In biology, Bateman's principle suggests that in most species, variability in reproductive success, or "reproductive variance," is greater in males than in females. This is ultimately a consequent of anisogamy. Females, especially mammalian females, almost always invest more energy into producing offspring than males invest. Bateman's principle anticipated and is consistent with Robert Trivers's theory of Parental investment—in most species females are a limiting factor over which males will compete. This competition results in some males being more successful than others, leading to greater reproductive variance among males than females. It is named for English geneticist Angus John Bateman (1919–1996).
Typically it is the females who have a relatively larger investment in producing each offspring. Bateman attributed the origin of the unequal investment to the differences in the production of gametes: sperm are cheaper than eggs. A single male can easily fertilize all female's eggs: she will not produce more offspring by mating with more than one male. A male is capable of fathering more offspring if he mates with several females. By and large, a male's potential reproductive success is limited by the number of females he mates with, whereas a female's potential reproductive success is limited by how many eggs she can produce. This results in sexual selection, in which males compete with each other, and females become choosy in which males to mate with. As a result of being anisogamous, males are fundamentally promiscuous, and females are fundamentally selective.
Bateman's observations came from his empirical work on mating behaviour in fruit flies (Drosophila melanogaster). Bateman hypothesized that male reproductive success increases with number of mates, whereas female reproductive success does not. He believed that this hypothesis could be supported by illustrating the variance in number of mates between females and males, and by plotting reproductive success versus number of mates.
To test this, Bateman crossed virgin parent fruit flies that were each heterozygous for a unique dominant mutant phenotype. He placed 3–5 flies of each sex in milk bottles for 3–4 days, allowed the females to lay eggs, then removed the parent flies and counted the offspring once hatched. Because most (75%) of the offspring expressed the phenotypes of one or both parents, Bateman deduced how many mates each individual had by observing the offspring’s mutations. He judged reproductive success by counting the relative number of offspring sharing each parental phenotype (Bateman 1948). Bateman concluded that 1) the variation in number of mates for males was greater than for females, and 2) "The males show direct proportionality between number of mates and fertility... The females, provided they have been mated with at least once, show absolutely no effect of number of mates" (Bateman 1948).
Flaws in Bateman’s original study
However, whatever the flaws in Bateman's original research, most biologists accept the general validity of his principle. Parker and Birkhead (2013) suggest that "Despite recent criticisms, the contribution of the early pioneers of sexual selection, Darwin and Bateman, remains generally valid..."  Schmitt (2013) noted that over 60 years "...since Bateman, and the empirical evidence clearly shows males have higher RS variability across a wide variety of species... It is almost always the case that males have more RS variance than females. ...In humans, there is near-universal evidence of greater RS variance in men than women." 
Batman's study was also criticised by feminist authors for only emphasizing the male role. The critique however have no bearing on the validity of the results. Bateman's principle has been reformulated by American evolutionary psychologist Geoffrey Miller to view it from a female perspective. In his wording, the females are not sexually active as such, but rather are more sexually selective than males, as their fitness is more tied to the quality of the genes the male can provide rather than quantity.
Sex-role reversed species: Exceptions that prove the rule
The most well-known exceptions to Bateman's principle are the existence of sex-role reversed species such as pipefish (seahorses), phalaropes and jacanas in which the males perform the majority of the parental care, and are cryptic while the females are highly ornamented and territorially aggressive (Emlen & Oring 1977;Knowlton 1982; Berglund, Widemo & Rosenqvist 2005).
However, sex role reversed species are the exceptions that prove the rule. In these species, the typical fundamental sex differences are reversed: females have a faster reproductive rate than males (and thus greater reproductive variance), and males have greater assurance of genetic parentage than do females (Flinn 2004). Consequential reversals in sex roles and reproductive variance are consistent with Bateman's Principle, and with Parental investment theory of Robert Trivers.
- Gowaty, Patricia; Kim, Anderson (11 June 2012). "No evidence of sexual selection in a repetition of Bateman’s classic study of Drosophila melanogaster". Proceedings of the National Academy of Sciences of the United States of America 109: 11740–11745. doi:10.1073/pnas.1207851109. Retrieved 15 December 2012.
- Parker, G.A. & Birkhead, T. R. (2013). Polyandry: the history of a revolution. Phil. Trans. R. Soc. B 5 March 2013 vol. 368 Published online January 21, 2013 doi: 10.1098/rstb.2012.0335 PDF
- Schmitt, D. P. (2013) Much Ado About Sex Differences In Reproductive Success. Psychology Today.
- Miller, G. (2000), The Mating Mind: How Sexual Choice Shaped the Evolution of Human Nature, London: Heineman, ISBN 0-434-00741-2 (also Doubleday; ISBN 0-385-49516-1).
- Ridley, Mat (2002), The Red Queen: Sex and the Evolution of Human Nature
- Baker, Robin (2003), Sperm Wars: The Science of Sex
- Bateman, A.J. (1948), "Intra-sexual selection in Drosophila", Heredity 2 (Pt. 3): 349–368, doi:10.1038/hdy.1948.21, PMID 18103134
- Berglund, A.; Widemo, M.S.; Rosenqvist, G. (2005), "Sex-role reversal revisited: choosy females and ornamented, competitive males in a pipefish", Behavioral Ecology 16 (3): 649–655, doi:10.1093/beheco/ari038
- Birkhead, T. (2001), Promiscuity: An Evolutionary History of Sperm Competition, Cambridge: Harvard University Press, ISBN 0-674-00666-6
- Brooker, MG; Rowley, I; Adams, M; Baverstock, PR (Mar 1990), "Promiscuity: An inbreeding avoidance mechanism in a socially monogamous species?" (PDF), Behavioral Ecology and Sociobiology 26 (3): 191–199, doi:10.1007/BF00172086
- Darwin, C.R. (1871), The Descent of Man and Selection in Relation to Sex, Hurst and Co
- Emlen, S.T.; Oring, L.W. (1977), "Ecology, sexual selection, and the evolution of mating systems", Science 197 (4300): 215–223, doi:10.1126/science.327542, PMID 327542
- Flinn, Mark (2004), "Sexual selection: monkeys, apes, and humans", Lecture notes for Anth 1500, University of Missouri-Columbia, retrieved 2008-06-28
- Hewett, Caspar (2003), Theory of Sexual Selection - The Human Mind and the Peacock's Tale, The Great Debate, retrieved 2008-06-28
- Huxley, J.S. (1938), "The present standing of the theory of sexual selection", in de Beer, G.R., Evolution: Essays on aspects of evolutionary biology, Oxford: Clarendon Press, pp. 11–42
- Judson, Olivia (2002), Dr. Tatiana's Sex Advice To All Creation, New York: Metropolitan Books, ISBN 0-8050-6331-5
- Knight, J (Jan 2002), "Sexual stereotypes", Nature 415 (6869): 254–7, doi:10.1038/415254a, PMID 11796975
- Knowlton, N. (1982), "Parental care and sex role reversal", in King’s College Sociobiology Group, Current problems in sociobiology, Cambridge, UK: Cambridge University Press, ISBN 0-521-24203-7
- Méry, F; Joly, D (Feb 2002), "Multiple mating, sperm transfer and oviposition pattern in the giant sperm species, Drosophila bifurca", Journal of Evolutionary Biology 15 (1): 49–56, doi:10.1046/j.1420-9101.2002.00364.x
- Pruett-Jones, S; Tuttle, EM (Feb 2007), "Fairy-wren sperm counts: a correction", Animal Behavior 73 (3): e1–e2, doi:10.1016/j.anbehav.2006.10.003
- Snyder, BF; Gowaty, PA (Nov 2007), "A reappraisal of Bateman's classic study of intrasexual selection", Evolution 61 (11): 2457–68, doi:10.1111/j.1558-5646.2007.00212.x, PMID 17725639
- Thornhill, Randy (2008), The Evolutionary Biology of Human Female Sexuality
- Williams, GC (1966), Adaptation and natural selection: a critique of some current evolutionary thought, Princeton, N.J: Princeton University Press, ISBN 0-691-07900-5
- Wolff, JO; Macdonald, DW (Mar 2004), "Promiscuous females protect their offspring", TRENDS in Ecology and Evolution 19 (3): 127–33, doi:10.1016/j.tree.2003.12.009, PMID 16701243
- Angeloni, L.; Bradbury, J.W.; Charnov, E.L. (2002), "Body size and sex allocation in simultaneously hermaphroditic animals", Behavioral Ecology 13 (3): 419–426, doi:10.1093/beheco/13.3.419
- Charnov, E.L. (1982), The Theory of Sex Allocation, Princeton, NJ: Princeton University Press, ISBN 0-691-08311-8
- Maynard Smith, J. (1978), The Evolution of Sex, Cambridge, UK: Cambridge University Press, ISBN 0-521-29302-2