Abstract
Phenotypic plasticity of size at maturation is commonly described using size–age maturation reaction norms (MRNs). MRNs for age and size at maturation are analyzed and classified into three general categories related to different size scalings of growth and mortality. The underlying model for growth and mortality is based on processes at the level of the individual, and is motivated by the energy budget of fish. MRN shape is a balance between opposing factors and depends on subtle details of size dependence of growth and mortality. MRNs with both positive and negative slopes are predicted, and for certain mortality conditions also a lower critical spawning mass. The model is applied to predict a generic fishery-induced evolutionary response and allows assessment of climate change impact on MRNs. Our work stresses the importance of using realistic size dependence of mortality and growth, since this strongly influences the predicted MRNs and sensitivity to harvest pressure.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andersen, K. H., & Brander, K. (2009). Expected rate of fisheries-induced evolution is slow. Proc. Nat. Acad. Sci., 106(28), 11,657–11,660.
Andersen, K. H., Farnsworth, K. D., Thygesen, U. H., & Beyer, J. E. (2007). The evolutionary pressure from fishing on size at maturation of Baltic cod. Ecol. Model., 204(1–2), 246–252. doi:10.1016/j.ecolmodel.2007.01.002.
Berrigan, D., & Koella, J. (1994). The evolution of reaction norms: Simple models for age and size at maturity. J. Evol. Biol., 7(5), 549–566.
Blanchard, J., Dulvy, N., Jennings, S., Ellis, J., Pinnegar, J., Tidd, A., & Kell, L. (2005). Do climate and fishing influence size-based indicators of Celtic Sea fish community structure? ICES J. Mar. Sci., 62(3), 405–411. doi:10.1016/j.icesjms.2005.01.006.
Browman, H. I., Law, R., & Marshall, C. T. (2008). The role of fisheries-induced evolution. Science, 320(5872), 47.
Chambers, R. C. (1997). Environmental influences on egg and propagule sizes in marine fishes. In Chambers, R. C., & Trippel, E. A. (Eds.), Early life history and recruitment in fish populations (pp. 63–102). London: Chapman & Hall.
Cury, P., Shannon, L., Roux, J., Daskalov, G., Jarre, A., Moloney, C., & Pauly, D. (2005). Trophodynamic indicators for an ecosystem approach to fisheries. ICES J. Mar. Sci., 62(3), 430–442. doi:10.1016/j.icesjms.2004.12.006.
Day, T., & Rowe, L. (2002). Developmental thresholds and the evolution of reaction norms for age and size at life-history transitions. Am. Nat., 159(4), 338–350.
Day, T., & Taylor, P. (1997). Von Bertalanffy’s growth equation should not be used to model age and size at maturity. Am. Nat., 149(2), 381–393.
Dunlop, E. S., Heino, M., & Dieckmann, U. (2009). Eco-genetic modeling of contemporary life-history evolution. Ecol. Appl., 19(7), 1815–1834.
Dunlop, E. S., Shuter, B. J., & Dieckmann, U. (2007). Demographic and evolutionary consequences of selective mortality: Predictions from an eco-genetic model for smallmouth bass. Trans. Am. Fish. Soc., 136(3), 749–765. doi:10.1577/T06-126.1.
Ernande, B., Dieckmann, U., & Heino, M. (2004). Adaptive changes in harvested populations: Plasticity and evolution of age and size at maturation. Proc. R. Soc. B: Biol. Sci., 271(1537), 415–423. doi:10.1098/rspb.2003.2519.
Gårdmark, A., & Dieckmann, U. (2006). Disparate maturation adaptations to size-dependent mortality. Proc. R. Soc. B: Biol. Sci., 273(1598), 2185–2192. doi:10.1098/rspb.2006.3562.
Heino, M. (1998). Management of evolving fish stocks. Can. J. Fish. Aquat. Sci., 55(8), 1971–1982.
Heino, M., & Dieckmann, U. (2008). Detecting fisheries-induced life-history evolution: An overview of the reaction-norm approach. Bull. Mar. Sci., 83(1), 69–93.
Heino, M., Dieckmann, U., & Godø, O. (2002). Measuring probabilistic reaction norms for age and size at maturation. Evolution, 56(4), 669–678.
Jobling, M. (1994). Fish and fisheries series : Vol. 13. Fish bioenergetics. London: Chapman & Hall.
Jørgensen, C., Enberg, K., Dunlop, E. S., Arlinghaus, R., Boukal, D. S., Brander, K., Ernande, B., Gaerdmark, A., Johnston, F., Matsumura, S., Pardoe, H., Raab, K., Silva, A., Vainikka, A., Dieckmann, U., Heino, M., & Rijnsdorp, A. D. (2007). Ecology—managing evolving fish stocks. Science, 318(5854), 1247–1248. doi:10.1126/science.1148089.
Law, R. (2000). Fishing, selection, and phenotypic evolution. ICES J. Mar. Sci., 57(3), 659–668.
Law, R. (2007). Fisheries-induced evolution: present status and future directions. Mar. Ecol. Progr. Ser., 335, 271–277.
Law, R., & Grey, D. (1989). Evolution of yields from populations with age-specific cropping. Evol. Ecol., 3(4), 343–359.
Mylius, S., & Diekmann, O. (1995). On evolutionarily stable life histories, optimization and the need to be specific about density dependence. Oikos, 74(2), 218–224.
Peters, R. (1983). The ecological implications of body size. Cambridge: Cambridge University Press.
Quince, C., Abrams, P. A., Shuter, B. J., & Lester, N. P. (2008). Biphasic growth in fish I: Theoretical foundations. J. Theor. Biol., 254(2), 197–206. doi:10.1016/j.jtbi.2008.05.029.
Reiss, M. J. (1991). The allometry of growth and reproduction. Cambridge: Cambridge University Press.
Stearns, S., & Koella, J. (1986). The evolution of phenotypic plasticity in life-history traits. Predictions of reaction norms for age and size at maturity. Evolution, 40(5), 893–913.
Taborsky, B., Dieckmann, U., & Heino, M. (2003). Unexpected discontinuities in life-history evolution under size-dependent mortality. Proc. R. Soc. B: Biol. Sci., 270(1516), 713–721. doi:10.1098/rspb.2002.2255.
Thorpe, J. E. (2007). Maturation responses of salmonids to changing developmental opportunities. Mar. Ecol. Progr. Ser., 335, 285–288.
Thygesen, U., Farnsworth, K., Andersen, K., & Beyer, J. (2005). How optimal life history changes with the community size-spectrum. Proc. R. Soc. B: Biol. Sci., 272(1570), 1323–1331. doi:10.1098/rspb.2005.3094.
Vinberg, G. G. (1956). Rate of metabolism and food requirements of fishes. Fish. Res. Board Can., 194, 1–253.
Ware, D. M. (1975). Growth, metabolism, and optimal swimming speed of a pelagic fish. Fish. Res. Board Can., 32(1), 33–41.
West, G. B., Brown, J. H., & Enquist, B. J. (2001). A general model for ontogenetic growth. Nature, 413, 628–631.
Wright, P. J. (2007). Understanding the maturation process for field investigations of fisheries-induced evolution. Mar. Ecol. Progr. Ser., 335, 279–283.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Christensen, A., Andersen, K.H. General Classification of Maturation Reaction-Norm Shape from Size-based Processes. Bull Math Biol 73, 1004–1027 (2011). https://doi.org/10.1007/s11538-010-9550-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-010-9550-3