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The Effects of Predator Evolution and Genetic Variation on Predator–Prey Population-Level Dynamics

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Abstract

This paper explores how predator evolution and the magnitude of predator genetic variation alter the population-level dynamics of predator–prey systems. We do this by analyzing a general eco-evolutionary predator–prey model using four methods: Method 1 identifies how eco-evolutionary feedbacks alter system stability in the fast and slow evolution limits; Method 2 identifies how the amount of standing predator genetic variation alters system stability; Method 3 identifies how the phase lags in predator–prey cycles depend on the amount of genetic variation; and Method 4 determines conditions for different cycle shapes in the fast and slow evolution limits using geometric singular perturbation theory. With these four methods, we identify the conditions under which predator evolution alters system stability and shapes of predator–prey cycles, and how those effect depend on the amount of genetic variation in the predator population. We discuss the advantages and disadvantages of each method and the relations between the four methods. This work shows how the four methods can be used in tandem to make general predictions about eco-evolutionary dynamics and feedbacks.

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Acknowledgements

SP was supported by the American Association of University Women Dissertation Fellowship to SP and the Austrian Science Fund (FWF) Grant P25188-N25 awarded to Reinhard Burger at the University of Vienna.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Utah State University, Logan, UT, 84322, USA

    Michael H. Cortez

  2. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria

    Swati Patel

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Correspondence to Michael H. Cortez.

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Cortez, M.H., Patel, S. The Effects of Predator Evolution and Genetic Variation on Predator–Prey Population-Level Dynamics. Bull Math Biol 79, 1510–1538 (2017). https://doi.org/10.1007/s11538-017-0297-y

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