Table 1.
Symbols and Notation.
Figure 1.
The consequences of a negative correlation between fitness and immigration rate.
A) shows the fitness distributions for two phenotypes in a closed population. In the simple case of two individuals, one with and one with
(so
), the slightly higher expected fitness of
individuals causes the expected change in mean phenotype to be negative. B) shows the situation with variable immigration (and no emigration). Immigration rate is independent of the fitness of
individuals, but negatively correlated with the fitness of
individuals. Though the mean phenotype of immigrants is lower than the mean phenotype in the deme, and selection in the deme favors a lower phenotypic value, mean phenotype is expected to increase in this case because of the fact that
individuals do best at those times when low immigration leads to low deme growth rate. The same pattern holds in a deme of size
when
, individuals with a particular phenotypic value always do well or poorly together, and the number of immigrants fluctuates between 0 and
.
Figure 2.
The influence of the variance in immigration rates, , on the expected change in mean phenotype.
In this example, selection favors (the fitness distributions are shown in the inset figure) while immigrants have
. The dots in the main figure represent the means of 10,000 runs of an individual based simulation with the same expected immigration rate (
) but different variances in
. In each case, the initial deme size was 50, and emigration was independent of both immigration and phenotype.
Figure 3.
The relation between variance in immigration, , selection, and
in an island-continent model.
The colored lines represent on the island as a function of current mean island phenotype for different variances in immigration rate (each colored dot represents the mean of 10,000 runs of an individual based simulation). Selection on the island favors
(inset figures).
,
, and
. Colored “
” symbols mark the values of mean island phenotype at which
. A) Relatively weak selection on the island. B) Stronger selection on the island.
Figure 4.
Hypothetical example of a local population in which immigration () and within deme mean reproductive rate (
) vary over time.
with probability 0.9 and
with probability 0.1, and
with probability 0.8,
with probability 0.1, and
with probability 0.1. In this case,
and
. Emigration is independent of both
and
. If immigration were independent of
and of emigration, then the effective migration rate is
. If, however, immigration and within deme reproduction are strongly correlated, so that immigrants always arrive during times of high within deme reproduction (as illustrated), then
, so
.