Behavior: Males put more time and effort into pursuing prospective mates, while females put more time and effort into raising the young. Females put little or no effort into seeking mates, and males put little or no effort into raising the children.
Males, on the other hand, produce tiny little gametes which are little
more than DNA with tails. They can move around and are so easy to make
they represent almost no energy or effort by the male.
If a female makes a bad choice of mate and her offspring dies because of
it, then she has incurred a substantial loss of investment. If the male
makes a bad choice of mate, however, he can simply turn around and mate
again, none the poorer.
"a struggle between the individuals of one sex, generally male, for the possession of the other sex."This is similar to natural selection- they act on the same mechanism, but sexual selection refers only to those traits which affect mating success.
From flies: They put a bunch of tagged flies together and watched who mated with whom. All the females mated either one or two times. The males, however, ranged from no times to four times.
From red-tailed deer: 36% of the females had no matings at all, while 45% of the males had no matings at all. However, the females had quite a narrow range of number of offspring living to maturity, while the males' numbers went all the way up to 24!
From elephant seals: Most females had one or two offspring, but the males either had none or they had 100-200!
From red colobus: Some males had up to 30 offspring, while females all had 0, 1, or 2.
From Kipsigis: (Polygynous traditional pastoralists in Kenya) The females had 15 kids at the most, while several males had over 25 kids.
To sum up, males have much more varied reproductive success than females.
This is all well and good for things like flies where the female lays the egg, the male fertilizes it, they both fly away and that's the end of their respective investments in the offspring. In primates, there's still tremendous investment to be done after the laying of the egg.
There's gestation- energy that must be spent carrying
the developing child inside your own body.
There's lactation- energy spent providing food for the
child for the first stages of its life.
There's carrying- energy spent lugging the child around
from one place to another which, as anyone who has carried around a
two-year-old can tell you, mounts up real quick.
Parental investment as defined by Trivers:
"Any investment by the parent in an individual offspring that increases the offspring's chance of surviving (and hence reproductive success) at the cost of the parent's ability to invest in other offspring."
So, basically, males can increase their reproductive success by getting more women, while females can increase their reproductive success by turning food into eggs as a faster rate. Remember, "Where one sex invests considerably more than the other, members of the latter will compete among themselves to mate with members of the former." Of course, this is a more generalized account of things- it's not always males doing chasing and females being choosy. If the investment by each sex changes, then the competition should change as well. So, if males were to invest more than the females, we would expect the females to compete among themselves for the males.
There are all kinds of species with all different levels of parental involvement. There is a South American frog, denderbates, called the poison dart frog. The females lay their eggs on the backs of the males. The males then climb up and find little pools of water in the crotches of trees where they put the eggs. The males will climb back up the trees every day to check on the progress of the tadpoles, bringing them food and water, and even moving them if the pool looks like it is drying up. Meanwhile, the female goes blithely along finding guys who will let her lay her eggs on their backs. The males act all coy, and the females will fight viciously among themselves if they encounter each other.
There are no role-reversal species in primates. Nor in mammals, for that matter, since having breasts predisposes the females to invest more than the males. However, there are all different degrees of parental investment. The more monogamous the species, the less sexual selection there is and the less difference between the sexes there is in reproductive success. The more polygynous a species is, the more sexual selection there is and the more differences in reproductive success there is.