Estimation of additive genetic variance when there are gene-environment correlations: pitfalls, solutions and unexplored questions.

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British Ecological Society
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1. Estimating the genetic variation underpinning a trait is crucial to understanding and predicting its evolution. A key statistical tool to estimate this variation is the animal model. Typically, the environment is modelled as an external variable independent of the organism, affecting the focal phenotypic trait via phenotypic plasticity. We studied what happens if the environment is not independent of the organism because it chooses or adjusts its environment, potentially creating non-zero genotype–environment correlations. 2. We simulated a set of biological scenarios assuming the presence or absence of a genetic basis for a focal phenotypic trait and/or the focal environment (treated as an extended phenotype), as well as phenotypic plasticity (the effect of the environment on the phenotypic trait) and/or ‘environmental plasticity’ (the effect of the phenotypic trait on the local environment). We then estimated the additive genetic variance of the phenotypic trait and/or the environment by applying five animal models which differed in which variables were fitted as the dependent variable and which covariates were included. 3. We show that animal models can estimate the additive genetic variance of the local environment (i.e. the extended phenotype) and can detect environmental plasticity. We show that when the focal environment has a genetic basis, the additive genetic variance of a phenotypic trait increases if there is phenotypic plasticity. We also show that phenotypic plasticity can be mistakenly inferred to exist when it is actually absent and instead environmental plasticity is present. When the causal relationship between the phenotype and the environment is misunderstood, it can lead to severe misinterpretation of the genetic parameters, including finding ‘phantom’ genetic variation for traits that, in reality, have none. We also demonstrate how using bivariate models can partly alleviate these issues. Finally, we provide the mathematical equations describing the expected estimated values.
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Funding information: Norges Forskningsråd, Grant/Award Number: 325826 and PID 302619; Spanish Ministry of Science and Innovation, Grant/Award Number: CGL2016-79483-P and PID2019-108971GB-I00; Spanish Ministry of Universities, Grant/Award Number: FPU17/06268; Swedish Collegium for Advanced Study The peer review history for this article is available at https://w w w.w e b o f s c i e n c e . c o m /a p i /g a t e w a y/ w o s /p e e r- r e v i ew/10.1111/2041-210X.14098. Code to simulate the data is available from Zenodo repository at (Munar-Delgado et al., 2023). Additional supporting information can be found online in the Supporting Information section at the end of this article: Supplementary Material I. About considering the extended phenotype as a focal trait. Supplementary Material II. Supplementary Results. CGL2016-79483- P PID2019-108971GB- I00 FPU17/06268
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