Population dynamics of mutualism and intraspecific density dependence: How θ-logistic density dependence affects mutualistic positive feedback

Abstract Mutualism describes the biological phenomenon where two or more species are reciprocally beneficial, regardless of their ecological intimacy or evolutionary history. Classic theory shows that mutualistic benefit must be relatively weak, or else it overpowers the stabilizing influence of intraspecific competitionand leads to unrealistic, unbounded population growth. Interestingly, the conclusion that strong positive interactions lead to runaway population growthis strongly grounded in the behavior of a single model. This model—the Lotka–Volterra competition modelwith a sign change to generate mutualism rather than competition between species—assumes logistic growth of each species plus a linear interaction term to represent the mutualism. While it is commonly held that the linear interaction term is to blame for the model's unrealistic behavior, we show here that a linear mutualism added to a θ -logistic model of population growthcan prevent unbounded growth. We find that when density dependenceis decelerating, the benefit of mutualism at equilibrium is greater than when density dependenceis accelerating. Although there is a greater benefit, however, decelerating density dependencetends to destabilize populations whereas accelerating density dependenceis always stable. We interpret these findings tentatively, but with promise for the understanding of the population ecologyof mutualism by generating several predictions relating growth rates of mutualist populations and the strength of mutualistic interaction.