A MODEL FOR HEAT-TRANSFER IN A HONEY-BEE SWARM

A swarm is a temporary structure formed when several thousand honey be es leave their hive and settle on some object such as the branch of a tree. They remain in this position until a suitable site for a new hom e is located by the scout bees. A continuum model based on heat conduc tion and heat generation is used to predict temperature profiles in sw arms. Since internal convection is neglected, the model is applicable only at low values of the ambient temperature T-a. Guided by the exper imental observations of Heinrich (1981a-c, J. Exp. Biol. 91, 25-55; Sc ience 212, 565-566; Sci. Am. 244, 147-160), the analysis is carried ou t mainly for non-spherical swarms. The effective thermal conductivity is estimated using the data of Heinrich (1981a, J. Exp. Biol. 91, 25-5 5) for dead bees. For T-a = 5 and 9 degrees C, results based on a modi fied version of the heat generation function due to Southwick (1991, T he Behaviour and Physiology of Bees, PP 28-47. C.A.B. International, L ondon) are in reasonable agreement with measurements. Results obtained with the heat generation function of Myerscough (1993, J. Theor. Biol . 162, 381-393) are qualitatively similar to those obtained with South wick's function, but the error is more in the former case. The results suggest that the bees near the periphery generate more heat than thos e near the core, in accord with the conjecture of Heinrich (1981c, Sci . Am. 244, 147-160). On the other hand, for T-a = 5 degrees C, the hea t generation function of Omholt and Lonvik (1986, J. Theor. Biol. 120, 447-456) leads to a trivial steady state where the entire swarm is at the ambient temperature. Therefore an acceptable heat generation func tion must result in a steady state which is both non-trivial and stabl e with respect to small perturbations. Omholt and Lonvik's function sa tisfies the first requirement, but not the second. For T-a = 15 degree s C, there is a considerable difference between predicted and measured values, probably due to the neglect of internal convection in the mod el.