Rejuvenating functional responses with renewal theory

Abstract

<jats:p>Functional responses are widely used to describe interactions and resource exchange between individuals in ecology. The form given to functional responses dramatically affects the dynamics and stability of populations and communities. Despite their importance, functional responses are generally considered with a phenomenological approach, without clear mechanistic justifications from individual traits and behaviours. Here, we develop a bottom-up stochastic framework grounded in renewal theory that shows how functional responses emerge from the level of the individuals through the decomposition of interactions into different activities. Our framework has many applications for conceptual, theoretical and empirical purposes. First, we show how the mean and variance of classical functional responses are obtained with explicit ecological assumptions, for instance regarding foraging behaviours. Second, we give examples in specific ecological contexts, such as in nuptial-feeding species or size-dependent handling times. Finally, we demonstrate how to analyse data with our framework, especially highlighting that observed variability in the number of interactions can be used to infer parameters and compare functional response models.</jats:p>

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

“…As a result, experimenters should consider scale and setting carefully, and more importantly, determine how laboratory results translate to natural conditions in the field, when possible. In addition to the recommendations for future work on the effects of physiology, allometry and habitat structure on predatory functional responses provided above, other important avenues for research include exploring the impacts of predator and prey behavioural plasticity (individual as well as reciprocal plasticity [105]) on functional response shapes, accounting for stochasticity in interactions among individuals within the functional response framework [106,107], quantifying the consequences of induced prey defences [108], and determining the effects of prey condition on predator foraging and prey avoidance behaviour.…”

Technical review on derivation methods for behavior dependent functional responses

“…Functional responses are often generated in optimal foraging theory using renewal theory (e.g., Andrews 1968, Cressman et al 2014, Hassell 1978, Holling 1966, Houston and McNamara 1985, 1999, McNamara et al 2006, Stephens and Krebs 1986, Yearsley 2003. Recently, Billiard et al (2018) developed a bottom-up stochastic framework grounded in renewal theory showing how functional responses depend on the relative density of the individuals through the decomposition of interactions into different activities. They have derived the stochastic versions of classical functional responses: Holling's I, II and III.…”

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

“…Random times involved in ecological or biological interactions are in general nonexponentially distributed, see [DKPvG15,BBC18] and references therein. Indeed, handling or manipulation times may have small standard deviations compared to the mean, while exponential distribution forces the value of variance once the mean is fixed.…”

“…We also obtain new features due to the fact that mortality depends on prey consumption and life length is not exponentially distributed. Following in particular [BBC18] and references therein, we model the interaction by a renewal process for each predator, with two status. Each predator successively searches during a random time and then manipulates during an other random time, which may include rest or other interactions.…”