Modelling inducible defences in predator–prey interactions: assumptions and dynamical consequences of three distinct approaches

Abstract

Inducible defences against predation are widespread in the natural world, allowing prey to economise on the costs of defence when predation risk varies over time or is spatially structured. Through interspecific interactions, inducible defences have major impacts on ecological dynamics, particularly predator–prey stability and phase lag. Researchers have developed multiple distinct approaches, each reflecting assumptions appropriate for particular ecological communities. Yet, the impact of inducible defences on ecological dynamics can be highly sensitive to the modelling approach used, making the choice of model a critical decision that affects interpretation of the dynamical consequences of inducible defences. Here, we review three existing approaches to modelling inducible defences: Switching Function, Fitness Gradient and Optimal Trait. We assess when and how the dynamical outcomes of these approaches differ from each other, from classic predator–prey dynamics and from commonly observed eco‐evolutionary dynamics with evolving, but non‐inducible, prey defences. We point out that the Switching Function models tend to stabilise population dynamics, and the Fitness Gradient models should be carefully used, as the difference with evolutionary dynamics is important. We discuss advantages of each approach for applications to ecological systems with particular features, with the goal of providing guidelines for future researchers to build on.

Predator coexistence through emergent fitness equalization

“…This mechanism is highly general, independent of details such as the predators’ functional responses, the exact way that defense affects the predators, or whether defense traits are unidirectional or bidirectional. It is also independent of whether adaptation occurs through evolution or phenotypic plasticity, as they can both be described by the adaptive dynamics approach used here (Abrams , Yamamichi et al ). The generality of the mechanism makes it widely applicable to coexistence of predators, herbivores, parasites, and any other consumer‐resource system with adapting prey.…”

“…Following the framework of adaptive dynamics (Abrams ), the direction and speed of trait changes are determined by the fitness gradient:where w x represents the prey per capita net growth rate and G determines the speed of trait changes relative to ecological dynamics. Even under contemporary (“rapid”) evolution, trait changes are still generally slower than population dynamics (DeLong et al ); however, the adaptive dynamics approach also represents trait changes driven by phenotypic plasticity (Yamamichi et al ), which are generally expected to be faster than evolutionary changes. G = 0.02 was chosen as the standard value (see Table for all parameters and values used), but I confirm that changing the speed of adaptation does not affect the equilibrium location or stability (Appendix : Sections S2 and S3), although it of course affects how rapidly the equilibrium is reached.…”

The ecology of fear and inverted biomass pyramids

“…Predators are known to induce both morphological (Kondoh ) and behavioral (Ives and Dobson ) anti‐predator responses in their prey, affecting the predator–prey system (Yamamichi et al ). Anti‐predator behaviors are of particular interest because they are likely to occur immediately in response to changes in population sizes (Ives and Dobson , Křivan , ), making feedbacks between behavior and community structure even more pronounced.…”

How long do Red Queen dynamics survive under genetic drift? A comparative analysis of evolutionary and eco-evolutionary models

“…We do, however, briefly explore the effects of including more genotypes and 298 mutation as a means to revive genotypes. There is an increasing effort to openly discuss how 299 verbal models and biological assumptions enter into models [27,75]. Making the assumptions clear 300 and readily available should be the standard for future publications.…”

“…To this end we compare models from evolutionary game theory, 73 that do not include population size changes and theoretical ecology models that do. The models 74 have been widely used in the literature and represent the simplest case of Red Queen dynamics 75 with a matching allele interaction profile (for details see the Methods below and additional file). 76…”