Regressions for Estimating Gastropod Biomass with Multiple Shell Metrics Author(s): Adam Obaza & Clifton B. Ruehl Source: Malacologia, 56(1–2):343-349. 2013. Published By: Institute of Malacology URL: http://www.bioone.org/doi/full/10.4002/040.056.0224

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REGRESSIONS FOR ESTIMATING GASTROPOD BIOMASS WITH MULTIPLE SHELL METRICS

Adam Obaza1,2* & Clifton B. Ruehl1,3*

INTRODUCTION power and provide more accurate biomass es- timates for snails because they exhibit a diver- Snails are among the most important primary sity of shapes. Comparisons among possible consumers in freshwater ecosystems. They eat regression models may reveal that different large amounts of periphyton, facilitate nutrient metrics or combinations of metrics are better regeneration for the resources they consume, predictors of a particular mass measure for a and in ecosystems with greater than two trophic given group (e.g., AFDM vs. wet mass). OHYHOVVQDLOVDUHDYLWDOFRQGXLWIRUHQHUJ\ÀRZ In this study, we consider three common, to upper trophic levels by serving as prey to nu- structurally diverse freshwater snail genera merous invertebrate and vertebrate predators , Pomacea and Haitia to examine (Dillon, 2000). Estimates of individual biomass the utility of using multiple length measures to (mass/individual) enable calculations of stand- predict multiple soft-tissue mass measures. ing stock (mass/area) and production (mass/ Planorbella () are pulmonate snails area/time). These measures are superior to with planispiral shells that grow sinistrally (left GHQVLW\ QRDUHD IRUDVVHVVLQJWKHLQÀXHQFH handed). Haitia (Physidae) are small pulmo- of on communities and ecosystems nates with a sinistrally growing conispiral shell. because they incorporate size-structured Pomacea (Ampulariidae) are large caenogas- DVSHFWVRIHQHUJ\ÀRZ 5HJHVWHUHWDO tropods that have globose, conispiral shells Rosas-Luis et al., 2008). that are generally dextral (right handed) with Length-mass regressions enable quick DQRSHUFXOXP$GGLWLRQDOO\ZHUHSRUWWKH¿UVW estimation of individual biomass to assist length-to-mass regression for 3RPDFHDÀDJHO- estimating standing stock and production. lata Say, 1827. Regressions provide mass estimates without VDFUL¿FLQJDQLPDOVZKLFKPD\QRWEHIHDVLEOH for protected taxa or desirable because repeat- METHODS edly sampling the same population can cause bias (Cahill et al., 2002). Obtaining biomass We collected P. duryi Wetherby, 1879 data from preserved specimens is facilitated ±PPVKHOOOHQJWKn = 89) and H. by regressions because length is a relatively cubensis 3IHLIIHU  ± PP VKHOO stable measure compared to mass (Wetzel et length, n = 30) from populations maintained al., 2005). However, historically most studies of at the Daniel Beard Research Center in Ev- freshwater snails report density without mea- erglades National Park. These populations VXUHVRIELRPDVV *DUQHU +DJJHUW\ originated from collections made throughout Ruehl & Trexler, 2011). Among those studies the Everglades and were supplemented an- that report biomass data, few report regres- nually with wild-caught individuals. Pomacea sions that include more than one measure of paludosa 6D\ ±PPn = 19) length (e.g., shell length or width) or mass (e.g., were obtained from live-caught animals and wet mass or ash-free dry mass, a measure of their offspring. Pomacea paludosa sample size organic content) and rarely combine multiple was comparatively small, but we believe it is measures of length to improve mass estimates VXI¿FLHQWIRURXUSXUSRVHEHFDXVHSUHOLPLQDU\ HJ(FNEODG%RHUJHU&ROOLQV UHJUHVVLRQVLQGLFDWHGWKDWPRGHO¿WZDVYHU\ %HQNHHWDO*RQ]iOH]HWDO good. 3RPDFHD ÀDJHOODWD ± PP n = Deichmann et al., 2008). Combining multiple 49) were collected from Mexico (Sian Kaan, length measures should improve predictive Quitana Roo, 19.20°N, 87.89°W) and Belize

1Department of Biological Science, Florida International University, 3000 NE 151st Street, North Miami, Florida 33181, U.S.A. 2Ocean Associates, Inc., 501 W. Ocean Blvd, Suite 4200, Long Beach, California 90802, U.S.A. 3Department of Biology, Columbus State University, Columbus, Georgia 31907, U.S.A. *Corresponding author: [email protected]

343 344 OBAZA & RUEHL

FIG. 1. Graphical description of how aperture width and length, and shell length were mea- sured P. duryi. Shell length is the lateral distance from anterior to posterior, aperture length is the distance across the aperture from anterior to posterior, aperture width is the length across the aperture at its widest point using calipers to 0.01 FIG. 3. Graphical description of how aperture and PP6FDOHEDU PP width, length, and shell length were measured for P. paludosa and 3ÀDJHOODWD. Shell length is the lateral distance from anterior to pos- terior, aperture length is the distance across the &UDE&DWFKHUODJRRQ2UDQJH:DONƒ1 aperture from anterior to posterior, aperture width ƒ: )DFLOLWLHVZHUHQRWDYDLODEOHWRJHW is the length across the aperture at its widest point dry and ash mass of 3 ÀDJHOODWD. All snails and opercula length and width that correspond with aperture length and width measurements ZHUHVDFUL¿FHGE\IUHH]LQJIRUK 1LHOVHQ  using calipers to 0.01 mm. Scale bar = 10 mm. Gosselin, 2011). Shell measurements were made to the near- est 0.01 mm with calipers and weighed to the furnace and reweighed. We subtracted the nearest 0.0001 g. Shell length and aperture ashed mass from the dried mass to calculate width and length were measured on Planorbella AFDM. (Fig. 1) and Haitia (Fig. 2). We measured shell We quantified the capacity for multiple length, aperture width and length as well as length measures to predict mass compared operculum width and length on P. paludosa to single measures using a model selection (Fig. 3). After measurements, the soft tissue procedure with regression. Regressions were was separated from the shell with forceps. Soft used to determine relationships between mass tissue and shell were weighed and then dried (wet, dry, and AFDM) and shell size (length, DWƒ&WRDFRQVWDQWPDVV'ULHGVRIWWLVVXH width, operculum length, operculum width). shell, and opercula were weighed and then :HWHVWHGDOOPHWULFFRPELQDWLRQVWR¿QGWKH FRPEXVWHGDWƒ&IRUIRXUKRXUVLQDPXIÀH best model for each measure of mass for each . Models were compared using the information-theoretic approach proposed by Burnham & Anderson (2002). Each model was ranked relative to the others using second order Akaike’s Information Criterion for small sample sizes (AICc) where the lowest value LQGLFDWHG WKH EHVW ¿W7KH$,&c calculation adds another parameter to the AIC formula WKDWIXUWKHUSHQDOL]HVPRGHO¿WIRULQFOXGLQJ more independent variables. Models were considered equal if the difference between FIG. 2. Graphical description of how aperture the calculated AICc value and the lowest AICc width and length, and shell length were measured YDOXHIRUHDFKGDWDVHWZDV” &RPSWRQHW for H. cubensis. Shell length is the lateral distance al., 2002). Model weights facilitated better from anterior to posterior, aperture length is the distance across the aperture from anterior to UHVROXWLRQRIPRGHOVZLWK$,&FYDOXHV”'DWD posterior, and aperture width is the length across were natural-log (ln) transformed because a the aperture at its widest point using calipers to plot of mass by length suggested a power 0.01 mm. Scale bar = 3 mm. relationship. BIOMASS FROM MULTIPLE LENGTH METRICS 345

RESULTS AND DISCUSSION measurements changed depending on the mass measurement, but always included The information-theoretic approach revealed shell length. Wet mass was predicted best by that in many cases, multiple measures of shell shell length and aperture length or width for morphology predicted tissue mass better than P. duryi (Table 1). Similarly, a combination of single shell measurements. Model weights, the shell length and aperture width, or these and relative probability of model accuracy, indicated aperture length, predicted wet mass best in that inclusion of a length and width parameter H. cubensis. However, models that included provided more robust models (Table 1). Even only shell length and aperture width predicted ZKHQWKHǻ$,&FYDOXHVIRUPRGHOVZLWKRQO\ dry mass best for P. duryi, while shell length one parameter were low, the model weight with aperture length best predicted dry mass was correspondingly low meaning that it was in H. cubensis. Finally, a combination of shell unlikely that single parameter models provided length and aperture width best predicted AFDM WKHEHVW¿W,QFOXVLRQRIH[WUDSDUDPHWHUVDOVR for both P. duryi and H cubensis. Therefore, increased the R2 value (Table 2). For the two regardless of mass measurement, we recom- pulmonate species, the best combination of mend gathering data on shell length and ap-

TABLE 1. Lowest AIC values out of all possible model variations including shell length (SL), aperture width (AW), aperture length (AL), operculum length (OpL) and operculum width (OpW) for each species DQGPDVVPHDVXUH0XOWLSOHPRGHOVDUHLQFOXGHGLIǻ$,&”0RGHOZHLJKWLVWKHUHODWLYHOLNHOLKRRG DJLYHQPRGHOSURYLGHVWKHEHVW¿W

Species Mass Measure Parameters ǻ$,&F Model Weight

P. duryi Wet SL, AW, AL 0  Wet SL, AL 2.12 0.22 Dry SL, AW 0  Dry SL, AW, AL 2.21 0.2 AFDM SL, AW 0  AFDM SL, AW, AL 2.28 0.2 H. cubensis Wet SL, AW 0 0.71 Wet SL, AW, AL 1.91 0.27 Dry SL, AL 0  Dry SL, AL, AW 2.4 0.2 AFDM SL, AW 0 0.3 AFDM SL  0.28 AFDM SL, AL 0.35 0.25 AFDM SL, AW, AL  0.13 P. paludosa Wet OpL 0  Wet AL, OpL 2.4 0.11 Dry AW, OpL 0  Dry OpL 1.31 0.13 Dry AW, AL 1.39 0.13 AFDM AW, OpL 0 0.35 AFDM OpL  0.09  OBAZA & RUEHL

TABLE 2. Top two regression equations as selected by AIC and the equation for shell length (SL) to provide a comparison with the exception of H. cubensis AFDM where SL was one of the top two regression equations. Regressions are of transformed SL, aperture width (AW), and length (AL) and operculum width (OpW) and length (OpL) to ln transformed wet mass, dry mass and AFDM for P. duryi (n = 89), P. paludosa (n = 19) and H. cubensis (n = 30).

Mass P. duryi P. paludosa H. cubensis

Wet 6/$:$/ 3.09 OpL - 7.97 6/$: R2 = 0.87 R2 = 0.98 R2 = 0.73 6/$/ $/2S/ 6/$:$/ R2  R2 = 0.98 R2 = 0.73 6/ 2.85 SL - 8.33 2.83 SL - 9.34 R2 = 0.84 R2 = 0.97 R2  Dry 6/$: $:2S/ 6/$/ R2 = 0.81 R2 = 0.92 R2  6/$:$/ 2.89 OpL - 9.01 6/$:$/ R2 = 0.80 R2 = 0.91 R2  6/ 6/ 3.13 SL - 12.18 R2 = 0.80 R2 = 0.89 R2  AFDM 6/$: $:2S/ 6/$: R2  R2  R2 = 0.5 6/$:$/ 2S/ 2.44 SL - 11.05 R2  R2 = 0.95 R2 = 0.49 2.48 SL - 10.57 2.80 SL -10.08 R2  R2 = 0.93 erture width for species that are shaped like P. by adding variability. For example, tissue mass duryi or H. cubensis, and adding the aperture within a globose shell may weigh the same as length measure to increase accuracy. Adding tissue from a longer shell but not be consistent this extra measure requires little effort but pro- with the relationship between the two estab- vides three-dimensional information on shell lished by the regression. A similar case might shape and improves biomass estimates. exist if more resources were allocated to shell Presence of predators and variable nutrient thickness than tissue growth. Caution should be concentrations often alter shape and life history exercised when applying these regressions to WUDLWVWKDWPD\LQÀXHQFHOHQJWKPDVVUHJUHV- samples taken in areas with only one predator sions. Predators induce different shell shapes, type or during extremes in resource availability shell thickness, and life history traits in both (e.g., eutrophication, drought). Despite this SK\VLGDQGSODQRUELGVQDLOV 'H:LWWHWDO limitation, these general regressions are appli- +RYHUPDQHWDO$XOG 5HO\HD cable for studies calculating energy budgets for Ruehl & Trexler, 2013). Differential allocation HFRV\VWHPVRUHQHUJ\ÀRZLQIRRGZHEV of resources represents a tradeoff with repro- Comparing regressions for P. paludosa ductive effort and is situation dependent with a revealed that operculum length alone or com- size limited predator: in times of low resources, bined with aperture width or length yielded individuals will mature early and risk predation the lowest AICc for all mass measures. While to reproduce quickly, while in times of abundant all three models were equivalent according resources individuals will attempt to grow to a to the AICc value (Table 1), model weights VL]HUHIXJHEHIRUHUHSURGXFLQJ &KDVH LQGLFDWHG2S/KDGWKHEHVW¿WIRUZHWPDVV Crowl & Covich, 1990). Snails that differentially 2S/ DQG$: JDYH WKH EHVW ¿W IRU GU\ PDVV allocate resources or induce shape variation and AFDM. Therefore, for two of the metrics PD\DIIHFWWKH¿WRIOHQJWKZHLJKWUHJUHVVLRQV multiple measures were the best predictors. BIOMASS FROM MULTIPLE LENGTH METRICS 347

Some Pomacea species have shown sexual The error structure in a non-linear model is dimorphism (Cazzaniga, 1990) that may have assumed to be normal and additive while error affected the accuracy of our regressions. How- structure in a log-transformed linear model is ever, the reported R2 values were higher than assumed to be lognormally distributed and multi- those found in the literature: Sykes (1987) and plicative (Xiao et al., 2011). While there is some Cattau et al. (2010) documented a R2 of 0.75 debate as to which error structure is most realis- and Bourne & Berlin (1982) found a maximum tic for biological studies, use of log-transformed, R2RI7KHUHJUHVVLRQVIURPWKLVVWXG\PD\ multiplicative error structures have been found bias results if estimating mass for one gender, WREHPRUHUHOLDEOH .HUNKRII (QTXLVW EXWWKLVVFHQDULRLVQRWOLNHO\IRU¿HOGFROOHFWLRQV ;LDRHWDO 7KHUHIRUHZHDUHFRQ¿GHQW because even though brood sex ratios are in our use of log-transformed data. highly variable in Pomacea the population sex Few gastropod studies report length-mass ratio is not (Yusa & Suzuki, 2002). regressions for wet mass, dry mass and Youens & Burks (2008) found similar results AFDM together (but see Collins, 1992), but to our P. paludosa regressions when comparing studies that use biomass report data using wet mass to shell height and shell length (they each of the three measures. We report all referred to our operculum length as operculum three mass measures to facilitate application width). They agreed with Guedes et al. (1981) of the technique and because each measure that operculum length is analogous to the base potentially conveys different information. Wet of an elaborate shell and therefore represents mass provides an estimate of the live mass of the most reliable measure of wet mass. Another the and is probably most useful when possible explanation is that because the oper- comparing among closely related taxa that culum grows from the tissue, it is more likely to have similar shapes. Dry mass includes both be indicative of body mass. Use of operculum organic and inorganic matter in estimates and OHQJWKIRUPDVVHVWLPDWLRQKDVDQFLOODU\EHQH¿WV could be reported instead of wet mass when For example, intact opercula are easily retrieved comparing among taxa that differ greatly in IURP JXW FRQWHQWV RI PROOXVFLYRUHV D UHJUHV- the water content of their tissue. Ash-free dry sion that predicts mass from operculum length mass reveals the organic content of tissue, provides an estimate of energy transfer through which is an indicator of the differential alloca- the food web and offers potential insight into size- tion of resources between hard and soft tissues selective predation by different molluscivores within an individual or among taxa. Therefore, +XOVH\HWDO $GGLWLRQDOO\RSHUFXODDUH depending on the scope and level of taxonomic occasionally found in the fossil record and could comparison, researchers might report different provide estimates of standing stock for snails in forms of mass measurements, but reporting all an ecosystem from the past (Martín & Francesco, three regressions will enable the conversion of  $SHUWXUHDQGRSHUFXOXPVL]HDUHXQGRXEW- one to the other for meta-analytic purposes. edly related and possibly redundant as factors, Because snails exhibit a wide diversity of however our results show the value of including form, one single measurement is unlikely these parameters in our analysis. Models of best to be adequate for all taxa. To address this ¿WIRUDOOWKUHHPDVVPHDVXUHVLQFOXGHERWKRSHU- challenge, we recommend reporting multiple culum and aperture measurements. In addition, length measures that will improve comparisons aperture and operculum length are the only pa- among studies by increasing consistency and rameters in one of the wet mass models. Because accuracy. Furthermore, we suggest research to the AIC method penalizes additional parameters, examine the accuracy of these regressions to these models would not have had low AIC scores different species within genera to aid in deter- unless both were necessary. Therefore, we felt mining the extent of their applicability. Finally, the inclusion of both aperture and operculum using multiple length measures simultane- measurements was important. ously to predict biomass offers more accurate Only shell length and wet mass measures and precise estimates of snail mass to better were available for P. ÀDJHOODWD (y = 2.593x - SUHGLFWWKHLQÀXHQFHRIVQDLOVRQFRPPXQLWLHV 7.923, R2 = 0.83). We include this regression and ecosystems. We propose this study as EHFDXVH LW LV WKH ¿UVW UHSRUWHG OHQJWKPDVV D ¿UVW VWHS WRZDUGV HQFRXUDJLQJ WKH XVH RI relationship for this species. Though we do multiple measures of shell length for predict- not have the same depth of information for this ing biomass that will facilitate estimates of species as the others, the information we have standing stock and production in ecosystems reported will aid future studies on this species IRUJUHDWHUXQGHUVWDQGLQJRIHQHUJ\ÀRZDQG and the ecosystems where it lives. ecosystem function. 348 OBAZA & RUEHL

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