Figure 2. Predictions of the SRD for a set of parameters giving potential tree mortality.

a) The density of beetles settling in dead trees (brown), living trees (green) or migrating (blue) in one flight season as functions of swarm density (N). Here K_D = 5, K_L = 10, median Ω = 0.6, α = 1, c₀ = 0.2, c_T = −2, β = 0.05, c₁ = 0.5, a₁ = −1, a₂ = 5,R = 10, τ = 0.5. The threshold T = 15 is marked and shows where living trees would be colonized with P = 0.5 if all beetles had joined attacks. b) The resulting fitness functions (expected number of offspring per capita) when early-arriving individuals are able to monopolize resources (dotted lines) and when they are not solid). The grey line shows the probability of successful colonisation of living trees increasing with population density. c) The colours show total population growth rates as a function of beetle distributions, showing the stable distributions as predicted by the IFD (dotted) and SRD (green and brown solid) lines. Below the diagonal, the horizontal axis shows population density(N), the vertical axis the number of beetles settling in dead trees (N_d). Above the diagonal, the vertical axis shows population density, the horizontal axis the number of beetles settling in living trees (N_s). d) As in (c), except that colours show per cent difference in fitness between beetles in dead and living trees. Following the brown (dead-tree) line, we see that at low densities (interval A) both the SRD and IFD predict all beetles to settle in dead trees. As living trees are settled (interval B) we see marked deviations from the IFD as individuals colonizing living trees enjoy increased fitness. However, as population density increases further, the SRD and IFD converge (interval C) as both resources become crowded.