Optimal experimental design for predator–prey functional response experiments

Abstract

Functional response models are important in understanding predator-prey interactions. The development of functional response methodology has progressed from mechanistic models to more statistically motivated models that can account for variance and the over-dispersion commonly seen in the datasets collected from functional response experiments. However, little information seems to be available for those wishing to prepare optimal parameter estimation designs for functional response experiments. It is worth noting that optimally designed experiments may require smaller sample sizes to achieve the same statistical outcomes as non-optimally designed experiments. In this paper, we develop a model-based approach to optimal experimental design for functional response experiments in the presence of parameter uncertainty (also known as a robust optimal design approach). Further, we develop and compare new utility functions which better focus on the statistical efficiency of the designs; these utilities are generally applicable for robust optimal design in other applications (not just in functional response). The methods are illustrated using a beta-binomial functional response model for two published datasets: an experiment involving the freshwater predator (an aquatic insect) preying on (a small crustacean), and another experiment involving a ladybird beetle ( L.) preying on the black bean aphid ( Scopoli). As a by-product, we also derive necessary quantities to perform optimal design for beta-binomial regression models, which may be useful in other applications.

Laboratory measurement of the functional and numerical responses of the predaceous mite, Typhlodromus (T.) setubali to Panonychus ulmi (Phytoseiidae: Tetranychidae)

“…Modeling a prey-predator system has progressed considerably to more mathematically tted models, which correct errors related to certain classical aspects of calculation [24]. The logistic regression delivered a signi cantly negative linear coe cient (P 1 < 0) and a positive quadratic coe cient (P 2 > 0) for the seven classes of prey offered, suggesting that T. (T.) setubali performs a type II functional response to P. ulmi immatures (Table 1), which assumes that the predation rate increased according to the increase in prey density, levelling off to a maximum of 18 prey.…”

Predator size affects the intensity of mutual interference in a predatory mirid

“…Understanding the relationship between per capita predator consumption in increasing prey density, that is, the functional response (Solomon, 1949), is crucial for describing and estimating the feeding interactions between a consumer and a resource (see, e.g., Abrams, 1989; Englund et al., 2011; Jeschke et al., 2002; Sentis, Hemptinne, & Brodeur, 2012, 2013) and essentially the cornerstone for most quantitative ecological studies (Moffat et al., 2020; Zhang et al., 2018). Holling (1959a) proposed various types of functional response; in type I and II, the prey consumption is assumed to increase linearly with prey density or increase asymptotically, respectively, reaching a plateau, while in a type III functional response, the prey consumption is supposed of a sigmoid form as prey density increases.…”

Systematic bias in studies of consumer functional responses

“…That said, we offer no rule of thumb for determining what sample size is enough; as noted above, the sample size necessary to effectively reduce bias will depend on the variance‐generating processes of the system in question and the experimental designs and models with which these processes are studied. Continued developments in the areas of symbolic regression and optimal experimental design should have much insight to offer in reducing the logistical burden that will be required (Okuyama and Bolker, 2012; Martin et al ., 2018; Zhang et al ., 2018; Moffat et al ., 2020). This notwithstanding, the most fundamental advance that is needed is a conceptual one regarding a clarity of purpose.…”