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Evolutionary tradeoff and equilibrium in an aquatic predator-prey system

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Abstract

Due to the conventional distinction between ecological (rapid) and evolutionary (slow) timescales, ecological and population models have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has been recently established and may be critical to understanding how populations persist in changing environments. In this paper we examine the relationship between ecological and evolutionary dynamics, focusing on a well-studied experimental aquatic predator-prey system (Fussmann et al., 2000, Science, 290, 1358–1360; Shertzer et al., 2002, J. Anim. Ecol., 71, 802–815; Yoshida et al., 2003, Nature, 424, 303–306). Major properties of predator-prey cycles in this system are determined by ongoing evolutionary dynamics in the prey population. Under some conditions, however, the populations tend to apparently stable steady-state densities. These are the subject of the present paper. We examine a previously developed model for the system, to determine how evolution shapes properties of the equilibria, in particular the number and identity of coexisting prey genotypes. We then apply these results to explore how evolutionary dynamics can shape the responses of the system to ‘management’: externally imposed alterations in conditions. Specifically, we compare the behavior of the system including evolutionary dynamics, with predictions that would be made if the potential for rapid evolutionary change is neglected. Finally, we posit some simple experiments to verify our prediction that evolution can have significant qualitative effects on observed population-level responses to changing conditions.

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References

  • Abrams, P. A. (2000). The evolution of predator-prey interactions: theory and evidence. Annu. Rev. Ecol. Systematics 31, 79–105.

    Article  Google Scholar 

  • Abrams, P. and M. Vos (2003). Adaptation, density dependence, and the responses of trophic level abundances to mortality. Evol. Ecol. Res. 5, 1113–1132.

    Google Scholar 

  • Ashley, M. V., M. F. Willson, O. R. W. Pergams, D. J. O’Dowd, S. M. Gende and J. S. Brown (2003). Evolutionarily enlightened management. Biol. Conservation 111, 115–123.

    Article  Google Scholar 

  • Cousyn, C., L. De Meester, J. K. Colbourne, L. Brendonck, D. Verschuren and F. Volckaert (2001). Rapid, local adaptation of zooplankton behavior to changes in predation pressure in the absence of neutral genetic changes. Proc. Natl. Acad. Sci. USA 98, 6256–6260.

    Article  Google Scholar 

  • Cushing, J. M., R. F. Costantino, B. Dennis, R. A. Desharnais and S. M. Henson (2002). Chaos in Ecology: Experimental Nonlinear Dynamics, Theoretical Ecology Series I, San Diego: Academic Press.

    Google Scholar 

  • Dercole, F., J. O. Irisson and S. Rinaldi (2003). Bifurcation analysis of a prey-predator coevolution model. SIAM J. Appl. Math. 63, 1378–1391.

    Article  MathSciNet  Google Scholar 

  • Dieckmann, U. (1997). Can adaptive dynamics invade? Trends Ecol. Evol. 12, 128–131.

    Article  Google Scholar 

  • Ellner, S. P. and N. G. Hairston Jr (1994). Role of overlapping generations in maintaining genetic variation in a fluctuating environment. Am. Nat. 143, 403–417.

    Article  Google Scholar 

  • Fussmann, G. F., S. P. Ellner and N. G. Hairston Jr (2003). Evolution as a critical component of plankton dynamics. Proc. R. Soc. Lond. B 270, 1015–1022.

    Article  Google Scholar 

  • Fussmann, G. F., S. P. Ellner, K. W. Shertzer and N. G. Hairston Jr (2000). Crossing the Hopf bifurcation in a live predator-prey system. Science 290, 1358–1360.

    Article  Google Scholar 

  • Grant, P. R. and B. R. Grant (2002). Unpredictable evolution in a 30-year study of Darwin’s finches. Science 296, 707–711.

    Article  Google Scholar 

  • Hairston, N. G., W. Lampert, C. E. Cceres, C. L. Holtmeier, L. J. Weider, U. Gaedke, J. M. Fischer, J. A. Fox and D. M. Post (1999). Lake ecosystems: rapid evolution revealed by dormant eggs. Nature 401, 446.

    Article  Google Scholar 

  • Johnson, M. T. J. and A. Agrawal (2003). The ecological play of predator-prey dynamics in an evolutionary theatre. Trends Ecol. Evol. 18, 549–551.

    Article  Google Scholar 

  • Khibnik, A. I. and A. S. Kondrashov (1997). Three mechanisms of Red Queen dynamics. Proc. R. Soc. Lond. B 264, 1049–1056.

    Article  Google Scholar 

  • Law, R. and D. R. Grey (1989). Evolution of yields from populations with age-specific cropping. Evol. Ecol. 3, 343–359.

    Article  Google Scholar 

  • Le Galliard, J. F., R. Ferriere and U. Dieckmann (2003). The adaptive dynamics of altruism in spatially heterogeneous populations. Evolution 57, 1–17.

    Google Scholar 

  • Levin, S. A. and H. C. Muller-Landau (2000). The evolution of dispersal and seed size in plant communities. Evol. Ecol. Res. 2, 409–435.

    Google Scholar 

  • Marrow, P., U. Dieckmann and R. Law (1996). Evolutionary dynamics of predator-prey systems: an ecological perspective. J. Math. Biol. 34, 556–578.

    Google Scholar 

  • Morin, P. (1999). Community Ecology, Oxford: Blackwell Science.

    Google Scholar 

  • Mueller, L. D. and A. Joshi (2000). Stability in Model Populations, Monographs in Population Biology, 31, Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Pickett-Heaps, J. D. (1975). Green Algae: Structure, Reproduction and Evolution in Selected Genera, Sunderland, MA: Sinauer Associates.

    Google Scholar 

  • Reznick, D. N. and C. K. Ghalambor (2001). The population ecology of contemporary adaptations: what empirical studies reveal about the conditions that promote adaptive evolution. Genetica 112–113, 188–198.

    Google Scholar 

  • Reznick, D. N., F. H. Shaw, F. H. Rodd and R. G. Shaw (1997). Evaluation of the rate of evolution in natural populations of Guppies (Poecilia reticulata). Science 275, 1934–1937.

    Article  Google Scholar 

  • Shertzer, K. W., S. P. Ellner, G. F. Fussmann and N. G. Hairston Jr (2002). Predator-prey cycles in an aquatic microcosm: testing hypotheses of mechanism. J. Anim. Ecol. 71, 802–815.

    Article  Google Scholar 

  • Sinervo, B., E. Svensson and T. Comendant (2000). Density cycles and an offspring quantity and quality game driven by natural selection. Nature 406, 985–988.

    Article  Google Scholar 

  • Stockwell, C. A., A. P. Hendry and M. T. Kinnison (2003). Contemporary evolution meets conservation biology. Trends Ecol. Evol. 18, 94–101.

    Article  Google Scholar 

  • Thompson, J. N. (1998). Rapid evolution as an ecological process. Trends Ecol. Evol. 13, 329–332.

    Article  Google Scholar 

  • Yoshida, T., L. E. Jones, S. P. Ellner, G. F. Fussmann and N. G. Hairston Jr (2003). Rapid evolution drives ecological dynamics in a predator-prey system. Nature 424, 303–306.

    Article  Google Scholar 

  • Yoshida T., N. G. Hairston Jr and S. P. Ellner, Evolutionary trade off between defense against grazing and competitive ability in a simple unicellular alga, Chlorella vulgaris. Submitted to Proceedings of the Royal Society of London, Biology [PRSLB] (submitted).

  • Zimmer, C. (2003). Rapid evolution can foil even the best-laid plans. Science 300, 895.

    Article  Google Scholar 

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Correspondence to Laura E. Jones.

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Jones, L.E., Ellner, S.P. Evolutionary tradeoff and equilibrium in an aquatic predator-prey system. Bull. Math. Biol. 66, 1547–1573 (2004). https://doi.org/10.1016/j.bulm.2004.02.006

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  • DOI: https://doi.org/10.1016/j.bulm.2004.02.006

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