3.3.1. 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 characterized by their allelic value \(A_{Z, l, k}\) (with \(k \in [1, 2, ... n_{Z, l}]\)).
Following classical quantitative genetics [Lynch et al., 1998], we assume that the genotypic values \(G_Z(i)\) of trait \(Z\) in the population follow initially a normal distribution:
with \(\overline{G_Z}(0)\) the initial genotypic mean and \(\sigma^2_{A, Z}(0)\) 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 \(N\left(0, \dfrac{\sigma^2_{A, Z}(0)}{2 l_Z}\right)\) [Soularue and Kremer, 2012]. This allelic model defines allelic values as deviations around the initial genotypvic 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 ones 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 characterized 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 \(\dfrac{1}{n_{b,l}}\).