# Rejuvenating functional responses with renewal theory

## TL;DR

This paper introduces a mechanistic, stochastic framework based on Renewal Theory to derive and analyze ecological functional responses from individual behaviors, improving understanding and empirical inference.

## Contribution

It presents a bottom-up approach linking individual traits to population-level functional responses using Renewal Theory, with applications for modeling and data analysis.

## Key findings

- Explicit formulas for mean and variance of functional responses.
- Application to specific ecological contexts like nuptial-feeding species.
- Method for inferring parameters from interaction variability.

## Abstract

Functional responses are widely used to describe interactions and resources 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 behaviors. Here, we develop a bottom-up stochastic framework grounded in Renewal Theory showing 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 behaviors. Second, we give examples in specific ecological contexts, such as in nuptial-feeding species or size dependent handling times. Finally, we demonstrate how to analyze 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.