Footnote 1 The debate on the functional response (see Jost and Ellner 2000, for a comprehensive discussion) largely fluctuates around the functional specification and subsequent estimation of the so-called predation function in continuous time. The instantaneous rate of prey consumption per predator-the so-called functional response-is both an essential feature of PP interaction and an important dimension for structuring a broad variety of continuous time PP models (see Jost and Ellner 2000, for an overview). In the ecological and biological literature so-called predator-prey (PP) models have become an established framework to describe patterns of predation, i.e., the killing and consumption of one species (the prey) by another (the predator). 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. Results from an unrestricted structural model are in line with core axiomatic assumptions of predator-prey models.

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. (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. 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. 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. In ecology, the concept of predation describes interdependent patterns of having one species (called the predator) killing and consuming another (the prey).

Predator vs prey conclusion example