Sexual Desire

Sexual desire is an instinctive reaction in animals. If the desire isn't there, neither is the possibility of reproduction. If it is there, it is based on an individual's perception of a suitable mate. That perception usually is a set of criteria that the opposite sex must meet, or at least approximate. An individual regards a member of the opposite gender that meets or exceeds (at least, within the available pool of possibilities) those criteria as being superior to others of that gender. It is therefore the individual that provides the chance for the highest quality offspring with the best chance of survival. When the criteria are not met, sexual desire does not occur.
The criteria can include coming into heat, showing strength, clearly being healthy, providing a safe environment for offspring, being readily available as a sexual partner, some other factor or factors, or any combination. It all depends on what the organism's reproductive strategy deems important. (Please always bear in mind that, in all but humans (as far as we know) there is no conscious element to reproductive strategy -- instinctive reaction guides it.)
Such criteria must, of course, be reciprocal. Simply because she meets his criteria does not mean he meets her's, and vice versa. It is when both partners' criteria overlap enough for both partners to accept them that mating takes place.
Again, the chicken and the egg: the hen's criteria for sexual desire are those that would allow the best combination of genes. If the rooster is good enough to satisfy the criteria, it is superior to one that does not meet them. Thus, its qualities are those that should combine with her's and pass on, and he's the rooster with which she mates.
Because of the costs of sex, the criteria a potential mate must meet or approximate differ greatly, depending on whether the animal applying them is male or female.
One aspect of any reproductive strategy that I should mention now is that of numbers. In numbers there is chance: chance for survival, chance for superiority, chance for further offspring. The more offspring any species can produce, the better that species' chances of survival and future.
This results in each organism trying to produce as many offspring as possible as long as possible. It is at this point we run into the major difference between male and female attitudes towards sex.