DOI: 10.5061/dryad.0000000g8
title: Higher genetic variance of prey defense promotes fluctuation-dependent species coexistence

description: Understanding the stable coexistence of competing species despite the
 competitive exclusion principle has been a central topic in ecology.
 Previous studies revealed that rapid contemporary evolution can promote
 species coexistence, but the mechanisms behind coexistence are not fully
 understood. A recent study showed that predator evolution can promote
 fluctuation-dependent species coexistence. Here, I propose a new mechanism
 where prey rapid evolution due to high genetic variance can also promote
 fluctuation-dependent coexistence of competing predator species. Previous
 experimental and theoretical studies demonstrated that the rapid evolution
 of a prey defense trait can cause predator-prey population cycles.
 Although those studies focused on a system with a single predator species,
 I show that the population fluctuations driven by prey rapid evolution can
 promote the coexistence of two competing predator species via a
 gleaner-opportunist trade-off. By expanding the framework of modern
 coexistence theory, I further show how prey rapid evolution can increase
 the niche difference of competing predators and simultaneously affect the
 competitive ability difference via population cycles. Given the propensity
 for oscillatory dynamics and prey rapid evolution (due to large population
 sizes and genetic variance) in nature, I argue that this expansion of
 coexistence theory provides an important solution to the coexistence
 paradox.
description: # Higher genetic variance of prey defense promotes fluctuation-dependent
 species coexistence Dataset DOI:
 [10.5061/dryad.0000000g8](10.5061/dryad.0000000g8) ## Description of the
 data and file structure A Mathematica notebook (.nb and .pdf) to analyze
 ordinary differential equations for understanding how higher genetic
 variance of prey defense promotes fluctuation-dependent species
 coexistence. ### Files and variables * SupplementaryMaterial.nb This file
 can be opened by Wolfram Mathematica. * SupplementaryMaterial.pdf A PDF
 version of "SupplementaryMaterial.nb". ### Contents 1.
 Quantitative trait model (Figs. 1, S1-S3, Appendices S1-S2) 1. Appendix
 S1: General analyses of the quantitative trait model 2. Appendix S2:
 Detailed analyses of a model based on Abrams & Matsuda (1997)
 *Evolution* 3. Fig. 1a: Competitive exclusion when the prey genetic
 variance is low 4. Fig. S1a: The gleaner-opportunist trade-off 5. Fig.
 S1b: The growth-defense trade-off for disruptive selection 6. Fig. 1c: A
 bifurcation plot along the prey genetic variance without an opportunist 7.
 Fig. S2c: A bifurcation plot along the density-dependent parameter without
 an opportunist 8. Fig. 1d: A bifurcation plot along the prey genetic
 variance with an opportunist 9. Fig. S2a-b: Competitive exclusion or
 coexistence depending on the density-dependent parameter 10. Fig. S2d: A
 bifurcation plot along the density-dependent parameter with an opportunist
 11. Fig. 1b: Coexistence when the prey genetic variance is high 12. Fig.
 1f: The niche and competitive ability differences with fluctuations 13.
 Fig. 1e: A phase diagram of coexistence along the prey genetic variance
 and handling time 14. Fig. S3: Coexistence of three predator species 2.
 Coevolution model (Figs. 2, S4-S5, Appendix S3) 1. Fig. S4a: The
 foraging-mortality trade-off for stabilizing selection 2. Fig. S4b: A
 phase diagram of cycles without a gleaner along the prey and predator
 genetic variance (*V*~1~ and *V*~2~) 3. Fig. 2a: A phase diagram of
 coexistence along the prey and predator genetic variance 4. Fig. S4c-d:
 Dynamics when (*V*~1~, *V*~2~) = (0.02, 0.1) 5. Fig. 2b-d: Dynamics when
 (*V*~1~, *V*~2~) = (0.05, 0.1), (0.1, 0.1), and (0.05, 0.6) 6. Fig. 2e: A
 bifurcation plot along the prey genetic variance when *V*~2~ = 0.1 7. Fig.
 2f: A bifurcation plot along the predator genetic variance when *V*~1~ =
 0.05 8. Fig. S5a: A phase diagram of coexistence along the prey and
 predator genetic variance 9. Fig. S5b: A bifurcation plot along the
 predator genetic variance when *V*~1~ = 0.27 10. Fig. S5c-d: Dynamics when
 (*V*~1~, *V*~2~) = (0.27, 0.1) and (0.27, 0.6) 3. Clonal model (Figs. 3,
 S6) 1. Fig. 3a: A bifurcation plot along the defended clone's trait
 without an opportunist 2. Fig. 3c: Coexistence when prey trait variation
 is high 3. Fig. S6: The gleaner-opportunist trade-off 4. Fig. 3d: The
 niche and competitive ability differences with fluctuations 5. Fig. 3b: A
 bifurcation plot along the defended clone's trait with an opportunist
 4. van Velzen (2020)'s quantitative trait model (Appendix S4, Fig.
 S7) 1. Fig. S7: The niche and competitive ability differences in van
 Velzen (2020) *Ecology* ## Code/software Wolfram Mathematica 14.3.0.0