Trees wanted--dead or alive! Host selection and population dynamics in tree-killing bark beetles

Abstract

Bark beetles (Coleoptera: Curculionidae, Scolytinae) feed and breed in dead or severely weakened host trees. When their population densities are high, some species aggregate on healthy host trees so that their defences may be exhausted and the inner bark successfully colonized, killing the tree in the process. Here we investigate under what conditions participating with unrelated conspecifics in risky mass attacks on living trees is an adaptive strategy, and what this can tell us about bark beetle outbreak dynamics. We find that the outcome of individual host selection may deviate from the ideal free distribution in a way that facilitates the emergence of tree-killing (aggressive) behavior, and that any heritability on traits governing aggressiveness seems likely to exist in a state of flux or cycles consistent with variability observed in natural populations. This may have implications for how economically and ecologically important species respond to environmental changes in climate and landscape (forest) structure. The population dynamics emerging from individual behavior are complex, capable of switching between "endemic" and "epidemic" regimes spontaneously or following changes in host availability or resistance. Model predictions are compared to empirical observations, and we identify some factors determining the occurrence and self-limitation of epidemics.

Figure 1. Schematic overview of the model, summarizing the steps and equations.

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.

Figure 3. Population dynamics of the SRD.

a) Offspring density as a function of swarm density shows three non-zero equilibrium points (blue dots), and the population trajectories have two attractor basins; a lower (endemic) and higher (epidemic). b) As (a), showing one endemic (brown arrows) and one epidemic (green arrows) trajectory. A population may be transported from one attractor basin to the other by several mechanisms in either direction (blue and yellow arrows). For instance a large windfelling (giving a brief doubling of K_D, upper grey line, blue arrows), or a winter of poor survival (a decreased R, lower grey line, yellow arrows).

Figure 4. Predictions of the SRD.

a) The effect of varying the random sampling coefficient (τ) – i.e., the chance that a beetle bores into a living tree, possibly piercing resin channels and transferring fungi, before settling in a dead tree. We see that beetle species/populations with low a sampling rate are predicted to be less likely to colonize trees, and less likely to sustain continued epidemic states. b) The brown points show the number of dead trees (i.e., logs) and green points the number of living trees that were observed to be colonized by I. typographus at a site over a period of 100 days (data from Grégoire 1996). The colonization sequence predicted by the model (brown line for beetles settling in dead trees, green for live trees and blue for migration) is highly consistent with these observations (see Analysis and Results sections).

Figure 5. Comparisons with observations.

a) Field data on the number of offspring per adult Ips cembrae as a function of gallery density (black line with ±2SD), showing a strong negative density-dependence. This is consistent with the model density dependence (red line; part of eq. 3, see below as eq. 8) b) The density per m² of newly emerging I. typographus for 68 trees with fitted regression lines. Partially defended trees (i.e. trees with partial root contact, grey points) are colonized together with lower dead-wood densities, corresponding to expectations (see Results).

Figure 6. Comparisons with other model formulations.

a) Comparing the offspring density for the model (red) with an established resource-based bark beetle model by Økland and Bjørnstad (2006), see Analysis section (blue lines, upper line scaled for better fit). The dotted blue line is the population model presented here, but with the simplification that living trees are colonised immediately when N>T, as is implicit in most current population models that do not take adaptive behaviour into account. b) Swarm density for which colonizing living trees has a 50% chance of success, as a function of colonization threshold (T) and dead trees present (K_d). The interaction is strongly non-linear.