Transition Matrix Population Model for Dust MiteDermatophagoides pteronyssinus(Acari: Pyroglyphidae)

Abstract

A transition matrix model of the population dynamics of the European house dust mite, Dermatophagoides pteronyssinus (Trouessart) (Acari: Pyroglyphidae), is described. It can model continuously varying conditions by forming transition matrices by interpolation between known transition matrices constructed from experimental data. Finite carrying capacity is modeled by modifying the population distribution vector at each time-step by using a form of the Skellam model, which is derived from the assumption that in competition each successful animal gets all it requires, and the unsuccessful animals get insufficient resources for survival or reproduction. The transition matrix model does not require all mites to have the same survivorship, life-stage durations, fecundity, and so on. Life table data to drive the model is taken from two sources, one source of which requires using the mean and standard deviation of the duration of each stage to synthesize a range of duration times and a range of transition probabilities to the next stage, thus ensuring variability between mites. Where synthesized data are used, significant long-lasting oscillations in dust mite levels are modeled, which does not happen when modeling with unsynthesized data, and is unlikely to occur in the field. Under conditions normally met with in the microenvironment (bedding, base of carpet, soft furnishing) of D. pteronyssinus, finite carrying capacity is essential to prevent unbounded population growth. The model is compared with other workers' field data with fair agreement. It is argued that shortcomings in the available data rather than the model are the principal reasons for differences between field and modeled results.