Allee dynamics generated by protection mutualisms can drive oscillations in trophic cascades

Abstract

Understanding the relative effect of top predators and primary producers on intermediate trophic levels is a key question in ecology. Most previous work, however, has not considered either realistic nonlinearities in feedback between trophic levels or the effect of mutualists on trophic cascades. Here, we develop a realistic model for a protection mutualism that explicitly includes interactions between a protected herbivore and both its food plant and generalist predators. In the absence of protection, herbivores and plant resources approach a stable equilibrium, provided that predation is not so high as to cause herbivore extinction. In contrast, adding protection by mutualists increases the range of dynamical outcomes to include unstable equilibria, stable and unstable limit cycles, and heteroclinic orbits. By reducing the impact of predators, protection by mutualists can allow herbivores to exert strong negative effects on their host plants, which in turn can lead to repeated cycles of overexploitation and recovery. Our results indicate that it may be essential to consider protection mutualisms to understand the dynamics of trophic cascades. Conversely, it may be essential to explicitly include dynamical feedback between plants and herbivores to fully understand the population and community dynamical consequences of protection mutualism.

Numerical responses in resource-based mutualisms: A time scale approach

“…Fishman and Hadany (2010) derived a Beddington-DeAngelis functional response in the specific case of bee pollination, by considering details such as flower and patch states, and flower-nest traveling times. And for protection mutualisms Morales et al (2008) employed time scale arguments in order to simplify the study of ant protection mutualisms.…”

Model selection analysis of temporal variation in benefit for an ant-tended treehopper

“…Predation was modeled as in Morales et al (2008) under the assumption that predators equilibrate rapidly to changes in treehopper and ant abundance. The predation rate was modeled mechanistically by assuming a constant immigration and attack rate for predators, and by allowing the rate at which predators leave aggregations to vary as a function of treehopper and ant density.…”

“…1 E-mail: mmorales@williams.edu for the population dynamics of mutualism (Holland et al 2002). Despite the close linkage between studies of context-dependent variation in the costs and benefits of mutualism and density-dependent costs and benefit, however, the density-dependent pattern of net benefit is typically viewed as fixed for a given system (Morales et al 2008, Morris et al 2010. In reality, both the magnitude and density-dependent pattern of benefit is likely to vary as the ecological conditions change.…”

Dispersal and spatial heterogeneity allow coexistence between enemies and protective mutualists

“…However, numerical experiments reveal that when is satisfied, the mutualist may invade when its initial density is above a threshold (Amarasekare , ; Morales et al. ). To find the critical value of the mutualist population density above which it can invade ( m *), we substitute m for M in eqn () and solve at the equilibrium to yield …”

“…No solution simultaneously satisfies inequalities (10) and (4), indicating that for the mutualist to invade; its net effect U must be negative (i.e., it may have a partial positive effect by decreasing enemy abundance, but its overall effect on the host is antagonistic). However, numerical experiments reveal that when (4) is satisfied, the mutualist may invade when its initial density is above a threshold (Amarasekare 1998(Amarasekare , 2004Morales et al 2007). To find the critical value of the mutualist population density above which it can invade (m*), we substitute m for M in eqn (1a-b) and solve at the equilibrium to yield…”