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------8713662
Hendrickson, Dean Arthur
GEOGRAPHIC VARIATION IN MORPHOLOGY OF AGOSIA CHRYSOGASTER, A SONORAN DESERT CYPRINID FISH
Arizona State University PH.D. 1987
University Microfilms International 300 N. Zeeb Road, Ann Arbor, Ml48106
. ··-·------·-·-· ~------·------·~----- GEOGRAPHIC VARIATION IN MORPHOLOGY OF AGOSIA CHRYSOGASTER, A SONORAN DESERT CYPRINID FISH by
Dean A. Hendrickson
A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy
ARIZONA STATE UNIVERSITY
May 1987
------·------GEOGRAPHIC VARIATION IN MORPHOLOGY OF AGOSIA CHRYSOGASTER, A SONORAN DESERT CYPRINID FISH by
Dean A. Hendrickson
has been approved
t1ay 1987
APPROVED:
.Chairoerson
Supervisory Committee
ACCEPTED:
-~::?d~--Dean, Graduate College
------···---·- ···------· ------. --··. ABSTRACT
Morphometric analyses of Agosia chrysogaster
northern morph native to Bill Will lams, Gila, Sonoyta and de la
Concepcion basins of Arizona, New Mexico and Sonora, and a southern form from Willcox Playa of Arizona and Rios Sonora, Yaqui, Mayo,
Fuerte an~ Sinaloa of Sonora and Sinaloa, Mexico. The latter is
smaller, and less sexually dimorphic, but has longer pre- and
postdorsal body lengths. Populations in the geographically
intermediate Rios Sonoyta and Sonora are morphologically intermediate.
Males differ more between morphs than do females. Meristic characters overlap between morphs, but the northern form has higher mean lateral line scale counts. Highly tuberculate nuptial males, characteristic
of the northern morph, were not found in the south, nor were •spawning• pits associated with spawning of the former. Morphs differ on a multivariate axis on which temporal variation at single localities is also reflected. Distances among some intra-locality samples on this axis were greater than least inter4norph distances. Measures of morphological disimilarity were
weakly correlated with inter-sample differences in elevation; latitude, and longitude, but more highly correlated with an index of
hydrologic isolation among localities. Differentiation among basins thus appears to reflect hydrographic isolation, rather than ecological
conditions.
Electrophoretic data on&· chrysogaster produced relationships
patterns largely incongruent with results of the morphological
analyses, and with unexpected geographic area relationships.
iii
--- -··- ----· ·------·-· ---·-- ··--···· ACKNOWLEDGEMENTS
Many people provided assistance that enabled me to complete this study. Primarily I wish to thank my wife, Sherry, and son, Garrett, who, along with my parents, supported me throughout this project and tolerated many hours in which my focus was on this instead of them. This work, and many others I have simultaneously undertaken, would have been impossible without their help and understanding. Dr. W. L. Minckley has been an endless source of support and intellectual stimulation throughout, and has made it possible for me to participate in several other professionally profitable, and enjoyable, endeavors.
My work with him has greatly broadened my scientific background and for that I am forever grateful.
Much field work for this study was supported by various grants from the Department of Zoology at Arizona State University, which also provided me with part-time teaching and museum assistantships for four years. I wish to thank all collectors mentioned in the 1 ist of samples for their field help, and all museum curators who lent specimens. Ms. Susan Zneimer did the electrophoretic analyses in the lab of Dr. Don Buth at University of California, Los Angeles. I also wish to thank Terry Johnson for his flexibility in allowing me time to complete this study while employed under his supervision at Arizona Game and Fish Department. Michael E. Douglas and members of my committee provided many suggestions which greatly improved the dissertation.
iv
------TABLE OF CONT8NTS
Page LIST OF TABLES vii
LIST OF FIGURES viii INTRODUCTION Objectives
Distribution, Biology and Ecology of Agosia chrysogaster 4
Taxonomic History 10
METHODS AND MATERIALS 12
Morphometric and Meristic analyses 12
Electrophoretic Analyses 15
RESULTS 17
Univariate Analyses 17
Multivariate Analyses of Morphometric Data 20
Allometric Differences Between Morphs 31
Shape Reconstructions 33
Temporal Variation in Morphology of Agosia chrysogaster 38
Classification of Unknowns to Morph and Basin 47
Results of Analyses of Meristic Data 50
Correlations with Ecology and Geography 51
Other Characters which Corroborate Morphometric Analyses 56
Results of Analyses of Electrophoretic Data 58
DISCUSSICJI.I 75
Physiography and Distribution of Morphotypes 85
Other Fishes 88
v
---· ----.------Page
CONCLUSIONS 93
REFERENCES 97
APPENDIX 112 Appendix A. Acronyms and descriptions of morphometric variables. 112 Appendix B. Descriptions of samples used in analyses 114
Appendix C. Means and 9~/. confidence intervals <±2 standard errors) for all variables by sex and basin 120 Appendix D. Nonlinear regression statistics by sex and morph for all ·variables regressed on SL. 127 Appendix E. Composition of native fish faunas of river basins where Agosia chrysogaster is native. 136
vi
--- -·-·· ·------· ----·------·-- LIST OF TABLES
Page
Table 1. Mean Coefficient of Variation for all variables measured 5 times on each of 5 specimens. 18
Table 2. Summary of meristic characters of Agosia chrysogaster. 49
Table 3. Numbers of specimens of each genotype found in a survey of 15 1oc i i n 25 pop u 1 at i on s from 22 ge ogr ap h i c localities. 51
Table 4. Numbers of specimens of each genotype found in a survey of 15 loci in 25 populations from 22 geographic 1 oc a 1 i t i e s • 59
Table 5. Genetic similarities among samples- Nei 1 s <1978) unbiased genetic identity above diagonal, and Rogers 1 <1972) genetic similarity below diagonal. 62
vii
------·-·· LI ST OF FI GURES
Page Figure 1. Map of distribution of Agosia chrrsogaster with localities of samples used 5
Figure 2. Lateral and ventral views of female Agosia chrysogaster and dorsa 1 v i ew of rna 1e 13
Figure 3_. Plot of sample mean scores on first canonical variates from 3 separate DFA~s maximizing distances among samples
Figur~ 4. Scatter plot of scores on first two canonical variates of pooled, within-sample covariance matrix of females. 25
Figure 5. Plot of scores for all basins on sheared 2nd and 3rd components
and southern (stars> morphs of Agosia chrysogaster at grand mean SL. 34 Figure 7. Overlaid average shapes of females of northern (solid line) and southern (dotted line) morphs of Agosia chrysogaster at grand mean SL. Average measures at mean SL were predicted for each morph from non-linear regressions of each variable on SL. 36
Figu~e 8. Overlaid average shapes of males Figure 9. Overlaid average shapes of males Figure 11. Percentages of total numbers of specimens used in morphometric analyses by month of collection and morph viii ------· Page Figure 12. Relationship of Mahalanobis' multivariate distances among samples based on 49 morphometric variables, and •Pair level.• 53 Figure 13. Phenogram of genetic relationships of samples of Agosia chrysogaster 66 Figure 14. Unrooted Wagner network of relationships of samples of Agosia chrysogaster derived by clustering of Roger's (1972) genetic distance coefficients <1 -similarity) with the distance Wagner procedure of BIOSYS-1 Figure 16. Plot of S. i X INTRODUCTI~ Objectives A number of major problems confront biogeographers analyzing evolutionary histories of western North American fishes. Studies of geology and paleoecology are complete enough that hypotheses of area relationships can be formulated for testing against biological data distributions required for such tests Cracraft, 197S; Craw and Weston, 1984; Hendrickson, 1986; Nelson and Platnick, 1981; Nelson and Rosen, 1981; Rosen, 197S, 1978, 1979>, are inadequate or entirely lacking for the region's fishes. This study partially ameliorates the paucity of systematic data on Western North American fishes. The genus Agosia was chosen primarily because it occurs in one of the ichthyologically least-studied regions of North America. Taxonomy within the genus has not been examined since the 18B9s (Jordan, 1886, 1891>, although Miller <19S9> and McNatt (1974> suggested that specimens from the Rio Yaqui system were taxonomically distinct from those of the Gila River basin. Additionally, a second taxon 198S>, shares much of its distribution with Agosia. If both fishes attained their distributions via the same geologic events, they would display congruent phylogenies and area relationships. Failure in this ---- . ------···· 2 regard would indicate either independent derivations of distributions, differential dispersals of species, or errors in reconstruction of phylogenies. Development of phylogenetic hypotheses for Agosia is thus required before the biogeographic hypothesis that it and f. occidentalis share the same history can be tested in the sense of vicariance biogeographers After preliminary analyses, a detailed phenetic approach to relationships analysis was decided upon for several reasons. First, samples from throughout the range of Agosia indicated little inter-sample differentiation, and a lack of discernible osteological or other anatomical characters appropriate for use in a strict cladistic analysis. Furthermore, metric characters appropriate for recoding to discontinuous character states of measurements 1985; Winans, 1984) and Jshearing' of Principal Components et al ., 1981; Strauss, 1984; Bookstein et al ., 1985), provide powerful methods of analyzing morphometric data and comparing shapes and shape ------·-··- -- ·--·· ·------··--·----· 3 changes among groups. Such analyses can lead to discovery of characters useful in cladistic analyses. Several hypotheses, stated as follows, were addressed with the morphometric data set: 1. Populations of each major river basin will be morphologically differentiated from one another. Genetic isolation by hydrographic divides and genetic drift or differential selection since time of isolation are the means by which such differentiation may have evolved. If morphological divergence is constant in rate, and convergence is absent, patterns of phenetic relationships should approach the true phylogeny. 2. Morphological distances among populations will be positively and linearly related to hydrographic distance among them. While panmixia should prevent significant morphological differentiation among local, hydrographically proximal populations, deviation from panmictic conditions will increase as a function of inter-locality distance. Deviations from 1 inearity in this relationship reflect either variations in gene flow, heterogeneity of differentiation rates, or polyphyletic origins of single basin populations. Since drainage distance .is believed the parameter most correlated with extent of genetic exchange, various other measures of inter-locality geographic distances 3. Morphology will be uncorrelated with measures of ecological conditions. Endler <1982a, b, 1983) and Chernoff <1982) have pointed out some difficulties and importance of discriminating ------·-----~- ~~-- -~- ·-·-- -~~ 4 ecological from phylogenetic causes of variation. If morphology is not affected by ecology, usefulness of morphological differentiation as an indicator of phylogeny is increased. 4. Patterns of morphological variation will match patterns of independently analyzed meristic, electrophoretic, and other data sets .on relationships among populations of Agosia chrysogaster. Congruent patterns should be evident as well in phylogenetic relationships of other groups similarly affected by the same events in earth history. Failure to find congruence among independent data sets indicates failure of data to depict true phylogenies or differences in history among the groups being tested. Distribution, Biology and Ecology of Agosia chrysogaster The natural geographic range of Agosia chrysogaster extends from the Bill Williams River drainage <350 N> of Arizona, U.S.A. 1989; Hendrickson, 1984>. It occurs in all major, intervening tributaries of the Sea of Cortez apparent exception of the Rio Matape of Sonora the taxon is associated with a diverse m~alian, avian and herpetofauna of La Brean age Non-native populations of Agosia, apparently the result of use of ------··- --·------····----·--- 5 Figure 1. Map of distribution of Agosia chrysogaster with localities of samples used. Outlined area is approximate natural distribution of the species. Open circles mark samples used in morphometric analysis only. Solid circles are for those used in both electrophoretic and morphometric analyses. Half-solid circles indicate those used only in electrophoresis. ------6 RIO GRANDE HUALAPAI LAKE BILL WILLIAMS _ __.-.~ MIMBRES GILA ..,1.~""'--,.,.. COLORADO~ SONOYTA -..,_..;1-4 CONCEPCION WILLCOX PLAYA SONORA MATAPE -~_; YAQUI COCORAQUI MAYO-- 0 200 400 km FUERTE SINALOA ------7 the species as bait Grande No specimens have been taken in recent studies in the Virgin RiverJ Arizona and Nevada (e.g., Cross, 1985; unpublished data, J. E. Deacon, pers. comm.>. That population Desert region to which Agosia chrysogaster is native were recently reviewed by Turner and Brown <1982>, and aquatic habitats of the region described by Hendrickson et al. <1981>, Hinckley and Brown (1982>, and Hendrickson and Hinckley <1985>. Paleoclimatology was reviewed by Hinckley et al. <1986>, who further described the region's geologic history. Aoosia chrrsogaster is typically the most abundant fish in Soncran Desert stre~s. While mostly at low to mid-elevation (less than 1500 m>, it penetrates to 2873 m elevation Hinckley, 1981; Schreiber, 1978; Schreiber and Hinckley, 1982; Fisher et al ., 1981> cyprinid is highly successful and apparently well adapted to low-order tributaries, persisting through a broad, highly fluctuant and unpredictable spectrum of conditions ranging from dramatic flash floods ~·~'nckley and Meffe, in press>, and individuals survived under algal mats in stream reaches lacking daytime surface flqws.{Minc~ley, 1973; Deacon and Hinckley, 1974), Decreased nocturnal evapo-transpiration renewed surface discharge and allowed the fish to leave algal mats to forage. High fecundity and prolonged reproductive period Barber, 1979; Rinne, 1975; Lewis, 1978a; Kepner, 1982> provide rapid recovery from events which reduce populations. An apparent high vagil ity adaptability were provided by Lewis <1978b>, who provided data on tolerance of Agosia chrysogaster to toxic mine effluents, Lowe et al. <1967>, who studied its survival in low concentrations of dissolved oxygen, and by Marsh and Hinckley's <1982> record of the species from Phoenix metropolitan area irrigation canals. Breeding behavior and spawning habitats of a. chrysogaste~ in the Gila River basin have been described by Hinckley and Barber <1979>, ---·-···------9 Hinckley <1973>, Lewis (197Bb>, and Kepner <1982). Saucer-shaped nests are excavated to a depth of 1 - 4 em in sand or gravel of shallow areas (3- 18 em) with little current, generally at mouths of backwaters. Males do not defend territories, but move with apparent randomness over nesting areas. Single females enter the area and spawn in a brief flurry of sand, with one or rarely 2 males, in the depressions. Females quickly depart from spawning areas and males resume patrolling. Eggs are non-adhesive. Any one female generally carries ova in 3 stages of development. Spawning periodicity is multimodal, and at least some eggs appear ready to be spawned at almost any time of the year. Individuals reach maturity asynchronously, but spawning activity of populations peaks in spring and autumn. Fecundity ranged from 8 to 379 ova per female in Kepner~s (1982) study. Low numbers of eggs per nest indicate fractional spawning and distribution of egg complements across numerous nests. Postlarval anatomy and development have been described by Winn and Miller <1954). Agosia chrysogaster is parasitized by a diversity of organisms significant biological impacts ------· Taxonomic History The genus Agosia has a relatively simple taxonomic history. Girard <1856) described 2 species, a. chrrsogaster and a. metallica, respectively from the Santa Cruz and San Pedro rivers of the Gila River drainage, and shortly afterwards published figures These taxa were subsequently synonymized with B· chrysogaster page priority) by Evermann and Rutter <1895). In the interim, Cope and Yarrow <1875) examined other material from Fort Lowell, Arizona, on the Gila River, which they described as Hyborynchus siderius. Jordan and Gilbert (1883) referred these specimens to the genus Zophendum. Jordan (1891) noted the Camp Lowell Zophendum did not differ from specimens of a. chrysogaster from the Rio Sonora. Over the last 59 years, taxonomic status has been stable, and the genus has been accepted as monotypic aside from comments by Miller <1959> and McNatt <1974> who noted that Rio Yaqui populations may represent a distinct, undescribed form. Relationships of North American cyprinids have long been unclear, and phyletic affinities of the genus Agosia remain so. Many taxa now believed to be distant relatives of AQosia have at one time been placed into the genus and Miller (1948a) considered Moapa to be its nearest relative. Coad 1 inked Moapa with Eremichthys, at some distance from the group containing Agosia. Recently, Hinckley et al. (1986) 1 based on recent geological data, speculated that relationships of various western North ------·-~-- ·----···-· ---- . ---·-·------···-· 11 American taxa may I ie to the south, and in particular that nearest relatives of Agosia may be found within Algansea, a central Mexican endemic. At least phenetically, some taxa currently in Algansea Algansea aphanea) are remarkably similar to Agosia. However, Barbour and Miller (1978> hypothesized the sister group of Algansea to be subgenus Temeculina of genus Gila. This relationship, which makes Gila paraphyletic, is based principally on a single synapomorphy taxonomy of certain taxa assigned provisionally to Notropis Although I do not further address relationships of the genus Agosia, a comment relevant to future studies is appropriate. While taxa previously hypothesized as its sister groups are western North American forms, such need not be the case. For example, Howes (1984) considers that Pogonichthys and Ptychocheilus may be North American representatives of the otherwise eastern Asian aspinine cyprinids. His work lends support to earlier speculations of such trans-Pacific relationships Morphometric and Meristic Analyses Specimens were collected by seines and electrofishing, preserved in 19/. formalin and transferred to 70/. ethanol after rinsing in water. Host preserved material is in the Co11 ect ion of Fishes, Arizona State University specimens from the same samples used for morphometric analyses. Meristics data were compiled on at least one sample of 39 specimens from each major basin. A truss system dimensions, was used for morphometric measurements. Data were taken on 49 dimensions specimens representing 69 spatially and/or temporally separated samples the IBM 3981 and 3999 mainframe computers at ASU, employing programs in versions 5.98 and 5.16 of the Statistical Analysis System Figure 2. Lateral and ventral views of female Agosia chrysogaster and dorsal view of mate.· Measurements used in moprhometric analyses are indicated. ------·-- ·-··-·- 14 15 characters were ambiguous. Each major sub-basin of the Gila River drainage was represented by similar sample sizes. Morphometric data en non-native populations of Hualapai Lake, Mimbres River, and Rio Grande drainages also were analyzed. Data were subjected to descriptive, univariate statistical analyses specimen deletion. Unless otherwise specified, all analyses were conducted separately on each sex and significance levels of PS.05 applied in all tests. Since sexual dimorphism confounded many analyses, results presented here are of analyses on females only unless stated otherwise. Multivariate analyses of morphometric data were done using SAS routines the PROC MATRIX code presented by Bookstein et al. (1985); after corrections of minor errors, including those pointed out by Rohlf (in press), Electrophoretic Analyses Electrophoretic analyses were done by Zneimer <1986>. Specimens were frozen fresh on dry ice in the field and maintained at -800 C for a maximum of 5 years prior to analysis. Populations used in the ------·· ------·-·--····------· ------. ·-··-·· 16 electrophoretic survey are indicated in Appendix B. Buffer systems and stains employed to survey 15 presumptive loci resolved from mixed tissue extracts are described in Zneimer <1986>. All analyses of electrophoretic data were done using BIOSYS-1 Univariate Analyses Measurement precision was analyzed by compiling 5 repeated measurements of all variables on each of 5 individual specimens of varied size and sex from 5 different collections. Means, standard errors and coefficients cf variation Measurement precision varied over nearly 3 orders of magnitude among characters, but most <42 of 49} were measured relatively precisely, with cv~s ranging from 9.118 to 9.747. Greatest lengths Sex-specific means and 9~/. confidence intervals for all raw variables are summarized in Appendix C. 18 VARIABLE MEAN CV VARIABLE MEAN CV VARIABLE MEAN CV NARORB 3.227 SNTBARB 0.458 HEADW 0.274 ISTHMUS 1.934 OPERNAR 0.425 DOOPERCO 0.264 NARL 1.684 MOUT!id 0.429 DORSFL 0.250 BARB ORB 1.264 BODYW 0.404 PCFL 0.237 PECOPER 9.747 PELVGW 0.490 BPECTO 0.216 NARSNT 0.735 IORB 0.392 PECDO 0.209 OPERCORB 9.704 PELFL 0.372 ANFL 0.205 I NARES 0.677 ORBDIA 0.372 PECOPELO 0.203 IPREMAX 9.629 PELOANO 0.370 PELODI 0.180 SNTBMEM 0.618 ALIPB 8.367 NPECTO 0.172 I BARB 9.616 AN BASE 8.360 ANODO 0.167 PLIPB 0.506 CAUDPD 0.356 PELODO 0.137 BOPERCO 9.505 ANOHP 0.349 HEADD 0.124 DORSBASE 0.501 IOPERCO 0.315 HEADL 9.110 LOPERCO 9.485 ANODI 9.396 SL 9.068 BARBNAR 9.466 HPDORSI 9.284 FL 9.953 TL 0.035 Table 1. Mean Coefficient of Variation for all variables measured 5 times on each of 5 specimens. CV was computed for each specimen, then averaged across specimens. See Appendix A for acronyms and descriptions of variables. Since size differences were present ~ong samples, basins and sexes, it was desirable to isolate these effects. Bookstein et al. <1985) recently reviewed methods of isolating size effects from those of shape in morphometric studies. Basically, three methods have been employed: Principal Components Analysis 1978; Albrecht, 1978; Hills, 1978; Pimentel, 1979; Humphries et al ., 1981; Mosimann and James, 1979; Blackith and Reyment, 1984; Bookstein e t a 1 • , 1985) . Regression techniques were applied to partition variance into size-related and size-free components. For each sex, plots of raw variables ·against SL revealed non-1 inear relationships, which remained after log transformations. Log-log 1 inear regression consistent deviations from linearity. The same was true if individual variables were regressed onto scores of the first principal component indicating better fit to the data. Therefore "size-free• data for each sex were produced by non-linear regression of measures onto the first principal component of pooled, within-sample, covariance matrices. Resultant residuals were used in subsequent analyses. The possibility that the pooled population displayl\'d heterogeneity of allometric relationships was also investigated by regression techniques. Tests revealed differences in regression parameters ~ong basins, which are discussed later. ---· ,_, ______213 Multivariate Analyses of Morphometric Data PCA was used not only to summarize the data set and analyze relationships ~ong variables, but as a means of evaluating •natural• groupings of observations. PCA of the pooled covariance matrix of log-transformed raw measures of all variables produced a single cluster of data points on all plots of component scores. Upon closer ex~ination, however, mean scores for some drainage basins differ~d from others, despite broad overlap in scatters for individual specimens. All variables loaded heavily and positively on the first component Component 2 loaded heavily <-.92) on the imprecisely measured ISTHMUS, with the next largest being ANFL (0.13). Component 3 may be interpreted as a contrast of several vertical and horizontal measures in the anterior head region (loading on BARBORB is 8.38, NARSNT 8.33, NARORB 9.29) with predorsal body lengths NARORB Upon failure of PCA to resolve •natural• clusters in the morphometric data set, DFA was applied. While PCA extr-acts 1 inear combinations of variables (components> accounting for maximal ~ounts ------·------·------21 of variation, it does this with no constraints on orientation of components other than that they be orthogonal and uncorrelated. The first component is oriented on the axis of greatest overall variation, and subsequent components describe sequentially lesser proportions of total variance. DFA likewise extracts 1 inear combinations of variables describing sequentially decreasing amounts of total variance, but does so under the constraints that they maximize inter-class variance while simultaneously minimizing intra-class variation. The technique thus requires some a priori basis of classification of observations. It has a further drawback when compared to PCA. Whereas loadings of individual variables onto components can be interpreted in PCA as shedding 1 ight on structure, intercorrelations among variables greatly confound such interpretations of 1 inear Discriminant Functions. Thus, although these functions may provide discrimination among groups, contributions of indi~Jidual variables remain largely unknown. DFA performed on log-transformed raw measurements for all variables and all specimens produced a discriminant function maximizing multivariate distances among samples, yet a plot of scores on the first 2 canonical variates revealed 1 ittle discrimination among them. Figure 3 illustrates that although scatters of scores for each sample are broadly overlapping, sample means on the first axis The same DFA 1 s were also run on data segregated by sex. Each sex 22 Figure 3. Plot of sample mean scores on first canonical var·iates from 3 separate DFA~s maximizing distances among samples ------23 w ...J :>:"- a: (F) ...... "'I z tn ex IXl IJ) "'I I 24 had comparable patterns of relationships among samples and basins. Based on analyses of raw, log-transformed data on all variables for each sex, and using major group as the class variable in DFA, morphological separation of the 2 major groups was greatest among males Use of size-free data in DFA improved segregation of the same 2 groups. Separation of the forms on the first discriminant function of size-free residuals input to DFA classifying samples was roughly comparable to that of the second discriminant function of raw data on the pooled, within-basin covariance matrix. The 2 major groups were, as found with raw data, a northern one consisting of samples from the Bill Williams, Gila, Sonoyta and Concepcion basins and a southern one comprised of samples from all remaining drainages The function developed from the southern group successfully classified 97/. of females and 99/. of males from the northern form, the northern group 1 s function correctly classified all females, but only 55/. of ·- -··· -- ---·-··------.-----. 25 Figure 4. Scatt~r plot of scores on first two canonical variates of pool~d, within-sample covariance matrix of females. Matrix was of residuals of 49 morphometric variables from nonlinear regressions on PCl from a pooled, within sample covariance matrix of females. Specimens of northern morph indicated by"+", those of southern morph by •x•. CANONICAL DISCRNINANT ANALYSIS ON RESIDUALS OF NONLINEAR REGRESSION ON PC1. CLASS =SAMPLE. CAN2 6 6 X X 4 X X + + ++ + X -1-t +* 3 X lE,c" ~ X +if.-11-,~t+ ++ + ~ ~ )C Xx X .+ +of~-++ + :1=1:+ +-fl'"+ .... +..&...... 2 XX X X~ + i" • X X lC ilf. *X ~ X 't.jJ/ X~ X X ~ x,j6c ~X Xx ~ X :x 0 X lC\l )( XX X X X X )( X x· X X c -1 X ~ X,CX ~ X xX X~ ~ >§c X ~ ~ ~ )( X X X X X )0( XX X -~ A x x *xxx XX x -2 X X ~X >)c X X X X~ XX X N X X X X X X xlll: X ~ X 2 -3 XX X Xx XX -4 -6 -6 -7 -8 -9 I -8 -7 -6 -6 -4 -3 -2 -1 0 2 3 4 5 6 CAN1 X • WUCOX, VACU. SONORA, + • BlJ.. WLLJAUS. COCOlAQU, UAVO, FlERTE SONOYTA&~ t-v &stW.OA 0.. males of the other group. Generalized multivariate (all variables included) distance between sexes was 11.7 in the southern, and 15.8 in the northern group. As was the case with PCA's on pooled matrices, initial sheared components from the matrix of all variables failed to discriminate samples, but on closer analysis provided slightly less overlap among basins than did PCA. Shearing components on the major groups recognized from DFA slightly improved discrimination between them, but still left extensive overlap between scatters of the 2 apparent morphs. Although these sheared components did not provide the high levels of inter-group discrimination seen with DFA, interpretabl il ity in terms of morphology makes PCA of interest at this point since at least some discrimination exists and loadings on Discriminant Functions are not easily interpretted. Although variance within each major group was high, differences between them were present on components which have interpretable loading structures. Sheared PC-3 for females, for example, on which differences between morphs were detected, contrasted measures of the anterior head region with pre-dorsal and pre-pelvic body lengths and depths. Since certain imprecisely-measured characters consistently loaded highly on principal components extracted from all variables, and interpretation of loadings from 49 variables was complex, sub-sets of variables were input to sheared PCA analyses to simplify analyses. First, variables were ranked by overall estimates of measurement precision, and the 36 most precise characters were used with major grcup (mor~~) as the grouping variable. This reduced data set provided 28 slightly more graphical separation of major groups on PC plots than those based on the entire data matrix. Differences between major groups were greatest for males on H3 (sheared PC3>, which principally described variation H4 which is a combination of PELOANO <-.51), CAUDPD <.36) 1 and HPDORSI (-.42). By focusing on discrete areas of body shape, the character set was further reduced, yet still retained discriminatory power. Using only four characters from the anterior body region, and producing sheared PC's on the pooled within-group covariance matrix, H2 of the analysis on males becomes a contrast between PELODO (-.8) and DOOPERCO (,5). The major groups differ noticeably on mean scores on this axis major groups on these axes is more complete, and interpretation of loadings is clearer than for axes based on the full data set. After some experimentation with effects of various subsets of variables on outcome of sheared PCA, a 19-variable subset was selected that maximized inter-basin and inter-morph discrimination. While not as distant as in plots of discriminant functions, the same groups recognized with DFA are evident in Figure 5, a plot of scores on sheared components extracted from this subset of variables for males. ------·- -- ·- --· ·---·-·· ------. ···- -·· 29 Figure 5. Plot of scores for all basins on sheared 2nd and 3rd components H2 H3 SNTBARB 9.732 -9.337 BODYW 9.199 9.391 DOOPERCO -9.288 -0.379 PECDO -0.216 -9.059 PECOPELO 0.162 -9.038 PELODI -9.933 -9.299 ANODO -9.235 0.251 PELODO 9.105 IL269 HPDORSI -9.038 0.596 PELOANO -9.444 -9.263 30 (J) (V")' . N I ~~------~------~~ ~ ~ (Y') L() I • . I 0 . ·-·· ------31 Plots of the same components from females only display an equivalent geometry of relationships, but with slightly less distance between basins. Allometric Differences Between Morphs After recognition of morphometric heterogeneity, a variation on the regression method of size correction applied earlier to pooled data was performed on partitioned data sets for variable-by-variable analysis of among-group differences. Appendix D presents r.onl inear regression statistics for each variable regressed on SL by sex in each major group. These relationships were later used in shape reconstructions (see below>, but also demonstrate differences in allometries between groups and sexes. For example, a large proportion of variables have nonlinear log-log relationships with SL in at least one sex in one or both major groups. In the northern group, 35 <7~/.) of the 48 variables regressed on SL had significantly nonlinear relationships with that variable in at least one sex. Twenty-three (66/.) were positively nonlinear in both sexes while 4 <11/.) had negative quadratic terms. Twelve were nonlinear in males only <5 negative, 7 positive). In contrast, the southern group had only one variable nonlinearly related to SL in both sexes. A total of 14 additional variables were non-linear on SL in one sex only <14 positive, 1 negative), Females had a positive quadratic term on 19 variables, in which the same term was positive for both sexes in the other major group. Non-linearity with SL was demonstrated for only 3 variables (2 positive, 1 negative) in males of the southern group, besides the one for which both sexes are non-1 inear. Non-linearity was found in 3 variables in the southern group, for which no significant deviations from I inearity were indicated in the northern group, 2 of these were in males. Only one character, pectoral fin length As indicated by lack of overlap of asymptotically-estimated, 9~/. confidence intervals, a number of variables differed in one or more regression parameters between sexes and/or major groups. Within the northern group, sexes were significantly different in each intercept, slope and quadratic term of the pelvic-fin-length to SL. Differences between sexes were not demonstrated in the southern group for the relationship of any variable to SL. Although not different between sexes in the northern group, barbel to nares other variables differed in regression relationships on SL between opposite sexes of different major groups. 33 Shape Reconstructions The truss system of measurement is a geometrically logical improvement over traditional means of morphometric data collection, which often included measurements between non-homologous points and typically were heavily biased toward disjointed and compounded length dimensions as well as disjunct depth measures 1982; Bookstein et al ., 1985; Strauss and Fuiman, 1985). Perhaps greatest advantages of the truss system result from an ability to derive average shapes for groups of observations, permitting graphic comparison of size-free shape differences among groups relationship, provide graphic confirmation of results from DFA and PCA. Again, it is obvious that greatest differences between major groups in each sex are in pre-dorsal the head, especially the mouth variation from the overall Size/SL relationship. Overlaid reconstructions of mean shape for each sex within the ------·------34 Figure 6. Overlaid average shapes of males of northern (dashes) and southern ------35 ~ :1 ·-1 :; ==- 12:=· I ...... '.,~\ i2 \ ...... , ...... I ..••••••••••- ...... - . 36 Figure 7. Overlaid average shapes of females of northern ·------· ·----·· ----- ·-··. ..,.., •J{ mm..... '''''''' 38 major groups illustrate the trend toward greater body depths and shorter fins of females in each major group. Overall, the extent of sexual dimorphism is slightly greater in the northern than in the southern major group. This fact is evident from overlaid shape reconstructions Temporal Variation in Morphology of Agosia chrrsogaster A series of 8 samples taken from a single locality over a period of 39 months (7 over a 12-month period) was used to assess extent of temporal variation. Since growth and changes in condition factor were expected among samples in this series, it was not surprising that DFA of raw data discriminated among samples. Inputting size-free data for females into DFA, which maximized distances among samples, revealed that samples taken less than 2 months apart had mean scores on that axis that are as different as means on the same axis of the nearest inter-major group pairs Figure 8. Overlaid average shapes of males (dashes) and females . ------43 --- I I I I I I I I I I I I I I I ------41 Figure 9. Overlaid average ~hapes of males -·-·------· ·---·--·------··------· ------. --·-·-. 42 • I ._, .... J:: ...... IJ ...... li I '\ . \ I- ~·-·-...... ------~ 43 Figu~e 10. Mean scores for samples on first two canonical variates of pooled, within-morph covariance matrix of females. Matrix was of residuals of 19 morphometric variables ------·- --- ·--· -----····------·--·· 44 m (..) "' m 01 "' "" "'m Ill ., m "' "" m < 0 0 :z ct u :z 0 ct UJ :z:: > > > "' "' > 30 "' C\J o .... ' "'"' "' "' 0 ... en ~ N -.--.-.. -.·:--· . .--~~~~-r~~--~~~~-r~-T~~~-r~----~-C\J_L~ "'~--- 0 u ' :z ct w :0: 45 both inter-morph and intra-locality differences are great along the s&me axis indicates that temporal variaton parallels shape differences between the major morphological groups. On discriminant functions constructed to maximize between-morph and minimize within-morph variance, distances &mong Bonita Creek samples became small in comparison to inter-morph distances, but still encompassed the full range of variation within the northern morph on this improved between-morph discriminator. The same geometry of inter-morph and inter-sample 19-variable reduced data set. Although multiple, temporally-isolated samples from single localities in the range of the southern morph were not available for detailed analyses, temporally discrete pairs of samples were available for 2 localities. These also display large multivariate distances on the same inter-morph discriminators. Thus the morphs apparently do not differ in the way their shapes vary over time. High levels of temporal variability indicated that morphs detected by DFA could be an artifact of seasonal variation, if seasonal distributions of samples differed significantly between the 2 geographic areas. To evaluate this possibility, frequency distributions of numbers of specimens by month of collection for each group were compared Despite distributional differences, the average time of collection of --- ~ ------~ ~ ------~--~ ~~. 46 35 + ss I I ss I I ss I I ss ss I I ss ss 38 + I ss ss I ss ss I I tfl ss ss I I ss tfl ss ss I I ss tfl ss ss 25 + tfl ss ss I ss I ttl I ss ss ss p I ss tfl ss I ss E I tfl I ss ss ss R I ss tfl ss ss c + tfl 28 I ss ss ss E I ss tfl tfl ss ss I N I tfl tfl I ss ss ss T I ss tfl tfl ss ss I A I ss tfl tfl ss ss G + tfl tfl 15 I ss ss ss E I tfl tfl I ss ss ss I ss ttl tfl ss I ss I ss tfl tfl ss ss I I ss tfl tfl tfl ss ss 18 + tfl tfl tfl I ss ss ss I ss tfl tfl tfl ss ss I I tfl tfl tfl tfl ss ss ttl I ss I ss tfl tfl tfl tfl ss ss tfl I I ss tfl tfl tfl ttl ss tfl ss tfl tfl 5 + ss tfl tfl tfl tfl ss tfl ss tfl ss tfl tfl tfl tfl I I ss tfl tfl tfl ttl ss tfl ss tfl ss tfl tfl tfl ttl : ttl ss ttl ttl ttl ttl ss tf-1 ss tf-1 ss tf-1 ttl ttl ttl : tfi ss tfl tfi tfl tfl ss tfi ss tfi ss tfi tfl tfl ttl : tfi ss tfl tfi ss tfi tfi ss tfi ss tfi ss tfi tfi tfi tfi ------J F 11 A 11 J J A s 0 N D Figure 11. Percentages of total numbers of specimens used in morphometric analyses by month of collection and morph ------47 southern morph specimens is only about one month earlier than that for the northern form. Additionally, temporal variation at Bonita Creek on canonical variates scores from refined DFA~s maximizing discrimination between major groups (by utilization of subsets of variables and a priori classification to major groups) is proportionally far less than seen on canonical variates maximizing inter-sample distances. Therefore, differences between major groups appear to be fixed exaggerations of seasonal morphological variation. Classification of Unknowns to Morph and Basin Using a subset of 19 morphometric variables, mostly from the body-trunk region, a series of classification functions was derived from a subset of 769 specimens of mixed sex. The first of these, designed to provide classification to morphotype, correctly classified 418 (more than 9~/.) of the 443 mixed-sex specimens not used in its development. Interestingly, 11 specimens), were from a single sample Sonoyta, and 19 of those were females. Only one female, but 16 of 17 males, from that sample were correctly classified by this function. Despite this, the function was relatively successful and data on all specimens were used to derive a similar discriminant function usable for classification of future unKnowns. Scores on this discrimator, which maximizes between basin distances, but also provides accurate classification to morphotype, may be computed using the following formula: ------~- -~------~------· 48 X= 12.94966592 - 19.61163418 + 4.57912251 + 15.11293161 where values entered for each variable are logarithms (base 19) of the measurement in millimeters. Specimens of the northern morph score higher on this function than those of the southern group. Using a score of -6.95 as the point of division, this function misclassified to morph only 4.95/. <69 of 1212 total specimens- 21 of 471 males and 39 of 741 females) of all specimens used in this study. Although classification of single specimens to basin of origin is less accurate, the classification of unknown, relatively small samples to basin of origin should be possible. Basin mean scores on this function 9~1. confidence limits>, as well as maxima and minima, are presented in Table 2. ------···- 49 BASIN MEAN L(l.JER95"/.C I UPPER95"/.C I Mimbres -2.9966 -3.634159 -2.179959 Hualapai -3.3942 -3.848842 -2.759558 Concepcion -3.6403 -3.868214 -3.412386 Gi 1a -3.8422 -3.935474 -3.748926 Bi 11 Wi 11 i ams -4.1677 -4.493588 -3.931812 Sonoyta -5.3749 -5.689682 -5.967318 Sonora -6.4728 -6.681924 -6.264576 Yaqui -7.2993 -7.479387 -7.128213 Cocoraqui -7.7926 -8.333794 -7.251496 Fuerte -8.1631 -8.369244 -7.965956 Wi 11 cox Playa -8.2491 -8.462812 -8.917388 Mayo -8.4819 -8.669519 -8.393281 Sinaloa -8.7326 -9.346988 -8.119112 Table 2 - Mean and 95"/. confidence intervals <±2 Standard Errors) of the mean for scores on the 19-variable discriminant function defined in text. Statistics based on analysis of all specimens of Agosia chrysogaster 1 isted in Appendix B. Efficiency and accuracy of this discriminating function clearly demonstrate morphologic distinctiveness of the 2 morphotypes, and, in some instances, differ·entiation among basins. Intermediacy of scores on th1s discriminator for specimens fr-om Rios Sonoyta and Sonora is notable, as is the nature of misclassified specimens. Rio Sonoyta specimens, though previously indicated as part of the southern morphotype, are misclassed with a frequency of 32.~/. <21 of 64). Although 56.~/. of the Rio Sonoyta fish are females, 71.4/. of those misclassified were of that sex, indicating a pronounced tendency toward northern morphology in females. Fish from Rio Sonora were similarly misclassified <27.96/.) 1 with a tendency for males to be most liKely erroneously categorized. The female/male ratio in combined samples from the basin was 1.66, while the ratio for misclassified specimens was 1.39. Specimens of all other basins were accurately ------·· -·-· - ·-··· ·-·· ··--·. ·------. -·· .. 50 classified to morphotype by the 10-variable function. Remaining misclassified specimens were from Rios de la Concepcion (1) 1 Fuerte (2) 1 Yaqui <4>, and the Gila basin (9). For all these basins, rates of correct classification to morph are >911.. Using the same 10-variable discriminant function, 24 specimens from 2 populations (1 and 67 1 Appendix B> introduced outside the native range of Agosia were classified to the northern morphotype. Mean scores from these samples are greater than any basin mean Results of Analyses of Meristic Data ANOVA was used to test the null hypotheses of no differences among basin and morphotype means for each meristic variable. Among basins, significant differences were found for number of scales in the lateral 1 ine DF=10, P=.0992) and number of pectoral fin rays P=.9095), However, significant differences between morphotypes indicated by morphometric analyses, occurred only in lateral-1 ine scales Std. Mean Error- Min. Max. Lateral 1 ine scales (northern morph) 75.10379 9.3763599 69 89 (southern morph) 78.12969 9.3674279 64 89 Dorsa 1 fin rays (northern morph) 8.97925 9.9189748 8 11 (southern morph) 8.95035 9.0299361 8 10 Anal fin rays (northern morph) 7 .975Hl 9.0139592 7 9 (southern morph) 7.97872 0.0187459 7 9 Pectoral fin rays (northern morph) 15.99879 9.9753949 6 18 (southern morph) 15.87949 9 .1908959 6 18 Pelvic fin rays (nor-ther-n morph) 8.96224 9.9227996 7 9 Correlations with Ecology and Geography Mahalanobis' distances from DFA of all 49 size-free morphometric variables from females and classifying on sample were correlated with various measures of inter-locality geographic distance. Straight-1 ine distances among all pairs of localities were geometr-ically computed from latitude/longitude coordinates. Drainage distances between localities were extracted from drainage maps using a rotameter and following coastlines between mouths of basins. Elevational differences among paired localities were also used, as was an index of hydrographic relationships of localities. In the latter, drainages were partitioned into major hydrographic subbasins ~- -~------~----~- C''")_,_ intra-subbasin (2) and intra-locality (1), The last level consists of comparisons of temporally isolated samples from single localities. Of all geographic distance measures, highest correlation of morphological distances among localities was with Pair-level (r2 = 0.49), MahalanobisJ distance is correlated with drainage distance (r2 = 0.23>, while the same statistic for correlation with straight 1 ine distance is r2 = 9.20. Elevational difference between samples shows 1 ittle correlation with inter-locality Mahalanobis distances, whether analyzed within or among·basins. The relationship of Mahalanobis distance to Pair-level is presented in Figure 12. Scores on the first Discriminant Function maximizing inter~orph distances with all morphometric variables were correlated with latitude . Adding latitude to a multiple regression model explains no more variation alone Similar correlations of Principal Components scores (from the pooled within-morph covariance matrix) were also analyzed. Size r2=,133) 1 but not with longitude were correlated with latitude elevation 3 variables at P<.0091 (r2=,337, .089, and .979, respectively). A correlation between latitude and elevation ----·---~- -~-·---~-~------~~---~-~------53 Figure 12. Relationship of Mahalanobis' multivariate distances among samples based on 49 morphometric variables, and "Pair level." Pair level = 1 for comparisons of temporally isolated samples from single localities, 2 for comparisons of geographically separate localities within the same hydrographic subbasin of a major drainage, 3 for inter-subbasin comparisons within single drainages, and 4 for inter-drainage comparisons. Score for· each comparison is indicated by •+•, Means and their 9~/. confidence intervals <±2 Standard Errors) are indicated by vertical 1 i nes. ------54 IMAHALANOBIS DISTANCE AND PAIR LEVEL I PALEVEL lj + + IH 111111_1_ II 3 + * + I IIIIIIIIIIIIIRIIBIIIP••IIIHII'.IIII HI Ill !I -llH+I- 2 + + + -tt+ 1&1 t -itH- + + ++++ + #+t-tt+- -tH- + * 0 2 3 lj 5 6 7 8 9 10 11 12 13 MAHALD PAIRLEVEL INTRA-LOCALITY •1 INTRA-SUBBASIN • 2 INTRA-BASIN • 3 INTER-BASIN • 4 ------._1._1"'"' demonstrates a sampling confuses interpretation of correlations with aspects of morphology. High elevations were sampled only in the Gila River basin; all collections available from southern basins wer·e from low-elevation localities. However·, weak relation:.hips of PC1 the restricted latitudes of the Gila River basin. Linear regressions of meristic variables onto latitude, longitude, and elevation were done to evaluate possible effects of ecology on meristic characters. The highest single correlation was that of lateral-1 ine scales with latitude (r2 = 9.37>. Lateral-1 ine scales correlate little with elevation (r2 = 0.17) and longitude (r2 = 9.12). Other meristic characters were not significantly, or poorly correlated (r2 < 9.99) with these same environmental variables. This was true whether analyses were performed separately on sub-samples An additional indication that morphological characters defining morphs is not highly influenced by ecological conditions was provided by experimental starvation of a sample of fish. Two s~ples <19 and 11) were taken on the same date from a single population. One apparent starvation at the time the remainder were preserved. Subsequent inclusion of these samples in multivariate analyses ------· ------·---···· 56 demonstrated them to differ less on axes which discriminated morphs than did any of the temporally-separated pairs of samples from other localities (see below). Other Characters which Corroborate Morphometric Analyses Preliminary evidence compiled on other characters appears to corroborate the outcome of morphometric analyses. Principal among these development of tuberculation in nuptial males and the possible failure of the southern form to construct a spawning pit. Based on series examined in this study, and many others not specifically used, it appears that tuberculation in southern~. chrysogaster does not reach levels commonly seen in specimens of the northern morphotype. Additionally, I have not observed spawning pits associated with southern~· chrysogaster and know of no reports of such pits by others. Both of these observations may be biased, however, by inadequate representation of samples from Mexico during the breeding season. Though~· chrysogaster in the Gila River basin spawn periodically over a protracted period, a major peaK in reproduction occurs in spring (January- April) tuberculate males are rare during all other seasons Seasonality of reproduction in the southern morphotype has not been studied. Frequency distributions of numbers of specimens used in the morphometric analysis by month of collection light on this matter. Some months are not represented among southern samples, in particular those of what might be peaK spawning periods, ------57 but, unless spawning occurs over a much more restricted time period in the south than it does in the north, highly tuberculate males should have been observed. Mean time of collection of southern specimens is about a month earlier than for northern specimens. In the northern morphotype, large, coarse, cream-colored, horny, dermal tubercles develop profusely within a matrix of fine, evenly distributed, sandpaper-1 iKe tubercles on dorsal and lateral aspects of the cranium of adult, breeding males. Tuberculated area of the head extends from nape anteri·orly to about the anterior edge of the nares. Tubercles are largest on the dorsal surface where arranged in an apparently-random pattern; the size and density decrease only slightly over the preopercle and opercle. Concentrations of tubercles are sometimes found along the dorsal and ventro-posterior rim of the orbit. All fins bear tubercles. Those on paired fins develop only on dorsal surfaces of major rays, from fin base distally to approximately 7~/. of fin length. On the pectoral fin, tuber·cles ar·e 1 imited to 2 parallel rows on the first ray. Each pelvic ray may be vested with a single tubercle row. All medial fins are bilaterally tuberculated, with single rows that may appear on all rays. The first dorsal ray, however, has 2 anteriorly-direch>d, par·allel rows of tubercles on its leading edge. Tubercles do not extend completely to the distal margin on medial fins, but dorsal and caudal rays may have tubercles extending from the base along 59-7~1. of their lengths. Anal fin rays bear tubercles only on medial areas. Each scale of the dorsal and lateral body surfaces may also bear fine tubercles, similar to those of the head. ---- . ---··-··----- ··-- 58 The large, coarse, heavy tuberculation of the head in northern breeding males appears absent in the southern group, as is body tuberculation. However, the same fine, evenly-distributed tubercles which cover the head of the northern subspecies, similarly cover dorsal and lateral head surfaces of this form. Distribution of tubercles on fins appears the same as that in the northern group. While aspects of breeding behavior of e. chrrsogaster from the Gila River basin have been reported (Winn and Miller, 1954; Hinckley and Barber, 1979; Lewis, 1978a; Kepner, 1982), comprehensive studies are not available, and observations on the southern morphotype have not been made. However, as previously noted, nests, or spawning pits such as reported by Hinckley and Barber <1979) and Kepner (1982) for the northern form were not observed during the course of extensive field collections for this study and others in the range of the southern morphotype. Results of Analyses of Electrophoretic Data Isoz~es of Agosia chrysogaster were studied electrophoretically by Zneimer <1986) using specimens from collections also analyzed in this study. Relevant parts of her results are presented here also for comparison with results of morphometric analyses. Table 4 presents numbers of specimens of each genotype found in each population for all loci sampled electrophoretically. Genetic heterozygosity of populations 9.035±9.91). Both Rogers' (1972> and Nei's <1978) indices of overall 59 Table 4. Numbe~s of specimens of each genotype found in a su~vey of 15 loci in 25 populations from 22 geographic localities. Samples numbered as in Appendix B. Adapted from Zneime~ ( 1986). 6B I I SAMPLE : ------:2 5 9 14 18 23 32 33 35 37 38 44 46 : LOCUS ~ru : ======:I I 1. Cbp-1 aa 12 12 18 12 8 18 19 19 18 18 12 12 12 : 2. Ck-A ------:aa 12 18 18 12 14 18 19 19 18 18 12 12 12 : ------:ab : 3. Pep-A bb 12 18 18 18 14 18 19 22 18 8 12 7 : be 5 6 4 : ee 5 12 I : ------: 4. Pep-B aa 12 18 18 12 14 12 13 22 18 12 12 13 12 : ------:aa 1 11 13 : 5. Est-1 ab 1 4 4 1 : bb 18 IB 4 1 14 18 18 19 17 18 18 13 11 : ------: 6. Gp-1 aa 12 17 17 12 14 18 18 18 18 18 12 12 6 : ------: aa 2 13 13 1 ab 2 4 4 11 7. Gpi-A bb 9 18 1 1 14 18 18 18 15 18 18 k 2 cr 1 ------:aa 9 2 17 18 13 16 17 17 14 2 : 8. Gpi-8 ab 3 4 1 2 1 I 3 4 : bb 11 18 18 12 6 : be : ------: 9. Ldh-A aa 12 12 9 9 14 12 13 13 18 12 12 12 12 : ab 3 3 : ------: 18. Ldh-B aa 12 13 12 9 14 12 13 13 18 12 12 12 12 : ~ 3 : ------:aa 12 18 18 18 15 18 19 18 18 13 12 : 1t. 11-Hdh-A ab 1 : ce 18 18 : 12. S-Hdh-8 ------:aa 12 18 18 18 14 18 19 19 18 18 18 13 12 : ------~------: ab 1 : 13. 11-He-A bb 12 18 18 18 8 16 19 18 18 17 14 13 12 : be 6 2 5 : 14. S-He-A ------:aa 12 18 18 18 13 18 19 18 18 18 18 12 12 : ~ : I ------:I aa I 15. PIJ1-A ab I bb 12 18 18 16 14 18 19 19 18 18 18 13 12 : be 2 :I I ·-··------61 Tabl~ 31 eontinu~d !W!PLE ------:47 48 58 51 52 53 56 61 62 63 65 68 l I ======LOCUS ALLELE I 1. Cbp-1 aa 18 12 18 18 18 18 18 12 29 18 12 14 l ------: 2. Ck-A aa 16 18 18 18 18 18 18 18 29 18 12 14 l ------: ~ 2 l 3. Pep-A bb 16 19 18 18 18 18 18 18 18 18 9 6 l be l ee l ------: 4. P~p-8 aa 16 13 12 12 18 12 12 12 18 12 12 12 l ------: aa l 5. E~t-1 ab 1 l bb 16 19 18 18 18 18 17 18 29 18 13 15 l ------: 6. Gp-1 aa 16 18 18 18 18 18 18 18 16 18 12 6 l ------·aa 4 4 ab 5 8 7. Gpi-A bb 16 18 18 3 6 5 9 6 19 18 18 13 be 3 3 6 2 ee 12 6 7 aa 16 18 16 17 16 15 14 18 4 12 B. Gpi-8 ab 2 1 2 2 3 2 1 bb 1 18 17 1 l be 1 l 9. Ldh-A ------:aa 16 13 12 12 18 12 12 12 18 12 12 12 l ab l ------: 18. Ldh-B aa 16 13 12 12 18 12 12 12 18 12 12 12 l ab l ------: aa 16 19 18 18 18 18 18 18 18 18 12 19 l l 11. M-Hdh-A ab I ee I ------: 12. S-Hdh-B aa 16 19 18 18 12 18 18 18 18 18 13 11 : ------:ab 1 l 13. M-H~-A bb 12 18 18 17 18 18 18 16 14 18 9 18 l be 4 1 2 4 2 l ------: 14. S-H~-A aa 16 18 18 18 18 18 12 18 16 18 11 18 l ab 2 l ------:I aa 6 1 2 18 18 18 4 I 15. PS1-A ab 9 18 8 1 7 bb 1 1 8 17 18 28 18 1 11 be -----· --·- --· ------·· ----··--··-----·· --···. 62 TableS. Genetic similarities among samples- Nei's (1978) unbiased genetic identity above diagonal 1 and Rogers' <1972> genetic similarity below diagonal. Samples numbered as in Appendix B. Data from Zneimer (1986). 63 Sfl'IPLE 2 5 9 14 18 23 32 33 35 37 38 44 46 2 .97 .98 .92 1.88 1.88 1.88 1.80 1.88 .87 .83 .95 .98 5 .94 .92 .a6 .96 .97 .97 .96 .97 .92 .8a 1.88 1.88 9 .94 .aa .97 .96 .96 .96 .96 .96 .81 .77 .98 .93 14 .a8 .a2 .94 .as .86 .87 .87 .86 .75 .71 .83 .88 18 .97 .94 .91 .98 1.88 1.88 1.88 1.88 .85 .82 .94 .97 23 .98 .95 .92 .98 .99 1.98 1.88 1.88 .86 .82 .94 .97 32 .98 .95 .93 .98 .98 1.88 1.88 1.88 .86 .82 .94 .97 33 .98 .95 .93 .98 .98 .99 1.88 .9a .86 .82 .94 .97 35 .98 .95 .92 .91 .97 .98 .99 1.88 .87 .83 .95 .98 s 37 .a3 .a9 .77 .71 .a3 .a4 .a4 .84 .84 .99 .92 .92 A 38 .a8 .as .73 .67 .81 .81 .81 .81 .88 .96 .88 .98 f1 44 .93 .98 .a6 .88 .92 .93 .94 .93 .94 .98 .87 .95 p 46 .94 .97 .a8 .a2 .92 .93 .93 .93 .94 .89 .86 .99 L 47 .93 .98 .a8 .a2 .95 .95 .94 .94 .93 .79 .77 .88 .88 E 48 .96 .93 .91 .85 .96 .97 .97 .97 .96 .82 .78 .91 .91 58 .96 .93 .98 .as .96 .97 .9a .97 .97 .82 .7a .92 .91 51 .87 .83 .83 .81 .87 .sa .sa .88 .88 .72 .69 .82 .82 52 .a9 .as .a5 .at .as .98 .98 .98 .98 .74 .71 .a4 .a4 53 .a9 .as .a4 .at .a8 .a9 .89 .a9 .98 .74 .71 .a4 .a4 56 .92 .96 .a7 .a3 .89 .91 .91 .91 .92 .sa .87 .99 .99 61 .91 .95 .a6 .83 .98 .91 .91 .98 .91 .a7 .87 .99 .98 62 .97 .95 .91 .as .98 .99 .98 .98 .9a .84 .83 .95 .98 63 .98 .95 .93 .87 .98 .99 1.88 1.88 .98 .a4 .a2 .93 .97 65 .93 .98 .87 .81 .93 .94 .93 .93 .94 .88 .at .93 .95 68 .98 .95 .93 .87 .98 .99 1.88 1.88 .98 .85 .a2 .93 .97 Sfl'IPLE 47 48 58 51 52 53 56 61 62 63 65 68 2 .97 .99 .99 .98 .92 .91 .94 .94 1.88 1.88 .97 1.88 5 .93 .95 .96 .86 .88 .88 .99 .98 .97 .96 .95 .96 9 .93 .96 .96 .87 .8a .Sa .98 .98 .96 .96 .93 .96 14 .a7 .98 .98 .a4 .85 .a4 .a7 .a7 .98 .98 .aa .98 18 .97 .99 .99 .a9 .91 .91 .93 .92 1.88 1.88 .97 1.88 23 .97 .93 .93 .a9 .92 .91 .93 .93 1.88 1.88 .97 1.88 32 .97 .99 .99 .89 .92 .91 .93 .93 1.88 1.88 .97 1.88 33 .97 .99 .99 .a9 .92 .91 .93 .92 1.98 1.88 .97 1.88 35 .97 .99 .99 .98 .92 .92 .94 .94 1.88 1.88 .97 1.88 s 37 .82 .84 .as .75 .77 .77 .91 .91 .a7 .as .84 .a4 A 38 .7a .81 .81 .71 .73 .74 .a4 .84 .82 .88 .78 .88 f1 44 .98 .93 .93 .a3 .86 .86 .97 .97 .93 .93 .as .93 p 46 .93 .96 .96 .86 .89 .89 .94 .93 .93 .93 .98 .93 L 47 .99 .99 .95 .97 .97 .86 .86 .94 .95 .97 .95 E 48 .97 1.88 .93 .95 .95 .89 .88 .96 .98 .95 .98 58 .97 1.98 .93 .95 .95 .89 .a8 .96 .97 .95 .97 51 .92 .98 .98 1.88 1.88 .82 .82 .87 .88 .91 .88 52 .93 .92 .92 .98 1.88 .84 .84 .88 .98 .93 .98 53 .92 .91 .92 .98 .99 .84 .84 .88 .89 .93 .89 56 .a9 .92 .92 .84 .a6 .a6 .99 .98 .91 .a7 .91 61 .89 .91 .92 .84 .86 .86 1.88 .91 .98 .87 .98 62 .97 .99 .99 .89 .91 .91 .94 .94 1.88 .94 .98 63 .97 .99 .99 .98 .92 .91 .92 .92 .98 .93 1.88 65 1.88 .99 1.98 .96 .9a .98 .92 .92 .97 .97 .93 68 .97 .99 .99 .98 .92 .91 .92 .92 1.88 1.88 .97 ---·------· 64 genetic similarity are in Table 5. Scores for genetically identical pairs of samples are 1.9 in both indices, with increasing divergence lowering scores. Minimum similarity between samples, as measured by Rogers' index, was 9.67, but 95.3/. of all 399 possible sample pairs had scores~ 9.89. Genetically identical sample pairs comprised 4.~/. of the tota 1 ; Zneimer <1986) found significant deviations from Hardy-weinberg expectations, indicating lack of gene flow, at both inter- and intra-basin levels in e. chrrsogaster. Great distances among localities and hydrographic divides may be responsible for impeding gene flow at these levels, however, 5 significant, intra-sample deviations from Hardy~einberg expectations were also noted 32, 46, 51 and 52>. Reasons for these are not known, however, 3 of the 5 deviations were at the Gpi-A locus. Five presumptive loci were monomorphic across all samples. Three polymorphic loci Yaqui) and Turkey Creek unique Peptidase allele Est-1 in Coon CreeK and Verde River rare; and synapomorphic presence of the b allele of Ldh-A only in Coon CreeK and Verde River samples <14 and 9). An UPGMA phenogr~ based on the genetic identity coefficient of Nei <1978) is presented in Figure 13. It clusters populations by the unweighted pair-group method with arithmetic means Electrophoretic data were input to BIOSYS-1 1972; Lundberg, 1972; SWofford, 1981) based on Rogers~ Genetic Similarity Coefficients the longest branch. Results are in Figure 14. Obvious discrepancies were noted between relation?hips patterns extracted from electrophoretic data and those indicated by morphology. Since lack of congruence between morphological and electrophoretic patterns might be the result of analysis of different sets of samples, the morphometric data set was re-analyzed after deletion of samples not represented in electrophoretic analyses. Re-analysis clearly indicated existence of the same northern and southern morphological groups indicated by analyses of the full morphometric data set. DFA designed 66 Figure 13. Phenogram of genetic relationships of s~ples of Agosia chrysogaster. Derived by clustering in BIOSYS-1 -----~ ----~-~~ ----- ~~---- GENETIC DISTANCE 0.16 0.12 0.08 0.04 0 .------.- 2 HUALAPAI 35 GILA 33 GILA 23 GILA 32 GILA 68 MIMBRES 63 CONCEPCION 62 CONCEPCION 18 GILA 65 SONOYTA 47 MAYO 48 MAYO 50 MAYO 5 BILL WILLIAMS • I 44 YAQUI 46 YAQUI I I ~~ ~g~g~~ L 9 GILA ------{:::::: 14 GILA 51 FUERTE 52 FUERTE 53FUERTE 38YAQUI 37 WILLCOX 0.84 0.88 0.92 0.96 1.00 GENETIC SIMILARITY ~ '-J 68 to maximize distances among various groupings of samples recognized by Zneimer (1986) 1 or apparent in the Wagner network, discriminated morphologically among them, but greatest differences were consistently between the 2 previously recognized, maJor morphological groups, and not those recognized electrophoretically ------69 Figure 14. Unrooted Wagner network of relationships of samples of Agosia chrrsogaster derived by clustering of RogerJs <1972> genetic distance coefficients (1 - similarity) with the distance Wagner procedure of BIOSYS-1 ------70 71 Figure 15. Plot of sample mean scores ------·------· -----· . --··------72 N N N N N N« N N "' "' PI N ....N ....N N N N N N N 'ill N .... N N N NN .. "' N N "' .., N .., z a: (.) .., ,., .., ..,.., -- "' - -.r_ -- .., -- 0 .., "'.:pr> N- --=------.., ...,~ ------=.::~~ -~-;.- - ~ .;: ------.- - _-c:. - .,::- - .., I .., ,.., -_..,; ------..... -- - .., .., _.., ------"' C\J ..,..,-- -- I "' .., .., tn ... I ... .., "' .., .., .., ::I' .., I "' ~ ~~------~------~------r------r------OT------T-----~N~------~------~~------~"? a: I I I u -----· ----·------73 Figure 16. Plot of sample mean scores (sexes combined) on Canonical Variates l and 2 of DFA on 49 log-transformed morphometric variables. Samples are those common to both electrophoretic and morphometric analyses. Canonical Variates maximize multivariate distances among smallest groups of Distance Wagner tree, lettered as in Figure 14. ------·-- . F F E [E F F F F { F F F f t E F EE rtf FE F f FF F E E E E c F F f £rEf fF E E FF ~ft ~ E E E E E E g F f' f FE F t ~ F~ E c E Ff F E E c F ~ ft:JE ~ F E E lj: F Vf F EE ,IE IF r E[E ~ : E c c c c c F EF E t- EjF E c c c c c F F jEEE Ef E E F E Fn: c cccec FEgFi E c c c r' E E E E 8 B c ccc c ~ c ~ c F f F B E E B B c r F r Cc ftQ:cc EB E ~ sm c B E B B c ~ Cl: cc!f:Cc E c c E F F'E E EB B EFiiBii B faa~ B a ccc c c c c c c 0 C C CC C F E E E B8 B BB sB \ B B ~Slit! B D C 8 C CC Q: C C(t C C C C 1119 B BBB CCC f E B ' 9 BB I!.. cc ccccc c 9 B It 88 B lj'fB BB c " Q; C D c E 8A 8 8 8. 8 BBB BB liB BB Bs D A B 8 8 B ~ c c c 9_ ?._% B B A B B -., B 8 B 8 ¥ BBB B B oD " B c B B 8 9 D A A A A A AA AA B B B AA. AA A BA.~ A B t A ---- " " A -."A" __," A A A D A A ""A A " A A A A A " A ~ A A " A A -6 -5 -II -3 -2 -I 0 2 3 li 5 6 1 CAN! ~-J .to DISCUSSION All analyses of the morphometric data set indicate existence of two distinct, allopatric morphs of Agosia chrysogaster. A northern morph is native to the Bill Williams, and Gila Rivers of Arizona and New Mexico, as well as Rios Sonoyta and de la Concepcion of Arizona and Sonora, while the southern morph is from the endorheic Willcox Playa, and rios Yaqui, Sonora, Cocoraqui, Mayo, Fuerte and Sinaloa. The southern morph, furthermore, shows indications of differentiation between populations of the Mayo, Fuerte and Sinaloa basins and those of the Willcox, Yaqui, Cocoraqui and Sonora basins, though these are morphologically more similar to one another than either is to the northern group. Fishes from Rios Sonoyta and Sonora show tendencies toward body shapes intermediate between morphs. Although the relationship between morphs is affected by size and sex, at average sizes the southern form has proportionately longer pre-dorsal and PECDO> lengths, but shorter post-dorsal barbel differ in size as well. Differences in size and shape appear to be the result of different growth relationships. While log-log relationships of individual variables to SL were significantly non-1 inear for most variables in the - ~----~~------~-~----- ~-~~ 76 northern morph, those of the southern were predominately not significantly different from 1 inearity. Northern males had significantly non-linear log-log relationships on SL for 35 of 48 variables; the same figure for females was 23. In the southern form, fewer non-linear relationships were found, and more were in females (10) than males (3). Though sexes are dimorphic in body and fin characters in both groups, differences are most pronounced in the northern. Morphology of &· chrysogaster in temporally separated samples from single localities varied in the same characters that discriminated between morphs. While there were differences between samples of each morph in distribution of times of collection, average month of collection for the southern morph was only about one earlier than that for the northern form. Aspects of morphology important in discrimination between morphs were correlated with latitude; correlations with longitude and elevation were not predictive. Correlation of morphology with latitude may be an artifact of its high correlation with distribution of the morphs. An experiment in which fish from a single sample were separated randomly into a treatment group starved before preservation and measuring, and another group preserved at time of sampling, also demonstrated lack of effects of environment on body shape characteristics. These specimens differed less on multivariate axes discriminating among basins and between morphs than did those from multiple collections from single localities at intervals over a year. It thus appears that aspects of morphology varying between morphs are ·--- 77 little influenced by ecological conditions. Despite temporal variation and that due to sexual dimorphism and size, it was possible to develop a classification function using 19 variables which should provide 9~/. correct classification of unknowns of either sex to morph, and will likely allow assignment of most ~all samples to basin of origin. Morphological patterns of variation were correlated with other observations. Though ranges were broadly overlapping, the southern form had on average about 3 more lateral-1 ine scales than in northern fish and apparently lacks development of large tubercles in nuptial males as in the northern form. Differences may also exist in breeding behaviour. Although either morphological or electrophoretic data set could be used to accurately identify many unknown samples to basin of origin, and morphology is capable of near-perfect discrimination of morphotypes, the two data sets produce different conclusions regarding relationships of the groups and leave morphologically-defined groups without isozymic definition. Similarly, isoyme-based relationships patterns are mostly unpredictive of morphology. For example, the UPGMA phenogram based on electrophoretic data of Zneimer <1986) introduced populations 1 ikely derived from that basin, cluster with those of Rio de la Concepcion in both electrophoretic and morphometric analyses, Verde River and Coon Creek samples that also cluster closely with other Gila basin populations in morphometric analyses are 1 inked only remotely to them in the phenogram of electrophoretic data. ------·------·--···------·------78 Distinctiveness of the San Bernardino Playa samples from other Rio Yaqui samples is also incongruent with morphology and results mostly from differentiation at both the Pep~ and M-Mdh~ loci. Morphologically, these 2 populations are only slightly differentiated from other populations of that major group. Additionally, the UPGMA tree places Rio Mayo samples in a group that includes Rio Sonoyta. This group is linked at a high level of genetic identity to a tight cluster composed of Rio de la Concepcion samples and most of the Gila basin samples, and is more remotely clustered to the Rio Fuerte group. Morphological data indicate specimens from Rio Sonoyta are clearly part of the northern morphotype, along with specimens from the Gila, Bill Williams and Concepcion systems, although they are in some ways intermediate between morphotypes. Morphologically, the fish of the southern morph which are most similar those of the Rio Sonoyta are from Rio Sonora, not from Rio Mayo as indicated by electrophoretic data. Geologic data and the shared distribution of Cyprinodon macularius in the Gila and Sonoyta river basins this pat tern. The UPGMA tree shows 1 itt 1e tendency to .1 inK samp 1es in such a pattern. Zneimer (1986) also produced an unrooted, unweighted Wagner network (Farris, 1979, 1972, 1981; Lundberg, 1972; Swofford, 1981> based on Rogers Genetic Similarity coefficients BIOSYS-1 this study and are presented in Figure 14. This relationship hypothesis is more congruent with relationships indicated by morphology ---·------79 than is that derived by UPGMA, but major incongruencies remain. Rooting of the tree through outgroup comparison might improve congruence. Although Gila robusta an outgroup for electrophoretic analysis set, combined with questions regarding appropriateness of choice for the outgroup resulted in a decision not to employ that taxon to root the tree. Rhinichthrs osculus, a taxon likely to be the actual sister group of Agosia chrrsogaster (Miller, 1959; Coad, 1976>, has been selected instead as the outgroup for future analyses. Without outgroup comparison for rooting, interpretation of the Wagner tree is complicated. Regardless of where the tree of Figure 14 might be rooted, however, there is no location which would produce full congruence with morphology, and there are no simple theories which might account for incongruence of electrophoretic and morphologic patterns. Any attempts to reconcile the two data sets leave some aspects (e.g., great electrophoretic distance of Coon Creek [sample 14] and Verde River [9J samples from the rest of the Gila basin, and geographically unexpected placement of samples from Rio Sonoyta [65] and Bill Williams [5] drainages) unexplained, however, greatest congruence would be obtained if the figure were rooted on the short branch between the central trichotomy and the tight cluster of Gila and Concepcion basin samples. The initial dichotomy would then correspond to the geographically-sensible split of the Gila/Concepcion lineage from the southern morph, and subsequent splitting of the latter into 80 Yaqui/Willcox/Sonora and Mayo/Fuerte 1 ineages. Such a pattern is congruent with morphology and an assumption of equitable rates of morphological divergence among all 1 ineages. If this is not the case, and the true ancestral condition lies elsewhere on the figure, then electrophoretically-distant terminal groups of the southern morph demonstrate remarkable morphological convergence achieved over the same time period in which the northern morph diverged morphologically, but with relatively 1 ittle isozymic divergence, from one or the other of them. A rooting position producing some congruence with morphologic data would be between the Mayo/Fuerte group <3> and the trichotomy. This might relate to geographically-possible divergence from an ancestral stock of Mayo/Fuerte and northern 1 ineages, with subsequent morphological convergence of a Yaqui/Willcox/Sonora lineage toward Mayo/Fuerte morphology after the former split from its Gila/Concepcion sister group. Rooting on the opposite side of the trichotomy, nearer the mid-point of the longest distance, implies not only the same type of convergence, but the unlikely occurrence of a geographicallY central dichotomy producing a central group bounded on both north and south sides by the other. Multivariate analyses of morphometric data also produced unrooted and purely phenetic relationships patterns, but these were geographically sensible and corroborated by evidence from meristics, tuberculation, and perhaps breeding behaviour. A suite of morphological character states non-linear relationships of most characters to SL, spawning pits, etc.) ------... 81 comprises autapomorphies of the northern group and synapomorphies uniting lineages of its drainages, while the alternate suite characterizes the southern morph and unites its diverse lineages. The lack of congruence between patterns of morphology- and isozyme-based estimations of relationships is not unique. Johnson <1975> and Mickevitch and Johnson <1976> reported congruency between relationships patterns as indicated by minimum-length Wagner trees independently derived from electrophoretic and morphometric data sets on the atherinid genus Menidia. However, these patterns were largely incongruent with those derived by phenetic Micl Selander, 1972; Turner, 1974; Sage and Selander, 1975; Kornfield et al ., 1982; Kornfield and Taylor, 1983; Turner and Grosse, 1989; Turner et al., 1983; Grudzien and Turner, 1984a 1 b). Others have reported physiological and behavioral divergences sufficient to result in reproductive isolation among forms differing 1 ittle electrophoretically Chapman, 1971) 1 while still others revealed considerable isozyme divergence in the face of 1 ittle or no apparent morphological ------. 82 divergence and Turner, 1984, 1985). In general, molecular similarities among conspecific populations of other North American fishes, including other cypriniforms, characteristically are >B.85 1979a, b, 19BB; Buth and Burr, 1978; Zimmerman et al ., 1989; Ferris et al., 1982; Turner, 1983; Grudzien and Turner, 1983). Some cypriniform species pairs, however, are about equally, or less, genetically differentiated al., 1989; Dowling and Moore, 1985) than are some pairs of populations analyzed here. It is thus obvious that genetic distance data are not consistently correlated with classical taxonomy, nor is it desirable that such a rate-dependent measure be so if taxonomy is to be a reflection of phylogeny. Existence in this study of clearly-discernable morphotypes, with contiguous geographic distributions, coupled with evidence of intermediates are in fact characteristic of subspecies. However, if morphs were considered subspecies, greatest genetic distances of Zneimer's <1986> study would fall within the southern one, and not between the two. Apparent lack of congruence between morphological and electrophoretic data sets obviously confuse taxonomic interpretation. Although there are no recognized criteria to determine what constitutes a subspecies, Hubbs <1943) suggested informal ones based on his fish research. His criteria were proposed more than 4 decades ago, however, and must be assessed in 1 ight of modern taxonomic perspectives. Hubbs ... ------···------· 83 <1943) was careful to point out that •systematic characters must have a genetic basis" and continued to say "Unless the systematics are excessively complicated, I would designate as a subspecies any genetic form which shows reasonable geographic or ecological consistency, and which can usually be distinguished on its totality of characters.• Mayr (1969) considered a subspecies to be • ••• an aggregate of phenotypically similar populations of a species, inhabiting a geographic subdivision of the range of a species, and differing taxonomically from other populations of the species.• Other definitions of subspecies include the long-used, but now disfavored "75/. rule" the result of phylogenesis rather than ecological adaptation. Although Zneimer's <1986) results would not have been predicted by this study of morphology, the only conclusion that may be drawn is that relatively few loci surveyed in her study failed to reveal differentiation congruent with morphology, While it seems likely that the diversity of morphological characters surveyed would be under polygenic control, it is possible that differentiation of morphs may relate to genetic alterations at one, or few, loci associated with --- ~~-~--~-~--~~~ 84 growth control and sexual dimorphism. That morphs clearly differ in allometric relationships for most characters may be evidence of such control systems. If few changes, perhaps related to general developmental processes, have occurred, it is 1 ikely they would not be sampled in an electrophoretic survey such as Zneimer's. Though isozyme studies have become an important tool of systematists during the past 2 decades, the technique is not without I imitations and problems 1982 1 1984; and references therein>. Configuration of relationships patterns developed with methodologies such as UPGMA and Distance Wagner may be unstable and highly sample dependent Bernardino) pair. Thus, there is little concordance between results from different methods of analysis of the electrophoretic data. Various measures of internal consistency (e.g., SoKal and Rohlf, 1962; Farris, 1972; Prager and Wilson, 1978; Fitch and Margoliash, 1967; Sokal and Rohlf, 1981) may also be employed to evaluate tree configurations. Based on these, the Wagner method produces best fit to the data 9.983ti• 9.864 for UPGMA tree>. Though not investigated by Zneimer or· here, structure of Zneim~r's data set, with most variation expressed at few loci and often in one or few samples, would 1 ikely produce considerable variation in configuration of trees produced from subsets of loci and/or samples. Relationships hypotheses derived from morphometric data, however, are highly stable when subsets, either of variables or samples, are used in their development. For example, the same 2 major groups are detectable with multivariate techniques on as few as 4 of the 49 variables and all samples Physiography and Distribution of Morphotypes Topographically, geographic ranges of the 2 morphotypes are isolated by considerable relief between the Rio de la Concepcion and Rio Sonora basins, though the latter is isolated from the Gila River basin by areas of relatively low rei ief in the area of Cananea, Sonora. Least rei ief between ranges of the 2 morphotypes occurs at the divide between the Willcox Playa and Aravaipa CreeK of the Gila River basin, ·--··- ---··------·--·------·----·----·------·. 86 where Aravaipa Creek is eroding headward into the northwest end of the broad Sulphur Springs Valley. Prior to extensive erosion of Aravaipa canyon, the Sulphur Springs Valley was obviously well isolated. There is no morphological evidence of contact between the northern and southern forms over this divide. Morphological tendencies toward intermediacy of specimens from the Rios Sonoyta and Sonora, and clear grouping of Rio de la Concepcion specimens with the Gila/Bill Williams group parallel electrophoretic patterns expressed in the Wagner tree and are consistent with physiographic intermediacy of those drainages. Although both drain some Basin and Range areas, each resembles the Gila River in having long northeast-to-southwest reaches, especially in their lower parts on the coastal plain. By contrast, the Rio Yaqui and more southern systems drain only Basin and Range topography and uplifted parts of the Sierra Madre Occidental, and are tightly constrained in all but short coastal-plain reaches. Alignment of major structural valleys of the Rios Bavispe and Moctezuma of the Rio Yaqui southward into the Rio Mayo system, then curving eastward to control nothwest-draining headwaters of the Rios Fuerte and Sinaloa drainages, respectively, is obvious in Figure 1. Another apparent Basin and Range alignment of drainages is that of the Gila basin's Verde River and Tonto Creek along the western rim of the Colorado Plateau with the Santa Cruz/San Pedro valleys Gila tributaries>. This same alignment continues through the upper Rio Sonora. If the Rio Sonora be simply described as streams in or entering that alignment, and .. ------87 basins to its west. At least one a posteriori scenario can be conceived, which reconciles some apparent incongruencies between phenetic relationships depicted by morphometric analysis and the Wagner Tree based on genetic identity coefficients derived from isozymic data. However, this scenario necessitates some major assumptions. If Gila/Concepcion, Yaqui/Sonora, and Mayo/Fuerte components were synchronously fragmented from an ancestral population distributed continuously across most or all of the present range of the species, the result would produce a phylogeny much like that depicted in the Wagner Tree of Figure 14. The three-way, synchronous disruption corresponds to the central trichotomy of the tree. To reconcile this scenario of cladogenesis with the morphometric analysis, and seemingly common sense, requires erroneous placement of the Verde River/Coon Creek, Sonoyta and Bill Williams branches by the Wagner method. Geographically, it seems far more 1 ikely that all these populations derived from the 1 ineage leading to the close-knit assemblage formed by the remaining Gila basin samples and those from Rio de la Concepcion. This scenario also implies failure of Rio Yaqui, Sonora, and more southern populations to undergo substantial phenetic divergence, while over the same time period the northern group evolved a significant apomorphic body shape prior to its fragmentation. While elaborate ad hoc hypotheses are required to reconcile relationships patterns based on isozymes with those derived from morphology, or any probable geologic or geographic scenario, morphological relationships reflect geography and geology of the area. ------· 88 Mexican drainages north and west of Rio Sonora drain generally low-relief areas of coastal plain and subsiding, highly alluviated basin and range terrain, and at least in their lower reaches are little controlled by topography. This 1ow-rel i ef area extends northward i rdo the Gila and Bill Williams drainages. By contrast, more eastern and southern drainages occupied by the southern morphotype of Agosia are characterized by considerable relief and topographic control of the Basin and Range physiographic province structural, fault-bounded valleys of this region, continuous throughout the range of the southern morphotype, have been previously proposed as pathways of fish dispersal Other Fishes Unfortunately, a large data base of phylogenetic hypotheses for taxa broadly sympatric with Agosia, which could be used in a vicariance biogeography approach to the problem, does not presently exist. The single appropriate published hypothesis of fish relationships is that based on electrophoretic data of Vrijenhoek et al. (1985) for Poeciliopsis occidental is, which shares 6 basins with~. chrysogaster. f. occidental is is in all basins south of the Bill Williams that are also inhabited by~. chrysogaster, with the exception of Rio Sonoyta and those south of Rio Mayo. Morphologic relationships of populations of the latter are partly congruent with electrophoretic relationships of the former. Relationships of Rio Sonora populations off • occidental is 1 ie with those of more northern basins, while .. ·-··-··- --····- -·--·-··------···-----··---··. 89 morphological data for a. chrysogaster indicate that Rio Sonora populations are nearest those of the Rio Yaqui and more southern basins, but intermediate in some characters. Additionally, the Wagner NetworK of f. occidental is reveals a third group from the upper Rio Mayo that corresponds geographically to the Mayo/Fuerte group of a. chrysogaster, which is discernable both electrophoretically patterns indicated by its morphology. Morphologically, Agosia of Rio Mayo are nearer those of the Rio Yaqui than they are to the northern morph. As for other sites of contention between morphology and electrophoretic data on Agosia, f. occidental is data are uninformative. f. occidental is no longer occurs naturally in the Verde River or Coon CreeK, if in fact it ever did they were known from less than about 59 Km downstream from those sites>, and was never Known from the Rio Sonoyta or Bill Williams River comprehensible morphological affinities. Along with electrophoretic data on f. occidentalis, distributions of other fishes (for which there are no phyletic relationships hypotheses) are congruent with morphometrically indicated relationships ---~ ------90 patterns in a. chrysogaster. Although faunas of single basins may be depauperate, a. chrysogaster co-occurs with a diversity of other fishes throughout its range. Information on the native ichthyofauna was recently reviewed by Hinckley et al. (1986); but other works dealing with fish faunas, including exotics, in the range of a. chrysogaster are: Rutter, <1896); Snyder, 1915; MeeK, 1904; Hubbs and Hiller <1941); Miller <1945 1 1959 1 1960 1 1961, 1976); Miller and Simon, 1943; De Buen, 1947; Hiller and Winn, 1951; Hiller and Lowe <1964); Branson et al ., 1969; Barber and HincKley (1966); Contreras-Balderas, 1969; Alvarez, 1979; LaBounty and Hinckley <1972); Hinckley and Deacon, 1968; Deacon and Hinckley <1974); Hubbard (1977>; Angus <1989>; Kepner <1989, 1981>; Schreiber and Hinckley <1982>; Moore, 1984; Silvey et al. (1984); Propst et al. 1985; Hinckley <1973, 1985); Hendrickson (1984); Hendrickson et al ., 1981; Burr, 1976; Hendrickson <1984) 1 Schultz (1977>; Vrijenhoek <1984); and Hendrickson and Juarez Romero (in prep.). A basin-by-basin account of fishes taken with a. chrysogaster No single species shares the entire distribution of Aqosia chrysogaster, though some are broadly syrnpatric with it and provide biogeographical information. Among these are other Poecil iopsis taxa, diversity of which increases rapidly from the lower Rio Yaqui southward. If the many unisexual clones of Poeciliopsis that reproduce through hybridogenesis or gynogenesis are considered together, they occur in all Mexican basins occupied by Agosia with exception of Rio Sonoyta. In actuality, however, these represent a complex, but well studied, group of distinct clones, each of which has apparently 91 dispersed from independent origins in the rios Mayo and Fuerte. If a questionable Rio Sonora (Miller and Lowe, 1964) is valid, and if catfishes south of Rio Yaqui are considered synonymous with that form 1976; Hendrickson, 1984). Within~. ornatum, Burr (1976) concluded that •extreme and rather irregular variability from drainage to drainage• characterized the taxon, and recognized no subspecific groupings. Catostomus insignis and~· bernardini are a sister-species pair with distributions largely congruent with those of the northern and southern morphotypes, respectively, of a. chrysogaster, though catostomids are lacking from Rios Sonoyta and de la Concepcion. A single record of~. bernardini from Rio Sonora, as well as one of~· wigginsi from the Rio Yaqui basin, were judged invalid by VanDevender et al, <1985). If valid, those records would increase congruency of their distributions with B· chrysogaster morphs. Relationships of~. wigginsi are not clear, but Siebert and Hinckley <1986) who "cursorily examined" relationships of~. leopoldi and~· cahita from the Rios Yaqui and Mayo, mention it. Their proposal that "Catostomus leopoldi and~· cahita (and 1 ikely ~· wigginsi) represent rel lets or derivatives of an old regional fauna• seems to imply that relationships of the last are likely not with the~. bernardini complex. However, Robert R. Miller (in litt., 1/39/1987) groups~· wigginsi with~. bernardini and ~· insignis on the basis of 1 ip characteristics. Catostomus of this 92 region obviously are in need of further study. Another species, Gila purpurea, ties together three basins occupied by the southern morph and most arid basins Matape and Cocoraqui, as well as Willcox Playa) are those from which Gila robusta is absent. Other fishes which occur with a. chrysogaster are local endemics other Gila and Colorado River basin fishes, as well as Gila ditaenia and the remaining Catostomus species>, or represent peripheral populations of taxa more widely distributed elsewhere plebe ius, Notropis formosus, Rhinichthys osculus, Cichlasoma beani, and Gobiesox fluviatilis). ------CONCLUSIIJIIS Morphological differentiation ~~ng Agosia chrysogaster from different basins, and in particular between groups of basins occupied by the 2 morphs, was evident in all analyses of the morphometric and meristic data sets, and indicated by tuberculation patterns and spawning behaviour. Thus, hypothesis 1 of this study, that ther·e is morphological divergence among basins, is supported. It is recognized, however, that phenetic techniques may not be good indicators of phylogeny due to influences of convergence and variations in rate of divergence. Despite that fact, conclusions based on the morphometric analyses, and congruence with them of several other character sets, strongly support a phylogeny involving an early dichotomy in ancestral a. chrysogaster, which gave rise to what are now the 2 morphs. Subsequent to that split, 1 ineages isolated in independent hydrographic basins continued to diverge. In the southern morph, 2 closely-related, morphological lineages are indicated, one in the Willcox Playa, Sonora and Yaqui basins, and the other in the rios Mayo, Fuerte and Sinaloa. Evidence of morphologically-intermediate morphs in geographically-intermediate drainages may result from reticulation in the phylogeny, which in turn suggests hydrographic inter-connections between drainages and lack of genetic isolation. Zneimer <1986>, on the other hand, found no electrophoretic evidence for the morphological groups of a. chrrsogaster. Ad hoc hypotheses which explain electrophoretic relationships patterns derived by Zneimer <1986) are themselves not parsimonious, and become even less ----- ·---··--·------·------94 so if attempts are made to explain evolution of morphologies within the context of genetic relationships indicated by electrophoresis. Geologic history of the region fails to support any attempt to explain hypotheses developed by Zneimer. By contrast, hypotheses which address phenotypic evolution of the 2 morphs are direct, uncomplicated, and correlate well with physiography and geologic history of the region. That a multivariate measure of morphologic distance between samples was correlated with stream distances among them supports the second hypothesis of this study. However, distance along drainages (and coast! ines) between localities was correlated to a lesser degree with morphologic distance than was an index of hydrographic affiliation. Thus, hydrographic isolation of basins appears more important in influencing evolutionary direction than distance individuals would travel to achieve gene flow. This result probably reflects inability of&· chrysogaster to utilize marine corridors between basins. The third hypothesis was similarly supported. While morphologic distance along a multivariate axis, which provides high levels of discrimination between morphs and among basins, is correlated with latitude, longitude and elevation, high levels of variation surround the relationships. Highest correlation was that with latitude , and multiple correlation of both morph and latitude indicates the latter adds insignificantly to total variation. Latitude may be coincidentally correlated with morphology because the morphs occur north and south of one another. Similar correlations ------·-····------·· 95 exist among scores on Principal Components, which discriminate among morphs and latitude, longitude and elevation. The correlation of elevation with morphology appears to be largely a result of sampling bias. For the Gila River basin alone, however, where such sampling bias was not as pronounced, a weak relationship with elevation was found for size and H2. Finally, hypothesis 4 1 that all data sets would produce patterns congruent to that of the morphometric analyses, was supported by all forms of morphological data, as well as by distributions and relationships of other taxa, but not by electrophoretic analyses. The electrophoretic analyses on Agosia, however, produced relationships patterns more similar to those from isozyme studies of Poeciliopsis occidental is than to those derived from morphology of Agosia. Reasons for lack of agreement between isozyme and morphometric studies are unKnown, but may be related to analytical problems inherent with electrophoretic data and 1 imited sample size in that study. As noted before, morphology does not appear greatly influenced by ecology, and distribution and degree of differentiation of morphs fit classical criteria for subspecies, which presume underlying genetic causation. In 1 ight of all evidence, it seems unlikely that lack of congruence between morphologic and electrophoretic data relates to failure of the former to reflect phylogeny. Thus, as a result of varied tests of initial and subsequently formulated hypotheses, I conclude that B· chrysogaster consists of 2 readily-distinguishable, allopatric morphs. The fact that fishes of 2 geographically intermediate basins ---··-·--·- -·· .. 96 intermediate in body shape indicates incompleteness, or past breakdown, of hydrographic isolation, and implies an ability of the morphs to interbreed. Reasons for lack of intermediacy of morphology in Rio de la Concepcion, geographically intermediate between Rios Sonoyta and Sonora, are unknown. The morphs also display differences in lateral 1 ine scale count, nuptial tuberculation, degree of sexual dimorphism, and perhaps breeding behavior. Shape of~. chrYsogaster appears 1 ittle correlated with general indicators of ecological conditions such as latitude and elevation, but, at least in the Gila basin, varies temporally in the same ways that morphs differ from one another. Despite temporal variation, all samples can be readily assigned to morphotype, and often to basin of origin, on the basis of a small subset of morphometric characters. It is clear that description of subspecies would be justified solely on the basis of morphology and distributions; however, electrophoretic data produce largely incongruent patterns. Morphological phenetic dissimilarity might, therefore, be disproportionate to true genetic similarity, and perhaps the result of alterations in regulation of growth patterns determined by few genes. Discrepancies between morphologic and electrophoretic analyses thus confuse phylogenetic interpretations, and it remains unknown which data set, if either, is a more accurate reflection of the true phylogeny. Since it is my opinion that taxonomy should reflect phylogeny, decisions regarding taxonomic treatment of the morphs are deferred pending additional data on questions of genetic relatedness of the morphs and mechanisms determining morphology. REFERENCES Adams, E. N., III. 1972. Consensus techniques and the comparison of taxonomic trees. Syst. Zool ., 21:399-397. Albrecht, G. H. 1978. Some comments on the use of ratios. Syst. Zool., 27:67-71. Alvarez, J. 1979. Peces Mexicanos Angus, R. A. 1989. Geographic dispersal and clonal diversity in unisexual fish populations. Am. Nat., 115:531-559. Arnold, E. N. 1981. Estimating phylogenies at low taxonomic levels. Zeit. Zool. Syst. Evol., 19:1-35. Atchley, W. R., C. T. GasKins, and D. Anderson. 1976. Statistical properties of ratios. I. Empirical results. Syst. Zool., 25:137-148. Atchley, W. R., and D. Anderson. 1978. Ratios and the statistical analysis of biological data. Syst. Zool ., 27:71-78. Avise, J. C. 1974. Systematic value of electrophoretic data. Syst. Zool ., 23:465-481. Avise, J. C., and C. F. Aquadro. 1982. A comparative summary of genetic distances in the vertebrates: patterns and correlations. Evol. Biol., 15:151-185. Avise, J. C., and F. J. Ayala. 1976. Genetic differentiation in speciose versus depauperate phylads: evidence from the California minnows. Evolution, 39:46-58. Avise, J. C., and R. K. Selander. 1972. Evolutionary genetics of cave-dwelling fishes of the genus Astyanax. Evolution, 26:1-19. Avise, J. C., and M. H. Smith. 1977. Gene frequency comparisons between sunfish Ball, I. R. 1975. Nature and formulation of biogeographical hypotheses. Syst. Zool., 24:497-439. 98 Barber, W. E., and W. L. Hinckley, 1966. Fishes of Aravaipa Creek, Grah~ and Pinal counties, Arizona. SW. Nat., 11:313-324. Barbour, C. D., and R. R. Miller. 1978. A revision of the Mexican cyprinid fish genus Algansea. Misc. Publs. Mus. Zool, Univ. Mi c h . , 155: 1-72. Blackith, R. E., R. A. Reyment, and N. A. Campbell, 1984. Multivariate Morphometries, 2nd edition. Academic Press, New York. Bookstein, F. L., B. c. Chernoff, R. L. Elder, J. M. Humphries, G. R. Smith, and R. E. Strauss. 1985. Morphometries in Evolutionary Biology, Spec. Publ. 15, Acad. Nat. Sci. Phil. Branson, B. A., C. J. McCoy, Jr., and M. E. Sisk. 1969. Notes on the freshwater fishes of Sonora, with an addition to the known fauna. Copeia, 1969:217-229. Burr, B. M. 1976. A review of the Mexican Stoneroller, Campostoma ornatum Girard Buth, D. G. 1984a. Allozymes of the cyprinid fishes; variation and application. Pages 561-589 ln: Evolutionary Genetics of Fishes. Buth, D. G. and B. M. Burr. 1978. Isozyme variability in the cyprinid genus Campostoma. Copeia, 1979:298-311. Chernoff, B. 1982. Character variation among populations and the analysis of biogeography. Am. Zool., 22:425-449. Chernoff, B., and R. R. Miller. 1981. Systematics and variation of the Aztec Shiner, Notropis sal lei, a cyprinid fish from Central Mexico. Proc. Biol. Soc. Coad, B. W. 1976. On the intergeneric relationships of North American and certain Eurasian cyprinid fishes Colless, D. H. 1988. Congruence between morphometric and allozyme data for Menidia species: A reappraisal. Syst. Zool ., 29:288-299. Collins, J.P., C. Young, J. Howell, and W. L. Hinckley, 1981. Impact of flooding in a Sonoran Desert stream, including elimination of an endangered fish population Cope, E. D., and H. C. Yarrow. 1875. Report upon the collections of fishes made in portions of Nevada, Utah, Colorado, New Mexico, and Arizona, during the years 1871, 1872, 1873, and 1874, Report of the Geographical and Geological Explorations and Surveys West of the 199th Meridian Cracraft, J, 1975. Historical biogeography and earth history: perspectives for a future synthesis. An. Miss. Bot. Gard., 62:227-258. Craw, R. C., and P. Weston. 1984. Panbiogeography: A progressive research program? Syst. Zool ., 33:1-13. Cross, J. N. 1985. Distribution of fish in the Virgin River, a tributary of the lower Colorado River. Environ. Biol. Fish, 12: 13-21 • Crowson, R. A. 1979. Classification and Biology, Aldine Publishing Company, Chicago. Deacon, J. E., and W. L. Hinckley. 1974. Desert Fishes. Pages 385-488 la: Desert Biology, Volume 2. ---··-···--·------·-·· 100 Echelle, A. A., and D. T. Mosier. 1981. All-female fish: a cryptic species of Menidia. Science, 212:1411-1413. Echelle, A. A., and D. T. Mosier. 1982. Menidia c1arKhubbsi 1 n. sp. Endler, J. A. 1982b. Problems in distinguishing historical from ecological factors in biogeography. Am. Zool ., 22:441-452. Endler, J. A. 1983. Testing causal hypotheses in the study of geographic variatiqn. Pages 424-443 ln: Numerical Taxonomy. (J. Felsenstein, ed.). Proceedings of the NATO Advanced Study Institute on Numerical Taxonomy, Bad Windsheim, Germany, 1982. Springer-verlag, Berlin. Evermann, B. w., and C. Rutter. 1895. The fishes of the Colorado basin. Bul. U.S. Fish Com., 14:473-486. Farris, J. S. 1979. Methods of computing Wagner Trees. Syst. Zool ., 19:83-92. Farris, J. S. 1972. Estimating phylogenetic trees from distance matrices. Am. Nat., 196:645-668. Farris, J. S. 1981. Distance data in phylogenetic analysis. Pages 3-23 In: Advances in Cladistics: Proceedings of the first meeting of the Willi Hennig Society. ------·--·--· 101 Fisher, S. G., L. J. Gray, N. B. Grimm, and D. E. Busch. 1982. Temporal succession in a desert stream following flash flooding. Ecological Monongraphs, 52:93-110. Fitch, W. M. and E. Margol iash. 1967. Construction of phylogenetic trees. Science, 155:279-284. Girard, C. 1856. Researches upon the cyprinoid fishes inhabiting the fresh waters of the United States of America, west of the Mississippi Valley, from specimens in the museum of the Smithsonian Institution. Proc. Acad. Nat. Sci. Phila., 8:165-213. Girard, C. 1859. Ichthyology of the Boundary. Pages 1-85 in: Report of the United States and Mexican Boundary Survey, made under the direction of the Secretary of the Interior, Volume 3, Grudzien, T. A., and B. J. Turner. 1983. Biochemical systematics of Allodontichthys: A genus of goodeid fishes. Biochem. Syst. Ecol ., 11:383-388. Grudzien, T. A., and B. J. Turner. 1984a. Direct evidence that the Ilyodon morphs are a single biological species. Evolution, 38:492-407. Grudzien, T. A., and B. J. Turner. 1984b. Genic identity and geographic differentiation in trophically dichotomous Ilyodon Hendrickson, D. A., W. L. Hinckley, R. R. Miller, D. J. Siebert, and P. H. Hinckley. 1981. Fishes of the Rio Yaqui Basin, Mexico and United States. J. Ariz.-Nev. Acad. Sci., 15:65-196. Hills, M. 1978. On ratios-- a response to Atchley, Gaskins and Anderson. Syst. Zool., 27:61-62. ~~~~ -~~ ------~~~ ----~- ~~-~ 102 Hoffman, G. L. 1958. Experimental studies on the Cercaria and Metacercaria of a Strigeoid Trematode, Posthodiplostomum minimum. Exper. Parasit., 7:23-59. Hoffman, G. L., and J. A. Hutcheson. 1979. Unusual pathogenicity of a commmon metacercaria of fish. J. Wildl. Dis., 6:199. Hopkirk, J. D. 1973. Endemism in Fishes of the Clear Lake Region. Univ. Cal if. Publ. Zool., 96:1-161L H~».~es, G. 1984. Phyletics and biogeography of the aspinine cyprirlid fishes. Bul. Brit. Mus. Nat. Hist. and loadings on the sheared components are as follows: