Population Dynamics and Mutualism: Functional Responses of Benefits and Costs

TLDR

The study develops a framework for analyzing mutualistic population dynamics using density‑dependent functional responses of benefits and costs. The authors formulate density‑dependent functional responses for mutualist growth, explore various benefit–cost dependencies, and apply the model to the senita cactus–moth system, examining egg distribution and fruit abortion as mechanisms shaping these responses. Net effects of mutualism are typically saturating or unimodal, and varying benefit–cost relationships can alter population dynamics and stability, with fruit abortion enabling a stable equilibrium that would otherwise be absent.

Abstract

We develop an approach for studying population dynamics resulting from mutualism by employing functional responses based on density-dependent benefits and costs. These functional responses express how the population growth rate of a mutualist is modified by the density of its partner. We present several possible dependencies of gross benefits and costs, and hence net effects, to a mutualist as functions of the density of its partner. Net effects to mutualists are likely a monotonically saturating or unimodal function of the density of their partner. We show that fundamental differences in the growth, limitation, and dynamics of a population can occur when net effects to that population change linearly, unimodally, or in a saturating fashion. We use the mutualism between senita cactus and its pollinating seed-eating moth as an example to show the influence of different benefit and cost functional responses on population dynamics and stability of mutualisms. We investigated two mechanisms that may alter this mutualism's functional responses: distribution of eggs among flowers and fruit abortion. Differences in how benefits and costs vary with density can alter the stability of this mutualism. In particular, fruit abortion may allow for a stable equilibrium where none could otherwise exist.