A hierarchical Bayesian approach for estimating freshwater mussel growth based on tag-recapture data

Abstract In fisheries stock assessment and management, the von Bertalanffy growth model is commonly used to describe individual growth of many species by fitting age-at-length data. However, it is difficult or impossible to determine accurate individual ages in some cases. Mark-recapture survey becomes an alternative choice to collect individual growth information. In mark-recapture studies, some tagged animals can be recaptured more than one time and ignorance of the autocorrelations for each individual may result in substantial biases in estimations of growth parameters. To investigate the existence of individual and sex variability in growth, we designed an experiment to collect mark-recapture data for one endangered freshwater mussel species ( Epioblasma capsaeformis ) and one common, non-imperiled species ( Actinonaias pectorosa ) by using a passive integrated transponder (PIT) technique. Models with individual and sex variability (M1), sex-related differences (M2), individual variability (M3) and nonhierarchy (M4) were developed to estimate growth of E. capsaeformis and A. pectorosa . Deviance information criterion (DIC) was used to measure the performance of these models. For E. capsaeformis , female mussels tended to have higher means of asymptotic length (44.96 mm) and growth rate coefficient (0.283/year) than males (42.18 mm and 0.213/year). The model M3 yielded the lowest DIC value for both species, indicating individual differences should be considered in parameter estimation. Thus, we suggest that a hierarchical approach be used to consider individual variability for modeling growth of mussels with mark-recapture data, especially when there is a high percentage of multiple recaptures.

[1]  R. Johnson.  Systematics and zoogeography of Plagiola (= Dysnomia = Epioblasma), an almost extinct genus of freshwater mussles (Bivalvia: Unionidae) from Middle North America , 1978 .

[2]  Fabens Aj,et al.  Properties and fitting of the Von Bertalanffy growth curve. , 1965 .

[3]  J. Downing,et al.  Length‐specific growth rates in freshwater mussels (Bivalvia: Unionidae): extreme longevity or generalized growth cessation? , 2001 .

[4]  C. Walters,et al.  Quantitative fisheries stock assessment: Choice, dynamics and uncertainty , 2004, Reviews in Fish Biology and Fisheries.

[5]  Terrance J. Quinn,et al.  Quantitative Fish Dynamics , 1999 .

[6]  S. A. Ahlstedt,et al.  Status of aquatic mollusks in the southeastern United States: a downward spiral of diversity , 1997 .

[7]  J. Downing,et al.  Molluscan shell growth and loss , 1993, Nature.

[8]  Stephen G. Walker,et al.  An improved method for estimating individual growth variability in fish, and the correlation between von Bertalanffy growth parameters , 2002 .

[9]  S. R. Kerr,et al.  Bioenergetic analysis of the effects of temperature and prey availability on growth and condition of northern cod (Gadus morhua) , 1997 .

[10]  Y. Jiao,et al.  Models and model selection uncertainty in estimating growth rates of endangered freshwater mussel populations , 2008 .

[11]  A. C. Miller,et al.  Empirically Derived Survival Rates of a Native Mussel, Amblema plicata, in the Mississippi and Otter Tail Rivers, Minnesota , 2001 .

[12]  L. Bertalanffy,et al.  A quantitative theory of organic growth , 1938 .

[13]  S. Balle,et al.  Individual growth pattern and variability in Serranus scriba: a Bayesian analysis , 2010 .

[14]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[15]  Ian James,et al.  Estimation of von Bertalanffy growth curve parameters from recapture data , 1991 .

[16]  J. Rhymer,et al.  PIT tags increase effectiveness of freshwater mussel recaptures , 2007, Journal of the North American Benthological Society.

[17]  Eric P. Smith,et al.  Model Selection Uncertainty and Bayesian Model Averaging in Fisheries Recruitment Modeling , 2009 .

[18]  Brian Dennis,et al.  Estimation of Growth and Extinction Parameters for Endangered Species , 1991 .

[19]  R. Hilborn,et al.  Fisheries stock assessment and decision analysis: the Bayesian approach , 1997, Reviews in Fish Biology and Fisheries.

[20]  You‐Gan Wang,et al.  A maximum likelihood approach for estimating growth from tag–recapture data , 1995 .

[21]  R. Arlinghaus,et al.  Documented and Potential Biological Impacts of Recreational Fishing: Insights for Management and Conservation , 2006 .

[22]  C. R. Fisher,et al.  Effects of intrapopulation variability on von Bertalanffy growth parameter estimates from equal mark-recapture intervals , 1997 .

[23]  Brian T. Watson,et al.  Life history and population biology of the endangered tan riffleshell (Epioblasma florentina walkeri) (Bivalvia: Unionidae) , 2001, Journal of the North American Benthological Society.

[24]  Keith Sainsbury,et al.  Effect of Individual Variability on the von Bertalanffy Growth Equation , 1980 .

[25]  Kevin S. Cummings,et al.  Conservation Status of Freshwater Mussels of the United States and Canada , 1993 .

[26]  D. Kimura.  Extending the von Bertalanffy growth model using explanatory variables , 2008 .

[27]  W. Cope,et al.  Evaluation of freshwater mussel relocation as a conservation and management strategy , 1995 .

[28]  Y. Jiao,et al.  Incorporating temporal variation in the growth of red abalone (Haliotis rufescens) using hierarchical Bayesian growth models , 2010 .

[29]  Daniel Pauly,et al.  Systematic distortions in world fisheries catch trends , 2001, Nature.

[30]  R. D. Stanley,et al.  Hierarchical Bayesian estimation of recruitment parameters and reference points for Pacific rockfishes (Sebastes spp.) under alternative assumptions about the stock–recruit function , 2010 .

[31]  Jess W. Jones,et al.  A HOLISTIC APPROACH TO TAXONOMIC EVALUATION OF TWO CLOSELY RELATED ENDANGERED FRESHWATER MUSSEL SPECIES, THE OYSTER MUSSEL EPIOBLASMA CAPSAEFORMIS AND TAN RIFFLESHELL EPIOBLASMA FLORENTINA WALKERI (BIVALVIA: UNIONIDAE) , 2006 .

[32]  K. Andrews,et al.  PIT Tagging: Simple Technology at Its Best , 2004 .

[33]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[34]  Malcolm Haddon,et al.  Modelling and quantitative methods in fisheries , 2001 .

[35]  Jess W. Jones,et al.  Influence of life-history variation on demographic responses of three freshwater mussel species (Bivalvia: Unionidae) in the Clinch River, USA , 2011 .

[36]  Jennifer Scott.  Population demographics of six freshwater mussel species (Bivalvia : Unionidae) in the upper Clinch river, Virginia and Tennessee , 1994 .

[37]  E. Deboer,et al.  An Analysis of Two Methods of Fitting the von Bertalanffy Curve to Capture-Recapture Data , 1988 .

[38]  David R. Smith,et al.  Estimating Survival and Recruitment in a Freshwater Mussel Population Using Mark-recapture Techniques , 2004 .

[39]  Thomas E. Helser,et al.  A Bayesian hierarchical meta-analysis of fish growth: with an example for North American largemouth bass, Micropterus salmoides , 2004 .

[40]  Alan Campbell,et al.  Use of Bayesian hierarchical models to estimate northern abalone, Haliotis kamtschatkana, growth parameters from tag-recapture data , 2009 .

[41]  K. Drinkwater,et al.  Density-versus temperature-dependent growth of Atlantic cod (Gadus morhua) in the Gulf of St. Lawrence and on the Scotian Shelf , 2003 .

[42]  G. Laslett,et al.  Consequences of assuming an incorrect error structure in von Bertalanffy growth models: a simulation study , 2007 .

[43]  A. Gelman.  Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) , 2004 .

[44]  R. Neves,et al.  Evaluation of Techniques for Age determination of Fresh water Mussels (Unionidae) , 1988 .

[45]  J. Ragle,et al.  IUCN Red List of Threatened Species , 2010 .

[46]  W. Ponder,et al.  The Global Decline of Nonmarine Mollusks , 2004 .