Individual-based modeling of the spread of pine wilt disease: vector beetle dispersal and the Allee effect

Pine wilt disease is caused by the pinewood nematode Bursaphelenchus xylophilus, which is vectored by the Japanese pine sawyer beetle Monochamus alternatus. Due to their mutualistic relationship, according to which the nematode weakens and makes trees available for beetle reproduction and the beetle in turn carries and transmits the nematode to healthy pine trees, this disease has resulted in severe damage to pine trees in Japan in recent decades. Previous studies have worked on modeling of population dynamics of the vector beetle and the pine tree to explore spatial expansion of the disease using an integro-difference equation with a dispersal kernel that describes beetle mobility over space. In this paper, I revisit these previous models but retaining individuality: by considering mechanistic interactions at the individual level it is shown that the Allee effect, an increasing per-capita growth rate as population abundance increases, can arise in the beetle dynamics because of the necessity for beetles to contact pine trees at least twice to reproduce successfully. The incubation period after which a tree contacted by a first beetle becomes ready for beetle oviposition by later beetles is crucial for the emergence of this Allee effect. It is also shown, however, that the strength of this Allee effect depends strongly on biological mechanistic properties, especially on beetle mobility. Realistic individual-based modeling highlights the importance of how spatial scales are dealt with in mathematical models. The link between mechanistic individual-based modeling and conventional analytical approaches is also discussed.