Targeted Gene Flow
To simulate a TGF action, we introduce a number of differently adapted individuals into the recipient population from a ‘source’ population. This source population is adapted to the future environment of the recipient location. Given an input value for c and m can solve for the frequency of favourable alleles required to be optimally adapted at management time M (see S4 for full workings).
\begin{equation} {\hat{f}}_{M}=\frac{v_{M}^{2}}{2n_{p}V_{G}+v_{M}^{2}}\nonumber \\ \end{equation}
We then explore a management space (described in S5), varying the timing of an introduction and the number of introductees. In our test case we introduce individuals adapted to t = 50, i.e. a population adapted to the environment at our management horizon at M = 50 years. Across this space we explore introduction times from 0 to 50 years, at two-year intervals. The proportion of introduced individuals ranges from 0 to 0.3, in step increments of 0.025, for each introduction time. This proportion is in relation to the population size at the time of the management action, Nt , and not to the carrying capacity, N* .
Results
Across all simulations we found that the success of a given gene flow action was strongly influenced by the timing of the introduction as well as the proportion of pre-adapted individuals introduced at a given timestep (Figure 1 and 3). The management objective (E(Y )) was optimised when a greater proportion of individuals (>10%) were introduced in the years prior (or during) the maximum level of demographic pressure experienced by our simulated populations (~ 25 years into the simulation). Although this pattern remained consistent throughout, adjusting the demographic parameters did alter the effectiveness of TGF, and the optimal management strategy (Figure 2, 4 and 5).
Trait heritability (h2 ) impacts the success of our simulated management actions. Higher heritabilities increased the expected return, with particular respect to scenarios where there is a lower carrying capacity (Figure 2). These broad patterns were also seen in the sensitivity analysis suggesting they are consistent trends robust to population dynamics. A high carrying capacity in the system seemed to negate the influence of a reduced heritability and the effects of faster environmental decay (Figure 2a). Across all scenarios, the optimal timing and size of an introduction favoured scenarios with a high number of individuals introduced in the years immediately prior to the greatest shift in the environment (Figure 2b).
The chosen shape of environmental shift changed the maximum expected return as well as the optimal location in management space (timing and size) (Figure 6). Scenarios with a gradual environmental shift produced a higher expected return than scenarios with a severe level of environmental shift. In addition, increased levels of demographic pressure constrained the optimal time to implement TGF, often clustering around the years immediately preceding the maximum rate of change (Figure 1c, 3a, b).
Outbreeding depression drastically reduced the success of TGF, in some cases generating no improvement in expected return above a “do nothing” scenario (Figure 3c). A 10% reduction in fitness produced relatively similar results to no outbreeding depression; however, a 50% reduction in fitness often vastly increased the probability of extinction, and our diversity measure, resulting in a reduced expected return. Simulation runs that coupled the maximum reproductive rate with a high carrying capacity were able to withstand high levels of outbreeding depression (S3). Across all remaining parameter sets, increasing the level of outbreeding depression generally tightened the window of opportunity in which to conduct TGF actions in an optimal way (e.g. Figure 2b). Higher levels of outbreeding depression reduced the expected return (Figure 4a), though the expected return was rarely worse than a “do nothing” scenario. These loses were partly combatted by higher levels of trait heritability within a population. The optimal management action was influenced by the level of outbreeding depression in the system, with high levels our outbreeding depression resulting in an apparently random optimum (Figure 4b). This is due to only tiny differences in the expected return across the management landscape coupled with the model’s inherent stochasticity (Figure 3c).