Holger Schielzeth

Assessing the biological relevance of variance components estimated using Markov chain Monte Carlo (MCMC)‐based mixed‐effects models is not straightforward. Variance estimates are constrained to be greater than zero and their posterior distributions are often asymmetric. Different measures of central tendency for these distributions can therefore vary widely, and credible intervals cannot overlap zero, making it difficult to assess the size and statistical support for among‐group variance. Statistical support is often assessed through visual inspection of the whole posterior distribution and so relies on subjective decisions for interpretation. We use simulations to demonstrate the difficulties of summarizing the posterior distributions of variance estimates from MCMC‐based models. We then describe different methods for generating the expected null distribution (i.e. a distribution of effect sizes that would be obtained if there was no among‐group variance) that can be used to aid in the interpretation of variance estimates. Through comparing commonly used summary statistics of posterior distributions of variance components, we show that the posterior median is predominantly the least biased. We further show how null distributions can be used to derive a p ‐value that provides complementary information to the commonly presented measures of central tendency and uncertainty. Finally, we show how these p ‐values facilitate the implementation of power analyses within an MCMC framework. The use of null distributions for variance components can aid study design and the interpretation of results from MCMC‐based models. We hope that this manuscript will make empiricists using mixed models think more carefully about their results, what descriptive statistics they present and what inference they can make.

Individuals differ in the way they judge ambiguous information: some individuals interpret ambiguous information in a more optimistic, and others in a more pessimistic way. Over the past two decades, such “optimistic” and “pessimistic” cognitive judgment biases (CJBs) have been utilized in animal welfare science as indicators of animals’ emotional states. However, empirical studies on their ecological and evolutionary relevance are still lacking. We, therefore, aimed at transferring the concept of “optimism” and “pessimism” to behavioral ecology and investigated the role of genetic and environmental factors in modulating CJB in mice. In addition, we assessed the temporal stability of individual differences in CJB. We show that the chosen genotypes (C57BL/6J and B6D2F1N) and environments (“scarce” and “complex”) did not have a statistically significant influence on the responses in the CJB test. By contrast, they influenced anxiety-like behavior with C57BL/6J mice and mice from the “complex” environment displaying less anxiety-like behavior than B6D2F1N mice and mice from the “scarce” environment. As the selected genotypes and environments did not explain the existing differences in CJB, future studies might investigate the impact of other genotypes and environmental conditions on CJB, and additionally, elucidate the role of other potential causes like endocrine profiles and epigenetic modifications. Furthermore, we show that individual differences in CJB were repeatable over a period of seven weeks, suggesting that CJB represents a temporally stable trait in laboratory mice. Therefore, we encourage the further study of CJB within an animal personality framework.