin width, PBW =penultimate band width. 130

1.0 .... / - 0.9 I I ( I 0.8 I I 0.7 I (]) 1-< I I ~ 0.6 I ::8 I 1:.1 0 0.5 ..... I ~ 0 I 0.. 0.4 I 0 1-< I r:t... 0.3 I I Female I • 0.2 I 0 Male I I Female Fit 0.1 I --- Male Fit I j 0.0 0 ()iiiii!J!!!I(~ • 20 30 40 50 60 70 80 90 Disc Width (em)

Figure 3. Relationship between maturity status and disc width for female (n=l26) and male (n=54) D. dipterura. Grey droplines mark median disc widths at maturity. 131

20 18 • ,-., 16 Ei (.) '--' 14 -B • bJ) 12 • ~ • ~ • • ..... 0 • •• v 10 0...

Figure 4. Relationship of disc width to inner clasper length for D. dipterura (n = 171). Maturity status was directly assessed for 55 specimens. 132

5 e Present Study (n=8) 0 Mariano-Melendez (1997; n=21)

0 0 0 0 0

• • 0 0 0 0 0 0 0 0

0 • 0 0 0 0 0 0 0 •

0 +---~----.----.-----.----.----.----.----.----.----.----. 62 64 66 68 70 72 74 76 78 80 82 84 Maternal disc width (em)

Figure 5. Relationship between observed fecundity and maternal disc width (em) in Dasyatis dipterura. Data from this study are combined with those of Mariano-Melendez (1997). The total number of gravid females recorded from each study is indicated within parentheses. 133

70

DMale 60 D Female

50 c;"' ;:l "0 :~ "0 40 .5 '+-< 0,_

10

0 20 25 30 35 40 45 50 55 60 65 70 75 80 85 Disc width (em)

Figure 6. Size frequency histogram of D. dipterura from which vertebrae were processed for ageing. A total of339 (191 females, 148 males) were prepared and assessed. The sample size for each sex-specific five em disc width bin is presented within the histogram. Sample sizes equal to or less than two are not indicated in the figure. Samples collected from embryos are not included in the histogram. 134

14

12

~

j 10 1-< ...... (]) (])

sCCI 8 ·-Q

s;:::1 ...... 1-< 6 ~ (]) u ~ CCI 4 • Free living (]) ::;8 0 Embryo Linear Fit 2 Quadratic Fit

0 0 10 20 30 40 50 60 70 80 90 100 Disc Width (em)

Figure 7. Relationship between mean centrum diameter and disc width for D. dipterura (n = 345). Measurements from embryonic and free-living specimens of both sexes are combined. 135

24 22 20 ro 1:g 18 <],) u 16 !-< 0 ·~:: 14 ~ IZl 0 12 • •• 0-. • i:f ;::l 10 • 0 • u 8 "'d § 6 t:O 4 2 0 • 0 2 4 6 8 10 12 14 16 18 20 22 24 Band Count, Anterior Centra

Figure 8. Bias plot for pairwise comparisons of final age estimates from centra collected from anterior and posterior locations (n=30). Female and male specimens combined. The 45° diagonal line represents 1:1 agreement. 136

40 A

35

30

25 0 ~ 20 8 0 0 15 0 0 0 4111 0 19 10 0 0 • 0 0 I o • 8 5 0 0 0 8 @ ~ ~ 9 0 +-----0-----o--o--o-~~.-----o-----.-----o--.--o-----, 0 2 3 4 5 6 7 8 9 40 B 35

30

25

~ 20

15

10 0 0 0 0 4111 : +-----~-----.----~)---~--~~--~!--~ __• ___ e~--~--~1 ______9 10 11 12 13 14 15 16

40 c 35

30

25

~ 20

15

10

16 17 18 19 20 21 22 23 24 25 26 27 28 29 Band Count

Figure 9. Individual Index of Relative Precision (D) values by sex and final band count represented for: (A) specimens aged 1-8.5 years; (B) specimens estimated as 9-15.5 years; and (C) individuals aged 16-28 years. Specimens estimated to be less than one year are not included in 8A. 137

8

'"d 6 0 ~ "OiiiOiiiGI• Oilll\lillillfHIIOOOOGiiiiGI••• • • • ill • 5 0 " • •

8 N '"d 6 ~ "

8 f<) '"d 6 ~ "

a -8 0 5 10 15 20 25 30 Round 4 Estimate

Figure 10. Differences in sample band counts between each round. All samples received a clarity grade between 1 and 4 (n=306). Each point represents one or more observations of a specimen. 138

100 90 ;;>-, (.) ~ Q) ;j 80 0.8 0"' Q) !-. j:.l.. 70 +-' ~ Q) (.) !-. 60 12 0.6 0::: Q) ! t:l-. ~ Q) 50 ~ 0.. 13 (1j ?' ::;sQ) Q) 40 0.4 bJ) '"0 r.LI 30 ;js .p ~ 20 uQ) 10 0 Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. n = (12) (19) (11) (18) (55) (9) (15)

I,. · ''"' Narrow Translucent L~~~~"l Broad Translucent ~ Narrow Opaque c:::==J Broad Opaque e MeanMIR

Figure 11. Monthly variation in centrum edge type (n=205) and mean monthly marginal increment ratios (MIR) ± 1 standard error (n=139) determined from pooled sexes and size classes. Values within the histogram represent the number of samples included in monthly centrum edge analyses. Sample sizes incorporated into MIR analysis are listed in parentheses below the x-axis. Samples were collected from four different years (1992, 1998-2001) were combined for analysis. 139

1.0 o.9 A 0.8 0.7

~ 0.6 § 0.5

1.0 13 0.9 B 5 0.8 0.7 24 I t ~ 0.6 ~ 6 § 0.5 16

0.0 -t----.----.----.----.----,----.----.----,----.----.----.----,-~

1.0 0.9 c 0.8 0.7 15 2 6 0::: 0.6 ~ I 0 § 0.5 2

Figure 12. Mean monthly marginal increment ratios (MIR) by size class: (A) small (20- 40 em DW) (n=23), (B) medium (41-55 em DW) (n=73), and (C) large (56-85 em DW) (n=44). The error bars represent ±1 standard error and the values above these bars indicate the sample size associated within each month. 140

90

A 0 80 0 00 g ~ 0 70 ---8----- ,....., s 60 C) '-" ..t::...... '"0 50 ~ C) UJ Q 40

30 3 Parameter VBGF 2 Parameter VBGF 20

10 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Band Count 70 B

60

50

sC) '-" ~ ~ 40

C)

-- 3 Parameter VBGF 20 --- 2 Parameter VBGF

0 2 4 6 8 10 12 14 16 18 20 22 Band Count

Figure 13. Two and three parameter von Bertalanffy growth functions fit to (A) female (n=l69) and (B) male (n=135) disc width at age data. Size at birth (DWo) was anchored at 21.3 em DW for both females and males in the two parameter model. 141

90

80 • •

70

s(.) '-" 60 ~ ·-~ (.) 50 fZl ·-Q 40 Female •0 30 Male

20 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Band Count

Figure 14. Gompertz growth models based on size (DW) fit separately to female (n=169) and male (n=135) disc width at age data. 142

28 26 A 0 24 ,.....- 22 20 18 ,----, bil ~ 16 '-" J:l 14 bil ·a; 12 ~ 10 8 6 --- Gompertz 4 -- VBGF Weight

0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 Band Count

12 0 11 B 0 10 0 9 8 0 8 ,----, 0 bil 7 ~ 0 '-"..... 6 0 ..0 bil 0 ·a; 5 ~ 4

3 0 2 --- Gompetiz -- VBGF Weight 0 0

0 2 4 6 8 10 12 14 16 18 20 Band Count

Figure 15. Weight based growth models for D. dipterura. Gompertz and von Bertalanffy growth function fits of (A) female (n=l30) and (B) male (n=77) weight at age data. CHAPTER3

Population dynamics and potential responses to fisheries exploitation of Dasyatis

dipterura in the Bahia Magdalena lagoon complex, B.C.S. Mexico

143 144

Introduction

Marine populations possess a diverse array of growth characteristics over spatial

and temporal scales. Assessing and forecasting these patterns and variability is

fundamental to understanding the evolution of life history traits and community relationships as well as for developing effective management strategies. Population

fluctuations can be attributed to changes in births, growth, mortality (these combined

factors are commonly termed "vital rates"), immigration, and emigration (Steams, 1992;

Krebs, 2001). This uncomplicated summation ofthe factors impacting population growth, however, is deceptive. Each of these factors, in tum, is influenced by genetic, ecological, and physical processes that result in dazzling complexities and permutations of these basic rates that dictate population growth characteristics and potential. The difficulty of sampling in marine enviromnents further complicates attempts to assess and forecast the dynamic range of growth characteristics in these populations.

Numerous analytical tools have been developed for examining population dynamics. Techniques range from correlative assessments oflife history traits (e.g.,

Holden, 197 4; Adams, 1980) to more sophisticated age-structured, nonlinear models

(Hilbom and Walters, 1992; Walker, 1998; Haddon, 2001). More advanced approaches may better replicate natural population growth, but require detailed biological information and long-term catch statistics that are usually available only for commercially important species among well established fisheries. Thus, model development is frequently restricted because of limited empirical data. Essential 145

biological data, including measures of age, growth, fecundity and maturity, are particularly difficult to obtain for long-lived species. Paradoxically, such data deficient, long-lived species tend to be the least resilient to fisheries exploitation and yet are among those populations most in need of assessment (Heppell et al., 1999; Musick, 1999).

Demographic modelling has emerged as a flexible, altemative method for evaluating population growth characteristics and simulating responses to perturbations among long-lived marine species (Crouse et al., 1987; Cortes, 1998; Heppell et al., 1999;

Hunter et al., 2000). Xiao (2002) demonstrated that demographic approaches are more applicable and produce better estimates than classic yield-per-recruit models. Life table­ and matrix-based demographic techniques developed from ecological theory relate age­ or stage-specific fecundity and survivorship probabilities to generate projections of population growth rates (Deevey, 1947; Ebert, 1999; Caswell, 2001). The resulting estimates of intrinsic and finite population growth provide a useful method for comparing life history characteristics among species and determine vulnerability to fisheries exploitation. The proportional contribution of each stage or vital rate in the life cycle to overall population growth can be assessed from demographic models using elasticity analysis (Weinberg et al., 1986; Benton and Grant, 1999; Heppell et al., 1999; Caswell,

2000, 2001). Life table models are frequently viewed as simplistic tabulations of population mortality rates (Caswell, 2001), but can be extended to calculate most of the parameters of which matrix formulations are capable (Cailliet, 1992; Ebert, 1999;

Goldman, 2002). Mollet and Cailliet (2002) and Cortes (2002) demonstrated that Leslie 146

matrices and life tables produced the same or similar estimates of population growth.

Neither modelling approach considers immigration or emigration, requiring the assumption of closed populations.

Elasmobranchs display a broad range of life history attributes, but may be generally categorized as species with low fecundity, slow growth rates, late ages of maturity, and long lives (Holden, 1973; Hoenig and Gruber, 1990; Cortes, 2000).

Elasmobranch fisheries have typically been smaller and provided limited yields, but are currently expanding in importance and magnitude (Pratt and Casey, 1990; Bonfil, 1994).

Due in part to a much more direct relationship between the number of adult females and recruitment, traditional fisheries stock assessment models such as surplus production and yield per recruit approaches have often produced overestimates of productivity for elasmobranchpopulations (Holden, 1974; Cortes, 1995, 1998; Musick, 1999). Poor species-specific life history or landing information is available for elasmobranchs that are taken incidentally, landed in artisanal fisheries, or directly targeted in emerging fisheries; thus precluding many model options. However, life table (Cailliet, 1992; Cailliet et al.,

1992) and matrix based (Hoenig and Gruber, 1990; Heppell et al., 1999) demographic techniques are well suited for and have been increasingly applied to elasmobranch populations (Au and Smith, 1997; Cmies, 2004).

Demographic models typically assume that a population's vital rates are unifonn and constant across age classes. However, considerable age-specific variability of vital rates has been demonstrated in populations (e.g., Emlen, 1970) and these processes are 147

rarely static in the real world (Tuljapurkar, 1997; Nations and Boyce, 1997). In addition to natural random variation and plasticity of life history traits, infonnation derived from empirical observations is prone to measurement and sampling error. Population projections based on uniform application of constant vital rates may provide inaccurate estimates that may lead to inappropriate management decisions. Among elasmobranchs, and other long-lived species, projection errors may be further amplified because of the general paucity of data from which to develop population models. Incorporation of

Monte Carlo simulation into demographic models addresses demographic stochasticity and unce1iainty in vital rates (Manly, 1997; Haddon, 2001). By introducing varied input parameters drawn from appropriate probability distributions over the course of multiple simulations, Monte Carlo methods allow the estimation of mean demographic parameters with associated confidence limits from life table or matrix models. Cortes (1999, 2002) was the first to refine elasmobranch demographic models using Monte Carlo simulations and prompted other investigators to consider these important sources of variability and uncertainty in population models (Beerkircher et al., 2003; Carlson et al., 2003).

The summary of individual life history characteristics described in the previous chapter indicates that Dasyatis dipterura is relatively long-lived, slow growing, and has low fecundity. Results of field surveys established that D. dipterura is a primary component of directed elasmobranch fisheries in the Bahia Magdalena lagoon complex

(Chapter 1). It also comprises a large proportion of artisanal fishery landings in the Gulf of California (Ocampo-Tones, 2001; Marquez-Farias, 2002) and is likely to be a 148

common constituent ofbycatch among trawl fisheries throughout the region (Flores et al.,

1995). Elasmobranchs with life history traits similar to D. dipterura have proven to be extremely vulnerable to fisheries exploitation (e.g., Hoenig and Gruber, 1990; Musick,

1999; Stevens et al., 2000). Furthennore, Thrush et al. (1991) have determined that rays regulate the populations of benthic organisms such as clams and wonns through their feeding habits. Rays modify and enhance soft-bottom habitats by creating large feeding and shelter pits (Orth, 1975; VanBlaricom, 1982; Probert, 1984). As a result, decline of ray populations may have significant and unpredictable cascading effects on the biological diversity of entire marine communities.

In light of the relatively limited information on the life history and population variability of D. dipterura, demographic analyses are an appropriate tool for establishing a basic understanding of the population dynamics and assessing vulnerability of the species to fisheries exploitation. The objectives ofthis research component are to: 1) generate the first estimates of population growth characteristics of D. dipterura using life table models incorporating uncetiainty and variability in vital rates using Monte Carlo simulation; 2) examine life history constraints and relative contribution of fertility and juvenile and adult survivorship to population growth; 3) assess the impact and population responses of simulated increases in mortality due to fisheries exploitation; and 4) compare the resulting demographic parameters with those previously estimated for other elasmobranchs. 149

Methods

Demographic Models

Density-independent, linear, age-structured models were constructed to describe the population dynamics of D. dipterura from the Bahia Magdalena lagoon complex using life history tables in Microsoft Excel spreadsheets. This method combines age­ specific estimates oflongevity (co), survivorship (Sx), sexual maturity (a), and fecundity

(mx) to produce projections of population growth (Deevey, 1947; Wilson and Bossert,

1971; Ebert, 1999). Population projections were based on simulated proportional responses of a single cohort to the previous variables over the progression of a life span.

All models were female-specific and structured using one-year projection intervals assuming a closed population.

Population projections were calculated from multiple scenarios using two distinct life table model approaches: detenninistic and probabilistic (Mertz, 1970). Parameters included in deterministic models were static, applied unifonnly, and representative of best-case life history parameters. Deterministic methods have been broadly applied in previous elasmobranch demographic analyses (e.g., Cailliet, 1992; Cortes, 1995;

Simpfendorfer, 1999a) and provided a comparative basis for best-case population growth characteristics. Unce1iainty in life history parameters was considered using probabilistic models by varying age-specific vital rates and population structure using Monte Carlo simulations (Caswell, 2001; Cortes, 2002). Stochastic catastrophic, enviromnental, and 150

genetic factors which additionally affect population growth are not integrated into these models. Therefore the term "probabilistic" is used to describe models developed here that incorporate uncetiainty rather than the tem1 "stochastic".

Following the approach of Cortes (2002; pers. comm.), life tables were expanded to provide a broader range of descriptive characteristics than traditionally included

(Ebert, 1999; Caswell, 2001). Demographic parameters estimated for the population included: intrinsic rate of natural increase (r), finite annual population growth rate (A.), net reproductive rate (Ro), rate of increase per generation (rT), and population doubling time

(tx2). Three measures of generation time were additionally obtained; time necessary for the population to increase by a factor of Ro (T), mean age of mothers of offspring produced by a cohort over its life span ().1 1), mean age ofthe parents of the offspring produced by a population at the stable age distribution (A). The theoretical proportion of individuals present in each age class given a constant environment, referred to as the stable age distribution (ex), and the age-specific reproductive contribution, or value, noted as ( vx) were also calculated.

Instantaneous and finite rates of population increase, r and A. (where A.= er), were iteratively solved for and refined using the discrete form of the Euler-Lotka equation

(Wilson and Bossert, 1971; Goodman, 1982):

llJ 1 = Le-rxz,mx X=l 151

where lx is the probability of an individual being alive at the beginning of age x, mx is the number of offspring produced annually by individuals at age x, and co is the maximum age. Initial values of lx (age 0) were set at 1.0. As all models are developed based on females only, mx relates to the age-specific number of female offspring produced per female armually. Mean values of rand A are reported for probabilistic models. The theoretical doubling time of the population Ctx2) was determined following Krebs (2001) as: In 2/r.

Net reproductive rates (R 0 ), the average number of female offspring produced by each female over her entire lifetime, were determined from the summation of survivorship Clx) and fecundity (mx) products as (Wilson and Bossert, 1971):

The rate of increase per generation (rT) was determined as (Fowler, 1988):

where r is the intrinsic rate of increase, x refers to age, ar1d Ro remains as defined above.

This is a dimensionless value that has been used to link evolutionarily determined life history strategies directly to equilibrium population density and growth characteristics

(Fowler, 1988). These results provide an integrated means of categorizing an organism's growth characteristics along the continuum of 'r-K' selection and enables comparison of life history patterns across taxa. 152

Among iteroparous populations, the determination of mean generation time is complicated due to repeated reproductive events. As a result, several definitions and approaches are commonly applied to these estimates (Caughley, 1967; Gregory, 1997;

Krebs, 2001). Measures of generation time were calculated following Caswell (2001):

R0 T=ln- , r

(j) A= Ie-rxxlxmx x=!

where formula elements R0 , r, lx, mx, x, and ro are the same parameters as applied to the previously described equations. Values for !lr were incorporated as generation time when determining rT. This calculation has most frequently been denoted as T and has served as the primary estimation of generation time in other publications (e.g., Caughley, 1966;

Steams, 1992; Ebe1i, 1999, Krebs, 2001).

The concept of a stable age distribution (ex) is an important principle of population ecology and assumption of demographic models (Me1iz, 1970; Ebert, 1999).

In seasonally breeding populations, a constant proportion of individuals will be attained within each age class, despite initial population size, given geometric population growth, a constant enviromnent, and fixed age-specific survivorship and fecundity rates. Once the hypothetical ex is achieved, age classes maintain constant growth rates and time- 153

specific population growth is described as "A (Ebert, 1999; Krebs, 2001). Although most natural populations are unlikely to demonstrate ex because of inherent variability in growth, moderate deviations from this structure typically do not alter the qualitative predictions of age distribution based on r and "A (Steams, 1992). The tenus associated with ex are as previously described and distributions were calculated as (Ebe1i, 1999):

Reproductive value (vx) was assessed to determine the potential age-specific contribution of females over the course of their life span (Goodman, 1982; Steams,

1992). This value weights the contribution of individuals from different age classes to r and has been considered as a measure of fitness in ecological and evolutionary studies

(Wilson and Bossert, 1971; Steams, 1992). Because newboms were defined as age 0, the distribution of reproductive eff01i was calculated following Goodman (1982) as:

where v0 is equal to 1 and indicates the reproductive value at birth, and} represents all

ages a female will pass through from x 0 to CD.

Elasticity analysis was conducted to assess the proportional contribution of changes in survival and reproduction to the population growth rate, "A (de Kroon et al.,

1986; Horvitz et al., 1997; Caswell, 2001). This fonn of sensitivity analysis has been increasingly used to assess species fitness or the impacts of environmental perturbations 154

and aid in directing management and conservation priorities (e.g., Silvertown et aL, 1996;

Benton and Grant, 1999; Hunter et al., 2000; van Tienderen, 2000). Survival and fecundity/fertility are inte1Telated life history traits that are measured on different scales.

Elasticity analysis relates the proportional contribution of these differing matrix or life table elements in relation to the population growth rate, A, (Caswell, 2001). A large elasticity value would indicate a relatively greater change in A, resulting from an alteration to the associated rate of fertility or survivorship. To estimate elasticity values for fertility, juvenile survivorship, and adult survivorship from each scenario, Leslie matrix elements were incorporated into the life table (Heppel et al., 1999,2000; Cortes, pers. comm.). Ebert (1999) also demonstrated a method for calculating sensitivity and elasticity from life table elements. Following Leslie matrix approaches, a fertility (Fx) column relating initial survivorship (So, often denoted as Po) to mx was added to all life tables (Caswell, 2001). Reproductive values (vx) were standardized to equall for the first age class and an additional column containing the age-specific product of Vx and ex

(inner product, VxCx) was included in life table models to provide the components necessary to obtain elasticity calculations. Using age-specific elements of the Vx and Cx columns, individual elasticities (eij) were calculated following Ebert (1999) and Cmies

(pers. comm.): 155

where aij is the element corresponding to row i of columnj (survivorship), A is the finite rate of increase, Vi is the value of row i in the reproductive value (vx) column, Wj is the value of row j in the stable age distribution (ex) column, and ( w, v) is the scalar product of

w row elements in the Cx and Vx distributions (VxCx, or, or l::V,Cx ). x;Q

Fertility elasticity values were calculated as the sum of Fx columns. Because this sum is calculated using S0, age 0 survivorship is also expressed within the resulting value.

Juvenile and adult survival elasticities were summed across related age classes. The sum of all elasticity components is equal to 1 (de Kroon et al., 1986). Juvenile and adult elasticities were adjusted to reflect that both life stages are present within the same age class due to a being equivalent to the age at 50% maturity. I calculated three elasticity ratios from each scenario (adult survival:fertility, juvenile survival:fertility, and adult survival:juvenile survival) to further examine the potential impacts of perturbations in reproductive output or survival rates on population growth (Heppell et al., 1999; Cortes,

2002). An adult to fertility ratio of 2.5, for example, indicates that a 10% reduction in adult survival would necessitate a 25% increase in fertility to maintain the observed annual A. Assessments of these compensatory requirements have proven to be useful summaries of elasticity analysis and help to identifY vulnerable components of a population (Cortes, 2002) and aid in formulating improved management strategies

(Heppell et al., 1999). The ratios obtained for D. dipterura are compared to those calculated for other elasmobranchs. 156

Monte Carlo Simulation

The assumption of constant vital rates, as typically included in deterministic

demographic models, is usually inappropriate (Nations and Boyce, 1997). Plasticity is

inherent in vital rates, resulting in changes of these rates over time. Additionally,

biological processes are never fully understood and data sources are subject to

observation and measurement en-or. These combined factors operate simultaneously and

may limit the applicability and accuracy of strictly dete1ministic models. This inevitable

variability and uncertainty in life history parameters was accounted for by incorporating

Monte Carlo simulation into life tables (Cortes, 2002). This approach involves random,

independent resampling of vital rates or life history parameters with replacement from theoretical probability distributions, also tenned probability density functions (Manly,

1997; Haddon, 2001).

Probability distributions were developed as separate Independent Identical

Distributions (liDs) for survivorship (Sx), longevity (m), age at 50% maturity (a), and fecundity (mx) (Tuljapurkar, 1997; Cortes, 2002). Demographic models that incorporated randomly varied vital rates and life history traits from these probability distributions are refened to as probabilistic for the purpose of this study. Simulations were conducted with

Microsoft Excel spreadsheet software equipped with Crystal Ball® proprietary add-in risk-assessment software (Decisioneering Inc.) and Microsoft Visual Basic for

Applications. Independent values were randomly drawn for each age class. The range 157

and mean of demographic parameters was calculated following 5,000 simulations and

97.5% upper and 2.5% lower confidence limits were determined for each probabilistic model. The rationale for establishing probability distributions is described for each life history parameter below.

Life Histmy Parameters

Because of the lack of published infonnation on the life history characteristics of

Dasyatis dipterura, all demographic models were developed based on the age, growth, and reproductive study detailed in the previous chapter. Eight indirect methods for estimating natural mmiality (M) were calculated (Appendix 1). The approaches of

Hoenig (1983; two methods), Chen and Watanabe (1989; one method), Jensen (1996; three methods), and Campana et al., (200 1; one method) are derived from correlative relationships between natural mortality and specific life history parameters including longevity, age at maturity, and growth coefficient (k). Values determined for female life

history traits were applied to the equations; where Lw = 92.4 em, k = 0.0546, t0 = -7.609, and age at maturity (a)= 10 years. Although Hoenig's (1983) regression equations provide estimates of total mortality (Z) and are intended for application to unexploited or lightly exploited populations, it is included for comparison in this study because of its widespread use in the literature. The method of Chen and Watanabe (1989) produces age­ specific ammal mmiality rates, whereas a single value to be uniformly applied to all age classes is obtained from the other techniques. Unlike the previous approaches, Peterson 158

and Wroblewski (1984; one method) related Mto empirical measurements ofbody

weight-at-age as a method of estimating age-specific mmual mortality rates. Although

these authors developed the equation using dry weights, Cortes (2002) concluded that wet

weight provided more realistic estimates for sharks. This variation of Peterson and

Wroblewski (1984) was incorporated to obtain additional estimates of age-specific

mortality for D. dipterura. Mean female wet weight (g) at age was detennined from

observed mass at age records. Due to sample size constraints, pooled weight at age

estimates were obtained for age classes greater than 18 years. Spring scales used during

field sampling were limited to recording a maximum of 25 kg, therefore weight at age

estimates in excess of 25 kg were extrapolated from the power equation, wet weight =

0 9021 (x · )* 1.3052; where wet weight was converted from kilograms to grams and x =age.

Probabilities of mmual survivorship (Sx) were determined from the indirect

estimates of Mpreviously described (Appendix 1), where Sx =e-M (Ebe1i, 1999). Age­

specific Sx rates determined the proportion of individuals that were present in the

subsequent age class (lx). Constant Sx values were applied to deterministic models to

simulate best-case scenarios. Survivorship was assumed to be markedly decreased during the first year of life, and So values in both deterministic and probabilistic models were

input based on doubled natural mmiality estimates (Hoenig and Gruber, 1990; Gruber et

al., 2001; Heupel and Simpfendorfer, 2002). No published empirical studies have provided evidence that one indirect approach of estimating M (and therefore Sx) produces more accurate estimates than another and available studies indicate that indirect methods 159

may produce a wide range of Mvalues for a single population (Simpfendorfer, 1999a).

Therefore, mmual survivorship values based on each of the eight indirect methods were considered to be equally probable. Extensive variability in survivorship among years and age classes has been reported among fish populations (e.g., Vetter, 1988, Heupel and

Simpfendorfer, 2002). Therefore, in all probabilistic models, Sx values were drawn from uniform distributions specific to each age class (e.g., Figure 1A), wherin the lowest and highest calculated values were set as the lower and upper bounds.

Longevity (CD) estimates based on the maximum observed age, 28 years, and theoretical maximum age, 63 years, following Ricker (1979; 5ln2/k, where k is the growth coefficient derived from the von Bertalanfzy equation) were used for stmcturing traditional deterministic and probabilistic life tables. Maximum observed age may be considered to be an initial underestimate of CD (Beukema, 1989). However, based on the size range and relatively large sample size included in the ageing study, the striking difference between maximum observed age and that of theoretical maximum CD brings to question the likelihood of the elevated theoretical value. An additional model was developed to introduce uncertainty and allow critical comparisons of variable CD estimates in relation to survivorship, fecundity, and age at maturity. I assumed CD to be represented by a triangular distribution that was truncated to incorporate a minimum of 25 and a maximum of39 years (Figure 1B). The maximum observed age of28 was considered to be the likeliest value. This range was developed to incorporate possible ageing en·or

(over-estimation) and included values lower than the maximum repmied age based on the 160

overall average percent error of 9% obtained from the age estimates. The maximum

observed age was arbitrarily increased by 40% to establish the upper boundary for this

distribution and thus incorporate uncertainty in co into the model.

I based a on the median age at maturity as detennined from a logistic ogive

(Chapter 2). The median age was thus estimated to be 10 years. All females with a band

count of 11 or more were found to be mature (1 00% maturity). Therefore, a was

established as the age at 50% maturity and only half of the coinciding age class was

assumed to be reproductively active at this age to best reflect the observed central

tendencies of the population. In deterministic models, a was fixed at 10 years. In

probabilistic life tables a was randomly varied between the ages of 8 and 10 based on a

truncated normal distribution (e.g., Figure lC). Values were drawn from a range between

- 7.5 and 10.4 years ( x = 10) and rounded to the nearest whole year. All females were

assumed to be reproductively active in successive years following a.

Reproduction in D. dipterura conforms well to that of a birth-pulse population in

which parturition is not continuous but is restricted to a relatively discrete ammal period.

Pupping in the Bahia Magdalena lagoon complex occurs in the late summer months.

Minimum and maximum litter sizes of D. dipterura were observed to be 1 and 4, respectively. The sex ratio at birth did not differ significantly from 1:1. Mean total

fecundity based on the observed number of embryos per gravid female was reduced by

half (1.36 ± 0.36 SD) to represent the annual number of female offspring produced per

adult female (mx). Litter size was not observed to increase with size or age. 161

Reproductive output (mx) was reduced by half at a to incorporate the observed variation

in age-specific maturity and simulate the response ofpmiurition with 50% ofthe

population. Projections from detenninistic models were based on a static optimal mx of two offspring. Fecundity in probabilistic life table simulations was represented by a

modified nonnal distribution with a mean of 1.36, standard deviation of 0.36, and range

of 0.5 to 3.5 (Figure ID). This range included values that accounted for the possibility of

unequal sex ratios or the maximum fecundity being greater than has been observed in the

field. Age-specific values of mx were drawn for and applied separately to each adult age

class in all simulations. Mature females were assumed to reproduce annually in all models.

Natural Mortality Scenarios

Five scenarios were developed to examine the population dynamics of D. dipterura assuming natural mmiality as the only source of loss to the population.

Deterministic life tables based on best-case survival and fecundity conditions were

stmctured on the basis of an observed maximum age of 28 years and theoretical maximum age of 63 years. These detenninistic base scenarios are tenned D-28 and D-

63. Probabilistic models were included to incorporate uncertainty and variability in life history traits and vital rates into demographic parameters. Two probabilistic models were stmctured with longevities fixed at 28 and 63 years. The fifth scenario introduced variation in CD over a possible 14 year range in addition to randomly assigning values for 162

Sx, a, and mx to each age class from pre-defined probability distributions. These

probabilistic scenarios are referred to as P-28, P-63, and PV to specify the longevity by

which the corresponding life tables were structured. Results from these scenarios were

compared with those obtained from published demographic studies of sharks and rays.

Fishery Exploitation Scenarios

I assessed the potential effects of fishery exploitation on the population growth

characteristics of D. dipterura by integrating a fishing mortality of 0.05 yea{1 into each of the five initial scenarios. No information is available on exploitation rates of

elasmobranchs from the Bahia Magdalena lagoon complex. The relatively low fishing mortality (F) of 0.05 was arbitrarily applied to provide a basis for evaluating fishery impacts on the population. Artisanal fisheries are capable of producing high, localized levels of F. Fishing mortality rates up to 0.46 were estimated from a directed fishery for the small coastal shark, Rhizoprionodon terraenovae in the southern Gulf of Mexico

(Marquez-Farias and Castillo-Geniz 1998).

The mean size of females observed in the directed batoid fishery at Puerto Viejo was 52.3 em DW and corresponded to ages of 5-8. Althoughjuvenile D. dipterura dominated the catches at Puerto Viejo, the smallest size classes -less than 35 em DW­ were infrequently captured. It is likely that these individuals reside in different habitats than targeted by gillnets, are less vulnerable to the mesh sizes used by fishers, or these combined factors result in low catch rates of the youngest stingrays. Because these rays 163

are primarily entangled in gillnets by their tail spine, smaller mesh sizes managed to provide landings of large as well as smaller size classes. Despite the use of differing mesh sizes, size classes of D. dipterura greater than 35 em DW or approximately 2-3 years of age may be similarly vulnerable to gillnet fisheries. Therefore, F was applied equally to all age classes in each scenario beginning at age 2.

Detenninistic scenarios were again developed using optimal vital rates; the predicted age at 50% maturity, and longevities of 28 and 63 years. Survivorship values from the previously designated unifonn probability distributions were restructured based on F. Reduced survivorship based on fishing pressure was simulated using 5,000 Monte

Carlo trials for each model. Variability and unceiiainty in longevity, fecundity, and age at 50% maturity was incorporated in fishery scenarios as previously described. In addition to comparing the impact ofF on population growth rates, influences on

generation times, R0 , tx2, rT, Vx, and ex were also examined. The intrinsic rate of increase

(r) was used as a surrogate of A, to estimate the value ofF at which a stationary population growth rate would be attained ("A=l.O or r=O) (Mollet and Cailliet, 2002).

Specific fishery exploitation scenarios are designated as D-28+F, D-63+F, P-28+F, P-

63+F, and PV+F throughout this study. 164

Results

Natural Mortality and Survivorship

Natural mortality estimates calculated for D. dipterura from eight methods produced a broad range of rates, from 0.027-0.347 per year for ro=63 years and 0.064-

0.347 per year based on the observed ro of28 years (Table 1). The choice of ro markedly altered M estimates of Hoenig (1983), Chen and Watanabe (1989), and Campana et al.,

(2001). The age-specific, weight-based method of Peterson and Wroblewski (1984) resulted in the highest M estimates. At age 18 and above, these weight-based M rates converged on estimates similar to those obtained using Jensen's (1996) a-based approach and that of Campana et al. 's (200 1) for ro=28 years. Life history based methods of Jensen

( 1996) provided contrasting results, with M derived from k equaling almost half of that obtained using the a-based calculation. The lowest M estimates resulted from the age­ specific method of Chen and Watanabe (1989). Assuming ro=28 years, the ammal Mfor ages 0-3 were similar to the rates detennined using Jensen's (1996) k-based fonnulas, but decreased to a minimum of 0.064 by age 28. All M estimates obtained using the Chen and Watanabe (1989) method structured for ro=63 years were less than 0.071 mmually.

Survivorship estimates for use in demographic models were calculated from all indirect M rates. Minimum and maximum age-specific Sx values were bounded by the estimates derived from Peterson and Wroblewski (1984) and Chen and Watanabe (1989), respectively. Annual Sx rates ranged from 0.707-0.938 when ro=28 years and 0.707- 165

0.973 when m=63 years (Appendices 2, 3). With the exception of the Sx value obtained

from the weight-based Peterson and Wroblewski (1984) method, age 0 survivorship rates

were decreased by 50% and ranged between 0.707-0.849 per year and 0.707-0.868 for

m=28 and m=63 years, respectively. The Sx estimate based on Jensen's (1996) formula:

M= 1.5*k, produced one ofthe highest values at 0.921 per year (Appendix 1). Because

this method produced the second highest Sx value and was not age-dependent, it was

applied to deterministic life table models to represent Sx in best-case scenarios.

Survivorship ranges used to develop age-specific unifonn probability distributions for

probabilistic models are listed in Appendix 2 and Appendix 3.

Demographic Analysis

Detenninistic life table models projected similar population growth

characteristics, despite the striking difference in their age structures. The model

developed based on the maximum observed age of28 years (D-28) projected increasing population growth rates (A.) of approximately 14% ammally based on the most optimistic input parameters (Table 2). The net reproductive rate (Ro) was estimated to be 7.75, population doubling time (tx2) 5.25 years, and rate of increase per generation (rT) was

2.047 under this scenario. Measures of generation time were 15.5, 14.3, and 17.0 years

forT, A, and J.li, respectively (Table 3). An increasing Aof 14% ammally was also

estimated from the model that was structured by the theoretical maximum longevity of 63 years (D-63, Table 2). The Ro was estimated to be 9.8 female offspring per female over a 166

lifespan, tx2 was 5.2 years, and rT was 2.82. The three differing assessments of

generation time were determined to be T=17.1, A=14.6, and ~-t 1 =21.5 years for model D-

63 (Table 3). The first five age classes were projected to comprise greater than 75% of

the population under a stable age distribution (ex) for both deterministic scenarios (Figure

2A, Figure 3A). Age 0 constituted 20.6% of the population in scenario D-28 and less

than 0.05% ofthe population was calculated to comprise age class 28 (Figure 2A).

Under scenario D-63, the first age class (0) accounted for 23.4% of the population and

age classes greater than 28 years represented a negligible percentage of the population

under the theoretical stable age distribution, summing to less than 0.0007% of the total in

scenario D-63 (Figure 3A).

Age-specific reproductive values (vx) indicate that the largest contribution to

population growth is produced by age class 11 in both deterministic scenarios D-28 and

D-63 (Figure 4A, C). Following the peak at age 11, Vx declines to the point at which values are equivalent to or less than pre-reproductive age classes by age 24 in D-28.

Decreases in Vx are more gradual under scenario D-63 and values obtained for age classes

12-38 remain similar to the peak estimate at age 11. Reproductive values were projected to sharply decrease in a curvilinear fashion after age 49 in D-63.

Probabilistic models developed to incorporate uncertainty and variability in vital rates produced substantially lower potential mmual population growth rate estimates than obtained from deterministic models (Table 2). All simulations produced positive values 167

of A and generated population growth rates of2.6%-13.6% mmually. Confidence limits were narrowly distributed around the mean values of all demographic parameters.

Scenario P-28 indicated an increasing r of 0.057 yea{1 and A of 5.9% yea{1 in the absence of fishing mortality for the Bahia Magdalena lagoon complex population of D. dipterura (Table 2). Uncetiainty and variability in the input parameters Sx, a, and mx

1 produced A estimates ranging from 1.012-1.138 yea{ , but the narrow 97.5% and 2.5% confidence limits suggest that the vast majority of simulations provided estimates

approximating the mean. Mean estimates of R0 , tx2, and rT were 2.4 female offspring per female over a lifespan, 12.1 years, and 0.9, respectively. Estimates of generation time ranged from 14.4 (A) to 15.7 ()l1) years (Table 3).

Scenario P-63 produced a slightly higher mean of 6.9% yea{1 for A than obtained from the other probabilistic models (Table 2). Under this scenario, mean Ro was estimated to be 3.1, tx2 was 11.1 years, and rT was 1.2. Mean generation times estimated for the species ranged from 15.1 (A) to 18.7 (!li) years (Table 3). Upper and lower 95% confidence limits were similarly narrow in their distribution around mean demographic parameters.

The final probabilistic model (P-V) incorporated variability in m in addition to that in Sx, a, and mx rates. Estimates of demographic parameters derived from scenario

P-V were similar to those calculated in P-28 (Table 2). Mean A was 1.060 yea{1 with

1 simulations producing a range from 1.014-1.126 year- • Scenario P-V yielded a mean Ro of2.5, tx2 of 12.9 years, and rTof0.9. The three approaches to calculating generation 168

time resulted in estimates ranging from 14.6 (A) to 16.1 (!l I) years when incorporating variable w of28-39 years in the life table model (Table 3). Confidence limits were again nanowly distributed around the mean values of these demographic parameters.

Mean stable age distributions were dominated by the first five age classes in each of the three probabilistic scenarios. The ex theorized for P-28 decreased from approximately 21% of the population within age class 0 to 0.12% remaining at the maximum age of 28 years (Figure 2A). A similar trend was indicated for scenario P-V in which the initial distribution of individuals within each age class decreased from approximately 21% at age 0 to< 0.001% within age class 39 (Figure 2B). The mean ex of scenario P -63 decreased from approximately 21% of the individuals comprising age 0 to <0.00 1% remaining at age 58 (Figure 3B). Only minute fractions of the population were predicted to contribute to ex at the maximum age of 63 years.

The mean distribution of Vx indicated marked differences in age-specific reproductive efforts based on the differing w structures of probabilistic models.

Scenarios P-28 and P-V produced similar results, attaining maximum Vx values at 12 years which gradually decrease to pre-reproductive estimates ofvx by ages 25 and 27, respectively (Figure 4A, B). Maximum Vx was not obtained until age class 38 under the conditions of scenario P-63 (Figure 4C). A gradual increase in Vx is indicated at age 11 and is followed by a plateau that decreases to pre-reproductive levels after age 60. The extended adult period modelled in scenario P-63 predicts a significant reproductive contribution of age classes that were not observed in the natural population. 169

Variation in a accounted for a greater influence on A than did estimates of co.

Mean A was assessed in relation to co and a in scenario P-V based on 5,000 Monte Carlo simulations (Figme 5). Over the full range oflongevities (25-39 years), maximum mean

A estimates were projected when a=8 years. Finite annual growth rates decreased with increasing a. When a= 10 years, little variability in mean A occurred across the potential life span.

Elasticity Analysis

Elasticity patterns indicate that population growth rates of D. dipterura are more strongly influenced by survival of the juvenile and adult stages than survival of neonates or changes in fecundity. Potential effects of proportional changes in reproductive output on A may be considered as minor for this species. Deterministic and probabilistic scenarios generated similar proportional elasticity values and ratios (Table 4; Figure 6).

Fertility elasticities ranged from 0.062 in scenario P-63 to a maximum of 0.065 in scenarios D-28 and P-28. Juvenile elasticities ranked as the highest values in all simulations. Juvenile elasticity values ranged from a minimum of 0.480 in D-63 to a maximum of 0.579 in P-28.

Elasticity ratios are useful for describing the extent of compensation necessary to maintain A given a reduction in fertility, juvenile survival, or adult survival. The mean juvenile survival to fertility elasticity ratio (8.95) resulting from scenario P-Vindicates 170

that a 10% decrease in juvenile survival would require a 89.5% increase in fertility or age

0 survival to return the population to its original growth rate (Table 4). In comparison, only a 6.4% increase in adult survival would be necessary to compensate for a 10% decrease in juvenile survival rates. Minimum and maximum ratios of adult survival to fertility, juvenile survival to fertility, and adult survival to juvenile survival ranged from

3.8-8.2, 7.5-9.5, and 0.4-1.0, respectively based on 5,000 Monte Carlo simulations of scenario P-V. Juvenile to fertility and adult to fertility elasticity ratios were high in all scenarios (Table 4).

Mean elasticity values were minimally influenced by changes in co or a (Figure

7). Adult survival elasticity values increased slightly with greater co in scenario P-V.

Small increases in juvenile survival elasticities were observed to occur with decreasing a.

However, fertility elasticities varied minimally based on changes in these demographic input parameters. Confidence intervals around mean elasticity values were generally narrow. Simulations in which a was equal to 8 years produced the broadest range within calculated 95% confidence intervals.

Fisheries Impacts

Due to the relatively low intrinsic rates of increase projected for D. dipterura under even the most optimistic scenarios, the introduction of a relatively low fishing mortality (F = 0.05) resulted in marked decreases in demographic parameters (Table 2).

Deterministic models suggest that a fishing mortality of 0.13 yea{ 1 would result in a 171

stationary population (/c=l.O). Probabilistic models indicate that the Bahia Magdalena lagoon complex population would decrease if exposed to a mean mmual F equal to or

1 greater than 0.07 year- . It should be noted that declining annual A (<0.99) were estimated from each of the probabilistic models in 2-5% of the simulations that incorporated F. These minimum estimates of/cas a result of fishing pressure and variability or uncertainty in demographic parameters ranged between 0.967 (P-28+F) and

0.975 (P-63+F). Striking declines in Ro and rTwere produced by the inclusion ofF into life table simulations. Decreases in Ro ranged between 44-57% and a maximmn reduction of 77% in rT resulted in scenario P-28+F. Simulated fishery pressure also produced considerable variability in tx2. Estimates of generation time and elasticities were only slightly altered from the initial scenarios in response to fisheries exploitation (Tables 3,

4).

Minor stmctural shifts in Cx and Vx occurred in response to the incorporation ofF into life tables. The first five age classes dominated ex in all scenarios; however, a general reduction in the proportion of individuals present within age 0 was evident in all cases (Figures 2, 3). Variation of proportional age distributions from fishing pressure was greatest in scenario D-63 (Figure 3A). Although minimal or no decline in reproductive values were observed in the earliest and latest age classes, these values were shifted downward over the majority of the reproductively active years as a result ofF

(Figure 4A, B, C). In scenario D-63+F, the peak Vx was obtained two years later (among age class 40) than projected under conditions of M only. 172

Discussion

Mortality and Survivorship

Life history theory suggests that long-lived, late-maturing species with low fecundity, such as D. dipterura, have low natural mortality rates (e.g., Emlen, 1970;

Gadgil and Bossert, 1970; Adams, 1980; Steams, 1992). The eight indirect methods used to estimate natural mortality in this study generated relatively low values of M, supporting this generality (Table 1). Previous indirect estimates of M among batoids have produced much higher rates of natural mortality (Holden, 1974; Waring, 1984; Neer and Cailliet, 2001; Frisk et al., 2002; Mollet and Cailliet, 2002). Yokota (1951) calculated an mmual natural mortality of0.94 based on catch curve analysis for Dasyatis akajei. This estimate, however, was based on an unsound ageing method and w1equal fishing pressure among described age classes that likely resulted in a gross overestimate of M. Among the batoids, only the threatened sawfishes (Pristis pectinata and P.

1 perotteti) have been estimated to have natural mortality rates (0.07-0.16 yea{ ) approximating those obtained for D. dipterura (Simpfendorfer, 2000). By comparison to sharks, natural mo1iality estimates of D. dipterura were of similar magnitude to those of

1 1 Triakis semifasciata (0.14 yea{ ; Cailliet, 1992) and Sphyrna lewini (0.12 yea( ; Liu and

Chen, 1999) using one ofHoenig's (1983; Appendix 1, Equation 1) approaches, the large

1 coastal shark, Carcharhinus obscurus, (0.082-0.086 yea{ ) applying Jensen's (1996) von 173

Bertalanffy based methods (Simpfendorfer, 1999b), and the pelagic species, Alopias

1 pelagicus, based on longevity and the Campana et al. (2001) formula (0.15 yea{ )

(Mollet and Cailliet, 2002). Although these species represent a diverse and disparate

grouping based on phylogeny, habitat preference, or trophic level, each is characterized

by similar age at maturity and longevity.

Indirect calculations of natural mortality for D. dipterura provided plausible

survivorship rates but produced a broad range of possible values. Predation has been

assumed to be the most influential factor on natural mortality, but age, water temperature,

disease, parasites, food availability, and population density may also have significant

impacts (Vetter, 1998). Based on anecdotal information and observations of artisanal

fishery landings, I suggest that the Bahia Magdalena lagoon complex serves as a nursery

ground for bull sharks, C. leucas, scalloped, Sphyrna lewini, and smooth hammerheads,

S. zygaena. These species commonly prey on stingrays and may represent a significant

source of mortality for D. dipterura (Compagno, 1984; Snelson et al., 1984). However,

decades of directed miisanal fishing effort for large sharks may have resulted in reduced

numbers of these predators and increased stingray survivorship in recent years. El Nifio

and La Nifia large-scale oceanographic events significantly alter water temperature and

impact the distribution and abundance of potential predators as well as prey. These

environmental and associated biotic influences on mmiality may produce marked inter­

aruma! variability in survivorship. The use of Monte Carlo simulation and the broad range of age-specific and constant mortality values may account for and incorporate 174

much of the potential variability of survivorship from these and other sources of mortality

(Tuljapurkar, 1997; Cortes, 2002).

Approaches for estimating natural mortality based on life history parameters may not provide accurate estimates (Vetter, 1988). Despite good fits, prediction of natural mortality from correlative regressions may include significant errors, but estimates of error associated with predicted values have rarely been considered (Vetter, 1988; Pascual and Iribame, 1993). It is unlikely that a single, constant value as calculated by most indirect techniques adequately incorporates the variability of M that would occur over neonate, juvenile, and adult phases. Age-specific estimates calculated after Peterson and

Wroblewski (1984) were substantially different than other approaches and produced the lowest survivorship estimates through age 18. Mollet and Cailliet (2002) argue that this weight-based method may not be applicable for large, pelagic sharks because of the range of mass magnitudes included in the calculation and a lack of convincing empirical relationships between mortality and mass among sharks. However, McGurk (1986) concluded that the Peterson and Wroblewski (1984) method provided a good fit and predictability of mortality rates for many taxa, including invertebrates, pelagic fishes, and whales. Further support of this relationship was provided by Lorenzen ( 1996) who successfully modelled Mas a power function of weight for fishes from captive, fanned environments as well as natural ecosystems. Body weight has also been demonstrated to be a useful predictor of other life history parameters including longevity and r (Blueweiss et al., 1978). The Peterson and Wroblewski (1984) teclmique has been favored, with 175

slight modifications, by Cortes (2002) and applied to a suite of shark species. Goldman

(2002) found the method to provide the highest estimates of survivorship among most

age classes of salmon, Lamna ditropis, and sandtiger, Carcharias taurus, sharks. In contrast, survivorship estimates for the sawfish, P. pectinata, were estimated to be considerably lower during the first 8-10 years using the mean weight at age estimates based on Peterson and Wroblewski (1984) than were calculated using Hoenig (1983) equations (Simpfendorfer, 2000). Although empirical evidence is necessary to evaluate the accuracy of each indirect mortality estimate, the markedly lower survivorship rates estimated using the Peterson and Wroblewski (1984) technique may indicate that these estimates based on relationships of pelagic species may have limited applicability to benthic elasmobranchs. Because of the uncertainty surrounding indirect natural mortality estimation and the sensitivity of demographic models to this essential parameter, comparative assessments of multiple direct and indirect techniques must be completed.

Accurate measurements of natural mortality have proven to be complex and difficult to obtain from marine populations, but are essential for understanding population dynamics and responses to perturbations. The reliability of life history-based mortality measures for elasmobranchs has only recently been examined through direct studies. The regression equations of Hoenig (1983) were found to produce lower estimates of mortality than those resulting from catch curve analysis (Cortes and Parsons, 1996;

Simpfendorfer, 1999a). Heupel and Simpfendorfer (2002) compared multiple indirect methods of estimating natural mortality with the results derived from a telemetry study of 176

age 0 blacktip sharks, Carcharhinus limbatus. Indirect estimates typically

underestimated observed mortality rates and thus provided elevated survivorship values.

Juvenile survivorship was found to be highly variable, ranging between 44-61% annually.

However, the indirect methods of Hoenig (1983) and Jensen (1996), modified from Pauly

(1980), produced values within this observed range. A similar pattern of marked inter­

annual variation of 38-65% in age 0 survivorship was documented by Gruber et al.

(2001) among lemon sharks, Negaprion brevirostris. Although commonly applied techniques of indirect mortality estimation may not minor direct estimates among these species, the high variability among survivorship rates highlights the importance of calculating multiple estimates of mortality and incorporating Monte Carlo procedures to simulate uncertainty and variability in these rates. If indirect methods generally underestimate mortality rates (Cmies and Parsons, 1996; Heupel and Simpfendorfer,

2002), overly optimistic survivorship and population growth rates would result even with the inclusion of Monte Carlo uncertainty analysis.

Refinement of mortality estimates would greatly enhance projections of population dynamics based on demographic models. Direct M estimates obtained through a tagging program and fishery-independent derived catch curve analysis would enable a comparison with indirect estimates and provide an empirical basis for modelling survivorship. Although adult mortality rates are often considered to be relatively constant, juvenile survivorship even among relatively long-lived species may fluctuate considerably (Chamov, 1986). An emphasis on the assessment of juvenile mortality rates 177

would, therefore, provide the most essential details for improvement of survivorship parameters. Although survivorship values were drawn from a range that included age­ specific rates following Peterson and Wroblewski (1984) and Chen and Watanabe (1989), in all instances survivorship probabilities increased with age. However, evidence suggests that after a certain age survivorship is likely to decline (e.g., Beverton and Holt,

1959; Eberhardt, 1985; Chen and Watanabe, 1989). Modifications of age-specific survivorship that integrate this likely population characteristic through the use of modified probability distributions or methods of indirect mortality estimation may provide improved estimates from demographic simulations.

Demographic Analysis

Deterministic models based on the most optimistic survivorship and fecundity probabilities projected annual rates of population increase of 14.1-14.3% in the absence of fishing motiality. These simulations may represent the maximum likely potential for population growth and associated demographic descriptors. The similarity of population growth rates generated by these deterministic models indicates that differences in longevity between models had minimal impact on population projections. Stable age distributions derived from the theoretical maximum longevity of 63 years predicted extremely negligible propmiions of the population to extend beyond 28 years. Despite the fact that the largest females included in the age and growth study were at least 14 em less than the maximum reported disc width for the species, it is unlikely that any achieve 178

such extended longevity even under optimal conditions in the Bahia Magdalena lagoon complex. As illustrated by theoretical stable age distributions, the method of Ricker

(1979) for determining maximum longevity may generally overestimate longevity because of the asymptotic relationship nature of the von Bertalanffy growth function from which it is derived. The approach for estimating longevity following Fabens (1965) would also produce biologically unreasonable estimates of up to 88 years. However, demographic models in this study were minimally impacted by increases in longevity, demonstrating that other vital rates and life history characteristics are more influential on population growth.

Demographic analyses of D. dipterura produced estimates of A, comparable to C. obscurus, P. pectinata, and P. perotteti based on deterministic models and best-case or optimal conditions (Table 5). Despite often large differences in longevity, generation time, and fecundity among these species, projections from life tables produced similar rates of increase. In relation to other elasmobranchs, D. dipterura reflects a moderate potential for population growth under optimal conditions. The pelagic congener, D. violacea, has a life span less than half that of D. dipterura and a slightly greater fecundity, but also possesses a moderate estimated A of 1.20 yea{1 (Mollet and Cailliet,

2002). The lowest potential population growth rates calculated from deterministic demographic models under best-case scenarios range from 1.02-1.05 yea{1 for small and large coastal sharks. 179

Results from probabilistic life table models that incorporated uncertainty and variability in age at maturity, survivorship, and fecundity provide more flexible and probable demographic assessments. Because longevity is varied (in addition to other parameters) and the possibility that m may be less than observed because possible ageing error is included in the associated probability distribution, I suggest that scenario P-V provides the most realistic and applicable demographic results produced in this study.

However, estimates generated from scenario P-V produced very similar values to those obtained from the probabilistic scenario P-28, in which longevity was fixed at the maximum observed age of 28 years.

Potential population growth based on the most likely demographic model (P-V) produced a mean ammal A. of 1.06 (6%). In a review oflife history traits among long­ lived marine species, Musick (1999) concluded that populations with ammal intrinsic rates less than 10% were particularly vulnerable to increases in mortality. The mean rate of increase per generation (r1) was estimated as 0.93 and further indicates a limited capacity for the population to respond to increased mortality. This measure integrates demographic statistics to provide a description of population growth scaled over a period of evolutionary significance rather than absolute time and thus allows another useful characterization of species life history strategies (Fowler, 1988; Cortes, in press). The low estimate of rT obtained for D. dipterura is much more similar to estimates obtained for marine mammals than other fish species (Fowler, 1988). These low rates of mmual population growth and increase per generation are indicative of slow growing, late 180

maturing, long-lived, organisms that possess a relatively low fecundity. Species that possess these K-selected characteristics represent an extreme of the generalized rl K life history continuum (MacArthur and Wilson, 1967) and tend to exhibit low potential fishery yields, slow recoveries to fishery-induced mmiality, and increased risks of extinction (e.g., Adams, 1980; Hoenig and Gmber, 1990; Musick, 1999; Steams, 1992).

Studies of elasmobranch population dynamics have only recently incorporated

Monte Carlo simulation to account for unce1iainty and variability in life history parameters (Cortes, 1999, 2002; Frisk et al., 2002; Goldman, 2002; Beerkircher et al.,

2003; Carlson et al., 2003). Mean projections of population growth rates and generation times of D. dipterura are most similar to those previously calculated for the large coastal shark, Negaprion brevirostris and the small coastal shark, Rhizoprionodon terraenovae

(Table 6). The mean A, estimated for D. dipterura falls within the middle of the range of those estimated for other elasmobranchs using Monte Carlo procedures and lies within the range of species noted for low potential population growth rates (Cortes, 2002).

Other batoids that have been the focus of concem because of population declines and shifts in abundance in the North Atlantic appear to have considerably greater capacities for population growth (Frisk et al., 2002). Comparisons of the results obtained from this study with those from the literature are drawn to illustrate generalities and should not be considered absolute. Observed differences or similarities in demographic parameters may have resulted from differing model assumptions, selection of probability 181

distributions, or approaches to life table or matrix structure rather than actual life history variation (Cailliet, 1992; Gregory, 1997).

Variation in age at maturity and adult and juvenile survivorship were the most influential factors on A. Probabilistic models were generally insensitive to variability in longevity and fecundity. Although D. dipterura possesses a highly efficient mode of aplacental viviparity, reproduction appears to be the most constrained life history trait due to a single functional ovary and relatively low fecundity. No indication of an increase in litter size with maternal size was detected. My observations suggest, instead, that the largest females produced larger offspring. This tactic would likely confer improved survivorship to these offspring. However, increases in fecundity or reproductive periodicity are unlikely compensatory responses to perturbations within this population. High degrees of sensitivity to changes in age at maturity have previously been revealed by demographic models for many shark species (Smith et al., 1998;

Simpfendorfer, 1999a; Cortes, 2002). Other studies have detennined that small changes in natural mortality produced relatively large changes in A (Heppell et al., 1999;

Simpfendorfer, 1999b). Although combinations of low survivorship and late age of

1 maturity produced extreme estimates of A equal to 1. 01 yea{ , these instances were rare among simulations and age at maturity of D. dipterura typically accounted for the greatest single influence on A (Figure 5). Correlation analysis would provide a more detailed assessment of the effects of variability in age at maturity and survivorship on model output (Cortes, 2002). 182

Elasticity Analysis

Elasticity analyses of detenninistic and probabilistic model projections indicated

that population growth rates of D. dipterura are more strongly influenced by survival of

juvenile and adult stages than survival of neonates or changes in fecundity. This

elasticity pattern conforms to the general trend observed among sharks, rays, and other

long-lived vertebrates (Heppell et al., 1999, 2000; Cortes, 2002; Mollet and Cailliet,

2002). The proportional influence of fertility, juvenile survival, and adult survival

parameters on A, described for D. dipterura were most similar to mean elasticity values

previously obtained for Lamna ditropis, Squatina californica, and Triakis semifasciata

(Table 6) (Cortes, 2002; Goldman, 2002). Few demographic studies ofbatoid

populations have been conducted, but available elasticity analyses reflect similar patterns to that observed in D. dipterura. Survivorship of juvenile and adult Dipturus batis, Raja

clavata (Walker and Hislop, 1998), and D. violacea (Mollet and Cailliet, 2002) were

found to provide much greater contributions to population growth rates than fertility or

age 0 survivorship.

Population growth among species characterized by K-selective traits is often more heavily influenced by juvenile survivorship (Read and Harvey, 1989; Heppell et al.,

2000). The relatively small litter size of D. dipterura and observation of greater offspring size instead of increased fecundity with larger female size suggests selection of the juvenile life history stage as an important ecological and evolutionary trade-off for 183

optimizing fitness. Mean reproductive values provide further evidence of the extent and contribution of juvenile stingrays to projected population growth rates. However, the adult elasticity ranking calculated for D. dipterura was higher than observed among many elasmobranchs and signifies a large proportional contribution to A (Table 6).

Elasticity values with low rankings may be associated with high variance and should not be dismissed due to their potential for producing large effects on population growth rates

(Pfister, 1998; Mills et al., 1999). Although fertility appears to be constrained in D. dipterura, the potential for plasticity in adult and age-0 survivorship should be acknowledged and may contribute more to the variation in A than indicated by the elasticity values (Horvitz et al., 1997; de Kroon et al., 2000).

Large ratios of adult survival to fertility and juvenile survival to fertility were calculated for D. dipterura from deterministic and probabilistic models. Heppell et al.

(1999) applied elasticity ratios as measures ofthe density-dependent compensation necessary to return populations to a desired A in response to fisheries exploitation.

Elasticity ratios calculated in this study indicated that the extent of compensation required for fertility to offset even a 10% reduction in juvenile or adult survival of D. dipterura would be biologically unreasonable (Table 4). Cortes (2002) demonstrated that similar elasticity patterns were typical of shark species with late ages of maturity.

The consequences of perturbation to survivorship and fertility on population growth rate are assessed using elasticity analysis assuming that the current enviromnent is maintained (de Kroon et al., 2000). Elasticity values may vary under alternative 184

conditions and are impacted by measurement en-or, natural variation, and uncertainty of the input parameters. These sources of variability and uncertainty were included in the generated elasticity values through the incorporation of Monte Carlo simulation in life table models. Relative elasticity values and rankings were developed to assess the impact of small changes in vital rates on A and may provide inaccurate estimates in the case of large perturbations (Mills et al., 1999; Caswell, 2000). However, deviation of elasticity estimates because of the nonlinearity of these matrix or life table derivatives have been found to produce robust qualitative and fairly accurate quantitative results of moderate perturbations (Mills et al., 1999; Caswell, 2000; de Kroon, 2000). Elasticity rankings, values, and ratio proportions for D. dipterura deviated minimally from previous estimates in response to simulated fishing mortality. The predictions drawn from elasticity analysis in this study are likely to be robust and provide a reliable indicator of population perturbations on A.

Fisheries Impacts and Conservation Implications

Dasyatis dipterura is a primary component of directed artisanal elasmobranch fisheries in the Bahia Magdalena lagoon complex and Gulf of California. It is likely to be commonly taken as bycatch among trawl fisheries operating throughout the Gulf of

California and Pacific coast of Mexico. Historical and present fishing effort for this species is essentially unknown. The extent of these fisheries and mmuallandings are poorly documented, but catches appear to be greatest during reproductive and parturition 185

events in the summer and early fall. The introduction of a relatively low fishing mortality

1 (0.05 yeaf ) into deterministic and probabilistic models produced sharp declines in

projected net reproductive rates (Ro), age-specific reproductive values (vx), and rates of

increase per generation (rT). Demographic analyses indicate that tllis population is of

low productivity and would decline tmder moderate levels of exploitation.

The vulnerability of elasmobranchs to fishing pressure has been well established

(e.g., Holden 1973; Holden 1977; Pratt and Casey 1990; Walker 1998; Stevens et al.,

2000). Sustainable elasmobranch fisheries may be achieved, but rapid depletion and slow recoveries are common and typical of those species with low 'A values (Walker, 1998;

Musick, 1999; Stevens, 1999). Projections of 'A for D. dipterura were consistent with those of elasmobranchs at the lower end of the generalized r-K continuum, indicating a very limited fishery potential for this species (Cortes, 2002). Although Mexico has one of the largest elasmobranch fisheries in the Americas, no management plans for this historically susceptible group have been enacted.

Results of elasticity analyses are commonly used to aid in formulating conservation and management strategies (Crouse et al., 1987; de Kroon et al., 2000;

Heppell et al., 1999). The relative contribution of life stages that provide the greatest propmiion to population growth rate can be identified and targeted to maximize the influence of conservation efforts. Elasticities are convenient assessments of potential population responses to exploitation, but are not intended to provide a sole basis for management rationales (Mills et al., 1999; Ehrlen et al., 2001 ). The high juvenile 186

survival elasticity values calculated for D. dipterura suggest that the population growth rate would best be maintained or compensated for by management efforts intended to

improve juvenile survival under fisheries exploitation (de Kroon et al., 2000; Heppell et al., 2000). Juvenile stingrays dominated the catch composition in Puerto Viejo and were predicted to comprise the majority of the population based on stable age distributions. In the demersal gillnet fisheries that typify much of Mexico's miisanal elasmobranch fishing effort, myliobatiform rays are entangled by their tail spine and therefore vulnerable to a broad range of mesh sizes. Tlus observed lack of size selectivity in relation to gear complicates and restricts the ability to establish size-selective fisheries. I suggest that seasonal, or spatial fishery closures would provide a more effective mechanism for managing these populations. In response to expanding or emerging fisheries and the absence of management measures, marked declines and localized population depletions of D. dipterura are likely to occur.

The abundance, structure, and composition of skate populations in the North Sea have been reported to alter dramatically in response to industrial trawl fisheries (e.g.,

Walker and Hislop, 1998; Dulvy et al., 2000). In these studies, populations oflarger skate species were found to decline and smaller, potential competitor, species appeared to have increased in biomass following a period of extended exploitation. If vulnerability to fisheries and decreased productivity are correlated to body size among myliobatifonn rays, large species such as D. brevicaudata, D. centroura, D. longa, or D. thetidis may be much less capable of sustaining fishing pressure than D. dipterura. Indirect fishing 187

pressure alone may have the potential to produce declining population growth rates among these species. However, COlTelations of life history and demographic patterns to body length have not provided strong or consistent relationships among sharks (Cortes,

2000, 2002) and additional life history and empirical data would be required to further evaluate the population dynamics and potential responses to perturbation for these spec1es.

Model Limitations, Potential Improvements and Conclusions

The results of this study provide the first demographic analysis incorporating uncertainty in life history parameters for myliobatifonn rays. Until recently, demographic analyses were based primarily on deterministic life tables. Although multiple scenarios have often been considered in these studies the full range of likely input values has not been considered, potentially causing measurement en-or to be magnified. The use of Monte Carlo simulation was implemented in probabilistic models to potential measurement en-or and to reflect uncertainty of life history parameters based on probability distributions. These simulations address many of the limitations of traditional dete1ministic models.

The effectiveness of demographic models in describing population dynamics is greatly restricted by the quality of the input parameters and estimates of vital rates.

Although demographic models were developed from the best available life history data and included uncertainty in these parameters, additional information on litter size, 188

maturity, maternal size-fecundity relationships, age, and growth would enhance these

projections. Age and longevity were based on validated age and growth estimates based

on the semi-direct method of marginal increment analysis. Improved confidence in

model structure would be gained through validation of age estimates. Estimates of

natural mortality based on direct tag-recapture or fishery-independent catch curve would

greatly refine population projections. The implementation of a tag-recapture study would

also facilitate an assessment of fishing mortality and also provide a basis for validating

age estimates.

Conclusions drawn from dete1ministic and probabilistic matrix or life table models assume that populations increase at a geometrically constant rate regardless of population size. However, population density has long been recognized as an essential factor of population regulation (e.g., Krebs, 2001). The contribution and extent of density-dependent factors on population growth are difficult to demonstrate, but are commonly accepted to influence changes in age at maturity, fecundity, size at birth, individual growth rates, and mortality (e.g., Holden, 1973; Haddon, 2001; Rose et al.,

2001 ). Incorporation of potential compensatory responses to changes in population density into demographic models may provide more reliable projections of population dynamics in response to perturbations. Modelling these factors may best be accomplished through the application of nonlinear equations and has been successfully implemented in matrix models and elasticity analysis (Cushing, 1997; Caswell, 2001;

Grant and Benton, 2003). Density-dependent compensation has successfully been 189

incorporated into modified linear, age-structured demographic models (Au and Smith,

1997; Smith et al., 1998; Goldman, 2002) and more complex, nonlinear, data-intensive stock assessments (e.g., Wood et al., 1979; Punt and Walker, 1998) for shark populations.

Empirical evidence of compensatory density-dependent responses in life history parameters is unavailable for D. dipterura and most elasmobranchs in general (Cortes,

1998), but should be incorporated into future models. Consideration should also be given to potential reductions in population growth (i.e., Allee effects) as a consequence of reduced population densities in elasmobranch population modelling (Fowler and Baker,

1991; Gascoigne and Lipcius, 2004 ).

Matrix and life table models assume population growth based on a stable age distribution and a constant environment. Population age structure is subjected to constant variation and hypothetical stable age distributions, if achieved, are not maintained

(Steams, 1992; Krebs, 2001 ). However, moderate divergence from this structure typically does not alter the qualitative predictions of r and 'A in demographic models

(Steams 1992). In contrast, significant deviations from a stable age distribution in the study population may have resulted from historical and present fishing effort causing population projections to be inaccurate or overestimated. Elasmobranch populations, and other species characteristic of K-selected life history attributes, are thought to be less prone to fluctuations in response to enviro1m1ental variability (Caswell, 1982; Walker,

1998). However, the population dynamics described in this study should be considered as reflective of recent conditions in the Bahia Magdalena lagoon complex and should not 190

be assumed as transferable to future populations of D. dipterura exposed to different envirmm1ental conditions.

All modelling attempts represent over-simplifications of natural processes and are therefore limited in their predictive abilities. Demographic analysis based on life table or matrix teclmiques is an invaluable tool for describing population growth characteristics, comparing life history traits, assessing vulnerability to exploitation, and categorizing the influence of specific life stages to population growth (Cailliet, 1992; Cortes, 1998;

Caswell, 2001 ). Development of demographic models does not require estimates of population size and can be accomplished with relatively minimal life history data. Life table models are not as restrictive as has often been assumed. Life table and Leslie matrices are extremely flexible and can be extended to incorporate density-dependent compensation, effects of gear selectivity, diapause, both sexes, and uncertainty and variability in life history parameters (Tuljapurkar, 1997; Cortes, 2002, 2004; Beerkircher et al., 2003).

The present study maximizes the use of available life history infonnation and provides the first assessment of the population dynamics of the commercially exploited stingray, D. dipterura, with insights into vulnerability to fisheries exploitation.

Probabilistic models developed in this study did not assume that all females were reproductively active at a as most often applied, but instead simulated proportional maturity within the population based on directly observed tendencies and variability among females. EITor and uncertainty in modelled longevity and age estimates included 191

both the likelihood of overestimation as well as underestimation. Deterministic and probabilistic demographic analyses indicate that the Bahia Magdalena lagoon complex population of D. dipterura has a relatively low intrinsic growth potential and possesses a limited resilience to fishing pressure. Additional research focused on the movements, direct measurements of natural mortality, and age validation would advance and refine the understanding of D. dipterura population dynamics gained from this study. 192

LITERATURE CITED

Adams, P.B. 1980. Life history patterns in marine fishes and their consequences for fisheries management. Fishery Bulletin 78: 1-11.

Au, D.W. and Smith, S.E. 1997. A demographic method with population density compensation for estimating productivity and yield per recruit of the leopard shark (Triakis semifasciata). Canadian Journal of Fisheries and Aquatic Sciences 54: 414-420.

Benton, T.G. and Grant, A. 1999. Elasticity analysis as an important tool in evolutionary and population ecology. Trends in Ecology and Evolution 14(12): 467-471.

Beerkircher, L., Shivji, M., and Cortes, E. 2003. A Monte Carlo demographic analysis of the silky shark (Carcharhinus falciformis): implications of gear selectivity. Fishery Bulletin 101: 168-174.

Beukema, J.J. 1989. Bias in estimates of maximum life span, with an example ofthe edible cockle, Cerastoderma edule. Netherlands Journal of Zoology 39(1-2): 79- 85.

Beverton, R.J.H. and Holt, S.J. 1959. A review ofthe lifespan and mortality rates offish in nature and their relation to growth and other physiological characteristics. In CIBA Foundation Colloquia on Ageing. Volume 5. (G. Wolstenholme and M. O'Connor, eds.), p. 142-177. Little, Brown, and Company, Boston, MA.

Blueweiss, L., Fox, H., Kudzma, V., Nakashima, D., Peters, R. and Sams, S. 1978. Relationships between body size and some life history parameters. Oecologia 37: 257-272.

Bonfil, R. 1994. Overview of world elasmobranch fisheries. F AO Fisheries Technical Paper 341, 119 p.

Cailliet, G.M. 1992. Demography of the central California population of the leopard shark (Triakis semifasicata). Australian Journal of Marine and Freshwater Research 43:183-189.

Cailliet, G.M., Mollet, H.F., Pittenger, G.G., Beford, D., and Natanson, L.J. 1992. Growth and demography of the Pacific angel shark (Squatina californica), based on tag returns off California. Australian Journal ofMarine and Freshwater Research 43:1313-1330. 193

Campana, S., Marks, L., Joyce, W., and Harley, S. 2001. Analytical assessment of the porbeagle shark (Lamna nasus) population in the Northwest Atlantic, with estimates of long-term sustainable yield. Canadian Stock Assessment, Research Document 2001/067, Ottowa, Ontario. 59 p.

Carlson, J.K., Cortes, E., and Bethea, D.M. 2003. Life history and population dynamics of the finetooth shark (Carcharhinus isodon) in the northeastern Gulf of Mexico. Fishery Bulletin 101: 281-292.

Caswell, H. 1982. Life history theory and the equilibrium status of populations. The American Naturalist 120(3): 317-339.

Caswell, H. 2000. Prospective and retrospective perturbation analyses: their roles in conservation biology. Ecology 81(3): 619-627.

Caswell, H. 2001. Matrix Population Models: Construction, Analysis, and Interpretation. 2nd edition. Sinauer Associates, Inc., Sunderland, MA. 722 p.

Caughley, G. 1966. Mmiality patterns in mammals. Ecology 47(6): 906-918.

Caughley, G. 1967. Parameters for seasonally breeding populations. Ecology 48(5): 834-839.

Chamov, E.L. 1986. Life history evolution in a "recruitment population": why are adult mortality rates constant? Oikos 47: 129-134.

Chen, S. and Watanabe, S. 1989. Age dependence of natural mortality coefficient in fish population dynamics. Nippon Suisan Gakkaishi 55(2): 205-208.

Compagno, L.J. 1984. Food and Agriculture Organization species catalog. Sharks ofthe world. An mmotated and illustrated catalogue of shark species known to date. Carcharhinifonnes. FAO Fisheries Synopsis 125, Volume 4, Part 2: 251-655.

Cortes, E. 1995. Demographic analysis ofthe Atlantic sharpnose shark, Rhizoprionodon terraenovae, in the Gulf of Mexico. Fishery Bulletin 93: 57-66.

Cortes, E. 1998. Demographic analysis as an aid in shark stock assessment and management. Fisheries Research 39: 199-208. 194

Cortes, E. 1999. A stochastic stage-based model for the sandbar shark in the western North Atlantic. American Fisheries Society Symposium 23: 115-136.

Cortes, E. 2000. Life history patterns and correlations in sharks. Reviews in Fisheries Science 8( 4): 299-344.

Cortes, E. 2002. Incorporating uncertainty into demographic modeling: Application to shark populations and their conservation. Conservation Biology 16(4): 1048- 1062.

Cortes, E. 2004. Life history patterns, demography, and population dynamics. In Biology of Sharks and Their Relatives (J.C. Carrier, J.A. Musick, and M.R. Heithaus, eds.), p. 449-469. CRC Press, New York, New York.

Cortes, E. and Parsons, G.R. 1996. Comparative demography of two populations of the bom1ethead shark (Sphyrna tiburo). Canadian Journal ofFisheries and Aquatic Sciences 53: 709-718.

Crouse, D.T., Crowder, L.B., and Caswell, H. 1987. A stage-based population model for loggerhead sea turtles and implications for conservation. Ecology 68: 1412-1423.

Cushing, J.M. 1997. Nonlinear matrix equations and population dynamics. In Structured-Population Models in Marine, Terrestrial, and Freshwater Systems. (S. Tuljapurkar and H. Caswell, eds.), p. 205-243. Chapman and Hall, New York, NY.

de Kroon, H., Plaisier, A., van Groenendael, J., and Caswell, H. 1986. Elasticity: The relative contribution of demographic parameters to population growth rate. Ecology 67(5): 1427-1431.

de Kroon, H., van Groenendael, J., and Ehrlen, J. 2000. Elasticities: a review of methods and model limitations. Ecology 81(3): 607-618.

Deevey, E.S. Jr. 1947. Life tables for natural populations of animals. Quarterly Review ofBiology 22: 283-314.

Dulvy, N.K., Metcalfe, J.D., Flanville, J., Pawson, M.G., and Reynolds, J.D. 2000. Fishery stability, local extinctions, and shifts in community structure in skates. Conservation Biology 14(1): 283-293. 195

Eberhardt, L.L. 1985. Assessing the dynamics of wild populations. Joumal of Wildlife Management 49(4): 997-1012.

Ebert, T.A. 1999. Plant and Animal Populations: Lessons in Demography. Academic Press, San Diego, CA. 312 p.

Ehrlen, J., van Groenendael, J. and de Kroon, H. 2001. Reliability of elasticity analysis: reply to Mills et al. Conservation Biology 15(1): 278-280.

Emlen, J.M. 1970. Age specificity and ecological theory. Ecology 51(4): 588-601.

Fabens, A.J. 1965. Properties and fitting of the von Bertalanffy growth curve. Growth 29: 265-289.

Flores, J.O., Rodriguez, M., Shimizu, M., and Machii, T. 1995. Evaluation of demersal fishery resources of the Gulf of Califomia using Mexican shrimp trawlers. Joumal of the National Fisheries University 44 (1): 9-19.

Fowler, C.W. 1988. Population dynamics as related to rate of increase per generation. Evolutionary Ecology 2: 197-204.

Fowler, C.W. and Baker, J.D. 1991. A review of animal population dynamics at extremely reduced population levels. Report of the Intemational Whaling Commission41: 545- 554.

Frisk, M.G., Miller, T.J., and Fogarty, M.J. 2002. The population dynamics of the little skate Leucoraja erinacea, winter skate Leucoraja ocellata, and bamdoor skate Dipturus laevis: predicting exploitation limits using matrix analyses. ICES Joumal ofMarine Science 59: 576-586.

Gadgil, M. and Bossert, W.H. 1970. Life historical consequences of natural selection. American Naturalist 104: 1-24.

Gascoigne, J. and Lipcius, R.N. 2004. Alle effects in marine systems. Marine Ecology Progress Series 269: 49-59.

Goldman, K.J. 2002. Aspects ofthe age, growth, demographics and thennal biology of two lamnifonn shark species. Ph.D. Dissertation, College of William and Mary, Virginia. 220 p. 196

Goodman, D. 1982. Optimal life histories, optimal notation, and the value of reproductive value. American Naturalist 119(6): 803-823.

Grant, A. and Benton, T.G. 2003. Density-dependent populations require density­ dependent elasticity analysis: an illustration using the LPA model of Tribolium. Jomnal of Animal Ecology 72: 94-105.

Gregory, P.T. 1997. What good is Ro in demographic analysis? (And what is a generation anyway?). Wildlife Society Bulletin 25(3): 709-713.

Gruber, S.H., de Marignac, J.R.C., and Hoenig, J.M. 2001. Survival of juvenile lemon sharks at Bimini, Bahamas, estimated by mark-depletion experiments. Transactions of the American Fisheries Society 130: 376-384.

Haddon, M. 2001. Modelling and Quantitative Methods in Fisheries. Chapman and Hall/CRC Press, Boca Raton, FL. 406 p.

Heppell, S.S., Crowder, L.B., and Menzel, T.R. 1999. Life table analysis oflong-lived marine species with implications for conservation and management. In Life in the Slow Lane: Ecology and Conservation of Long-lived Animals. (J.A. Musick, ed.), p. 137-148. American Fisheries Society Symposium 23. Bethesda, MD.

Heppell, S.S., Caswell, H., and Crowder, L.B. 2000. Life histories and elasticity patterns: Perturbation analysis for species with minimal demographic data. Ecology 81(3): 654-665.

Heupel, M.R. and Simpfendorfer, C.A. 2002. Estimation of mortality of juvenile blacktip sharks, Carcharhinus limbatus, within a nursery area using telemetry data. Canadian Journal of Fisheries and Aquatic Sciences 59: 624-632.

Hilborn, R. and Walters, C.J. 1992. Quantitative Fisheries Stock Assessment: Choice, Dynamics, and Uncertainty. Chapman and Hall, New York, NY. 570 p.

Hoenig, J.M. 1983. Empirical use oflongevity data to estimate mortality rates. Fishery Bulletin 82(1): 898-903.

Hoenig, J.M. and Gruber, S.H. 1990. Life-history patterns in the elasmobranchs: implications for fisheries management. In Elasmobranchs as Living Resources: Advances in the Biology, Ecology, Systematics, and the Status of the Fisheries (H.L. Pratt, S.H. Gruber, and T. Taniuchi, eds.), p. 828-903. NOAA Technical Report NMFS 90. 197

Holden, M.J. 1973. Are long-term sustainable fisheries for elasmobranchs possible? Rappmis et Proces-verbaux des Reunions, Conseil International pour L'Exploration de laMer 164: 360-367.

Holden, M.J. 1974. Problems in the rational exploitation of elasmobranch populations and some suggested solutions. In Sea Fisheries Research. (J.A. Gulland, ed.), p. 117-138. Elek Scientific, London, England.

Holden, M.J. 1977. Elasmobranchs. In Fish Population Dynamics (J.A. Gulland, ed.), p. 187-214. John Wiley and Sons, New York, NY.

Horvitz, C., Schemske, D.W., and Caswell, H. 1997. The relative "importance" oflife­ history stages to population growth: prospective and retrospective analyses. In Structured-Population Models in Marine, Terrestrial, and Freshwater Systems. (S. Tuljapurkar and H. Caswell, eds.), p. 247-271. Chapman and Hall, New York, NY.

Hunter, C.M., Moller, H., and Fletcher, D. 2000. Parameter uncertainty and elasticity analysis of a population model: setting research priorities for shearwaters. Ecological Modelling 134: 299-323.

Jensen, A.L. 1996. Beve1ion and Holt life history invariants result from optimal trade­ off of reproduction and survival. Canadian Journal of Fisheries arid Aquatic Sciences 54: 987-989.

Krebs, C.J. 2001. Ecology: The Experimental Analysis of Distribution and Abundance. 5th edition. Benjamin Cummings, San Francisco. 695 p.

Liu, K.M. and Chen, C.T. 1999. Demographic analysis of the scalloped hammerhead, Sphyrna lewini, in the Northwestern Pacific. Fisheries Science 65(2): 218-223.

Lorenzen, K. 1996. The relationship between body weight and natural mortality in juvenile and adult fish: a comparison of natural ecosystems and aquaculture. Journal ofFish Biology 49: 627-647.

MacArthur, R.H. and Wilson, E.O. 1967. The theory of island biogeography. Princeton University Press, Princeton, NJ. 203 p.

Manly, B.F.J. 1997. Randomization, Bootstrap, and Monte Carlo Methods in Biology. 2nd edition. Chapman and Hall, London. 399 p. 198

Marquez-Farias, F.J. 2002. The artisanal ray fishery in the Gulf of California: development, fisheries research, and management issues. IUCN/SSC Shark Specialist Group. Shark News 14: 1-5.

Marquez-Farias, J.F. and Castillo-Geniz, J.L. 1998. Fishery biology and demography of the Atlantic sharpnose shark, Rhizoprionodon terraenovae, in the southern Gulf of Mexico. Fisheries Research 39: 183-198.

McGurk, M.D. 1986. Natural mortality of marine pelagic fish eggs and larvae: role of spatial patchiness. Marine Ecology Progress Series 34: 227-242.

Mertz, D.B. 1970. Notes on methods used in life-history studies. In Readings in Ecology and Ecological Genetics. (J.H. Connell, D.B. Mertz, and W.W. Murdoch, eds.), p. 4-17. Harper and Row, New York, NY.

Mills, S.L., Doak, D.F., and Wisdom, M.J. 1999. Reliability of conservation actions based on elasticity analysis of matrix models. Conservation Biology 13( 4): 815- 829.

Mollet, H.F. and Cailliet, G.M. 2002. Comparative demography of elasmobranchs using life history tables, Leslie matrices and stage-based matrix models. Marine and Freshwater Research 53: 503-516.

Musick, J.A. 1999. Ecology and conservation oflong-lived marine animals. American Fisheries Society Symposium 23: 1-10.

Nations, C.S. and Boyce, M.S. 1997. Stochastic demography for conservation biology. In Structured-Population Models in Marine, Terrestrial, and Freshwater Systems. (S. Tuljapurkar and H. Caswell, eds.), p. 451-469. Chapman and Hall, New York, NY.

Neer, J.A. and Cailliet, G.M. 2001. Aspects ofthe life history ofthe Pacific electric ray, T01pedo californica (Ayres). Copeia 2001(3): 842-847.

Ocampo-Torres, A.I. 2001. Descripci6n y analisis de la pesca artisanal de elasmobranquios de Sinaloa, Mexico. M.S. thesis, Centro de Investigacion Cientifica y de Educaci6n Superior de Ensenada, B.C., Mexico. 117 p.

Orth, R.J. 1975. Destruction of eelgrass, Zostera marina, by the cownose ray, Rhinoptera bonasus, in Chesapeake Bay. Chesapeake Science 16: 205-208. 199

Pascual, M.A. and Iribarne, 0.0. 1993. How good are empirical predictions of natural mortality? Fisheries Research 16: 17-24.

Pauly, D. 1980. On the interrelationships between natural mortality, growth parameters, and mean environmental temperature in 175 fish stocks. Journal du Conseil Pennanent International pour L'Exploration de laMer 39(2): 175-192.

Peterson, I. and Wroblewski, J.S. 1984. Mortality of fishes in the pelagic ecosystem. Canadian Journal of Fisheries and Aquatic Sciences 41: 1117-1120.

Pfister, C.A. 1998. Patterns of variance in stage-structured populations: evolutionary predictions and ecological implications. Proceedings of the National Academy of Sciences 95: 213-218.

Pratt, H.L., Jr. and Casey, J.G. 1990. Shark reproductive strategies as a limiting factor in directed fisheries, with a review of Holden's method of estimating growth parameters. NOAA Teclmical Report NMFS 90: 97-109.

Probeli, P .K. 1984. Disturbance, sediment stability, and trophic structure of soft-bottom communities. Journal of Marine Research 42: 893-921.

Punt, A.E. and Walker, T.I. 1998. Stock assessment and risk analysis for the school shark Galerorhinus gale us (Li1maeus) off southern Australia. Marine and Freshwater Research 51: 719-731.

Read, A.F. and Harvey, P.H. 1989. Life history differences among the eutherian radiations. Journal of Zoology 219: 329-353.

Ricker, W.E. 1979. Growth rates and models. In Fish Physiology. Volume VIII. Bioenergetics and Growth. (W.S. Hoar, D.J. Randall, and J.R. Brett, eds.), p. 677-743. Academic Press, New York, NY.

Rose, K.A., Cowan, J.H., Winemiller, K.O., Meyers, R.A., and Hilbom, R. 2001. Compensatory density dependence in fish populations: importance, controversy, understanding and prognosis. Fish and Fisheries 2: 293-327.

Silve1iown, J., Franco, M., and Menges, E. 1996. Interpretation of elasticity matrices as an aid to the management of plant populations for conservation. Conservation Biology 10: 591-597. 200

Simberloff, D. 1988. The contribution of population and community biology to conservation science. Annual Review ofEcology and Systematics 19: 473-511.

Simpfendorfer, C.A. 1999a. Mortality estimates and demographic analysis for the Australian sharpnose shark, Rhizoprionodon taylori, from northem Australia. Fishery Bulletin 97: 978-986.

Simpfendorfer, C.A. 1999b. Demographic analysis ofthe dusky shark fishery in southwestem Australia. American Fisheries Society Symposium 23: 149-160.

Simpfendorfer, C.A. 2000. Predicting population recovery rates for endangered western Atlantic sawfishes using demographic analysis. Enviromnental Biology of Fishes 58: 371-377.

Sminkey, T.R. and Musick, J.A. 1996. Demographic analysis of the sandbar shark, Carcharhinus plumbeus, in the westem North Atlantic. Fishery Bulletin 94: 341- 347.

Smith, S.E., Au, D.W., and Show, C. 1998. Intrinsic rebound potentials of26 species of Pacific sharks. Marine and Freshwater Research 49: 663-678.

Snelson, F.F., Jr., Mulligan, T.J., and Williams, S.E. 1984. Food habits, occunence, and population structure of the bull shark, Carcharhinus leucas, in Florida coastal lagoons. Bulletin of Marine Science 34(1): 71-80.

Steams, S.C. 1992. The Evolution of Life Histories. Oxford University Press, New York, NY. 249 p.

Stevens, J.D. 1999. Variable resilience to fishing pressure in two sharks: the significance of different ecological and life history parameters. American Fisheries Society Symposium 23: 11-15.

Stevens, J.D., Bonfil, R., Dulvy, N.K., and Walker, P.A. 2000. The effects of fishing on sharks, rays, and chimaeras (chondrichthyans), and the implications for marine ecosystems. ICES Joumal ofMarine Science 57: 476-494.

Thrush, S.F., Pridmore, R.D., Hewitt, J.E., and Cummings, V.J. 1991. Impact of ray feeding disturbances on sandflat macrobenthos: do communities dominated by polychaetes or shellfish respond differently? Marine Ecology Progress Series 96: 245-252. 201

Tuljapurkar, S. 1997. Stochastic matrix models. In Structured-Population Models in Marine, Terrestrial, and Freshwater Systems. (S. Tuljapurkar and H. Caswell, eds.), p. 59-87. Chapman and Hall, New York, NY. van Tienderen, P.H. 2000. Elasticities and the link between demographic and evolutionary dynamics. Ecology 81 (3):666-679.

VanBlaricom, G.R. 1982. Experimental analyses of structural regulation in a marine sand community exposed to swell. Ecological Mongraphs 52(3): 283-305.

Vetter, E.F. 1988. Estimation of natural mortality in fish stocks: a review. Fishery Bulletin 86: 25-43.

Walker, P.A. and Hislop, J.R.G. 1998. Sensitive skates or resilient rays? Spatial and temporal shifts in ray species composition in the central and north-western North Sea between 1930 and the present day. ICES Journal ofMarine Science 55: 392- 402.

Walker, T.I. 1998. Can shark resources be harvested sustainably? A question revisited with a review of shark fisheries. Marine and Freshwater Research 49: 553-572.

Waring, G.T. 1984. Age, growth, and mortality of the little skate off the Northeast coast of the United States. Transactions of the American Fisheries Society 113: 314- 321.

Weinberg, J.R., Caswell, H., and Whitlatch, R.B. 1986. Demographic importance of ecological interactions: how much do statistics tell us? Marine Biology 93: 305- 310.

Wilson, E.O. and Bossert, J.S. 1971. A Primer of Population Biology. Sinauer Associates Inc., Sunderland, MA. 192 p.

Wood, C. C., Ketchen, K.S., and Beamish, R.J. 1979. Population dynamics of spiny dogfish (Squalus acanthias) in British Columbia waters. Journal of the Fisheries Research Board of Canada 36: 647-656.

Xiao, Y. 2002. Relationship among models for yield per recruit analysis, models for demographic analysis, and age- and time-dependent stock assessment models. Ecological Modelling 155: 95-125. 202

Y okata, T. 1951. Studies on the stocks of sharks and rays. 11. Age composition of the ray, Dasybatus akajei (Muller et Henle), as observed in the catch by trawlers landed at Totaro, Miyazaki prefecture during a period September, 1949 to May, 1950. Bulletin ofthe Japanese Society of Scientific Fisheries 16(12): 188-189. 203

Table 1. Natural mortality (M) estimates for Dasyatis dipterura based on eight indirect methods using life history parameters or wet body weight. The sources of each method are indicated below. Approaches that incorporate longevity (co) were calculated using both observed (28 years) and theoretical (63 years) co. The von Bertalanffy growth coefficient (k) and age at 50% maturity in years (a) were included in the Jensen (1996) fonnulas. Values in parentheses indicate the range of estimates obtained for age-specific methods.

Method M (per year) Hoenig (1983) la. co= 28 0.149 lb. co= 28 0.160 2a. co= 63 0.066 2b. co= 63 0.072

Peterson and Wrobleski (1984) 3a. co= 28 (0.151-0.347)

3b. (J) = 63 (0.125-0.347)

Chen and Watanabe (1989) 4a. ffi = 28 (0.064-0.087)

4b. (J) = 63 (0.027-0.071)

Jensen (1996) 5. k 0.082 6. a 0.165 7. k 0.087

Campana et al. (2001) 8a. ffi = 28 0.164

8b. (J) = 63 0.073 Table 2. Intrinsic and finite population growth rates (r, A.), net reproductive rate (R 0 ), population doubling time (tx1), and rate of increase per generation (rT) projected from deterministic and probabilistic life table models for Dasyatis dipterura. Fishing mortality was applied to age classes two and greater in fisheries exploitation scenarios (designated as +F). Numbers in parentheses indicate the 1 percent change in demographic parameters in response to F = 0.05 yea{ compared to the corresponding scenarios that incorporated loss due to natural mortality only. Mean values and upper 97.5% and lower 2.5 % confidence limits are presented for probabilistic models.

Scenario r LCL UCL 'A LCL UCL Ro LCL UCL t x2 LCL UCL rT LCL UCL D-28 0.132 1.141 7.75 5.25 2.05 D-63 0.133 1.143 9.80 5.20 2.28 P-28 0.057 0.057 0.058 1.059 1.059 1.060 2.40 2.38 2.41 13.14 13.00 13.28 0.89 0.89 0.90 P-63 0.067 0.066 0.067 1.069 1.069 1.070 3.06 3.04 3.08 11.05 10.96 11.14 1.24 1.23 1.25 P-V 0.058 0.058 0.059 1.060 1.060 1.061 2.47 2.45 2.48 12.93 12.80 13.07 0.93 0.92 0.94 D-28+F 0.089 (-33%) 1.093 (-4%) 3.78 (-51%) 7.79 (+48%) 1.33 (-35%) D-63+F 0.090 (-32%) 1.094 (-4%) 4.13 (-58%) 7.69 (+48%) 1.42 (-38%) P-28+F 0.014 (-75%) 0.014 0.015 1.015 (-4%) 1.014 1.015 1.25 (-48%) 1.24 1.26 12.82 (-2%) -24.74 50.38 0.20 (-77%) 0.20 0.21 P-63+F 0.023 (-65%) 0.023 0.024 1.024 (-4%) 1.023 1.024 1.45 (-53%) 1.44 1.46 -36.65 (-431%) -297.47 224.16 0.36 (-68%) 0.35 0.37 P-V+F 0.020 (-65%) 0.020 0.021 1.021 (-4%) 1.020 1.021 1.36 (-45%) 1.35 1.37 11.14 (-68%) -44.75 67.03 0.29 (-69%) 0.29 0.30 Table 3. Estimates of population generation time; where T is the time required for the population to increase by a factor of the net reproductive rate (Ra), Ill represents the mean age of the parents of the offspring produced by a cohort over its life span, and A is the average age of the parents of the offspring produced by a population given a stable age distribution. Measures of generation time calculated from probabilistic models are based on means calculated from 5000 Monte Carlo simulations. Upper 97.5% and lower 2.5% confidence limits are presented for probabilistic models. Numbers in parentheses indicate the percent change in demographic 1 parameters in response to F = 0.05 year- compared to the corresponding scenarios that incorporated loss due to natural mortality only.

Scenario T LCL UCL A LCL UCL Ill LCL UCL D-28 15.5 14.3 17.0 D-63 17.1 14.6 21.5 P-28 15.0 15.0 15.1 14.4 14.4 14.5 15.7 15.7 15.7 P-63 16.6 16.6 16.7 15.1 15.1 15.2 18.7 18.6 18.7 P-V 15.3 15.3 15.3 14.6 14.6 14.6 16.1 16.1 16.1 D-28+F 14.9 (-4%) 14.2 (-1%) 15.8 (-7%) D-63+F 15.7 (-8%) 14.5 (-1%) 17.5 (-19%) P-28+F 14.4 (-4%) 14.4 14.5 14.3 (-1%) 14.3 14.3 14.6 (-7%) 14.5 14.6 P-63+F 15.3 (-8%) 15.3 15.3 14.9 (-1%) 14.9 15.0 15.7 (-16%) 15.7 15.7 P-V+F 14.7 (-4%) 14.6 14.7 14.5 (-2%) 14.4 14.5 14.9 (-8%) 14.9 14.9 Table 4. Fertility, juvenile survivorship, and adult survivorship elasticities and corresponding elasticity ratios summed across relevant age classes based on deterministic (D) and probabilistic (P) model projections. Values derived from probabilistic models are mean estimates based on 5,000 Monte Carlo simulations.

Elasticity (Proportional) Elasticity Ratios Scenario Fertility Juvenile Aduh Aduh :Age 0 Juvenile :Age 0 Aduh :Juvenile

D-28 0.07 0.49 0.44 6.78 7.50 0.90 D-63 0.06 0.48 0.46 5.49 8.95 0.62 P-28 0.07 0.58 0.36 6.68 7.50 0.89 P-63 0.06 0.55 0.38 5.37 8.95 0.60 P-V 0.06 0.57 0.36 5.66 8.95 0.64 D-28+F 0.07 0.49 0.44 5.50 8.95 0.62 D-63+F 0.06 0.48 0.45 7.11 7.50 0.95 P-28+F 0.07 0.58 0.35 6.20 8.95 0.69 P-63+F 0.06 0.56 0.37 6.97 7.50 0.93 P-V+F 0.07 0.58 0.36 5.98 8.95 0.67

N 0 0\ Table 5. Estimates of longevity (co), fecundity (mx), annual population growth rates (/..), net reproductive rates (R 0 ), and generation times (!l1) of 16 elasmobranchs based on deterministic models using best-case or optimal scenarios. Fecundity was assumed to be constant over adult ages in these studies. Method abbreviations signify life table- (LT) or matrix- (MX) based demographic approaches. Species are presented by decreasing values of/...

Species Method Location co mx J.. Ro Ill Source Sphyrna tiburo LT Florida Bay, Florida 12 4.65 1.33 3.61 5.1 Cortes and Parsons (1996) Sphyrna tiburo LT Tampa Bay, FL 12 4.45 1.31 3.45 5.1 Cortes and Parsons (1996) Sphyrna lewini MX Northwest Pacific 15 12.90 1.23 4.74 7.6 Liu and Chen (1999) Torpedo californica LT Northeast Pacific 24 8.50 1.20 8.89 11.2 N eer and C ailliet (2 00 I) a Dasyatis v iolacea LT Captive 10 3.00 1.17 1.99 4.5 Mollet and Cailliet (2002) Carcharhinus obscurus LT Southeastern Indian Ocean 60 12.00 1.15 26.10 29.4 Simpfendorfer (1999) Prist is pectinata LT West Atlantic 50 17.50 1.14 23.18 NG Simpfendorfer (2000) Dasyatis dipterura LT Eastern Central Pacific 28 2.00 1.14 7.75 17.0 Present study Pristis perotteti LT West Atlantic 30 7.30 1.12 5.74 NG Simpfendorfer (2000) Cacharodon carcharias LT Combinedb 36 1.50 1.08 6.16 26.2 Mollet and Cailliet (2002) Carcharhinus obscurus LT Northwest Atlantic 30 1.38 1.08 1.93 9.5 Cortes (1998) Carcharhinus plumbeus LT Northwest Atlantic 30 2.10 1.06 3.54 20.4 Sminkey and Musick (1996) Squatina californica LT Northeast Pacific 35 3.00 1.06 2.25 14.5 Cailliet et aL (1992) Alopias pelagicus LT Northwest Pacific 30 1.00 1.06 2.00 13.3 Mollet and Cailliet (2002) Rhizoprionodon terraenovae LT Gulf of Mexico 10 1.00 1.05 1.28 5.8 Cortes (1995) C archarhinus lim bat us LT Northwest Atlantic 30 2.25 1.03 2.11 26.8 Cortes (1998) Negaprion brevirostiris MX Western Atlantic 26 2.50 1.02 1.27 16.2 Hoenig and Gruber (1990) a Life history data obtained primarily fi"om captive observations

b Life history data for demographic analysis synthesizedfi"om multiple study locations

N 0 --l Table 6. Comparative elasmobranch demography based on probabilistic models incorporating uncertainty and variability in vital rates. Abbreviations signify life table- (LT), Leslie matrix- (MX), or stage- (SMX) based demographic approaches. Mean population growth rates (/..,), generation times (A), and elasticity values expressed as a percentage are presented by decreasing values of A.

Elasticity (%) Juvenile Adult Species Method Location /.. A Fertility Survival Survival Source Sphyrna lewini LT,MX Western Pacific 1.600 5.1 15.1 53.5 31.4 Cortes (2002) Prionace glauca LT,MX Northwest Atlantic 1.401 7.0 12.6 55.8 31.7 Cortes (2002) Leucoraja erinacea MX North Atlantic 1.233 Frisk et al. (2002) Dipturus laevis SMX North Atlantic 1.221 Frisk et al. (2002) lvfustelus henlei LT,MX Northeast Pacific 1.163 4.7 18.1 34.4 47.5 Cortes (2002) Jsurus oxyrinchus LT,MX Northwest Atlantic 1.141 10.1 9.0 58.2 32.8 Cortes (2002) Leucoraja ocellata MX North Atlantic 1.139 Frisk et al. (2002) lvfustelus californicus LT,MX Northeast Pacific 1.132 4.6 18.5 34.7 46.8 Cortes (2002) Alopias vulpinus LT,MX Northeast Pacific 1.125 8.9 10.2 44.8 45.0 Cortes (2002) Carcharodon carcharias LT,MX Northeast Pacific 1.098 12.3 7.6 67.7 24.7 Cortes (2002) Carcharhinus porosus LT,MX Southwest Atlantic 1.086 8.4 10.7 58.2 31.2 Cortes (2002) Negaprion brevirostris LT,MX Northwest Atlantic, Gulf of Mexico 1.064 16.4 5.7 70.0 24.2 Cortes (2002) Dasyatis dipterura LT Eastern Central Pacific 1.060 14.6 6.5 57.9 35.6 Present study Rhizoprionodon terraenovae LT,MX GulfofMexico 1.056 4.9 16.9 47.5 35.6 Cortes (2002) Carcharinus falciform is LT Western Atlantic 1.049 5.9 67.3 26.8 Beerkircher et al. (2003) Carcharhinus isodon LT,MX GulfofMexico 1.042 6.9 12.6 47.7 39.7 Carlson et al. (2003) C archarhinus brev ipinna LT,MX GulfofMexico 1.037 10.4 8.8 61.4 29.8 Cortes (2002) C archarhinus obscurus LT,MX Northwest Atlantic 1.030 26.2 3.7 67.9 28.5 Cortes (2002) Carcharhinus plumbeus LT,MX Northwest Atlantic 1.022 19.8 4.8 69.3 25.9 Cortes (2002) Alopias pelagicus LT,MX Northeast Pacific 1.020 11.8 7.8 60.4 31.7 Cortes (2002) Squatina californica LT,MX Northeast Pacific 1.019 14.4 6.6 64.3 29.1 Cortes (2002) Triakis semifasciata LT,MX Northeast Pacific 1.016 18.5 5.1 63.9 31.0 Cortes (2002) Lamna ditropis LT Northeast Pacific, Alaska 1.012 13.1 7.1 56.8 36.1 Goldman (2002) Carcharias taurus LT Northwest Atlantic 0.989 17.1 5.5 54.9 39.6 Goldman (2002) Carcharhinus limbatus LT,MX Eastern GulfofMexico 0.974 10.0 9.3 60.0 30.6 Cortes (2002) Squalus acanthias LT,MX Northeast Pacific 0.893 55.6 1.8 62 36.2 Cortes (2002) C archarhinus acronotus LT,MX Gulf ofMexico 0.847 4.2 19.1 47.2 33.6 Cortes (2002)

N 0 00 A B

0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 24 26 28 30 32 34 36 38 40 Annual survivorship (age 0) Longevity (years)

0.6 0.6 c 0.5 0.5 D g g 0.4 :0 0.4 :0 ~"' ~"' 0.3 2 ....0 ~ 0.3 ~ OJ OJ .:':..,. ·'=..,. 0.2

0.0 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Age at maturity (years) Annual fecundity

Figure 1. Examples of probability density functions developed for (A) age 0 survivorship, (B) longevity, (C) age at 50% maturity, and (D) fecundity for use in Monte Carlo simulations. Note that fecundity represents the annual number of female offspring produced per adult female.

N 0 \D 210

DD28 0.25 A ID28-+F §P-28 0.2

~ ~ P-28-+F ~ 0 "€ 0.15 0 0., 0 l-< 5 0.1 X ~ 0.05

0 1 3 5 7 9 11 13 15 17 19 21 23252J'E

0.25 B ~ ~ 0.2

~ ~ ...... 0 t:: 0.15 0 0., 8 5 0.1 X ~ 0.05

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 Age (years)

Figure 2. Hypothetical stable age distribution (ex) of Dasyatis. dipterura based on the maximum observed age of (A) 28 years and (B) probabilistic models that varied longevity from 25 to 39 years using Monte Carlo simulations. The impact of fishing mortality on age structure was considered in each scenario designated by the letter F (F=0.05). Mean ex values are presented for probabilistic models. 211

DD-63 0.25 A IID-63+F

0.2

,-.... q 0 "-E 0.15 0 0.. 8 8 >< 0.1 (.)

0.05

0 ~~~~~~~""~~""'"~' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' DP-63 0.25 B II P-63+F

0.2

,-.... q ·-e0 0.15 0 0.. 0 I- ....___,0.. >< 0.1 (.)

0.05 -

0 ij~J~~~~~~~~~~~PI"'"ON"rn "" " ' ' " " ' ' " " ' " " " ' " " " " " 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 Age (years)

Figure 3. Hypothetical stable age distribution (ex) of Dasyatis dipterura based on (A) deterministic and (B) probabilistic models incorporating the presence and absence of fishing mortality (F=0.05). Age structure was based on the maximum theoretical longevity of 63 years. Mean ex values are presented for probabilistic models. 212

12 A 10 --D-28 8 ...... D- 6 28+F P-28 4 P-28+F 2 0 12 B 10

8 Vx 6 -·---·P-V __ P-V+F 4

2 0 12 10 ------8 ---- D-63 6 ...... D- 4 63+F P-63 2 ...... P-63+F

0 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64

Figure 4. Age-specific reproductive values (vx) generated from best-case deterministic (D) and probabilistic (P) demographic models. Models were structured based on a fixed maximum age of28 years (A), variable longevities of25-39 years (B), and static longevity of 63 years (C). The impact of fishing mortality on age structure was considered in each scenario designated by the letter F (F=O.OS). 213

1.10 1.09 ! 1.08 f ! ! ! ! ! ! ! ! f 1.07 Q Q Q Q Q Q 2 2 2 f -' Q 2 8 1.06 il) >-. I (:2 {:2 ~ Q ~ ~ ~ « 1.05 ~ ~ ~ ~ ~ f 1=1 T ! ('j il) ~ 1.04 1.03 • Maturity= 8 years 1.02 o Maturity = 9 years

1.01 0 Maturity = 10 years

1.00 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Longevity (years)

Figure 5. Influence oflongevity and age at maturity on population mean annual population growth rates (A.). Error bars indicate upper 95th and lower 5th percentiles of the respective confidence limits. Mean values are based on the results of 5,000 Monte Carlo simulations and represent population projections from the most likely scenario (P­ V) in the absence of fishing mortality. 1.0 D Adult 0.9 ffi1il Juvenile 0.8 Fertility 0.7

0.6 .,.....c -~...... 2@ 0.5 @ 0.4

0.3

0.2

0.1

0.0 D-28 D-28+F D-63 D-63+F P-28 P-28+F P-63 P-63+F P-V P-V+F

Figure 6. Fertility (age 0 survivorship), juvenile and adult survivorship elasticity values summed across relevant age classes. Model abbreviations indicate deterministic (D) or probabilistic (P) forms and the longevity on which the model was based. The letter V indicates that longevity was varied between 25 and 39 years during simulations. Fishing mortality was introduced into each scenario designated with +F. Probabilistic models reflect mean values based on 5,000 Monte Carlo simulations. 215

e Fe1iility (a=8) 0 Fertility (a=9) Fertility (a= 10)

£Juvenile Survivorship (a=8) .6..Juvenile Survivorship (a=9) Juvenile Survivorship (a= 10) liiAdult Survivorship (a=8) DAdult Survivorship (a=9) Adult Survivorship (a= 10)

0.7

- !:1: 0.6 ::k ,;i~ ~ rl: lk .-1· rr. 15 t:r t:r if=- f~ t:r ~ t:r ZJ; tS ~ ~ A • A a A :lt ~ * * * * * f A 0.5 0 :§...... U) 0.4 ~ ! II ~ ; 15 t;.i;'i- . 0 13 ~ ~. w.-r i ~ ~ ~~ Q a ~ ~ :::::: = = C\1 =

0.1 (!\ !l) @ t:f'1 ~ ~ "1..~· ~ ~ ~ ~ 0 ~ ~ ~ ® 0 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 Longevity (years)

Figure 7. Influence of longevity and age at maturity on mean fertility, juvenile survivorship, and adult survivorship elasticity values. Age at maturity (a) varied between eight, nine, and ten years. Error bars indicate upper and lower 95% confidence limits. Means are based on the results of 5,000 Monte Carlo simulations and represent population projections from the most likely scenario (P-V) in the absence of fishing mortality. 216

Appendix 1. Sources and equations used to calculate the eight indirect estimates of

instantaneous natural mmiality (M) for Dasyatis dipterura applied in this study.

Hoenig (1983);

1. lnM= 1.46- 1.01 * (ln CD)

Relationship obtained to describe the mortality rates of fishes, CD = maximum

age. Two estimates were obtained based on the maximum observed CD of 28

and theoretical maximum CD of 63.

2. ln M = 1.44- 0.982 * (ln CD)

Fonnula recommended by Hoenig for estimating M, based on 79 species of

mollusks, fishes, and cetaceans; CD= maximum age. Two estimates were obtained

based on the maximum observed CD of 28 and theoretical maximum CD of 63.

Peterson and Wroblewski (1984);

Where W = weight in grams.

Chen and Watanabe (1989);

4. Mx=- 1- e--x-to~( ) 217

Appendix 1. Continued.

Where x = any age prior the estimated onset of senescence, and the parameters k

and t 0 are obtained from fits of size-at-age data to the three parameter von

Bertalanffy growth equation. Senescence Cts) is defined as ages greater than:

Where k and t 0 are as previously described. Mortality following this age 1s

Where t = age, fmax is the end of the reproductive span and is equal to longevity

( m) in this study, k is the growth coefficient and t0 is the theoretical time when

size is zero from the three parameter von Bertalanffy growth equation. Age-

specific estimates of M were calculated based on observed m of 28 and theoretical

m of 63.

Jensen (1996);

5. M= 1.65/a

Where a = age at maturity, considered to be 10 years and equivalent to the age

at 50% maturity for this study.

6. M= 1.50 * k

Where K = growth coefficient (0.0546) and was obtained from the three

parameter von Betialanffy growth equation. 218

Appendix 1. Continued.

7. M= 1.6 * k

Where k =growth coefficient (0.0546) and was obtained from the three parameter

von Bertalanffy growth equation. The formula is a modification of the method

described by Pauly (1980).

Campana et al. (200 1);

_ M= -lnO.Ol 8 {J]

Where m = maximum age and was calculated based on estimates of 28 and 63

years. Assumes 1% of individuals remain at m. 219

Appendix 2. Minimum and maximum survivorship estimates incorporated into probability distributions for natural and fishing mortality scenarios based on the longevity (co) of28 years. Fishing mortality (F=0.05) applied to ages 2 and greater. Age co= 28 co= 28+F (x) Minimum Maximum Minimum Maximum 0 0.707 0.849 0.707 0.849 1 0.751 0.918 0.751 0.918 2 0.760 0.920 0.723 0.875 3 0.785 0.922 0.747 0.877 4 0.798 0.923 0.759 0.878 5 0.796 0.925 0.757 0.880 6 0.804 0.926 0.765 0.881 7 0.813 0.927 0.773 0.882 8 0.815 0.928 0.775 0.883 9 0.824 0.929 0.783 0.884 10 0.825 0.930 0.785 0.884 11 0.828 0.931 0.788 0.885 12 0.838 0.931 0.797 0.886 13 0.838 0.932 0.797 0.887 14 0.840 0.933 0.799 0.887 15 0.843 0.933 0.802 0.888 16 0.843 0.934 0.802 0.888 17 0.842 0.934 0.801 0.889 18 0.849 0.935 0.807 0.889 19 0.849 0.935 0.807 0.890 20 0.852 0.936 0.811 0.890 21 0.852 0.936 0.811 0.890 22 0.852 0.936 0.811 0.891 23 0.852 0.937 0.811 0.891 24 0.854 0.937 0.812 0.891 25 0.856 0.937 0.814 0.892 26 0.858 0.938 0.817 0.892 27 0.859 0.938 0.817 0.892 28 0.860 0.938 0.818 0.892 220

Appendix 3. Minimum and maximum survivorship estimates incorporated into probability distributions for natural and fishing mmiality scenarios based on the longevity (OJ) of 63 years. Fishing mortality (F=0.05) applied to ages 2 and greater. Age OJ= 63 OJ= 63+F (x) Minimum Maximum Minimum Maximum 0 0.707 0.868 0.707 0.868 0.751 0.933 0.751 0.933 2 0.760 0.934 0.723 0.888 3 0.785 0.935 0.747 0.889 4 0.798 0.936 0.759 0.890 5 0.796 0.936 0.757 0.891 6 0.804 0.937 0.765 0.891 7 0.813 0.938 0.773 0.892 8 0.815 0.938 0.775 0.892 9 0.824 0.939 0.783 0.893 10 0.825 0.939 0.785 0.893 11 0.828 0.940 0.788 0.894 12 0.838 0.940 0.797 0.894 13 0.838 0.940 0.797 0.895 14 0.840 0.941 0.799 0.895 15 0.843 0.941 0.802 0.895 16 0.843 0.941 0.802 0.895 17 0.842 0.942 0.801 0.896 18 0.849 0.942 0.807 0.896 19 0.849 0.942 0.807 0.896 20 0.852 0.942 0.811 0.896 21 0.852 0.943 0.811 0.897 22 0.852 0.943 0.811 0.897 23 0.852 0.943 0.811 0.897 24 0.854 0.943 0.812 0.897 25 0.856 0.944 0.814 0.897 26 0.858 0.944 0.817 0.898 27 0.859 0.944 0.817 0.898 28 0.860 0.944 0.818 0.898 29 0.861 0.944 0.819 0.898 30 0.862 0.944 0.820 0.898 221

Appendix 3. Continued. Age 0) = 63 m = 63+F (x) Minimum Maximum Minimum Maximum 31 0.863 0.945 0.821 0.898 32 0.864 0.945 0.822 0.899 33 0.865 0.945 0.823 0.899 34 0.866 0.945 0.823 0.899 34 0.866 0.945 0.823 0.899 35 0.867 0.945 0.824 0.899 36 0.867 0.945 0.825 0.899 37 0.868 0.945 0.826 0.899 38 0.869 0.945 0.826 0.899 39 0.870 0.946 0.827 0.899 40 0.870 0.946 0.828 0.900 41 0.871 0.946 0.828 0.900 42 0.872 0.946 0.829 0.900 43 0.872 0.946 0.830 0.900 44 0.873 0.946 0.830 0.900 45 0.873 0.946 0.831 0.900 46 0.874 0.947 0.831 0.900 47 0.875 0.947 0.832 0.901 48 0.875 0.947 0.832 0.901 49 0.876 0.947 0.833 0.901 50 0.876 0.947 0.833 0.901 51 0.877 0.948 0.834 0.901 52 0.877 0.948 0.834 0.902 53 0.878 0.948 0.835 0.902 54 0.878 0.948 0.835 0.902 55 0.879 0.949 0.836 0.903 56 0.879 0.949 0.836 0.903 57 0.880 0.950 0.837 0.904 58 0.880 0.951 0.837 0.905 59 0.880 0.952 0.837 0.906 60 0.881 0.955 0.838 0.908 61 0.881 0.959 0.838 0.912 62 0.882 0.973 0.839 0.926 63 0.882 0.973 0.839 0.926