UC Irvine

Cooperation in biology and diversification of species have been widely studied by both evolutionary biologists and mathematicians. In this work we examine both of these seemingly unrelated phenomena and propose that there could be a context where they are connected. We focus on a setting where individuals in a shared environment cooperate by sharing products of two distinct parts of a complex task. Different strategies can evolve: individuals can complete all parts of the complex task, choosing self-sufficiency over cooperation, or they may choose to split parts of the task and share the products for mutual benefit, such that distinct groups of the organisms specialize on a subset of elementary tasks. We first examine this possibility using a quasispecies system, and then by using the methodology of adaptive dynamics, both analytically and by stochastic agent-based simulations, to investigate the conditions where branching into distinct cooperating subgroups occurs. We show that if performing multiple tasks is associated with additional cost, branching occurs for a wide parameter range, and is stable against the invasion of non-cooperating non-producers (``cheaters''). We hypothesize that over time, this can lead to evolutionary speciation, providing a novel mechanism of speciation based on cooperation. In addition, we investigate whether microscopic assumptions of the interaction rules of the simulations may play a role in the resulting dynamics. To do this, we derive ordinary differential equations for the mean trait values for four models, which differ by (1) the number of interactions each individual engages in before the payoff is determined (interacting with the entire population vs interacting with one randomly chosen individual), and (2) the type of criterion (probabilistic vs deterministic) by which the winner of each competition is determined. We find that the mean trait dynamics are the same in all four cases when only one trait in a population of cooperators is evolving. However, when we include ``cheaters'' we find, surprisingly, that the rules do make a difference, and the steady state to which the system converges can depend both on the number of interactions and on the criterion for determining the winners.