# Nonlinear social evolution and the emergence of collective action

## TL;DR

This paper develops a mathematical framework to analyze how nonlinear social interactions influence the evolution of collective behaviors across diverse biological systems, incorporating spatial and kin structures.

## Contribution

It introduces a general mathematical condition for natural selection with nonlinear social interactions, applicable to complex population structures and kin relationships.

## Key findings

- Derived a condition for selection with synergistic interactions.
- Applied the condition to kin and spatial network models.
- Extended the concept of 'actor' to collectives in social evolution.

## Abstract

Organisms from microbes to humans engage in a variety of social behaviors, which affect fitness in complex, often nonlinear ways. The question of how these behaviors evolve has consequences ranging from antibiotic resistance to human origins. However, evolution with nonlinear social interactions is challenging to model mathematically, especially in combination with spatial, group, and/or kin assortment. We derive a mathematical condition for natural selection with synergistic interactions among any number of individuals. This result applies to populations with arbitrary (but fixed) spatial or network structure, group subdivision, and/or mating patterns. In this condition, nonlinear fitness effects are ascribed to collectives, and weighted by a new measure of collective relatedness. For weak selection, this condition can be systematically evaluated by computing branch lengths of ancestral trees. We apply this condition to pairwise games between diploid relatives, and to dilemmas of collective help or harm among siblings and on spatial networks. Our work provides a rigorous basis for extending the notion of ``actor", in the study of social evolution, from individuals to collectives.