Print PagePopulation dynamics are often modeled by a single differential equation involving only the species of study. Instead of directly modeling the effects of other factors, single species models include parameters that incorporate these effects indirectly. In particular, when density dependence is expected due to resource depletion, a logistic model predicts dynamics using consumer density but neglecting any direct measurement of resource density.
Recent theoretical work has questioned whether a single species model representing a simplified version of a consumer-resource system is robust enough to capture the expected density dependence curves. In exploring this question, a new theoretical perspective on how to find density dependent curves of a consumer-resource system has been introduced. Using algebraic and numerical techniques, we relate this perspective to more traditional ways of considering density dependence.
Moreover, considering three types of resource (abiotic, biotic, abiotic + biotic) and two types of consumer functional responses (Type I, Type II), we explore the scenarios in which the density dependent curves determined from both newer and more traditional perspectives can be utilized in single species models to accurately represent the dynamics of the more complicated consumer-resource system from which they were calculated.
Results/Conclusions
We find that the key to connecting more recent and more traditional perspectives on density dependence is considering each perspective’s inherent assumptions about initial resource density. By varying initial resource densities, we define cases when each perspective is appropriate for use in a single species model.
Despite each perspective assuming different initial resource levels, we find scenarios where “consumer per capita growth rate vs. consumer population density” curves coincide. For example, a population, which has a low natural death rate and exhibits a Type I functional response to an abiotic resource, will have very similar density dependent curves from both perspectives. In contrast, when a population is expected to oscillate towards a stable equilibrium, we find differences in the density dependence curves; however, such oscillatory dynamics are not necessary for the differing perspectives to yield different results.
This work has implications for the common use of the logistic model as the basis of nearly all species interactions and community models. It also provides guidance when conducting empirical investigations of density dependence.
