Statistical Quantification of Individual Differences (SQuID): an educational and statistical tool for understanding multilevel phenotypic data in linear mixed models

Abstract

Phenotypic variation exists in and at all levels of biological organization: variation exists among species, among-individuals within-populations, and in the case of l within-populations abile traits, within-individuals. Mixed-effects models represent ideal tools to quantify multilevel measurements of traits and are being increasingly used in evolutionary ecology. Mixed-effects models are relatively complex, and two main issues may be hampering their proper usage: (i) the relatively few educational resources available to teach new users how to implement and interpret them and (ii) the lack of tools to ensure that the statistical parameters of interest are correctly estimated. In this paper, we introduce Statistical Quantification of Individual Differences (SQuID), a simulation-based tool that can be used for research and educational purposes. SQuID creates a virtual world inhabited by subjects whose phenotypes are generated by a user-defined phenotypic equation, which allows easy translation of biological hypotheses into quantifiable parameters. Statistical Quantification of Individual Differences currently models normally distributed traits with linear predictors, but SQuID is subject to further development and will adapt to handle more complex scenarios in the future. The current framework is suitable for performing simulation studies, determining optimal sampling designs for user-specific biological problems and making simulation-based inferences to aid in the interpretation of empirical studies. Statistical Quantification of Individual Differences is also a teaching tool for biologists interested in learning, or teaching others, how to implement and interpret linear mixed-effects models when studying the processes causing phenotypic variation. Interface-based modules allow users to learn about these issues. As research on effects of sampling designs continues, new issues will be implemented in new modules, including nonlinear and non-Gaussian data.