Estimation of genetic variance in fitness, and inference of adaptation, when fitness follows a log-normal distribution

Timothée Bonnet, Michael B Morrissey, Loeske E B Kruuk

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Additive genetic variance in relative fitness (σ2A(w)) is arguably the most important evolutionary parameter in a population because, by Fisher’s fundamental theorem of natural selection (FTNS; Fisher RA. 1930. The genetical theory of natural selection. 1st ed. Oxford: Clarendon Press), it represents the rate of adaptive evolution. However, to date, there are few estimates of σ2A(w) in natural populations. Moreover, most of the available estimates rely on Gaussian assumptions inappropriate for fitness data, with unclear consequences. “Generalized linear animal models” (GLAMs) tend to be more appropriate for fitness data, but they estimate parameters on a transformed (“latent”) scale that is not directly interpretable for inferences on the data scale. Here we exploit the latest theoretical developments to clarify how best to estimate quantitative genetic parameters for fitness. Specifically, we use computer simulations to confirm a recently developed analog of the FTNS in the case when expected fitness follows a log-normal distribution. In this situation, the additive genetic variance in absolute fitness on the latent log-scale (σ2A(l)) equals (σ2A(w)) on the data scale, which is the rate of adaptation within a generation. However, due to inheritance distortion, the change in mean relative fitness between generations exceeds σ2A(l) and equals (exp(σ2A(l))−1)⁠. We illustrate why the heritability of fitness is generally low and is not a good measure of the rate of adaptation. Finally, we explore how well the relevant parameters can be estimated by animal models, comparing Gaussian models with Poisson GLAMs. Our results illustrate 1) the correspondence between quantitative genetics and population dynamics encapsulated in the FTNS and its log-normal-analog and 2) the appropriate interpretation of GLAM parameter estimates.
Original languageEnglish
Pages (from-to)383–395
Number of pages13
JournalJournal of Heredity
Issue number4
Publication statusPublished - 26 Jun 2019


  • animal model
  • fundamental theorem of natural selection
  • GLMM
  • heritability
  • quantitative genetics


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