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The longevity of a honeybee colony is far more significant than the lifespan of an individual honeybee, a social insect. The longevity of a honeybee colony is integral to the fate of the colony. We have proposed a new mathematical model to estimate the apparent longevity defined in the upper limit of an integral equation. The apparent longevity can be determined only from the numbers of adult bees and capped brood. By applying the mathematical model to a honeybee colony in Japan, seasonal changes in apparent longevity were estimated in three long-term field experiments. Three apparent longevities showed very similar season-changes to one another, increasing from early autumn, reaching a maximum at the end of overwintering and falling approximately plumb down after overwintering. The influence of measurement errors in the numbers of adult bees and capped brood on the apparent longevity was investigated.

A mathematical model to estimate the seasonal change in apparent longevity of bee colony