DOI: 10.5061/dryad.t4b8gtj76
title: Preferential cannibalism as a key stabilizing mechanism of intraguild predation systems with trophic polymorphic predators

description: Theory predicts intraguild predation (IGP) to be unstable despite its
 ubiquity in nature, prompting exploration of stabilizing mechanisms of
 IGP. One of the many ways IGP manifests is through inducible trophic
 polymorphisms in the intraguild (IG) predator, where a resource-eating
 predator morph competes with the intraguild (IG) prey for the shared
 resource while a top predator morph consumes the IG prey. Cannibalism is
 common in this type of system due to the top predator morph’s
 specialization on the trophic level below it, which includes the
 resource-eating predator morph. Here, we explore the consequences of
 inducible trophic polymorphisms in cannibal predators for IGP stability
 using an IGP model with and without cannibalism. We employ linear
 stability analysis and identify regions of coexistence based on the top
 predator morph's preference for conspecifics vs. heterospecifics and
 the IG prey's competitive ability relative to the resource-eating
 morph. Our findings reveal preferential cannibalism (i.e. the preferential
 consumption of conspecifics) stabilizes the system when the IG prey and
 resource-eating morph have similar competitive abilities for the shared
 resource. Though original IGP theory finds the IG prey must be a superior
 resource competitor as a general criterion for coexistence, this is not
 typically the case when the predator has an inducible trophic polymorphism
 and the resource-eating morph is specialized in resource acquisition.
 Preferential cannibalism may therefore be a key stabilizing mechanism in
 IGP systems with a cannibalistic, trophic polymorphic IG predators,
 providing further insight into what general mechanisms stabilize the
 pervasive IGP interaction.
description: <strong>Model(s) overview</strong>: To examine the effect of preferential cannibalism
 in a trophic polymorphic predator on IGP system stability, we compared two
 models of varying complexity (Fig. 1) under two scenarios pertaining to IG
 prey competitive ability. The first model (referred to herein as the
 “base” model) is an extension of the original Lotka-Volterra IGP model
 first proposed by Holt and Polis (1997) with the separation of the IG
 predator into two states: a resource-eating morph that competes with the
 IG prey for the shared resource, and a top predator morph that consumes
 the IG prey. Biomass moves from one state to the other as a function of
 resource density, which is intentionally general to encompass changes in
 frequency of morphs across generations or individuals switching between
 morphs in a lifetime. In the second model (referred to herein as the
 “full” model), we build upon the first model to include cannibalism in the
 IG predator, where the top predator morph consumes both the IG prey and
 the resource-eating predator morph. We further include a preference
 parameter, s, that controls the top predator morph’s preference for
 conspecifics (resource-eating predator morph) or heterospecifics (IG
 prey). We explore preference over a range of s values, specifically three
 values of s which represent preference for conspecifics
 (s=0.7), preference for
 heterospecifics (s=0.3), and
 no preference (s=0.5). <strong>Analysis</strong>: We explored
 stability in our models using linear stability analysis (Gurney and Nisbet
 1998; Murdoch et al. 2003; See SI 1). In short, we linearized eqs. 1 and 2
 around their interior equilibrium, and then examined the stability of
 these systems to small perturbations. We first solved for the equilibrium
 in which all species have positive, non-zero abundances using the “Solve”
 function in Mathematica (Wolfram Research, Inc., Mathematica, Version
 12.0, Champaign, IL, 2019). We then evaluated the Jacobian matrix at this
 solution and numerically computed the eigenvalues using the “Eigenvalues”
 function, selecting the eigenvalue(s) in which the real part is negative
 and therefore stable. We further performed numerical simulations to show
 the effects of preference and competitive superiority on dynamics and
 equilibrium densities in SI 2. Dynamics were simulated in the R
 programming language (R Core Team 2023) using the package
 “deSolve.” 
description: # Code for: Preferential cannibalism as a key stabilizing mechanism of
 intraguild predation systems with trophic polymorphic predators Status of
 MS: Published in Theoretical Ecology
 (https://doi.org/10.1007/s12080-024-00575-7) Authors: Clara A. Woodie and
 Kurt E. Anderson # Structure of Code 1. "Simulations.nb"
 provides code for manipulating multiple parameters and observing the
 effect on density (for base model and full model, both Type I and Type II)
 2. "Equilibrium TypeI Full Model.nb" solves for equilibrium
 across multiple parameter ranges, finds instances of bistability, and
 makes plots for the Type I Full Model 3. "Equilibrium TypeI Base
 Model.nb" solves for equilibrium across multiple parameter ranges,
 finds instances of bistability, and makes plots for the Type I Base Model
 4. "Equilibrium TypeII Full Model.nb" solves for equilibrium
 across multiple parameter ranges, finds instances of bistability, and
 makes plots for the Type II Full Model 5. "Equilibrium TypeII Base
 Model.nb" solves for equilibrium across multiple parameter ranges,
 finds instances of bistability, and makes plots for the Type II Base Model
 6. "Bifurcations.R" makes bifurcation diagrams for the Type II
 Full Model # Methods ### Figure 1: Visualization of Models # Results ###
 Fig 2: Ratio of prey to predator competitive superiority across preference
 parameter ### Fig 3: IG predation rate across carrying capacity ### Fig 4:
 IG predation rate across conversion efficiency ### Fig. 5: IG predation
 rate across cannibalism predation rate ### Table 1: Parameters used in
 analysis (Table1.pdf) # Supplemental ### Fig S1: Simulations within the
 three regions of Fig2 ### Fig S2: Equilibrium across carrying capacity ###
 Fig S3: Sensitivity to switching rates ### Fig S4: IG predation rate
 across carrying capacity for Type II full model ### Fig S5: Bifurcation
 diagram across preference parameter ### Fig S6: Bifurcation diagram across
 carrying capacity