The genotype and expected trait value
Each locus with phenotypic effects (within np )
has an equal and additive effect on the individuals expected trait
value, E(z ). Two alleles are possible at each locus, with alleles
having a value of either 0 or d , where d > 0.
This additive effect size d is calculated as a function of the
environmental variance (VE ), the trait
heritability (h2 ), and is chosen such that the
stated heritability is achieved at initialisation (givenVE , np , and the initial
frequency of alleles with effect size d ,f0 ):
\begin{equation}
h^{2}=\ \frac{V_{G}}{V_{G}+V_{E}}\nonumber \\
\end{equation}or, equivalently,
\begin{equation}
V_{G}=\ \frac{{h^{2}V}_{E}}{1-h^{2}}\nonumber \\
\end{equation}With a binomial distribution, the expected genetic variance is then
given as,
\begin{equation}
V_{G}\ =\ 2d^{2}n_{p}f_{0}(1-f_{0})\nonumber \\
\end{equation}Where f0 is the initial frequency of favourable
alleles present (i.e. those with effect sizes of d ) at the start
of the simulation. We vary this value of f0 in
our sensitivity analysis. Our effect size, d can be calculated
as:
\begin{equation}
d=\sqrt{\frac{h^{2}V_{E}}{2n_{p}f_{0}(1-h^{2})(1-f_{0})}}\nonumber \\
\end{equation}Each individual’s expected phenotype is given by:
\begin{equation}
E\left(z_{i}\right)=d\sum_{j=i}^{n_{p}}{\sum_{k=1}^{2}a_{i,j,k}}\nonumber \\
\end{equation}where aj,k references the allelic value k(either 0 or 1) of locus j . Here the individual is represented byi . In our reference case we set heritability of the trait in the
recipient population (h2 ) to 0.1. We explore
the impact of differing heritability values in the sensitivity analysis.
We centre the mean phenotype such that maximum fitness is conferred at
the start of the simulation.