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).