Tension between positive and negative feedback determines the dynamics and long-term persistence of consumer-resource interactions
Diversity results from coexistence mechanisms, all of which require that species limit themselves more than they do others. The challenge is to determine how the interplay between intra- and inter-specific interactions leads to such self-limitation. Previous theory focuses on the tension between different interaction types in terms of the sign or strength of the interactions. Strong interactions between trophic levels (e.g., consumer-resource, predator-prey, host-parasite) lead to oscillations in species abundances, which can predispose species to stochastic extinction during periods of low abundances. Non-trophic interactions (e.g., exploitative/apparent competition) within trophic levels can weaken the links between trophic levels, thus reducing the tendency for oscillations and the potential for stochastic extinction. This theory predicts that interactions in nature tend to be weak. Here, we recast ideas about interaction strength in terms of the tension between positive (destabilizing) and negative (stabilizing) feedback loops that operate within and between species. Our goal is to develop a theoretical framework which integrates ideas about interaction strength with feedback mechanisms operating in natural communities.
By non-dimensionalizing consumer-resource models, we identify important parameter groupings that illustrate how parameters inducing positive feedback (attack rates) and negative feedback (intra-specific competition within resource species) group together and influence species’ population dynamics. The key parameter groupings are attack rates and handling times, which scale with the strength of positive feedback relative to negative feedback, such that increased attack rates, for example, indicate that positive feedback is relatively strong compared to negative feedback. We quantify the tension between positive and negative feedback via species’ per capita growth rates. Thus, while interaction strength only incorporates positive feedback, our metric includes both positive and negative feedback (and hence the net effect of all interactions on the growth rate). We then derive the stability boundary (at which the onset of oscillations occurs) in terms of this metric for basic community modules. We show that modules with more non-trophic competitive links (which induce negative feedback) relative to trophic interactions (which induce positive feedback) tend to be less prone to oscillatory dynamics. While the ideas we build on are well-known, synthesizing them in a common framework leads to novel insights about the generation and maintenance of diversity.