Phenotype-structured nonlocal aggregation models I: signal production and response
Abstract
Individuals within a cellular or ecological population can exhibit substantial variation in their traits or phenotype. Such heterogeneity can fundamentally alter population-level behaviour, including the ability to aggregate and form spatial patterns. We investigate these effects by extending nonlocal aggregation models, widely used to model cell--cell adhesion and collective animal movement, to incorporate phenotype structure. We characterise how heterogeneity and switching between phenotypes affect whether patterns form, how phenotypes are distributed within them, and whether they are stationary or exhibit spatio-temporal oscillations. We show that pattern formation is promoted when phenotypes that produce stronger interaction signals also respond more strongly to them, whereas specialisation towards either signal production or response inhibits pattern formation. Increasing rates of switching between phenotypes dampen these effects. Heterogeneity can also enable weakly interacting, and even repulsive, individuals to pattern as part of the collective. Furthermore, movement in phenotype and physical space can interact to restructure patterns and generate spatio-temporal oscillations. A further key message of this study is the value of considering both discrete N-phenotype and continuous phenotype formulations. We develop both in parallel, demonstrating formal correspondences, but also advantages to each framework in terms of mathematical analyses and interpretability.
Related
- On a phenotype-structured Shigesada--Kawasaki--Teramoto model: Turing instability and pattern selection under fast phenotype switching
- Fitness is asymptotically irrelevant under uniform competition in phenotype-structured populations
- Activation of a tissue-specific stress response in the aqueous outflow pathway of the eye defines the glaucoma disease phenotype
- Age and sex alter the immune response in a chronic fibrosis model via changes in T cell and macrophage phenotype
- Progressive Actomyosin Remodeling Defining a Structured Podocyte Injury Response in Nephrotic Syndrome
BibTeX
@misc{jewell2026phenotypestructured,
title = {{Phenotype-structured nonlocal aggregation models I: signal production and response}},
author = {Thomas Jun Jewell and Andrew L. Krause and Philip K. Maini and Eamonn A. Gaffney},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29884},
eprint = {2610.29884},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29884},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Phenotype-structured nonlocal aggregation models I: signal production and response
AU - Thomas Jun Jewell
AU - Andrew L. Krause
AU - Philip K. Maini
AU - Eamonn A. Gaffney
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29884
UR - https://arxiv.org/abs/2610.29884
AB - Individuals within a cellular or ecological population can exhibit substantial variation in their traits or phenotype. Such heterogeneity can fundamentally alter population-level behaviour, including the ability to aggregate and form spatial patterns. We investigate these effects by extending nonlocal aggregation models, widely used to model cell--cell adhesion and collective animal movement, to incorporate phenotype structure. We characterise how heterogeneity and switching between phenotypes affect whether patterns form, how phenotypes are distributed within them, and whether they are stationary or exhibit spatio-temporal oscillations. We show that pattern formation is promoted when phenotypes that produce stronger interaction signals also respond more strongly to them, whereas specialisation towards either signal production or response inhibits pattern formation. Increasing rates of switching between phenotypes dampen these effects. Heterogeneity can also enable weakly interacting, and even repulsive, individuals to pattern as part of the collective. Furthermore, movement in phenotype and physical space can interact to restructure patterns and generate spatio-temporal oscillations. A further key message of this study is the value of considering both discrete N-phenotype and continuous phenotype formulations. We develop both in parallel, demonstrating formal correspondences, but also advantages to each framework in terms of mathematical analyses and interpretability.
ER -