Bayesian optimal designs for common single-driver experiments in ecology

Summary

When measuring the impact of continuous independent variables, regressions are the appropriate tool. Regression experiments in ecology typically follow a replicated uniform design with experimental units evenly spaced across the design space. While popular, uniform designs are often inefficient and waste precious experimental resources. Optimal designs maximize the information gained per experimental unit and have been shown to be more efficient than uniform designs. However, optimal designs are parameter-dependent for non-linear regressions, which limits their application. Bayesian optimal designs use 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. In this study, we developed Bayesian optimal designs with four different sample sizes for four common single-driver non-linear regressions measuring per-capita growth against nutrient concentration, light intensity, temperature and toxin concentration. We compared the optimal designs to corresponding uniform designs in terms of parameter inference and predictive ability. For parameter inference, we performed 1000 simulations for each function where we generated data through both designs and fit the model through Bayesian inference. We compared the resulting posteriors from each design using strictly proper scoring rules. We also used the median curves from each posterior to compare predictive ability across the design space. We found that optimal design broadly outperformed uniform designs in both parameter inference and predictive ability across all sample sizes, especially in the nutrient and toxin experiments. We thus demonstrated the superiority of Bayesian optimal designs over commonly used uniform designs and advocate for increased use of Bayesian optimal designs in ecology.

Outcomes reported

When measuring the impact of continuous independent variables, regressions are the appropriate tool. Regression experiments in ecology typically follow a replicated uniform design with experimental units evenly spaced across the design space. While popular, uniform designs are often inefficient and waste precious experimental resources. Optimal designs maximize the information gained per experimental unit and have been shown to be more efficient than uniform designs. However, optimal designs are parameter-dependent for non-linear regressions, which limits their application. Bayesian optimal designs use 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. In this study, we developed Bayesian optimal designs with four different sample sizes for four common single-driver non-linear regressions measuring per-capita growth against nutrient concentration, light intensity, temperature and toxin concentration. We compared the optimal designs to corresponding uniform designs in terms of parameter inference and predictive ability. For parameter inference, we performed 1000 simulations for each function where we generated data through both designs and fit the model through Bayesian inference. We compared the resulting posteriors from each design using strictly proper scoring rules. We also used the median curves from each posterior to compare predictive ability across the design space. We found that optimal design broadly outperformed uniform designs in both parameter inference and predictive ability across all sample sizes, especially in the nutrient and toxin experiments. We thus demonstrated the superiority of Bayesian optimal designs over commonly used uniform designs and advocate for increased use of Bayesian optimal designs in ecology.

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