Bayesian optimal designs for common single-driver experiments in ecology

Abstract

O_LIEcological experiments often characterize species responses to environmental drivers by estimating parameters of well-known nonlinear functions. However, the standard experimental designs used for these experiments waste precious experimental resources by making measurements at uninformative driver levels. C_LIO_LIClassical methods to optimize experimental designs require the parameter values we intend to estimate - circularity that undermines the usefulness of optimization. Bayesian Optimal Experimental Design (BOED) solves this problem by using prior distributions of the parameters to calculate designs that optimize properties of the posterior distribution. Thus, they circumvent the parameter dependence and result in robust, efficient experimental designs. C_LIO_LIHere, we develop and evaluate Bayesian optimal designs for four commonly used nonlinear drivers measuring per-capita growth rate against: nutrients/food (Monod or Holling type 2 function), light (Eilers-Peeters function), temperature (Norberg function) and toxins (log-logistic function). C_LIO_LIWe show using simulations that Bayesian optimal designs consistently outperform standard uniform designs in terms of parameter estimation and prediction accuracy, especially at low sample sizes. For some functions, Bayesian designs with 5 data points outperformed uniform designs with 15 data points. BOED can therefore allow us to allocate scarce experimental resources more efficiently. We provide detailed explanations and code to enable readers to apply these methods. We also provide rules of thumb that would improve experimental efficiency even without following the entire BOED procedure. C_LI