Ecogenetic Module Genetic Structure

Genetic structure

The genetic structure is described by a polygenic multi-allelic model with finite numbers of loci and alleles for both the functional and neutral parts of the genome. The value of trait $Z$ thus results from the expression of $l_Z$ functional loci, each of which has a pool of $n_{Z, l}$ (with $l \in [1, 2, ..., l_Z]$) possible alleles in the initial population characterised by their allelic value $A_{Z, l, k}$ (with $k \in [1, 2, ... n_{Z, l}]$).

Following classical quantitative genetics (LW+98), we assume that the genotypic values $G_Z(i)$ of trait $Z$ in the population follow initially a normal distribution:

$$ N(\overline{G_Z}(0), \sigma^2_{A, Z}(0)) $$

where $\overline{G_Z}(0)$ is the initial genotypic mean and $\sigma^2_{A, Z}(0)$ is the initial additive genetic variance. It follows (see justification in the next section) that the allelic values $A_{Z, l, k}$ of the $n_{Z, l}$ alleles of locus $l$ initially present in the population are randomly drawn from a normal distribution $N\left(0, \dfrac{\sigma^2_{A, Z}(0)}{2 l_Z}\right)$ (SK12). This allelic model defines allelic values as deviations around the initial genotypic mean $\overline{G_Z}(0)$ of the population and allows for heterogeneous allelic values across loci coding for the same trait, many of them with minor effects and a few with major effects.

Similarly, the neutral part of the genome is described by $l_b$ neutral loci, each of which has a pool of $n_{b, l}$ (with $l \in [1, 2, ..., l_b]$) possible alleles in the initial population characterised by their allelic identity $b_{l,k}$ (with $k \in [1, 2, ... n_{b, l}]$) with no effect of evolving trait values. The allelic identities $b_{l,k}$ of the alleles of locus $l$ initially present in the population are randomly drawn from a discrete uniform distribution with probability mass function $\dfrac{1}{n_{b,l}}$.

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LW+98Michael Lynch, Bruce Walsh, and others. Genetics and analysis of quantitative traits. Volume 1. Sinauer Sunderland, MA, 1998.

SK12Jean-Paul Soularue and Antoine Kremer. Assortative mating and gene flow generate clinal phenological variation in trees. BMC evolutionary biology, 12(1):1–14, 2012.