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.