Abstract
Temperature is the most significant factor controlling developmental timing of most temperate poikilotherms. In the face of climate change, a crucial question is how will poikilothermic organisms evolve when faced with changing thermal environments? In this paper, we integrate models for developmental timing and quantitative genetics. A simple model for determining developmental milestones (emergence times, egg hatch) is introduced, and the general quantitative genetic recursion for the mean value of developmental parameters presented. Evolutionary steps proportional to the difference between current median parameters and parameters currently selected for depend on the fitness, which is assumed to depend on emergence density. Asymptotic states of the joint model are determined, which turn out to be neutrally stable (marginal) fixed points in the developmental model by itself, and an associated stable emergence distribution is also described. An asymptotic convergence analysis is presented for idealized circumstances, indicating basic stability criteria. Numerical studies show that the stability analysis is quite conservative, with basins of attraction to the asymptotic states that are much larger than expected. It is shown that frequency-dependent selection drives oscillatory dynamics and that the asymptotic states balance the asymmetry of the emergence distribution and the fitness function.
Similar content being viewed by others
References
Bentz, B. J., Logan, J. A., & Vandygriff, J. C. (2001). Latitudinal variation in dendroctonus ponderosae (coleoptera: Scolytidae) development time and adult size. Can. Entomol., 133(3), 375–387.
Calabrese, J. M., & Fagan, W. F. (2004). Lost in time, lonely, and single: reproductive asynchrony and the Allee effect. Am. Nat., 164(1), 25–37.
Chesson, P., & Huntly, N. (1997). The roles of harsh and fluctuating conditions in the dynamics of ecological communities. Am. Nat., 150(5), 519–553.
Danks, H. V. (1987). Monograph series, No. 1. Insect dormancy: An ecological perspective. Ottawa: Biological Survey of Canada (Terrestrial Arthropods).
Gilbert, E., Powell, J. A., Logan, J. A., & Bentz, B. J. (2004). Comparison of three models predicting developmental milestones given environmental and individual variation. Bull. Math. Biol., 66, 1821–1850.
Gomulkiewicz, R., & Holt, R. D. (1995). When does evolution by natural selection prevent extinction. Evolution, 49(1), 201–207.
Hendry, A. P., Wenburg, J. K., Bentzen, P., Volk, E. C., & Quinn, T. P. (2000). Rapid evolution of reproductive isolation in the wild: Evidence from introduced salmon. Science, 290(5491), 516–518.
Holt, R. D. (1990). The microevolutionary consequences of climate change. Trends Ecol. Evol., 5(9), 311–315.
Jenkins, J. L., Powell, J. A., Logan, J. A., & Bentz, B. J. (2001). Low seasonal temperatures promote life cycle synchronization. Bull. Math. Biol., 63, 573–595.
Johnson, M. T. J., & Agrawal, A. A. (2003). The ecological play of predator-prey dynamics in an evolutionary theatre. Trends Ecol. Evol., 18(11), 549–551.
Lande, R. (1976). Natural selection and random genetic drift in phenotypic evolution. Evolution, 30, 314–334.
Lande, R. (1993). Risks of population extinction from demographic and environmental stochasticity and random catastrophes. Am. Nat., 142, 911–927.
Logan, J. A., Regniere, J., & Powell, J. A. (2003). Assessing the impacts of global warming on forest pest dynamics. Front. Ecol. Environ., 1(3), 130–137.
Logan, J. D. (2008). Phenologically-structured predator-prey dynamics with temperature dependence. Bull. Math. Biol., 70(1), 1–20.
Lynch, M., & Lande, R. (1993). Evolution and extinction in response to environmental change. In P. M. Kareiva, J. G. Kingsolver, & R. B. Huey (Eds.), Biotic interactions and global change (pp. 234–250). Sunderland: Sinauer Associates.
MacArthur, R. H., & Wilson, E. O. (1967). Island biogeography. Princeton: Princeton University Press.
Powell, J. A., & Logan, J. A. (2005). Insect seasonality: Circle map analysis of temperature-driven life cycles. Theor. Popul. Biol., 67(3), 161–179.
Powell, J. A., Jenkins, J. L., Logan, J. A., & Bentz, B. J. (2000). Seasonal temperature alone can synchronise life cycles. Bull. Math. Biol., 62, 977–998.
Reznick, D. N., & Ghalambor, C. K. (2001). The population ecology of contemporary adaptations: What empirical studies reveal about the conditions that promote adaptive evolution. Genetica, 112, 183–198.
Roy, M., Brodeur, J., & Cloutier, C. (2002). Relationship between temperature and developmental rate of stethorus punctillum (coleoptera: Coccinellidae) and its prey tetranychus mcdanieli (acarina: Tetranychidae). Environ. Entomol., 31(1), 177–187.
Skelly, D. K., Joseph, L. N., Possingham, H. P., Freidenburg, L. K., Farrugia, T. J., Kinnison, M. T., & Hendry, A. P. (2007). Evolutionary responses to climate change. Conserv. Biol., 21(5), 1353–1355.
Slatkin, M. (1980). Ecological character displacement. Ecology, 61(1), 163–177.
Taylor, F. (1981). Ecology and evolution of physiological time in insects. Am. Nat., 117(1), 1–23.
Thomas, C. D., Cameron, A., Green, R. E., Bakkenes, M., Beaumont, L. J., Collingham, Y. C., Erasmus, F. N., Ferreira de Siqueira, M., Grainger, A., Hannah, L., Hughes, L., Huntly, B., van Jaarsveld, A. S., Midgley, G. F., Miles, L., Ortega-Huerta, M. A., Townsend Peterson, A., Phillips, O. L., & Williams, S. E. (2004). Extinction risk from climate change. Nature, 427(6970), 145–148.
Thompson, J. N. (1998). Rapid evolution as an ecological process. Trends Ecol. Evol., 13(8), 329–332.
Visser, M. E. (2008). Keeping up with a warming world; assessing the rate of adaptation to climate change. Proc. R. Soc., Ser. B, 275, 649–659.
Yamanaka, T., Tatsuki, S., & Shimada, M. (2008). Adaptation to the new land or effect of global warming? An age-structured model for rapid voltinism change in an alien lepidopteran pest. J. Anim. Ecol., 77, 585–596.
Zaslavski, V. A. (1996). Essentials of the environmental control of insect seasonality as reference points for comparative studies in other invertebrates. Hydrobiologia, 320, 123–130.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cobbold, C.A., Powell, J.A. Evolution Stabilises the Synchronising Dynamics of Poikilotherm Life Cycles. Bull Math Biol 73, 1052–1081 (2011). https://doi.org/10.1007/s11538-010-9552-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-010-9552-1