Angus John Bateman (1919–1996), an English geneticist, suggested that in most species, variability in reproductive success (or reproductive variance) is greater in males than in females. This can be seen as the result of anisogamy. Bateman suggested that since males are capable of producing millions of sperm cells with little effort, while females invest much higher levels of energy in order to nurture a relatively small number of eggs, the female plays a significantly larger role in their offspring's reproductive success. Thus Bateman’s paradigm views females as the limiting factor of parental investment, over which males will compete in order to copulate successfully.
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 females' 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 initially published his review in 1948. He was a botanist, contributing to the literature of sexual selection only once in his lifetime. Bateman initially saw his study on Drosophila to be a test of Charles Darwin’s doctrine of sexual selection. He saw Darwin’s theory of natural selection not as flawed, but as incomplete. He felt that if he were to provide a concrete demonstration of how sexual selection played a role in the reproductive success of certain species, he could explain the gap between Darwin’s ideas and sexual dimorphism.
Although it is common to confuse Bateman's ideas with those of later scientists, his principle can be expressed in three simple statements. The first is that male reproductive success increases with the number of mates they attempt to copulate with, while female reproductive success does not. The second is that male reproductive success will show greater variance than female. The third is that sexual selection will have a greater effect on the sex with greater variance in reproductive success.
Throughout his research, Bateman conducted experiments using fruit flies in order to observe their copulation and sexual behavior. A total of six series of experiments were conducted with the fruit fly Drosophila melanogaster, using three to five individuals of each sex. Each trial ran for three or four days. Some ran to completion without the transfer of the Drosophila from one environment (bottle) to another. In the others, Bateman transferred the flies and their eggs to a new bottle every day. Bateman also varied the age of the flies depending on the experiment, with an age gap between one and six days total. He never watched the flies' copulations. The flies used were from several inbred strains, which meant they could be identified by their specific inbred strain. Therefore, he inferred the number of involved mates based on the number of offspring that were later found to have mutations from both a male and a female. The difficulty that arose was that if a female Drosophila had copulated with five males and only one larva survived, Bateman would not be able to account for the other four copulations.
Analysis of the data collected in sets one through four showed that the males' reproductive success, estimated as the number of sired offspring, increased at a steady rate until a total of three mates were reached. It is important to note that Bateman kept the sex ratio of males to females completely even throughout his trials. But after surpassing three mates, male reproductive success began to fall. Female reproductive success also increased with number of mates, but much more gradually than that of the males. The second series of data collected in sets five and six illustrated a dramatically different outcome. Male reproductive success increased at a steady and steep rate, never dropping. Female reproductive success, on the other hand, plateaued after a single mate. Bateman focused mainly on the second series of data when discussing his results. His main conclusion was that the reproductive success of females does not increase with an influx of mates, as one fit mate was enough to successfully complete fertilization. This is often referred to as Bateman’s Gradient.
More than 60 years later, Bateman’s Principle has received considerable attention. Sutherland argued that the males' higher variance in reproductive success may result from random mating and coincidence. Hubbell and Johnson suggested that variance in reproductive success can be greatly influenced by the time and allocations of mating. In 2005, Gowaty and Hubbell suggested that mating tendencies are subject to change depending on certain strategies. They argued that there are cases in which males can be more selective than females. Bateman suggested that his paradigm would be “almost universal” among sexually reproducing species. Critics proposed that females might be more subject to sexual selection than males, but not in all circumstances. An example of a species that refutes Bateman's principle is the pseudoscorpion, Cordylochernes scorpioides. Female pseudoscorpions that mated with more than one male had higher reproductive success. 
Experimental and statistical criticisms followed. Until approximately a decade ago, critics of Bateman’s model focused on his experimental design. In recent years, they have shifted attention to the actual experimental and statistical calculations Bateman had published throughout his trials. Birkhead wrote a 2000 review arguing that the female fruit fly, Drosophila melanogaster, can store sperm for up to four days. But since Bateman’s experiments lasted only three to four days, the female Drosophila may not have needed to mate repeatedly. Therefore, if Bateman had used another species in which females had to copulate more frequently in order to fertilize their eggs, the results might have been different. In 2007, Snyder and Gowaty conducted the first in-depth analysis of the data in Bateman’s 1948 paper. They found many sampling biases, mathematical errors, and even statistical misinterpretations.
Replication of Bateman's experiments
Throughout 2012 & 2013, Gowaty, Kim, and Anderson took it upon themselves to repeat Bateman’s experiment in its entirety. Upon reproducing his tests, the same fly strains and mutations were used in order to maintain the same methodology. However, one of the strains that Bateman used had gone extinct, and was thus left out. (Tang-Martinez 2010)
Gowaty, Kim, and Anderson found that upon combining certain strains with one another, the offspring were unable to survive to adulthood. (Gowaty, Kim, & Anderson 2012) Thus, Bateman’s numbers regarding the amount of individuals not having mated was higher than the actual number. Likewise, his estimate of those that mated with one or more mates was too low. This was valid for both the males and females of this species.
Gowaty desired to further explore the reasoning behind the premature death of the Drosophila. He began doing so by running monogamy trials between different strained flies and found that 25% of the offspring died due to becoming double mutants. (Gowaty 2013) Bateman thought his work fit within the lines of Mendel’s laws of genetics, while Gowaty proved otherwise. The 1948 experiments inferred reproductive success based on the number of adults living by the end of the trial. In reality, many factors were left out of the equation when calculating reproductive success as a function of the number of mates, which had the ability to completely dislodge the accuracy behind Bateman’s results. (Tang-Martinez 2016)
Nevertheless, Bateman’s paradigm should not be looked at as that of a failure. Many modern day experiments between the relationship of number of mates and the reproductive success of males and females support Bateman’s Principle. Julie Collet conducted an experiment with a population of red junglefowl. A total of thirteen replicate groups of 3 males and four females were monitored for ten consecutive days. In this experiment, the sex ratio was biased towards that of the females. The paternity success of a given male was calculated using the proportion of embryos fathered over the total number of embryos produced by all the females in which he mated with. The total sexual selection opportunity was calculated using the following formula.
The σ2 represents the variance in RS, while the[clarification needed] is the square mean of reproductive success of members of one sex in a group. Collets experiment proved that Bateman’s ideology was in fact on the right track. Although his data and statistical errors were thought of to be completely flawing of his paradigm, modern day experiments like this one prove otherwise. The opportunity Collet was able to prove through her experiment was nearly twice as high in males in comparison to females. (Collet ’14)
In 2013, Fritzsche and Arnqvist tested Bateman’s Principle by estimating sexual selection between males and females in four seed beetles. They used a unique experimental design in which proved sexual selection to be greater in males than in females. In contrast, sexual selection was also proven to be stronger for females within role-reversed species. Overall, upon concluding their research, they suggested that the Bateman gradient is typically the most accurate and informative measure of sexual selection between different sexes and species. (Fritzsche, K. & Arnqvist, G)
Rather, Bateman’s conclusions and efforts were much ahead of their time. Bateman conducted his experiments with up-to-date technology, statistical analysis, and imagination, all of which were uncommon during the 1940s. (Tang-Martinez 2016) In retrospect, his work has provided a stern foundation for modern studies in the field of sexual selection and will continue to do so for years to come.
Sex-role reversed species
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.
- Newcomer, Scott D.; Zeh, Jeanne A.; Zeh, David W. (1999-08-31). "Genetic benefits enhance the reproductive success of polyandrous females". Proceedings of the National Academy of Sciences. 96 (18): 10236–10241. doi:10.1073/pnas.96.18.10236. ISSN 0027-8424. PMID 10468592.
- 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 Behaviour, 73 (3): e1–e2, doi:10.1016/j.anbehav.2006.10.003
- 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
- Janicke, T.; Häderer, I. K.; Lajeunesse, M. J.; Anthes, N. (12 February 2016), "Darwinian sex roles confirmed across the animal kingdom", Science Advances, 2: e1500983, doi:10.1126/sciadv.1500983.
- Maynard Smith, J. (1978), The Evolution of Sex, Cambridge, UK: Cambridge University Press, ISBN 0-521-29302-2