From daylight to darkness: a nonlocal model of circadian activity cycles
Abstract
An animal's ability to perceive its surroundings, as well as the ecological interactions it experiences, can be strongly influenced by the sleep patterns of both itself and surrounding species. Animals with limited sensory capabilities may struggle to navigate their habitat at night, while in a predator-prey system, it may be detrimental for prey to be inactive while predators are awake and hunting. Here, we develop a general mathematical framework to study these interactions using partial differential equations, incorporating activity cycles and daylight-dependent perception into existing models of animal movement. We show that both the dominant sensory mode and the length of daylight are key factors determining the strength of aggregation in social species. Extending this framework to a two-species predator-prey system, we use game-theoretic approaches to show that the equilibrium sleep strategy of each species is shaped not only by its own sensory capabilities, but also by those of its ecological opponent. Depending on the sensory capabilities of the two species, equilibrium strategies may consist of a single sleep pattern or a combination of multiple sleep patterns.
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BibTeX
@misc{bell2026from,
title = {{From daylight to darkness: a nonlocal model of circadian activity cycles}},
author = {Dan Bell and Timothé Boyer and Hao Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22713},
eprint = {2609.22713},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22713},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From daylight to darkness: a nonlocal model of circadian activity cycles
AU - Dan Bell
AU - Timothé Boyer
AU - Hao Wang
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.22713
UR - https://arxiv.org/abs/2609.22713
AB - An animal's ability to perceive its surroundings, as well as the ecological interactions it experiences, can be strongly influenced by the sleep patterns of both itself and surrounding species. Animals with limited sensory capabilities may struggle to navigate their habitat at night, while in a predator-prey system, it may be detrimental for prey to be inactive while predators are awake and hunting. Here, we develop a general mathematical framework to study these interactions using partial differential equations, incorporating activity cycles and daylight-dependent perception into existing models of animal movement. We show that both the dominant sensory mode and the length of daylight are key factors determining the strength of aggregation in social species. Extending this framework to a two-species predator-prey system, we use game-theoretic approaches to show that the equilibrium sleep strategy of each species is shaped not only by its own sensory capabilities, but also by those of its ecological opponent. Depending on the sensory capabilities of the two species, equilibrium strategies may consist of a single sleep pattern or a combination of multiple sleep patterns.
ER -