An encounter rate model of bark beetle populations searching at random for susceptible host trees

Iterative equations were developed that predict the encounter rate between a population of moving animals and a population of stationary objects, where the animals cease to search upon finding an object. The encounter rate through time depends on the number of searching animals (bark beetles), number of stationary objects (host trees), average speed of the animals, average radius of the object, and area of the search arena. The iterative equations were used in a computer program to vary these parameters with regard to flight dispersal of the bark beetle Ips typographus (Coleoptera: Scolytidae) during their search for susceptible host trees of Norway spruce (Picea abies). Realistic parameters of flight speed, numbers of beetles and susceptible host trees, tree diameters, density of healthy trees, search area, and time searching were held constant while certain of these parameters were varied in computer model runs. In most cases, significant proportions of the modeled bark beetle population (of which individuals fly forward with a random component) found the relatively few susceptible host trees suitable for colonization. Only at very low effective flight speeds (due to longer stays on trees) or with widely distributed hosts of smaller diameter, did relatively few beetles find suitable hosts. Once the ‘pioneer’ beetles find susceptible hosts, release of aggregation pheromone would greatly increase the effective radius of the host and allow rapid concentration of the population on these trees. The model suggests that primary attraction to host tree volatiles is not mandatory for host finding and selection in many species of bark beetle. Evolution of an olfactory response to host volatiles is more probable in species with low population densities or widely dispersed host plants, or both. Also, there would be little selection pressure on a bark beetle species to evolve aggregation pheromones if they can respond over some meters to plant volatiles that reveal the location of a susceptible host.