Submitted to: International Journal of Acarology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 7/15/2004
Publication Date: 12/30/2004
Citation: DeGrandi-Hoffman, G., Curry, R. Description and Validation of a Mathematical Model of Varroa Mite (Varroa destructor) and Honeybee (Apis mellifera L.) Population Dynamics. 2004. Internat. J. Acarol. 2004. Vol. 30, No. 3. Interpretive Summary: A mathematical model was constructed to predict the growth of Varroa populations in honeybee colonies over time. The effect of Varroa mites on the survival of the honeybee population also is simulated. We validated the preductions from the model by comparing them with the growth of actual Varroa populations in colonies. The predictions very closely resembled actual Varroa population growth. The model also accurately predicted the mortality rate of Varroa in colonies treated with miticides. Predictions from the model are similar to population trends reported from actual honeybee colonies infested with Varroa. For example, mite populations achieve exponential growth in colonies, and the model predicts a similar growth pattern. The model predicts that mite populations increase at a greater rate in locations where brood is reared throughout the year. The model also predicts that economic threshold levels and the effectiveness of miticides in increasing colony survival are dependent on the geographic location of the colony and its effects on brood rearing. Regions with uninterrupted brood cycles are predicted to have lower economic threshold values for mites than regions where brood rearing stops in the fall and winter.
Technical Abstract: A mathematical model of population interactions between Varroa destructor and a honeybee colony is described. Predictions of Varroa and honeybee population dynamics from the model are based upon weather conditions and parameters specific to honeybee and Varroa biology. Comparisons were made between predicted Varroa population growth and actual values from the field. The model generates predictions that are similar to those from actual colonies. Furthermore, predictions of Varroa population growth from the model are similar to those reported in actual honeybee colonies including; daily population growth rates, exponential growth of Varroa populations, and Varroa populations increasing at a greater rate when brood is reared throughout the year. The model also predicts that economic threshold levels and the effectiveness of miticides in increasing colony survival are dependent on the geographic location of the colony and the yearly brood rearing cycle. Regions with uninterrupted brood cycles are predicted to have lower economic threshold values for Varroa than regions where brood rearing stops in the fall and winter. The model predicts that spring applications of miticides are not as effective at prolonging colony survival as fall applications in temperate environments. However, if brood rearing occurs throughout the year, the chance of colony survival after a single miticide treatment is predicted to be the same whether the application occurs in the spring or fall.