Summary
We examined the optimal reproductive strategies for eusocial insects with an annual life cycle. A model is constructed for the growth of workers and reproductives as a function of the resources allocated to each. We then compute the allocation schedule which yields the maximum number of reproductives by season's end. Field observations appear to confirm the prediction of our model: the optimal strategy is to invest in colony growth until approximately one generation before the season's end, whereupon worker production ceases and reproductive effort is switched entirely to producing queens and males. Similar all-or-none strategies are observed in other biological contexts, and their optimality is proven here. Finally, we calculate the fraction of the total season's resources allocated to reproductives from which we can estimate the ergonomic efficiency of the colony with respect to reproductive success.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson, E., Hubricht, L.: A method for describing and comparing blooming seasons. Bull. Torrey Botan. Club 67, 639–648 (1940)
Andrewartha, H., Birch, L.: The Distribution and Abundance of Animals. Chicago: Univ. Chicago Press, 1954
Auslander, D., Oster, G., Huffaker, C.: Dynamics of interacting populations. J. Franklin Inst. 297, 345–376 (1974)
Bodenheimer, F.: Population problems of social insects. Biol. Rev. 12, 393–430 (1937)
Brian, M.V.: Social Insect Populations. London: Academic Press, 1965
Cumber, R.: The biology of bumblebees, with special reference to the production of the worker caste. Trans. Roy. Ent. Soc. Lond. 100, 1–45 (1949)
Denholm, J.: Necessary condition for maximum yield in a senescing two-phase plant. J. Theor. Biol. 52, 251–254 (1975)
Eberhard, M.: The social biology of polistine wasps. Misc. Publ., Mus. Zool., Univ. Michigan 140, 1–101 (1969)
Fisher, R.A.: The Genetical Theory of Natural Selection. New York: Dover Publications Inc., 1958
Frankie, G.: Tropical forest phenology and pollinator plant coevolution. In: Coevolution of Animals and Plants (eds. L. Gilbert, P. Raven). Austin: Univ. Texas Press, 1975
Free, J.B., Butler, C.G.: Bumblebees. London: Collins 1959
Gadgil, M., Bossert, W.H.: Life historical consequences of natural selection. Am Naturalist 104, 1–24 (1970)
Heinrich, B.: Foraging behavior and resource partitioning of some Maine bumblebees, preprint (1974)
Heinrich, B.: Bee flowers: a hypothesis on flower variety and blooming times. Evolution 29, 325–334 (1975)
Hirshfield, M., Tinkle, D.: Natural selection and the evolution of reproductive effort. P.N.A.S. 72, 2227–2231 (1975)
Hocking, B.: Insect-flower associations in the high arctic with special reference to nectar. Oihos 19, 359–388 (1968)
Howard, R.: Dynamic Probabilistic Systems, Vol. I. Markov Models, Vol. II: Semi-Markov and Decision Processes. New York: John Wiley and Sons 1971
Intriligator, M.: Mathematical Optimization and Economic Theory, Englewood Cliffs, N.J. Prentice Hall 1971
Ishay, J., Bytinski-Salz, H., Shulov, A.: Contributions to the bionomics of the oriental hornet (Vespa orientalis Fab.). Israel J. Ent. 2, 45–106 (1967)
Johnson, N., Kotz, S.: Continuous Univariate Distributions-2. Boston: Houghton-Mifflin 1970
Leitmann, G.: An Introduction to Optimal Control, New York: McGraw-Hill 1966
Levins, R.: Limits to Optimization. Preprint (1976)
Lovgren, G.: A mathematical treatment of the development of colonies of different kinds of social wasps. Bull. Math. Biophys. 20, 119–148 (1958)
Oster, G.: Modelling social insect populations I. Ergonomics of foraging and population growth in bumblebees. Am. Naturalist 110 (to appear) (1976)
Oster, G., Perelson A., Mirmirani, M.: Optimal adaptations in the immune systems. J. Math. Biol. (to appear) (1976)
Plowright, R., Jay, S.: Caste differentiation in bumblebees (Bombus Latr. Hym.) I. The determination of female size. Insectes Soc. 15, 171–192 (1968)
Pontryagin, L., Boltyanskii, V., Gamkrelidaze, R., Mishchenko, E.: The Mathematical Theory of Optimal Processes. New York: John Wiley and Sons, 1962
Richards, O., Richards, M.: Observations on the social wasps of South America. Trans. Roy. Ent. Soc. Lond. 102, 1–170 (1951)
Rocklin, S., Oster, G.: Competition between phenotypes. J. Math. Biol. (to appear) (1976)
Roseler, P.: Unterschiede in der Kastendetermination zwischen den Hummelarten Bombus hypnorum und Bombus terrestris. Z. Naturforsch. 25, 543–548 (1970)
Savile, D.: General ecology and vascular plants of the Hazen Camp area. Arctic 17, 237–258 (1964)
Schaffer, W.M.: Selection for optimal life histories: the effects of age structure. Ecology 55, 291–303 (1974)
Sorensen, T.: Temperature relations and phenology of the northeastern Greenland flowering plants. Meddeleser om Gronland 125, 1–305 (1941)
Williams, G.C.: Adaptation and Natural Selection. A Critique of some Current Evolutionary Thought. Princeton, New Jersey: Princeton Univ. Press, 1966
Wilson, E.O.: Sociobiology. Cambridge: Harvard Univ. Press 1975
Yamane, S.: Preliminary observations on the life history of two polistine wasps, Polistes snelleni and P. biglumis in Sapporo. North. Japan. J. Fac. Sci. Hokkaido University Ser. VI Zool. 17, 78–105 (1969)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Macevicz, S., Oster, G. Modeling social insect populations II: Optimal reproductive strategies in annual eusocial insect colonies. Behav Ecol Sociobiol 1, 265–282 (1976). https://doi.org/10.1007/BF00300068
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00300068