Age-structured population models for species of pest mites
LE3 .A278 2007
Master of Science
Mathematics and Statistics
Mathematics & Statistics
Various species of pest mites pose significant challenges for apple growers worldwide. In Nova Scotia's Annapolis Valley, infestations of European red mites ('Panonychus ulmi'), among other species, threaten the region's apple orchards. In this thesis, two potential models for simulating the dynamics of 'P. ulmi' are described and analysed. The models considered explicitly incorporate the age structure of the mite population and so contain nonlinearities and delay terms, such that each is comprised of delay-differential equations. Consistent with the generational structure of the mites, each model assumes that the mite population follows delayed density-dependent fecundity, in which current adult population growth is dependent on the size of the adult population at a previous time. The models considered are non-seasonal, with environmental conditions assumed to be constant. With the equation based on Nicholson's blowflies data (Gurney ' et al.', 1980), the population is divided into discrete immature and adult life stages. In contrast, the full non-seasonal system described here incorporates three life stages: eggs, juveniles, and adults. Both models are analysed with respect to their linear stability properties, and each exhibits oscillating solutions under certain conditions.
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