scholarly journals Optimal experimental design for predator–prey functional response experiments

2018 ◽  
Vol 15 (144) ◽  
pp. 20180186 ◽  
Author(s):  
Jeff F. Zhang ◽  
Nikos E. Papanikolaou ◽  
Theodore Kypraios ◽  
Christopher C. Drovandi
Keyword(s):  
Experimental Design ◽  
Optimal Design ◽  
Functional Response ◽  
Optimal Parameter ◽  
Aphis Fabae ◽  
Optimal Experimental Design ◽  
Statistical Efficiency ◽  
Predator Prey ◽  
Designed Experiments ◽  
Robust Optimal Design

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 Notonecta glauca (an aquatic insect) preying on Asellus aquaticus (a small crustacean), and another experiment involving a ladybird beetle ( Propylea quatuordecimpunctata L.) preying on the black bean aphid ( Aphis fabae 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.

scholarly journals Sequential experimental design for predator–prey functional response experiments

2020 ◽  
Vol 17 (166) ◽  
pp. 20200156 ◽  
Author(s):  
Hayden Moffat ◽  
Markus Hainy ◽  
Nikos E. Papanikolaou ◽  
Christopher Drovandi
Keyword(s):  
Experimental Design ◽  
Functional Response ◽  
Statistical Models ◽  
Sequential Monte Carlo ◽  
Design Method ◽  
Computationally Efficient ◽  
Estimation Model ◽  
Predator Prey ◽  
Experimental Design Method ◽  
Experimental Runs

Understanding functional response within a predator–prey dynamic is a cornerstone for many quantitative ecological studies. Over the past 60 years, the methodology for modelling functional response has gradually transitioned from the classic mechanistic models to more statistically oriented models. To obtain inferences on these statistical models, a substantial number of experiments need to be conducted. The obvious disadvantages of collecting this volume of data include cost, time and the sacrificing of animals. Therefore, optimally designed experiments are useful as they may reduce the total number of experimental runs required to attain the same statistical results. In this paper, we develop the first sequential experimental design method for predator–prey functional response experiments. To make inferences on the parameters in each of the statistical models we consider, we use sequential Monte Carlo, which is computationally efficient and facilitates convenient estimation of important utility functions. It provides coverage of experimental goals including parameter estimation, model discrimination as well as a combination of these. The results of our simulation study illustrate that for predator–prey functional response experiments sequential design outperforms static design for our experimental goals. R code for implementing the methodology is available via https://github.com/haydenmoffat/sequential_design_for_predator_prey_experiments .

Multiple-objective criteria for optimal experimental design: application to ferrokinetics

1985 ◽  
Vol 248 (3) ◽  
pp. R378-R386 ◽  
Author(s):  
M. H. Nathanson ◽  
G. M. Saidel
Keyword(s):  
Experimental Design ◽  
Optimal Design ◽  
Objective Function ◽  
Information Matrix ◽  
Optimal Experimental Design ◽  
Multiple Objective ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Experimental Conditions ◽  
New Criterion

Optimal experimental design is used to predict the experimental conditions that will allow the "best" estimates of model parameters. A variety of criteria must be considered before an optimal design is chosen. Maximizing the determinant of the information matrix (D optimality), which tends to produce the most precise simultaneous estimates of all parameters, is commonly considered as the primary criterion. To complement this criterion, we present another whose effect is to reduce the interaction among the parameter estimates so that changes in any one parameter can be more distinct. This new criterion consists of maximizing the determinant of an appropriately scaled information matrix (M optimality). These criteria are applied jointly in a multiple-objective function. To illustrate the use of these concepts, we develop an optimal experimental design of blood sampling schedules using a detailed ferrokinetic model.

scholarly journals Estimating predator functional responses using the times between prey captures

2020 ◽  
Author(s):  
Kyle E. Coblentz ◽  
John P. DeLong
Keyword(s):  
Experimental Design ◽  
Statistical Method ◽  
Experimental Method ◽  
Functional Response ◽  
List Type ◽  
Proof Of Concept ◽  
Functional Responses ◽  
Predator Prey ◽  
Jumping Spiders ◽  
Wide Range

AbstractPredator functional responses, which describe how predator feeding rates change with prey densities, are a core component of predator-prey theory. Given their importance, ecologists have measured thousands of predator functional responses. However, most of these studies have used a single standard experimental method that is ill-suited to address many current, pressing questions regarding functional responses.We derive a new experimental design and statistical analysis that quantifies the parameters of predator functional responses by using the time between a predator’s feeding events and can be used with individual predators requiring only one or a few trials. We examine the feasibility of this experimental method and analysis by using simulations to examine the ability of the statistical model to estimate the ‘true’ functional response parameters from simulated data. We also perform a proof-of-concept experiment estimating the functional responses of two individual jumping spiders feeding on midges.Our simulations show that the statistical method is capable of reliably estimating functional response parameters under a wide range of parameter values and sample sizes. Our proof-of-concept experiment illustrates that the experimental design and statistical method provided reasonable estimates of functional response parameters and good fits to the data for individual jumping spiders using only a few trials per individual.By virtue of the fewer number of trials required to measure a functional response, the method derived here promises to expand the questions that can be addressed using functional response experiments and the systems for which functional responses can be measured. For example, this method is well-poised to address questions such as intraspecific variation in predator functional response parameters and the role of predator and prey traits and abiotic conditions on shaping functional responses. We hope, therefore, that this time-between-captures method will refine our understanding of functional responses and thereby our understanding of predator-prey interactions more generally.

scholarly journals Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sekson Sirisubtawee ◽  
Nattawut Khansai ◽  
Akapak Charoenloedmongkhon
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Impulsive Control ◽  
Positive Periodic Solution ◽  
Existence Condition ◽  
Predator Prey ◽  
Type Iv ◽  
Prey System ◽  
Existence And Stability ◽  
Predator Behavior

AbstractIn the present article, we propose and analyze a new mathematical model for a predator–prey system including the following terms: a Monod–Haldane functional response (a generalized Holling type IV), a term describing the anti-predator behavior of prey populations and one for an impulsive control strategy. In particular, we establish the existence condition under which the system has a locally asymptotically stable prey-eradication periodic solution. Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. Furthermore, numerical simulations for the proposed model are given to confirm the obtained theoretical results.

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