Modelling interaction patterns in a predator-prey system of two freshwater organisms in discrete time: an identified structural VAR approach

In ecology, the concept of predation describes interdependent patterns of having one species (called the predator) killing and consuming another (the prey). Specifying the so-called functional response of prey populations to predation is an important matter of debate which is typically addressed by means of continuous time models. Empirical regression or autoregression models applied to discrete predator-prey population data promise feasible steady state approximations of often complicated dynamic patterns of population growth and interaction. Ewing et al. (Ecol Econ 60:605–612, 2007) argue in favour of the informational content of so-called vector autoregressive models for the dynamic analysis of predator-prey systems. In this work we reconsider their analysis of dynamic interaction of two freshwater organisms, and design a structural model that allows to approximate the functional response in causal form. Results from an unrestricted structural model are in line with core axiomatic assumptions of predator-prey models. Conditional on population growth lagged up to three periods (i.e., 36 h), the semi-daily population growth of the prey Paramecium aurelia diminishes, on average, by 1.2 percentage points in response to an increase of the population growth of the predator Didinium nasutum by one percentage point.