Dynamics of mutualist populations that are demographically open.

1. Few theoretical studies have examined the impact of immigration and emigration on mutualist population dynamics, but a recent empirical study (A.R. Thompson Oecologia, 143, 61-69) on mutualistic fish and shrimp showed that immigration can prevent population collapse, and that intraspecific competition for a mutualistic partner can curb population expansion. To understand in a theoretical context the implications of these results, and to assess their generality, we present a two-species model that accounts explicitly for immigration and emigration, as well as distinguishing the impacts of mutualism on birth rates, death rates and habitat acquisition. 2. The model confirms that immigration can stabilize mutualistic populations, and predicts that high immigration, along with enhanced reproduction and/or reduced mortality through mutualism, can cause population sizes to increase until habitat availability curbs further expansion. 3. We explore in detail the effects of different forms of habitat limitation on mutualistic populations. Habitat availability commonly limits the density of both populations if mutualists acquire shelter independently. If a mutualist depends on a partner for habitat, densities of that mutualist are capped by the amount of space provided by that partner. The density of the shelter-provider is limited by the environment. 4. If a mutualism solely augments reproduction, and most locally produced individuals leave the focal patch, then the mutualism will have a minimal effect on local dynamics. If the mutualism operates by reducing rates of death or enhancing habitat availability, and there is at least some immigration, then mutualism will affect local dynamics. This finding may be particularly relevant in marine systems, where there is high variability (among species and locations) in the extent to which progeny disperse from natal locations. 5. Overall, our results demonstrate that the consequences of immigration and emigration for the dynamics of mutualists depend strongly on which demographic rate is influenced by mutualism. 6. By relating our model to a variety of terrestrial and aquatic systems, we provide a general framework to guide future empirical studies of the dynamics of mutualistic populations.