Predicting the effects of multiple predator assemblages is often difficult due to nonlinearities in the effects of predators on prey. Therefore, to predict the effects of predator communities on prey, we need estimates of predation parameters that characterize each predator’s functional response. These estimates often come from experiments where researchers manipulate prey density and fit a functional response equation to the data. However, experiments often involve depletion, prey size-structure, blocked designs and the re-use of predators, which makes parameter estimation challenging. Here, we developed statistical models to account for these experimental realities using Template Model Builder, which allows users to create a model template in C++, and estimate parameters using automatic differentiation and Laplace approximations. To test the model, we simulated datasets of prey consumption at various prey densities and sizes. We then estimated size-dependent functional response parameters using our model in TMB as well as mle2 (the most common current method) for comparison. We calculated the bias and coverage of each parameter estimate and explored the consequences of biased parameter estimation on the predictions of multiple predator assemblages.
Results/Conclusions
For our analyses, we focused on a Ricker size-dependence function and a Type II functional response, fitting the handling time, maximum attack rate, and the size at maximum attack rate for each experiment. For each functional response parameter, the TMB fit demonstrated no bias, and appropriate coverage. The random effect, however, was slightly negatively biased because in some instances we were unable to completely estimate the random effects using REML and were only able to integrate over a subset of the parameters. However, even with a slight bias in the random effect estimate, the other parameter estimates were better in terms of both bias and coverage than the estimates produced without accounting for depletion and random effects (in mle2). As a result, we were better able to predict the effects of multiple predator assemblages using parameters estimated with TMB than with previously available statistical tools.