Allelic diversity of the recipient population.
We track the allelic diversity of a population through time by initializing each individual with nh loci, which carry fixed differences between recipient (initialised with a = 0 or 1 with equal probability) and introduced (a = 2) individuals. We use this set of loci to generate a measure of allelic diversity taking into account the number of recipient alleles present (diversity) as well as the relative abundance of each allele (evenness). Because we assume all alleles have an equal and additive effect on an individual’s trait value (i.e. no disparity) we use the Gini-Simpson diversity index (D ) as our measure of diversity, defined as:
\begin{equation} 1-D=\sum_{i=1}^{j}{(\frac{n_{j}\left(n_{j}-1\right)}{\left(N\bullet{2n}_{h}\right)\left(N\bullet{2n}_{h}-1\right)}})\nonumber \\ \end{equation}
Where ni is the number of alleles from the recipient population (a != 2) across all individuals at locus j,N is the population size and 2nh is the total number of biallelic loci in the population. We subtract Dfrom 1 to give our final diversity measure a range from 0 (low diversity) to 1 (high diversity). As allelic richness and evenness increase, so diversity increases. We can then use this measure of allelic diversity in conjunction with extinction risk to optimise the timing and size of a TGF action.