Covariance reaction norms: A flexible approach to estimating continuous environmental effects on quantitative genetic and phenotypic (co)variances

Estimating quantitative genetic and phenotypic (co)variances plays a crucial role in investigating key evolutionary ecological phenomena, such as developmental integration, life history tradeoffs, and niche specialization, as well as in describing selection and predicting multivariate evolution in the wild. While most studies assume (co)variances are fixed over short timescales, environmental heterogeneity can rapidly modify the variation of and associations among functional traits. Here I introduce a covariance reaction norm (CRN) model designed to address the challenge of detecting how trait (co)variances respond to continuous environmental change, building on the animal model used for quantitative genetic analysis in the wild. CRNs predict (co)variances as a function of continuous and/or discrete environmental factors, using the same multilevel modeling approach taken to prediction of trait means in standard analyses. After formally introducing the CRN model, I validate its implementation in Stan, demonstrating unbiased Bayesian inference. I then illustrate its application using long-term data on cooperation in meerkats (Suricata suricatta), finding that genetic (co)variances between social behaviors change as a function of group size, as well as in response to age, sex, and dominance status. Accompanying R code and a tutorial are provided to aid empiricists in applying CRN models to their own datasets.