In biology, Bateman's principle is the theory that females almost always invest more energy into producing offspring than males, and therefore in most species females are a limiting resource over which the other sex will compete.
Typically it is the females who have a relatively larger investment in producing each offspring. A single male can easily fertilize all a female's eggs: she will not produce more offspring by mating with more than one male. A male is capable of fathering more offspring than any (one) female can bear, if he mates with several females.
By and large, a male's reproductive success increases with each female he mates with, whereas a female's reproductive success is not increased nearly as much by mating with more males. This results in sexual selection, in which males compete with each other, and females become choosy in which males to mate with.
Bateman's observations came from his empirical work on mating behaviour in fruit flies. He attributed the origin of the unequal investment to the differences in the production of gametes: sperm are cheaper than eggs. Animals are therefore fundamentally polygynous, as a result of being anisogamous.
"A female can have only a limited number of offspring, whereas a male can have a virtually unlimited number, provided that he can find females willing to mate with him. Thus females generally need to be much choosier about who they mate with." --Caspar Hewett, 2003
"A male can easily produce sperm in excess of what it would take to fertilize all the females that could conceivably be available. Hence the development of the masculine emphasis on courtship and territoriality or other forms of conflict with competing males." --Williams, 1966.
"in most animals the fertility of the female is limited by egg production which causes a severe strain on their nutrition.
In mammals the corresponding limiting factors are uterine nutrition and milk production, which together may be termed the capacity for rearing young. In the male, however, fertility is seldom likely to be limited by sperm production but rather by the number of inseminations or the number of females available to him...
In general, then, the fertility of an individual female will be much more limited than the fertility of a male... This would explain why in unisexual organisms there is nearly always a combination of an undiscriminating eagerness in the males and a discriminating passivity in the females." --Bateman, 1948.
"among polygynous species, the variance in male reproductive success is likely to be greater than the variance in female reproductive success." --Huxley, 1938.
"The female, with the rarest exceptions, is less eager than the male... she is coy, and may often be seen endeavouring for a long time to escape." --Darwin, 1871.