Moreover, the biological cost of generating offspring is generally substantially greater for the female, compared to the male. 

So, if the female is going to have offspring, it would be in their evolutionary interest that those offspring survive and reproduce. 

The more robust the mate, the more likely that the offspring will be genetically "well endowed" and likely to survive and reproduce, that is, the greater the return on the female's substantial investment.  

At the same time, the survival of offspring can be increased by the continued presence of the male, to protect the female and its (and their) offspring.

In many species the male's "investment" in the next generation is much less substantial.

Males can often maximize their reproductive success by mating with multiple females, or in some species, by helping the female to successfully produce and raise offspring.

Both males and females "know" these rules and may attempt to deceive each another.

A male may appear more robust than he actually is, a female may mate with multiple males in order to select the most robust sperm (sperm selection), or may mate with one male and bond with another, so that the second can help with raising the offspring.

In turn, males may respond by attempting to monopolize the female. This, of course, will require the male to spend energy in "guarding".

There are many variations to be found in the natural world and a full discussion is beyond the scope of this course. 

One of the most robust and reliable findings in the scientific literature on interpersonal attraction is the overwhelming role played by physical attractiveness in defining the ideal romantic partner (Hatfield & Sprecher, 1986; Jackson, 1992).

Both men and women express marked preference for an attractive partner in a noncommitted short-term (casual, one night stand) relationship (Buss & Schmitt, 1993).

For committed long-term relationships, females appear to be willing to relax their demand for a partner's attractiveness, especially for males with high social status or good financial prospects (for a review see Buss, 1999).

Males also look for various personality qualities (kindness, understanding, good parental skills) in their search for long-term mating partners, but unlike females, they assign disproportionately greater importance to attractiveness compared to other personal qualities (Buss, 1999).

The paramount importance of attractiveness in males' mate choices has been recently demonstrated by using the distinction between necessities (i.e., essential needs, such as food and shelter) and luxuries (i.e., objects that are sought after essential needs have been satisfied, such as a yacht or expensive car) made by economists.

Using this method, Li et al., (2002) reported that males treat female attractiveness as a necessity in romantic relationships; given a limited "mating budget," males allocate the largest proportion of their budget to physical attractiveness rather than to other attributes such as an exciting personality, liveliness, and sense of humor.

- from Mating strategies for young women by Devendra Singh (2004).

Sexual selection can lead to seemingly maladaptive traits. Consider the peacock's tail.  It takes a continuous supply of energy to generate a large, symmetrical and colorful tail.  It can also make the male more vulnerable to predators.

On the other hand, the presence of a gaudy tail implies that its owner is able to successfully compete with others for resources, and so is likely to be genetically "well endowed".

Once females notice tail size as a marker of success, they select as mates those males with the largest and most attractive tails.

This can lead to runaway' selection, the more prominent the male's tail the more likely he will find a mate, even though it may also have negative effects.  For example, the development of extremely large antlers, associated with male dominance and mate accessibility, as occurred in Megaloceros giganteous, can inhibit their ability to move through heavily wooded areas.

As their environment changed, their behavior and phenotypes could act to limit their ability to adapt fast enough to avoid extinction.

In the end, as with all adaptations, there is a balance between the positive effects, which lead to increased reproductive success (such as access to mates) and their negative effects, which can influence survival. 

The optimal form of a trait may not be stable over time, particularly if the environment is changing.