title: Inferring the temperature dependence of population parameters: the effects of experimental design and inference algorithm.
abstract: Understanding and quantifying the temperature dependence of population parameters, such as intrinsic growth rate and carrying capacity, is critical for predicting the ecological responses to environmental change. Many studies provide empirical estimates of such temperature dependencies, but a thorough investigation of the methods used to infer them has not been performed yet. We created artificial population time series using a stochastic logistic model parameterized with the Arrhenius equation, so that activation energy drives the temperature dependence of population parameters. We simulated different experimental designs and used different inference methods, varying the likelihood functions and other aspects of the parameter estimation methods. Finally, we applied the best performing inference methods to real data for the species Paramecium caudatum. The relative error of the estimates of activation energy varied between 5% and 30%. The fraction of habitat sampled played the most important role in determining the relative error; sampling at least 1% of the habitat kept it below 50%. We found that methods that simultaneously use all time series data (direct methods) and methods that estimate population parameters separately for each temperature (indirect methods) are complementary. Indirect methods provide a clearer insight into the shape of the functional form describing the temperature dependence of population parameters; direct methods enable a more accurate estimation of the parameters of such functional forms. Using both methods, we found that growth rate and carrying capacity of Paramecium caudatum scale with temperature according to different activation energies. Our study shows how careful choice of experimental design and inference methods can increase the accuracy of the inferred relationships between temperature and population parameters. The comparison of estimation methods provided here can increase the accuracy of model predictions, with important implications in understanding and predicting the effects of temperature on the dynamics of populations.
authors.affiliation: Department of Evolutionary Biology and Environmental Studies, University of Zurich Wintherthurerstrase 190, CH-8057, Zurich, Switzerland ; Computational Science Laboratory, Microsoft Research Cambridge, CB1 2FB, UK.
authors.forename: Gian Marco
authors.initials: GM
authors.lastname: Palamara
authors.affiliation: Department of Animal and Plant Sciences, University of Sheffield Sheffield, S10 2TN, UK.
authors.forename: Dylan Z
authors.initials: DZ
authors.lastname: Childs
authors.affiliation: Department of Evolutionary Biology and Environmental Studies, University of Zurich Wintherthurerstrase 190, CH-8057, Zurich, Switzerland.
authors.forename: Christopher F
authors.initials: CF
authors.lastname: Clements
authors.affiliation: Department of Evolutionary Biology and Environmental Studies, University of Zurich Wintherthurerstrase 190, CH-8057, Zurich, Switzerland.
authors.forename: Owen L
authors.initials: OL
authors.lastname: Petchey
authors.affiliation: Department of Evolutionary Biology and Environmental Studies, University of Zurich Wintherthurerstrase 190, CH-8057, Zurich, Switzerland.
authors.forename: Marco
authors.initials: M
authors.lastname: Plebani
authors.affiliation: Computational Science Laboratory, Microsoft Research Cambridge, CB1 2FB, UK.
authors.forename: Matthew J
authors.initials: MJ
authors.lastname: Smith
keywords: Activation energy; Arrhenius equation; MCMC; maximum likelihood; metabolic theory; microcosm experiments; state space models; stochastic simulations