Abstract
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.
Highlights
A lifespan of an animal, which is the period of time while an individual is alive, is an important index to evaluate individual activities
When we obtain the numbers of adult bees and capped brood in a field experiment, the following errors sometimes creep in: (1) Errors arising from a counting method, where a weighing method is apt to have much more errors than a direct counting method: (2) Errors arising from the timing of measurement, where a measurement just after dawn before foraging bees leave from their beehive contains less errors than that in the daylight
We estimated the apparent longevity of a honeybee colony in long-term field experiments
Summary
This work is focused on a proposal of a mathematical model to estimate only the apparent longevity, L(t), fairly accurately through all seasons. In order to estimate the apparent longevity as accurately as possible, the less parameters and the more plausible assumptions are better and it is desirable that the parameters can be determined from experimental data with high accuracy and the assumptions are closer to the truth. In this paper we propose a simple and realistic mathematical model whose parameters can be determined from the numbers of adult bees and capped brood obtained from the photos of combs and the inside of a beehive, which are comparatively easy to be accurately obtained from an experiment
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