Phenotypic Assortment and the Evolution of Cooperation in Finite Periodic Phenotype Spaces
Abstract
We study the evolution of cooperation in a finite haploid population whose individuals carry both a strategy and a phenotype on a finite periodic space. Cooperators help with a probability that decays exponentially with phenotypic distance, generating graded phenotype-dependent assortment. Under weak selection and a large-population mutation scaling, we combine coalescent arguments with the spectral representation of a random walk on the discrete torus to derive an explicit benefit-to-cost threshold for cooperation to be favored in stationary abundance. Stronger phenotypic discrimination and higher phenotype-space dimension strictly lower this threshold, whereas strategy mutation raises it. In contrast, phenotype mutation has a nonmonotone effect: the threshold diverges for both very rare and very rapid phenotype mutation and therefore attains at least one minimum at an intermediate rate. The high-mutation inhibition results from mixing on the finite phenotype space and distinguishes the periodic model from its unbounded-lattice counterpart.
Versions
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BibTeX
@misc{kroumi2026phenotypic,
title = {{Phenotypic Assortment and the Evolution of Cooperation in Finite Periodic Phenotype Spaces}},
author = {Dhaker Kroumi},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.21872},
eprint = {2608.21872},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.21872},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Phenotypic Assortment and the Evolution of Cooperation in Finite Periodic Phenotype Spaces
AU - Dhaker Kroumi
PY - 2026
DA - 2026/08/22
PB - arXiv
DO - 10.48550/arxiv.2608.21872
UR - https://arxiv.org/abs/2608.21872
AB - We study the evolution of cooperation in a finite haploid population whose individuals carry both a strategy and a phenotype on a finite periodic space. Cooperators help with a probability that decays exponentially with phenotypic distance, generating graded phenotype-dependent assortment. Under weak selection and a large-population mutation scaling, we combine coalescent arguments with the spectral representation of a random walk on the discrete torus to derive an explicit benefit-to-cost threshold for cooperation to be favored in stationary abundance. Stronger phenotypic discrimination and higher phenotype-space dimension strictly lower this threshold, whereas strategy mutation raises it. In contrast, phenotype mutation has a nonmonotone effect: the threshold diverges for both very rare and very rapid phenotype mutation and therefore attains at least one minimum at an intermediate rate. The high-mutation inhibition results from mixing on the finite phenotype space and distinguishes the periodic model from its unbounded-lattice counterpart.
ER -