Loci involved with incompatibility
To allow the model to explore outbreeding depression, each individual carries nc loci involved with genetic incompatibility. These loci carry fixed difference between recipient (a = 0) and source (a = 1) populations. These loci are used to implement outbreeding depression using a model of two-locus incompatibilities developed by Turelli & Orr (2000). The Turelli and Orr model implements the idea that lowered hybrid fitness can be explained by between-locus Dobzhansky-Muller incompatibilities and considers three types of incompatibility: those between heterozygous loci (H0 ), those between a heterozygous and a homozygous locus (H1 ), and those between homozygous loci (H2 ). Their model describes a ’hybrid breakdown score’ (E(S )) of an individual based on the frequency of each type of incompatibility in the individual’s genome. These are calculated from the proportion of loci that are homozygous from the recipient (p1 ) and source populations (p2 ), in addition to the proportion that are heterozygous for material from the two populations,pH . We use our set of ncincompatibility loci to calculate these values of p for each individual. Following Turelli and Orr, the hybrid breakdown score is given as
\begin{equation} E\left(S_{i}\right)=n_{c}[p_{1}p_{2}H^{2}+\left(p_{1}+p_{2}\right)p_{H}H_{1}+p_{H}^{2}H_{0}]\nonumber \\ \end{equation}
A negative exponential link is used to relate the hybrid breakdown scores to fitness,
\begin{equation} s_{i}=e^{-\alpha E(S)}\nonumber \\ \end{equation}
where alpha is a constant, and si is the probability of survival from outbreeding depression. When outbreeding depression is activated in the model, all individuals’ survival probabilities are multiplied by an individual’s s value (set to 1 otherwise), and survival is determined as a draw from a Bernoulli distribution with the resultant survival probability. A simple dosage ratio is used for the different classes of incompatibility to generate the hybrid breakdown score: (H1 ) = 0.5, (H2 ) = 1 and (H0 ) = 0.25. The value of alpha is varied to manipulate the strength of outbreeding depression in the model.