Simulation of the mate-finding behaviour of pine shoot beetles, Tomicus piniperda

An algorithm for animal searching behaviour was constructed that allows independent variation at random of movement parameters such as speed, duration, step size, and maximum right or left turn angle. The area, radius of the object searched for, and number of objects and searchers can also be varied. A capture algorithm is presented that can determine whether a searching animal intercepts a circle (object) irrespective of the step size. These two algorithms were incorporated into a computer simulation model of mate finding for walking male bark beetles, Tomicuspiniperda, in search of females that remained stationary when boring into the bark of Scots pine, Pinus sylvestris. The model showed that, for realistically chosen parameters, males were able to find 'females' at apparently natural rates without the need to enlarge the radius of the 'female' beyond the size of an actual female. This indicates that there may be little, if any, advantage in the evolution of a long-range pheromone, for which no chemical and behavioural evidence has yet been found. Simulation of animal movement is useful for understanding such areas of animal behaviour as kinesis (Rohlf & Davenport 1969; $Doucet & Drost 1985; Benhamou & Bovet 1989), dispersal (Skellam 1973) and optimal searching for mates, prey, food or oviposition sites (Jones 1976, 1977; Pyke 1978; Gries et al. 1989). Models of search behaviour have concerned random movement in four (Rohlf & Davenport 1969; Pyke 1978) or eight (Jones 1976, 1977; Gries et al. 1989) possible directions. A more realistic model of animal movement in all possible directions was outlined by Skellam (1973) for use in dispersal studies, but was not implemented by computer. A recent model allows random changes in path directions based on a normal distribution (Bovet & Benhamou 1988). In the majority of these models a more natural movement was achieved by not allowing a reversal of direction so that the 'animal' generally progressed forward. However, there have been few, if any, computer models that have simulated realistically the relationships of animal movements and mate (or prey) finding in bounded areas with respect to such parameters as speed, time, angle of turning, size of mate or prey, rate of turning and density. The model animal for my simulation study is the larger pine shoot beetle, Tomicus piniperda (L.). This bark beetle (Coleoptera: Scolytidae) is a serious pest of Scots pine, Pinus sylvestris L., in Europe and Asia. Its dispersal and host-seeking flight coincides with temperatures above 13°C in early spring (Byers et al. 1985; Lanne et al. 1987). Almost immediately at these temperatures, T. piniperda aggregates en masse on fallen Scots pine that have been damaged during winter storms. It is common to find several tens to hundreds of beetles of both sexes walking about on the trunk. Females soon locate suitable sites where they bore into the bark, but for several hours they are exposed to predators (clerid beetles, Thanasimus formicarius). Also at this time males wander in search of females that are boring into the bark. Upon encountering a female a male attempts to monopolize her by jousting with and displacing any resident male, during which time both males stridulate repeatedly (personal observations). These interactions between males usually occur for only a few seconds. Bark beetles that aggregate en masse on host trees mostly use pheromones (Byers 1989). An earlier study purported to find evidence of a longrange pheromone in T. piniperda (Schonherr 1972) while another report was inconclusive (Kangas et al. 1967). My colleagues and I (Byers et al. 1985) have demonstrated that T. piniperda are attracted equally to traps containing either infested or uninfested host logs in the field indicating that ( l ) there is no long-range aggregation pheromone and (2) host compounds are responsible for aggregation. @ 1991 The Association for the Study of Animal Behaviour