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.
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