# How range residency and long-range perception change encounter rates

## TL;DR

This paper develops new analytical models to understand how animals' non-uniform space use and perception range influence encounter rates, challenging traditional assumptions of uniform movement and local perception in ecological theory.

## Contribution

It introduces novel analytical expressions for encounter rates based on Ornstein-Uhlenbeck motion, accounting for non-uniform space use and variable home range sizes, extending beyond classical Brownian motion models.

## Key findings

- Non-uniform space use significantly alters encounter rate predictions.
- Perception range and home range size interaction biases encounter estimates.
- Realistic movement behaviors are crucial for accurate ecological modeling.

## Abstract

Encounter rates link movement strategies to intra- and inter-specific interactions, and therefore translate individual movement behavior into higher-level ecological processes. Indeed, a large body of interacting population theory rests on the law of mass action, which can be derived from assumptions of Brownian motion in an enclosed container with exclusively local perception. These assumptions imply completely uniform space use, individual home ranges equivalent to the population range, and encounter dependent on movement paths actually crossing. Mounting empirical evidence, however, suggests that animals use space non-uniformly, occupy home ranges substantially smaller than the population range, and are often capable of nonlocal perception. Here, we explore how these empirically supported behaviors change pairwise encounter rates. Specifically, we derive novel analytical expressions for encounter rates under Ornstein-Uhlenbeck motion, which features non-uniform space use and allows individual home ranges to differ from the population range. We compare OU-based encounter predictions to those of Reflected Brownian Motion, from which the law of mass action can be derived. For both models, we further explore how the interplay between the scale of perception and home range size affects encounter rates. We find that neglecting realistic movement and perceptual behaviors can systematically bias encounter rate predictions.