# The evolution of cooperation under local regulation and non-additive gene action: building on Hamilton’s ideas

## TL;DR

This paper explores how cooperation evolves in populations with local regulation and non-linear gene effects, extending Hamilton's rule.

## Contribution

The study introduces a new framework for analyzing cooperation under non-additive gene action and varying local regulation.

## Key findings

- Cooperation can spread under a generalized version of Hamilton's rule when local regulation is weak.
- Cooperation is eliminated when local regulation is strong and migration is low.

## Abstract

We study evolution of cooperation in a population structured in a large number of groups of variable size, connected by random migration at rate m. Social interactions, including cooperation and competition occur only inside the groups. Assuming that groups are large, we define a parameter λ that measures the strength of the local regulation, i.e., the rigidity of group sizes. Individuals are of two possible genotypes, one typically assumed to produce a non-cooperative phenotype and the other a phenotype that is cooperative with all members of its own group. Gene action may be additive, producing fitness functions that are linear in the number of cooperators in a group, or not. Assuming weak selection, we obtain the following two contrasting conclusions. (1) “Hamilton regime”: If λ << m, then cooperative behavior can spread under a certain condition, which in the additive, i.e., linear, case is precisely Hamilton’s rule. The general version of this condition is also relatively easy to apply and is based on Wright’s classical beta distribution for the frequency of alleles in infinite island models. We call it the “beta version of Hamilton’s rule”. (2) “Taylor regime”: If m << λ, then cooperation that is costly to the actor is eliminated by selection.