Trends in Growth Modeling in Fisheries Science
Abstract
:1. Introduction
2. Results
2.1. Peer-Reviewed Studies
2.1.1. Growth Modeling
2.1.2. Multi-Model Framework Studies
2.1.3. Multi-Model Non-VBGM Studies
2.1.4. Model Selection
2.2. Stock Assessments
3. Discussion
3.1. Growth Modeling
3.2. Model Selection
3.3. Stock Assessments
4. Materials and Methods
4.1. Peer-Reviewed Literature
4.2. Stock Assessments
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
References
- Pauly, D. On the interrelationships between natural mortality, growth parameters and mean environmental temperature in 175 fish stocks. J. Cons. Int. Explor. Mer. 1980, 39, 175–192. [Google Scholar] [CrossRef]
- Gislason, H.; Daan, N.; Rice, J.C.; Pope, J.G. Size, growth, temperature and the natural mortality of marine fish. Fish Fish. 2010, 11, 149–158. [Google Scholar] [CrossRef]
- Hixon, M.A.; Johnson, D.W.; Sogard, S.M. BOFFFFs: On the importance of conserving old-growth age structure in fishery populations. ICES J. Mar. Sci. 2013, 71, 2171–2185. [Google Scholar] [CrossRef] [Green Version]
- Smart, J.J.; Chin, A.; Tobin, A.J.; Simpendorfer, C.A. Multimodel approaches in shark and ray growth studies: Strengths, weaknesses and the future. Fish Fish. 2016, 17, 955–971. [Google Scholar] [CrossRef]
- Zhu, L.; Li, L.; Liang, Z. Comparison of six statistical approaches in the selection of appropriate fish growth models. Chin. J. Oceanogr. Limnol. 2009, 27, 457–467. [Google Scholar] [CrossRef]
- Lauerburg, R.A.; Temming, A.; Pinnegar, J.K.; Kotterba, P.; Sell, A.F.; Kempf, A.; Floeter, J. Forage fish control population dynamics of North Sea whiting Merlangius merlangus. Mar. Ecol. Prog. Ser. 2018, 594, 213–230. [Google Scholar] [CrossRef]
- Matthias, B.G.; Ahrens, R.N.; Allen, M.S.; Tuten, T.; Siders, Z.A.; Wilson, K.L. Understanding the effects of density and environmental variability on the process of fish growth. Fish. Res. 2018, 198, 209–219. [Google Scholar] [CrossRef]
- DeVries, D.A.; Grimes, C.B. Spatial and temporal variation in age and growth of king mackerel, Scomberomorus cavalla, 1977–1992. Fish. B-NOAA 1997, 95, 694–708. [Google Scholar]
- Helser, T.E.; Lai, H.L. A Bayesian hierarchical meta-analysis of fish growth: With an example for North American largemouth bass, Micropterus salmoides. Ecol. Model. 2004, 178, 399–416. [Google Scholar] [CrossRef]
- Midway, S.R.; Wagner, T.; Arnott, S.A.; Biondo, P.; Martinez-Andrade, F.; Wadsworth, T.F. Spatial and temporal variability in growth of southern flounder (Paralichthys lethostigma). Fish. Res. 2015, 167, 323–332. [Google Scholar] [CrossRef]
- Nieland, D.L.; Thomas, R.G.; Wilson, C.A. Age, Growth, and Reproduction of Spotted Seatrout in Barataria Bay, Louisiana. Trans. Am. Fish. Soc. 2002, 131, 245–259. [Google Scholar] [CrossRef]
- Curtis, T.D.; Shima, J.S. Geographic and sex-specific variation in growth of yellow-eyed mullet, Aldrichetta forsteri, from estuaries around New Zealand. N. Z. J. Mar. Fresh. 2005, 39, 1277–1285. [Google Scholar] [CrossRef]
- Chen, Y.; Jackson, D.A.; Harvey, H.H. A comparison of von Bertalanffy and polynomial functions in modelling fish growth data. Can. J. Fish. Aquat. Sci. 1992, 49, 1228–1235. [Google Scholar] [CrossRef]
- Bolker, B.M. Ecological Models and Data in R; Princeton University Press: Princeton, NJ, USA, 2009. [Google Scholar]
- Beverton, R.J.H.; Holt, S.J. On the Dynamics of Exploited Fish Populations, 1st ed.; Chapman and Hall: London, UK, 1957. [Google Scholar]
- Pearson, J.C. Natural history and conservation of redfish and other commercial sciaenids of the Texas coast. Bull. U. S. Bur. Fish. 1929, 44, 129–214. [Google Scholar]
- Ross, J.L.; Stevens, T.M.; Vaughan, D.S. Age, growth, mortality, and reproductive biology of red drums in North Carolina waters. Trans. Am. Fish. Soc. 1995, 124, 37–54. [Google Scholar] [CrossRef]
- Gompertz, B. On the nature of the function expressive of the law of human mortality and on a new mode of determining the value of life contingencies. Trans. R. Soc. Lond. 1825, 115, 515–585. [Google Scholar]
- Ricker, W.E. Computation and interpretation of biological statistics of fish populations. Bull. Fish. Res. Board Can. 1975, 191, 1–382. [Google Scholar]
- Pauly, D. Gill size and temperature as governing factors in fish growth: A generalization of von Bertalanffy’s growth formula. Ber. Inst. Meereskd. 1979, 62. [Google Scholar]
- Schnute, J.T.; Richards, L.J. A unified approach to the analysis of fish growth, maturity, and survivorship data. Can. J. Fish. Aquat. Sci. 1990, 47, 24–40. [Google Scholar] [CrossRef]
- Methot, R.D., Jr.; Wetzel, C.R. Stock synthesis: A biological and statistical framework for fish stock assessment and fishery management. Fish. Res. 2013, 142, 86–99. [Google Scholar] [CrossRef]
- Lee, R.M. An investigation into the methods of growth determination in fishes by means of scales. ICES J. Mar. Sci. 1912, 1, 3–34. [Google Scholar] [CrossRef]
- Pardo, S.A.; Cooper, A.B.; Dulvy, N.K. Avoiding fishy growth curves. Methods Ecol. Evol. 2013, 4, 353–360. [Google Scholar] [CrossRef]
- Minte-Vera, C.V.; Maunder, M.N.; Aires-da-Silva, A.M.; Satoh, K.; Uosaki, K. Get the biology right, or use size-composition data at your own risk. Fish. Res. 2017, 192, 114–125. [Google Scholar] [CrossRef]
- Katsanevakis, S. Modelling fish growth: Model selection, multi-model inference and model selection uncertainty. Fish. Res. 2006, 81, 229–235. [Google Scholar] [CrossRef]
- Katsanevakis, S.; Maravelias, C.D. Modelling fish growth: Multi-model inference as a better alternative to a priori using von Bertalanffy equation. Fish Fish. 2008, 9, 178–187. [Google Scholar] [CrossRef]
- Akaike, H. Information theory as an extension of the maximum likelihood principle. In Second International Symposium on Information Theory; Akademiai Kiado: Budapest, Hungary, 1973; pp. 267–281. [Google Scholar]
- Schwarz, G. Estimating the Dimension of a Model. Ann. Stat. 1978, 6, 461–464. [Google Scholar] [CrossRef]
- Shono, H. Efficiency of the finite correction of Akaike’s Information Criteria. Fish. Sci. 2000, 66, 608–610. [Google Scholar] [CrossRef]
- Burnham, K.P.; Anderson, D.P. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd ed.; Springer: New York, NY, USA, 2002. [Google Scholar]
- Murphy, M.D.; Taylor, R.G. Age, growth, and mortality of spotted seatrout in Florida waters. Trans. Am. Fish. Soc. 1994, 123, 482–497. [Google Scholar] [CrossRef]
- Dippold, D.A.; Leaf, R.T.; Hendon, J.R.; Franks, J.S. Estimation of the Length-at-Age Relationship of Mississippi’s Spotted Seatrout. Trans. Am. Fish. Soc. 2016, 145, 295–304. [Google Scholar] [CrossRef]
- Imai, C.; Sakai, H.; Katsura, K.; Honto, W.; Hida, Y. Growth model for the endangered cyprinid fish Tribolodon nakamurai based on otolith analyses. Fish. Sci. 2002, 68, 843–848. [Google Scholar] [CrossRef]
- Porch, C.E.; Wilson, C.A.; Nieland, D.L. A new growth model for red drum (Sciaenops ocellatus) that accommodates seasonal and ontogenetic changes in growth rates. Fish. B-NOAA 2002, 100, 149–152. [Google Scholar]
- Cailliet, G.M.; Smith, W.D.; Mollet, H.F.; Goldman, K.J. Age and growth studies of chondrichthyan fishes: The need for consistency in terminology, verification, validation, and growth function fitting. Environ. Biol. Fishes 2006, 77, 211–228. [Google Scholar] [CrossRef]
- Lorenzen, K. Toward a new paradigm for growth modeling in fisheries stock assessments: Embracing plasticity and its consequences. Fish. Res. 2016, 180, 4–22. [Google Scholar] [CrossRef]
- Gamito, S. Growth models and their use in ecological modelling: An application to a fish population. Ecol. Model. 1998, 113, 83–94. [Google Scholar] [CrossRef]
- Schnute, J. A versatile growth model with statistically stable parameters. Can. J. Fish. Aquat. Sci. 1981, 38, 1128–1140. [Google Scholar] [CrossRef]
- Silva, A.; Carrera, P.; Massé, J.; Uriarte, A.; Santos, M.B.; Oliveira, P.B.; Soares, E.; Porteiro, C.; Stratoudakis, Y. Geographic variability of sardine growth across the northeastern Atlantic and the Mediterranean Sea. Fish. Res. 2008, 90, 59–69. [Google Scholar] [CrossRef] [Green Version]
- Stewart, J.; Robbins, W.D.; Rowling, K.; Hegarty, A.; Gould, A. A multifaceted approach to modelling growth of the Australian bonito, Sarda australis (Family Scombridae), with some observations on its reproductive biology. Mar. Freshw. Res. 2013, 64, 671–678. [Google Scholar] [CrossRef]
- Piner, K.R.; Lee, H.H.; Thomas, L.R. Bias in estimates of growth when selectivity in models includes effects of gear and availability of fish. Fish. B-NOAA 2018, 116, 75–80. [Google Scholar]
- Francis, R.I.C.C. Are growth parameters estimated from tagging and age-length data comparable? Can. J. Fish. Aquat. Sci. 1988, 45, 936–942. [Google Scholar] [CrossRef]
- Francis, R.I.C.C.; Aires-da-Silva, A.M.; Maunder, M.N.; Schaefer, K.M.; Fuller, D.W. Estimating fish growth for stock assessments using both age-length and tagging-increment data. Fish. Res. 2016, 180, 113–118. [Google Scholar] [CrossRef]
- Wilson, K.L.; Matthias, B.G.; Barbour, A.B.; Ahrens, R.N.M.; Tuten, T.; Allen, M.S. Combining Samples from Multiple Gears Helps to Avoid Fishy Growth Curves. N. Am. J. Fish. Manag. 2015, 35, 1121–1131. [Google Scholar] [CrossRef]
- Goodyear, C.P. Modeling Growth: Consequences from Selecting Samples by Size. Trans. Am. Fish. Soc. 2019, 148, 528–551. [Google Scholar] [CrossRef] [Green Version]
- Burnham, K.P.; Anderson, D.P. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach; Springer: New York, NY, USA, 1998. [Google Scholar]
- Guthery, F.S.; Brennan, L.A.; Peterson, M.J.; Lusk, J.J. Information theory in wildlife science: Critique and viewpoint. J. Wildl. Manag. 2005, 69, 457–465. [Google Scholar] [CrossRef]
- Symonds, M.R.E.; Moussalli, A. A brief guide to model selection, mulitmodel inference and model averaging in behavioural ecology using Akaike’s information criterion. Behav. Ecol. Sociobiol. 2011, 65, 13–21. [Google Scholar] [CrossRef]
- Ye, M.; Meyer, P.D.; Neuman, S.P. On model selection criteria in multimodel analysis. Water Resour. Res. 2008, 44. [Google Scholar] [CrossRef]
- Brewer, M.J.; Butler, A.; Cooksley, S.L.; Freckleton, R. The relative performance of AIC, AICC and BIC in the presence of unobserved heterogeneity. Methods Ecol. Evol. 2016, 7, 679–692. [Google Scholar] [CrossRef]
- Serra-Pereira, B.; Figueiredo, I.; Farias, I.; Moura, T.; Gorda, L.S. Description of dermal denticles from the caudal region of Raja clavate and their use for the estimation of age and growth. ICES J. Mar. Sci. 2008, 65, 1701–1709. [Google Scholar] [CrossRef] [Green Version]
- Yamashita, H.; Katayama, S.; Komiya, T. Age and growth of black sea bream Acanthopagrus schlegelii (Bleeker 1854) in Tokyo Bay. Asian Fish. Sci. 2015, 2, 47–59. [Google Scholar]
- Matthias, B.G.; Ahrens, R.N.M.; Allen, M.S.; Lombardi-Carlson, L.A.; Fitzhugh, G.R. Comparison of growth models for sequential hermphrodites by considering multi-phasic growth. Fish. Res. 2016, 179, 67–75. [Google Scholar] [CrossRef]
- Tribuzio, C.A.; Kruse, G.H.; Fujioka, J.T. Age and growth of spiny dogfish (Squalus acanthias) in the Gulf of Alaska: Analysis of alternative growth models. Fish. B-NOAA 2010, 108, 119–135. [Google Scholar]
- Fischer, A.J.; Baker, M.S., Jr.; Wilson, C.A. Red snapper (Lutjanus campechanus) demographic structure in the northern Gulf of Mexico based on spatial patterns in growth rates and morphometrics. Fish. B-NOAA 2004, 102, 593–603. [Google Scholar]
- Maunder, M.N.; Crone, P.R.; Valero, J.L.; Semmens, B.X. Growth: Theory, Estimation, and Application in Fishery Stock Assessment Models. CAPAM Workshop Series Report 2. 2015. Retrieved from the Center for the Advancement of Population Assessment Methodology (CAPAM). Available online: http://www.capamresearch.org/sites/default/files/CAPAM_Growth%20Workshop_Series%20Report%202.pdf (accessed on 10 July 2018).
- Shmueli, G. To explain or to predict? Stat. Sci. 2010, 25, 289–310. [Google Scholar] [CrossRef]
- Midway, S.R.; White, J.W.; Roumillat, W.; Batsavage, C.; Scharf, F.S. Improving macroscopic maturity determination in a pre-spawning flatfish through predictive modeling and whole mount methods. Fish. Res. 2013, 147, 359–369. [Google Scholar] [CrossRef]
- Lee, Q.; Thorson, J.T.; Gertseva, V.V.; Punt, A.E. The benefits and risks of incorporating climate-driven growth variation into stock assessment models, with application to Splitnose Rockfish (Sebastes diploproa). ICES J. Mar. Sci. 2017, 75, 245–256. [Google Scholar] [CrossRef]
- Kimura, D.K. Extending the von Bertalanffy growth model using explanatory variables. Can. J. Fish. Aquat. Sci. 2008, 65, 1879–1891. [Google Scholar] [CrossRef]
- Ohnishi, S.; Yamakawa, T.; Okamura, H.; Akamine, T. A note on the von Bertalanffy growth function concerning the allocation of surplus energy to reproduction. Fish. B-NOAA 2012, 110, 223–229. [Google Scholar]
- Minte-Vera, C.V.; Maunder, M.N.; Casselman, J.M.; Campana, S.E. Growth functions that incorporate the cost of reproduction. Fish. Res. 2016, 180, 31–44. [Google Scholar] [CrossRef]
- He, J.X.; Bence, J.R. Modeling annual growth variation using a hierarchical Bayesian approach and the von Bertalanffy growth function, with application to lake trout in southern Lake Huron. Trans. Am. Fish. Soc. 2007, 136, 318–330. [Google Scholar] [CrossRef]
- Hatch, J.; Jiao, Y. A comparison between traditional and measurement-error growth models for weakfish Cynoscion regalis. PeerJ 2016, 4, e2431. [Google Scholar] [CrossRef] [Green Version]
- Froese, R.; Pauly, D. FishBase. World Wide Web Electronic Publication. Available online: www.fishbase.org (accessed on 10 February 2017).
- Mollet, H.F.; Ezcurra, J.M.; O’Sullivan, J.B. Captive biology of the pelagic stingray, Dasyatis violacea (Bonaparte, 1832). Mar. Freshw. Res. 2002, 53, 531–541. [Google Scholar] [CrossRef]
- Ricker, W.E. Growth rates and models. In Fish Physiology, III, Bioenergetics and Growth; Hoar, W.S., Randall, D.J., Brett, J.R., Eds.; Academic Press: New York, NY, USA, 1979; pp. 677–743. [Google Scholar]
- Hoese, H.D.; Beckman, D.W.; Blanchet, R.H.; Drullinger, D.; Nieland, D.L. A Biological and Fisheries Profile of Louisiana Red Drum Sciaenops Ocellatus; Fishery management Plan Series, Number 4, Part 1; Louisiana Department of Wildlife and Fisheries: Baton Rouge, LA, USA, 1991; 93p.
- Vaughan, D.S. Status of the Red Drum Stock on the Atlantic Coast: Stock Assessment Report for 1995; U.S. Department of Commerce, NOAA Technical Memorandum: Washington, DC, USA, 1996; NMFSF-SEFC-380; 50p.
- Condrey, R.; Beckman, D.W.; Wilson, C.W. Management implications of a new growth model for red drum. Appendix D. In Louisiana Red Drum Research; Shepard, J.A., Ed.; U.S. Dept. Commerce Cooperative Agreement NA87-WC-H-06122, Marine Fisheries Initiative (MARFIN) Program; Louisiana Department of Wildlife and Fisheries, Seafood Division, Finfish Section: Baton Rouge, LA, USA, 1988; 26p. [Google Scholar]
- Vaughan, D.S.; Helser, T.E. Status of the Red Drum Stock of the Atlantic Coast: Stock Assessment Report for 1989; U.S. Department of Commerce, NOAA Technical Memorandum: Washington, DC, USA, 1990; NMFS-SEFC-263; 53p.
- Gayanilo, F.C.; Pauly, D. The FAO-ICLARM Stock Assessment Tools (FiSAT) Reference Manual; FAO Computerized Infromation Series (Fisheries); FAO: Rome, Italy, 1997. [Google Scholar]
- Aragon-Noriega, E.A. Modeling the individual growth of the Gulf corvina, Cynoscion othonopterus (Pisces: Sciaenidae), using a multi-model approach. Cienc. Mar. 2014, 40, 149–161. [Google Scholar] [CrossRef] [Green Version]
- Richards, F.J. A flexible growth function for empirical use. J. Exp. Bot. 1959, 10, 290–300. [Google Scholar] [CrossRef]
- Balazik, M.T.; McIninch, S.P.; Garman, G.C.; Latour, R.J. Age and Growth of Atlantic Sturgeon in the James River, Virginia, 1997–2011. Trans. Am. Fish. Soc. 2012, 141, 1074–1080. [Google Scholar] [CrossRef]
- R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2019. [Google Scholar]
Model | Evaluated | Selected | Selection Rate |
---|---|---|---|
Schnute–Richards | 2 | 2 | 100% |
Double VBGM | 4 | 3 | 75% |
Seasonal VBGM | 10 | 5 | 50% |
Three-parameter VBGM | 79 | 31 | 39% |
Other | 32 | 12 | 38% |
Power | 6 | 2 | 33% |
Richards | 8 | 1 | 13% |
Two-parameter VBGM | 17 | 2 | 12% |
Three-parameter Gompertz | 40 | 4 | 10% |
Schnute | 14 | 1 | 7% |
Three-parameter Logistic | 31 | 2 | 6% |
Generalized VBGM | 10 | 0 | 0% |
Two-parameter Gompertz | 6 | 0 | 0% |
Two-parameter Logistic | 3 | 0 | 0% |
Linear VBGM | 1 | 0 | 0% |
Model | Migratory | Fresh | Marine |
---|---|---|---|
Double VBGM | 0 | 0 | 3 |
Gompertz | 0 | 1 | 4 |
Linear Regression | 1 | 0 | 1 |
Logistic | 0 | 0 | 3 |
Power | 0 | 0 | 2 |
Schnute-Richards | 0 | 0 | 5 |
Seasonal VBGM | 0 | 1 | 5 |
Specific | 0 | 1 | 10 |
VBGM | 8 | 35 | 107 |
Model Name | Model Equation | Parameter Description | Reference(s) |
---|---|---|---|
Two-parameter VBGM | L∞ = asymptotic length t = age L(t) = length at age t k1 = Brody growth parameter | [56] | |
Three-parameter VBGM | t0 = age at zero length | [15] | |
Two-parameter Gompertz | L0 = length at birth | [55,67] | |
Three-parameter Gompertz | k2 = rate of exponential decrease of relative growth with age | [18,55] | |
Three-parameter Gompertz | α = inflection point of the sigmoid curve | [19,55] | |
Three-parameter Logistic | k3 = relative growth rate parameter | [55,68] | |
Linear VBGM | b0, b1 = linear coefficients; b0 (intercept), b1 (slope) | [35,69,70] | |
Double VBGM | k4, k5 = instantaneous growth rate coefficients tp = “pivotal age” t1, t2 = age intercept parameters | [35,71,72] | |
Generalized VBGM | p = dimensionless factor | [20] | |
Seasonal VBGM | c = amplitude of oscillations ranging between 0 and 1 ts = the summer point or when growth rate is maximized, ranging between 0 and 1 | [41,73] | |
Schnute | τ1 = lowest age in the dataset τ2 = highest age in the dataset ρ = an incremental relative growth rate (incremental time constant) λ = relative growth rate (time constant) ι = size at age τ1 δ = size at age τ2 | [21,74] | |
Richards | δ = a shape parameter, and the sigmoidal Gompertz function k6 = relative growth parameter | [35,75,76] | |
Schnute–Richards | ν, δ, ϒ = dimensionless parameters k7 = units yr−ν | [21,26] | |
Power | a0 = y-intercept or the mean length at age 0 a1, b = parameters that describe the shape of the curve but have no biological interpretation | [26,27,76] |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Flinn, S.A.; Midway, S.R. Trends in Growth Modeling in Fisheries Science. Fishes 2021, 6, 1. https://doi.org/10.3390/fishes6010001
Flinn SA, Midway SR. Trends in Growth Modeling in Fisheries Science. Fishes. 2021; 6(1):1. https://doi.org/10.3390/fishes6010001
Chicago/Turabian StyleFlinn, Shane A., and Stephen R. Midway. 2021. "Trends in Growth Modeling in Fisheries Science" Fishes 6, no. 1: 1. https://doi.org/10.3390/fishes6010001