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ARS Home » Pacific West Area » Tucson, Arizona » Carl Hayden Bee Research Center » Research » Publications at this Location » Publication #335197
Title: Migration effects on population dynamics of the honeybee-mite interactions

Author
item MESSEN, KOMI - Arizona State University
item DeGrandi-Hoffman, Gloria
item CASTILLO-CHAVEZ, CARLOS - Arizona State University
item KANG, YUN - Arizona State University

Submitted to: Mathematical Modeling of Natural Phenomena
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 12/20/2016
Publication Date: 4/21/2017
Citation: Messen, K., Hoffman, G.D., Castillo-Chavez, C., Kang, Y. 2017. Migration effects on population dynamics of the honeybee-mite interactions. Mathematical Modeling of Natural Phenomena. 12(2):84-115. https://doi.org/10.1051/mmnp/201712206.
DOI: https://doi.org/10.1051/mmnp/201712206

Interpretive Summary: The survival of honey bee colonies is undermined by numerous factors, but most notably the parasitic Varroa mite (Varroa destructor Anderson and Trueman). A recent field study showed that migration of Varroa into hives on foraging bees greatly contributes to the rapid growth of mite populations in colonies. Motivated by this finding, a simple two-patch honey bee-Varroa model was constructed to explore how foraging behavior of honey bees in the presence of Varroa infested colonies might affect the population dynamics of honey bees and mites. The model revealed that when there are low rates of mite migration between patches with low mite populations, colonies and mites can coexist in both patches suggesting that low-level migration of mites on foragers could be a successful dispersal strategy for Varroa. However, high migration rates from infested to uninfested patches caused a rapid growth of the Varroa population in the uninfested patch, which in turn had a negative feedback on colony growth and survival. The theoretical framework for the interactions of colony and Varroa population dynamics provided by the model underscores the importance of area-wide Varroa control, because colonies with low mite infestations cannot survive when they are surrounded by highly infested hives.

Technical Abstract: Honeybees are amazing and highly beneficial insect species that play important roles in undisturbed and agricultural ecosystems. Unfortunately, honeybees are increasingly threatened by numerous factors, most notably the parasitic Varroa mite (Varroa destructor Anderson and Trueman). A recent field study showed that migration of mites into hives on foraging bees greatly contributes to the rapid growth of mite populations in colonies, and increases the mortality of honeybee colonies. Motivated by this, we propose a simple two-patch honeybee-Varroa model to explore how foraging behavior of honeybees in the presence of Varroa mite infestations affect the population dynamics of honeybees and mites. We provide a full analysis on the local and global dynamics of our proposed two-patch model that incorporates mite migration generated by honeybee foraging activities. The model revealed that under proper conditions, high mite migration rates could have the following effects: (1) save one honeybee colony from collapsing when honeybee colonies go extinct in both patches; (2) drive honeybee extinction in at least one patch. (c) Intermediate migration rate could generate multiple locally stable honeybee-mite coexistence equilibria, and drive mite extinction under proper environments. (d) An increase in migration rate causes a growth of the Varroa population, which in return has a negative feedback on the colony population. (e) Increasing mite migration from a healthy patch to a collapsing patch could reduce the extinction time in the collapsing patch. The theoretical results combined with numerical simulations including one and two dimensional bifurcation diagrams provide useful insights on how migration in mites affects the dynamics of honeybee and mite populations.