Mutualisms are ubiquitous in nature, provide important ecosystem
services, and involve many species of interest for conservation.
Theoretical progress on the population dynamics of mutualistic
interactions, however, has comparatively lagged behind that of trophic
and competitive interactions. Consequently, ecologists still lack a
generalized framework to investigate the population dynamics of
mutualisms. Here, we review historical models of two-species mutualisms
from over the last 90 years. We find that population dynamics of
mutualisms are qualitatively robust across derivations, including levels
of detail, types of benefit, and inspiring systems. Specifically,
mutualisms exhibit stable coexistence at high density and destabilizing
thresholds at low density. We distinguish between thresholds resulting
from Allee effects, low partner density, and high partner density, and
their mathematical and conceptual causes. The dynamics of stable
coexistence and thresholds in partner density emerge when benefits of
mutualism saturate, whether due to intrinsic or extrinsic density
dependence in intraspecific, interspecific, or both. These results
suggest that there exists a robust population dynamic theory of
mutualism that can make general predictions.