Abstract
A model is constructed to study the effects of local mate competition and multiple mating on the optimum allocation of resources between the male and female reproductive brood in social hymenopteran colonies from the ‘points of view’ of the queen (parental manipulation theory) as well as the workers (kin selection theory). Competition between pairs of alleles specifying different sex investment ratios is investigated in a game theoretic frame work. All other things being equal, local mate competition shifts the sex allocation ratio in favour of females both under queen and worker control. While multiple mating has no effect on the queen’s optimum investment ratio, it leads to a relatively male biased investment ratio under worker control. Under queen control a true Evolutionarily Stable Strategy(ess) does not exist but the ‘best’ strategy is merely immune from extinction. A trueess exists under worker control in colonies with singly mated queens but there is an asymmetry between the dominant and recessive alleles so that for some values of sex ratio a recessive allele goes to fixation but a dominant allele with the same properties fails to do so. Under multiple mating, again, a trueess does not exist but a frequency dependent region emerges. The best strategy here is one that is guaranteed fixation against any competing allele with a lower relative frequency. Our results emphasize the need to determine levels of local mate competition and multiple mating before drawing any conclusions regarding the outcome of queen-worker conflict in social hymenoptera. Multiple mating followed by sperm mixing, both of which are known to occur in social hymenoptera, lower average genetic relatedness between workers and their reproductive sisters. This not only shifts the optimum sex ratio from the workers’ ‘point of view’ in favour of males but also poses problems for the kin selection theory. We show that kin recognition resulting in the ability to invest in full but not in half sisters reverts the sex ratio back to that in the case of single mating and thus completely overcomes the hurdles for the operation of kin selection.
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References
Alexander R D 1974Ann. Rev. Ecol. Syst. 5: 325–383
Alexander R D and Sherman P W 1977Science 196: 494–500
Benford F A 1978J. Theor. Biol. 72: 701–727
Breed M D 1981Proc. Natl. Acad. Sci. U.S.A. 78: 2635–2637
Bulmer M G 1981J. Theor. Biol. 93: 239–251
Bulmer M G 1983Am. Nat. 121: 899–902
Charnov E L 1978aAm. Nat. 112: 317–326
Charnov E L 1978bJ. Theor. Biol. 75: 451–465
Charnov E L 1982The theory of sex allocation (Princeton: University Press)
Craig R 1979Evolution 33: 319–334
Craig R 1980aAm. Nat. 116: 331–323
Craig R 1980bJ. Theor. Biol. 87: 55–70
Crozier R H 1980 inDahlem konferenzen 1980 (ed.) H Markl (Weinheim Verlag Chemie GmbH) pp. 129–146
Crozier R H and Brückner D 1981Am. Nat. 117: 561–563
Fisher R A 1930The genetical theory of natural selection (Oxford: Clarendon Press)
Gadagkar R 1985aProc. Indian Acad. Sci (Anim. Sci.) 94: 309–324
Gadagkar R 1985bProc. Indian Acad. Sci. (Anim. Sci.) (submitted)
Gadgil M, Joshi N V and Gadgil S 1983J. Theor. Biol. 104: 21–42
Gadgil S, Nanjundiah V and Gadgil M 1980J. Theor. Biol. 84: 737–759
Getz W M and Smith K B 1983Nature 302: 147–149
Greenberg L 1979 Science 206: 1095–1097
Hamilton W D 1964aJ. Theor. Biol. 7: 1–16
Hamilton W D 1964bJ. Theor. Biol. 7: 17–52
Hamilton W D 1967Science 156: 477–488
Hamilton W D 1979 inSexual selection and reproductive competition in insects (eds.) M S Blum and N A Blum (New York: Academic Press) pp. 167–220
Herbers J M 1979Am. Nat. 114: 818–834
Herre E A 1985Science 228: 896–898
Klahn J E and Gamboa G J 1983Science 221: 482–484
MacNair M R 1978J. Theor. Biol. 70: 449–459
Maynard Smith J 1974J. Theor. Biol. 47: 209–221
Maynard Smith J 1982Evolution and the theory of games (Cambridge: University Press)
Metcalf R A 1980Am. Nat. 116: 642–654
Orlove M J 1975J. Theor. Biol. 49: 289–310
Oster G, Eshel I and Cohen D 1977Theor. Popul. Biol. 12: 49–85
Owen R E 1983Oecologia (Berlin) 59: 402–404
Owen R E and Plowright R C 1982Behav. Ecol. Sociobiol. 11: 91–99
Owen R E, Rodd F H and Plowright R L 1980Behav. Ecol. Sociobiol. 7: 287–291
Page R E and Metcalf R A 1982Am. Nat. 119: 263–281
Pamilo P 1982Am. Nal. 119: 638–656
Starr C K 1984 inSperm competition and the evolution of animal mating systems (ed.) R L Smith (New York: Academic Press) pp. 427–464
Taylor P D and Bulmer M G 1980J. Theor. Biol. 86: 409–419
Trivers R L and Hare H 1976 Science 191: 249–263
Uyenoyama M and Bengtsson B O 1981Theor. Popul. Biol. 20: 57–79
Werren J H 1980Science 208: 1157–1159
Werren J H 1983Evolution 37: 116–124
Wilson E O 1971The insect societies (Cambridge, Mass: Harvard University Press)
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Joshi, N.V., Gadagkar, R. Evolution of sex ratios in social hymenoptera: kin selection, local mate competition, polyandry and kin recognition. J. Genet. 64, 41–58 (1985). https://doi.org/10.1007/BF02923552
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DOI: https://doi.org/10.1007/BF02923552