Rejuvenating functional responses with renewal theory

From the distributions of times of interactions to preys and predators dynamical systems

We consider a stochastic individual based model where each predator searches and then manipulates its prey or rests during random times. The time distributions may be non-exponential and density dependent. An age structure allows to describe these interactions and get a Markovian setting. The process is characterized by a measure-valued stochastic differential equation. We prove averaging results in this infinite dimensional setting and get the convergence of the slow-fast macroscopic prey predator process to a two dimensional dynamical system. We recover classical functional responses. We also get new forms arising in particular when births and deaths of predators are affected by the lack of food.

Interactions between different predator-prey states: a method for the derivation of the functional and numerical response

In this paper we introduce a formal method for the derivation of a predator's functional response from a system of fast state transitions of the prey or predator on a time scale during which the total prey and predator densities remain constant. Such derivation permits an explicit interpretation of the structure and parameters of the functional response in terms of individual behaviour. The same method is also used here to derive the corresponding numerical response of the predator as well as of the prey.

Predator type influences the frequency of functional responses to prey in marine habitats

The functional response of a consumer to a gradient of resource density is a widespread and consistent framework used to quantify the importance of consumption to population dynamics and stability. Within benthic marine ecosystems, both crustaceans and fishes can provide strong top-down pressure on prey populations. Taxon-specific differences in biomechanics or habitat use, among other factors, may lead to variable functional response forms or parameter values (attack rate, handling time). Based on a review of 189 individual functional response fits, we find that these predator guilds differ in their frequency distribution of functional response types, with crustaceans exhibiting nearly double the proportion of sigmoidal, density-dependent functional responses (Holling type III) as predatory fishes. The implications of this finding for prey population stability are significant because type III responses allow prey persistence while type II responses are de-stabilizing and can lead to extinction. Comparing per capita predation rates across diverse taxa can provide integrative insights into predatory effects and the ability of predation to drive community structure.