Population dynamics of Varroa mite and honeybee: Effects of parasitism with age structure and seasonality

Authors: MESSAN, KOMI - Arizona State University; RODRIGUEZ MESSAN, MARISABEL - Brown University; CHEN, JUN - Arizona State University; DeGrandi-Hoffman, Gloria; KANG, YUN - Arizona State University

Submitted to: Ecological Modelling
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 11/4/2020
Publication Date: 11/18/2020
Citation: Messan, K., Rodriguez Messan, M., Chen, J., Hoffman, G.D., Kang, Y. 2020. Population dynamics of Varroa mite and honeybee: Effects of parasitism with age structure and seasonality. Ecological Modelling. 440. Article 109359. https://doi.org/10.1016/j.ecolmodel.2020.109359.
DOI: https://doi.org/10.1016/j.ecolmodel.2020.109359

Interpretive Summary: Honeybees play a major role in the production of more than a third of all agricultural crops. However, colonies are being lost at unsustainable levels from various stress factors. Field and theoretical studies have shown that parasitic Varroa mites (Varroa destructor Anderson and Trueman) and the viruses they transmit are a primary cause of colony losses worldwide. To understand better, how Varroa might affect the population dynamics of honey bee colonies, we constructed a brood-adult bee-mite interaction model where variation in queen egg laying rate with season of the year is considered. Changes in egg laying with respect to season affected the growth of the colony and Varroa population. The model revealed that seasonal fluctuations in egg laying rates and low adult worker mortality could keep mite levels low and colonies surviving for more than three years if colonies are established with low mite numbers. However, high mite infestations and the effects on brood and adult mortality caused colonies to perish regardless of colony size or growth rates. In actual apiaries, colonies established with low mite infestations can die from high Varroa populations in one year. The discrepancy between predicted Varroa populations based on mite reproduction and seasonal fluctuations of available brood to infest, and actual mite numbers underscores the impact that mites migrating from other colonies have on colony losses.

Technical Abstract: Honeybees play an important role in sustaining ecosystems and in the production of more than a third of agricultural crops. The decline of honey bee populations have sparked great concern worldwide. Field and theoretical studies have shown that the infestation of the parasitic Varroa mite (Varroa destructor Anderson and Trueman) could be one of the main reasons behind colony losses. To understand how Varroa affects the population dynamics of honey bee colonies, we constructed a brood-adult bee-mite interaction model in which the time lag from brood to adult bee is taken into account. Noting that the temporal dynamics of honey bee colony varies with respect to changes in seasonality, we validate the model and perform parameter estimations under both constant and fluctuating seasonality scenarios. Our analytical and numerical studies reveal the following: (a) In the presence of parasite mites, the large time lag from egg to adult bee could destabilize population dynamics and drive the colony to collapse; however the small natural mortality of adult bee population has the ability to promote a mite-free colony when time lag is small or at an intermediate level; (b) Low levels of l brood infestation could stabilize all populations at the unique interior equilibrium under constant seasonality while driving the mite population to perish when changes in seasonality are included; (c) Large brood infestation rates can destabilize colony dynamics leading to colony collapse depending on initial population size under constant and non-constant seasonal scenarios; (d) Results from our sensitivity analysis indicate that the queen's egg-laying may have the greatest effect on colony population size. The death rate of the brood and the colony size at which brood survivability is half-maximal were also shown to be highly sensitive with an inverse correlation to the colony population size. Our results provide insights on the dynamics generated by seasonality where colonies having low initial mite populations can coexist with Varroa due to reductions in brood rearing and subsequent declines in the Varroa population.