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Yasuhiro Yamada1,3, Toshiro Yamada 2,4 & Kazu Yasuhiro Yamada1,3, Toshiro Yamada 2,4 & Kazuko Yamada2,4
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 lifespan of an animal, which is the period of time while an individual is alive, is an important index to evaluate individual activities. In the colony composed of eusocial insects such as honeybees (Apis mellifera) which exhibit age-polyethism, the lifespan of each individual cannot always give an assessment as to the activities of a colony but the longevity of colony could give it more appropriately. The longevity of a colony will have greater significance than the lifespan of each individual of the colony. The life of colony diversely depends on the inborn lifespan of an individual, the labor division distribution ratio of each honeybee performing a particular duty, the natural environment such as the weather, the amount of food, pests and pathogens, the environmental pollution due to pesticides and so on. The honeybee length of life has been observed or estimated before in the four seasons, which have a distinct bimodal distribution in temperature zones. According to previous papers, honeybees live for 2–4 weeks1 and 30–40 days2 in spring, for 1–2 weeks1, 25–30 days2 and 15–38 days3 in summer, for 2–4 weeks1 and 50–60 days2 in autumn, and for 150–200 days3, 253 days2, 270 days4, 304 days5 6–8 months6 and 150–200 days3 in winter, where it has been estimated that the difference of life length among seasons may come from the brood-rearing load imposed on honeybees1 and may mainly come from foraging and brood-rearing activity2. Incidentally, the lifetime of the queen seems to be three to four years (maximum observed nine years). The average length of life of worker bees in laboratory cages was observed to range from 30.5 to 45.5 days7. The study on the influence of altitude on the lifespan of the honeybee has found that the lifespans are 138 days at an altitude of 970 m and 73 days at an altitude of 200 m, respectively8. Many papers have discussed what factors affect the length of life (lifespan, longevity, life expectancy) on a honeybee colony as follows: Proper nutrition may increase the length of life in a honeybee colony. Honeybees taking beebread or diets with date palm pollen (the best source for hypopharyngeal gland development) showed the longest fifty percent lethal time (LT50)9. The examination for the effect of various fat proteins on honeybee longevity have shown that honeybees fed diets of red gum pollen have the longest lifespan but those fed invert sugar have the shortest lifespan10. In the discussion on nutrition-related risks to honey bee colonies such as starvation, monoculture, genetically modified crops and pesticides in pollen and sugar, protein nutrient strongly affects brood production and larval starvation (alone and or in combination with other stresses) can weaken colonies11. And protein content in
1Department of Applied Physics, Graduate School of Engineering, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo, 113-8656, Japan. 2Graduate School of Natural Science & Technology, Kanazawa University, Kakuma-machi, Kanazawa, 920-1192, Japan. 3Present address: Department of Physics, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan. 4Present address: 2-10-15, Teraji, Kanazawa, Ishikawa, 921-8178, Japan. correspondence and requests for materials should be addressed to t.Y. (email: yamatoshikazu0501@yahoo.co.jp)
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