Influence of natural enemy specificity and functional response on victim coexistence

Natural enemies are thought to promote coexistence of competing victim species. Although existing theory suggests victim coexistence increases with enemy specialization, the dynamics and potential extinction of enemies is generally discounted. Where enemy dynamics have been considered, empirically atypical linear functional responses have been studied. These limitations could over-simplify inferences about enemy-mediated coexistence. We studied the dynamics of two competing victim species and two enemy species with a deterministic model. We derived equilibrium points, and used linear stability analysis, numerical simulations and Floquet theory to determine the influence of enemy specificity and non-linear functional responses on coexistence in this victim-enemy community. We found greater specificity could drive enemy equilibrium points to infeasible values. We found only accelerating enemy functional responses result in stable equilibrium point coexistence of otherwise equivalent competitor victims, in which case greater specificity results in greater stability. Linear and saturating responses produce complex dynamics (neutral or limit cycles, chaos) or extinction, with limit cycle stability highest at intermediate specificity. Our results indicate strict specificity may not maximize coexistence, and enemy functional response critically influences whether enemies promote victim coexistence. They highlight the need to incorporate enemy dynamics into the growing body of theory regarding enemy-mediated diversity maintenance.