Parameterising variable assimilation efficiency in predator-prey models

Our understanding of the dynamics of predator-prey systems has relied heavily on the use of models based on the standard Lotka-Volterra (LV) framework, dating back over 80 years. Although these models have been repeatedly analysed and refined since their initial inception, the way they describe the predator's growth rate has received surprisingly little attention; typically it is simply assumed that the predator's growth rate is linearly related to its ingestion rate according to a constant assimilation efficiency, e. However, for many consumers e is known to decrease at high prey densities. Models that ignore variable assimilation efficiencies overlook potentially important non-linearities, affecting the validity of predictions relating to conservation, invasion biology and pest control. Directly quantifying the relationship between e and prey abundance is, however, difficult. An alternative approach (the independent-response, IR, approach) is to not assume any direct link between the predator's functional response (the relationship between ingestion rate and prey abundance) and its growth response. This flexibility is invaluable when parameterising models from data; providing the model-fitting process is constrained to ensure that e never exceeds 1, this approach allows considerable insight into whether, and how, e varies with prey density. Here we examine the synergistic value of combining the IR and LV approaches. We illustrate these concepts through analysis of published functional and growth response data and show that, in many cases, e does vary with prey abundance. This paper is the first recognition that these two complementary approaches can be combined into a single framework that allows the relationship between a predator's functional and growth responses to emerge during the parameterisation process, thereby acting as a compromise between restrictive models that require this relationship to be defined a priori, and completely unrestrained models that allow assimilation efficiencies to exceed 1.