A Metaphysiological Population Model of Storage in Variable Environments

Abstract

ABSTRACT. We use mechanistic arguments to generalize a hierarchical metaphysiological approach developed by one of us to modeling biological populations (Getz, [1991, 1993]) and extend the approach to include a storage component in the population. We model the growth of single species and consumer‐resource interactions, both with and without storage. Our approach unifies modeling storage across trophic levels and is much simpler and more efficient to implement numerically than individual based approaches or population approaches that include integral, delay, or partial differential equation components in the model. Using intake functions (i.e., functional responses) that include the effects of interference competition, we apply the model to a hypothetical herbivore feeding on a resource that fluctuates seasonally and demonstrate the importance of a flow from storage that buffers the population against periods when resources are scarce or absent. We also apply the model to a hypothetical plant population that is driven by fluctuating resources and demonstrate the importance of a translocation flow from storage at the end of a dormant season, corresponding to periods when resources are most scarce. Finally, we couple these two populations for the case where the herbivore feeds exclusively on non‐storage biomass, and demonstrate how the population dynamics can be affected by the rates at which buffering and translocation flows transfer from storage to active tissue in the herbivore and plant populations. In particular, for certain buffering and translocation flow rates, 1‐year unimodal, 2‐year bimodal, and 2‐year unimodal cycles can emerge in the same herbivore population.

A Biomass Flow Approach to Population Models and Food Webs

“…In the early 1990s a fierce debate raged, as reviewed by Abrams and Ginzburg [2000], over whether the resource‐dependent functional response h ( x ) of or the ratio‐dependent functional response (Maynard Smith and Slatkin [1973], Getz [1984]) is more fundamental to characterizing resource extraction. Since both of these functional responses are special cases of the more general form h ( x , y ) in , which was introduced over 35 years ago, the argument appears in hindsight to be a storm in a tea cup and a question ultimately of the time scales over which the extraction rates are averaged (Getz and Schreiber [1999]).…”

Population and Evolutionary Dynamics of Consumer‐Resource Systems

“…As described in Getz & Owen-Smith (1998), the basic trophic Equations 7.30 can be augmented to include a storage component for each population. In this section, I provide an outline of this approach.…”

“…The allocation function p and the buffering and translocation flow rate functions f e and f w respectively can be expressed in a number of different ways and still be compatible with the assumptions made above.A particular set of expressions has been derived by Getz and Owen-Smith (1998), while a general theory for deriving such expressions from mechanistic principles has been proposed (Michalski & Getz unpublished manuscript). I will not pursue these details here, other than to remark that the existence of a storage component is critical to promoting the persistence of populations in highly variable resource environments.…”

Disease and the Dynamics of Food Webs

“…the per unit (e.g., per capita) growth rate of the component i , which from calculus is represented by is a function g i of its per unit consumption rate y i −1 (see [5] for a more detailed elaboration of g i and [33] for inclusion of a storage component);…”