Quantifying individual variation in reaction norms: Mind the residual

Abstract

Phenotypic plasticity is a central topic in ecology and evolution. Individuals may differ in the degree of plasticity (individual‐by‐environment interaction (I × E)), which has implications for the capacity of populations to respond to selection. Random regression models (RRMs) are a popular tool to study I × E in behavioural or life‐history traits, yet evidence for I × E is mixed, differing between species, populations, and even between studies on the same population. One important source of discrepancies between studies is the treatment of heterogeneity in residual variance (heteroscedasticity). To date, there seems to be no collective awareness among ecologists of its influence on the estimation of I × E or a consensus on how to best model it. We performed RRMs with differing residual variance structures on simulated data with varying degrees of heteroscedasticity and plasticity, sample size and environmental variability to test how RRMs would perform under each scenario. The residual structure in the RRMs affected the precision of estimates of simulated I × E as well as statistical power, with substantial lack of precision and high false‐positive rates when sample size, environmental variability and plasticity were small. We show that model comparison using information criteria can be used to choose among residual structures and reinforce this point by analysis of real data of two study populations of great tits (Parus major). We provide guidelines that can be used by biologists studying I × E that, ultimately, should lead to a reduction in bias in the literature concerning the statistical evidence and the reported magnitude of variation in plasticity.

Individual variation in reaction norms but no directional selection in reproductive plasticity of a wild passerine population

“…Such difference could be attributed to the difference in sample size, or a result of heterogeneity in individual variance across years. While this heterogeneity could be of interest in itself (Cleasby et al, 2015 ), we did not specifically tested for this in the models in this study, so as to prevent overfitting (Ramakers et al, 2020 ).…”

Great tits differ in glucocorticoid plasticity in response to spring temperature

“…With this model, we tested for among-individual variance in the elevation (Velevation) and slopes of corticosterone concentrations in response to temperature at capture (Vslopes), while also testing for the covariance and correlation among individuals’ elevation and slopes (COVelevations-slopes and relevations-slopes, respectively). Inappropriate modelling of residual variance (e.g., assuming residual homogeneity) can lead to erroneous inferences of slope variance in random regression models (for further detail, see Ramakers et al, 2020). Hence, we assumed residual effects to be year-specific (i.e., estimated residual variance for each of the 5 study years) and uncorrelated across years (i.e., diagonal residual error structure).…”

Effects of ambient temperatures on evolutionary potential of reproductive timing in boreal passerines

“…Possible heteroscedasticity of residual variance across spring temperatures was considered by estimating the residual variance for each equal‐interval group l of spring temperatures as (Ramakers, Culina, et al., 2018). The number of groups n was decided upon from four alternatives ( n = 4, 6, 8 or 10) based on model comparison using DIC values (Ramakers et al., 2020). For both species, n = 10 was selected.…”