Title Using geometric probability of mating to find the random and actual mating success of a honeybee.

Author Ronny DeJesus

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Abstract Honeybees are a member of the insect class insecta, are a part of the Apinea, and store liquid sugar or honey. The random geometric probability of mating success is estimated at approximately 7.5%. The actual probability of mating success increases to 100% if the number of queen bees mating with male bees increase. The male bees inject their semen into the queen bee while they are both in flight. Upon her arrival back to her hive, a little portion of the sperm goes into the spermatheca and the rest is discarded. The queen bee takes the semen and stores it in her oviducts and then fertilizes the eggs to determine gender.

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Introduction The body of the honey bee consists of stinger, legs, antennae, three segments of thorax, and six segments of abdomen. Included in the abdomen are the queen’s reproductive organs and stinger, the drone’s reproductive organs, and the worker’s stinger. The honey bee colony gets its nutrition from plants, specifically the nectar and honeydew. As for the larva and adult bees individually, their main diet consist of pollen which has proven to be an excellent source of protein. Prior to a mating ritual, bees from various colonies come together in specified locations. The drone bees, Apis, then find a queen bee or Apis mellifera as they swarm around in the air. Researchers estimated that approximately 25,000 drones coming from the surrounding 200 colonies were present at one mating site. A virgin queen mates with various mates while still in flight. During the male and female mating process, the number of male bees largely outweighs the number of female bees. Colonies produce thousands of males but only a few queens. Only a small percentage of males are successful in mating with a queen bee. Therefore the competition between males is fierce. Female bees may choose a mate and usually pick the fastest and most agile male bees. Researchers also found in a recent study that the size of a male bee plays a role in the amount of mating with females. Small males only mated with ½ of the number of females compared to normal-sized bees. The male drone gets onto the queen and injects his endophallus or ejaculating semen. As the queen mates with several other bees, each drone takes out the previous male’s semen and inserts its own. Shortly after 7 to 10 mates, drones quickly die because the semen is ripped from the male’s abdomen by the queen bee. The queen bee mating flights can range from 1 to 4 and she will not mate again throughout her 1-2 year life span. Following mating, the queen stores up to 100 million sperm within her oviducts. Queen bees determine gender by fertilizing eggs to produce females and queen bees. By not fertilizing the 3

eggs, she produces drone bees. Although female bees do not mate, they lay infertile eggs that become male bees. (Orkin.com) A new queen bee is reproduced by the existing queen who leaves to form a new nest along with a couple of adult bees. Method The larger rectangle represents the surface area of a female honeybee as seen by a male. The smaller circle or the bull’s-eye represents the surface area of her abdomen. This is the location of the queen bee’s reproductive organs where the male or drone injects his semen into the queen bee. The queen bee tears open the drone’s abdomen and deposits his sperm into her oviducts.

Figure 1: The honeybee images were retrieved from Google Images. The circle and larger rectangle represent the surface area of a honeybee. The smaller circle represents her reproductive organs. Results Female Target: 2 x 3.14 x 1^2 + 2 x 3.14 x 1 x 4= 6.28 + 25.12= 31,4 cm^2 Bull’s-eye insemination location 3.14 x 1^2- 3.14 x ,5^2= 3.14 - .78= 2.36 cm^2 The random probability of mating success: 2.36/31.4= 0.0751x 100%= 7.5 %

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There are 7.5 % chances out of 100 that random mating will be successful. Discussion After researching the mating success of honeybees, I found that the number of successful mating’s increase if the number of queen bee's mating increases. Therefore, there is a rate of 7 out of 100 chances that a male bee will successfully inject queen bees with their semen in flight. The geometric probability of mating success of honeybees is 7.5 %. The chances will increase to 100% if the number of males mating with queen bees increase. Honeybees gather from different colonies in specific locations to perform their mating ritual. The honeybees mate while still in flight. The male drone bees mount the queen bees and inject their endophallus or sperm. The queen bees are more likely to mate with male bees that are agile, fast, and of good stamina.

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References Brodschneider, R., & Crailsheim, K. (2010). Nutrition and health in honey bees. Apidologie, 41(3), 278-294.662. doi: 10.1051/apido/2010012 Couvillion, M. J., Hughes, W. O. H., Perez-Sato, J. A., Martin, S. J., Roya, G. G. F.M., & Ratnieks, F. L. W. (2010). Sexual selection in honeybees: Colony variation and the importance of size in male mating success. Behavioral Ecology, 21(3), 520-525. doi: 10.1093/beheco/arq016 Gary, N. E. (1963). Observations of mating behavior in the honeybee, J. apic. Res, 2(1), 3-13. ORKIN. (n.d.). Mechanics of honeybee mating. Retrieved from http://www.orkin.com/stinging-pests/bees/mechanics-of-honey-bee-mating Tarpy, D. R., & Page Jr., R. E. (2000). No behavioural control over mating frequency in queen honey bees (Apis mellifera L.): Implications for the evolution of extreme polyandry. The American Naturalist, 155(6), 820-827. doi: 10.1086/303358 Woyke, J. (1955). Multiple mating of the honeybee queen (Apis mellifica L.) in one nuptial flight. Bull. Acad. Polon. Sciences II, 3(5), 175-180.

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