Sexual selection is at the root of practically all the explanations for the origin of our large brains. To quote from Sue Blackmore:

An influential version of social theory is the ‘Machiavellian Intelligence’ hypothesis (Byrne and Whiten 1988; Whiten and Byrne 1997). Social interactions and relationships are not only complex but also constantly changing and therefore require fast parallel processing (Barton and Dunbar 1997). The similarity with Niccolò Machiavelli (1469–1527), the devious adviser of sixteenth-century Italian princes, is that much of social life is a question of outwitting others, plotting and scheming, entering into alliances and breaking them again. All this requires a lot of brain power to remember who is who, and who has done what to whom, as well as to think up ever more crafty wiles, and to double bluff the crafty wiles of your rivals – leading to a spiralling arms race. ‘Arms races’ are common in biology, as when predators evolve to run ever faster to catch their faster prey, or parasites evolve to outwit the immune systems of their hosts. The notion that some kind of spiralling or self-catalytic process is involved certainly suits what Christopher Wills (1993) calls ‘the runaway brain’, and this idea is common among theories that relate language evolution to brain size.

The idea that intelligence can play an important role in evolutionary change arises from the observation that intelligent agents are doing the selecting - in sexual selection. They get to use induction, deduction, analogies, prediction - the whole toolkit of intelligence - and the results are then reflected in the germ line of the next generation. Any idea that the loop between intelligence and brain design information has only closed recently - or has yet to close - is simply wrong. Human brains have been influencing human brain evolution for millions of years - in the same way that they have been influencing dog evolution for millions of years - by acting as the selective agent.

Brains don't just choose. They also create circumstances where there is a lot of information on which to make choices. The mating dance brainy-females often lead males on exposes their parasite load - and so their genetic quality - to selection. So: brains do not just select - they actively create opportunties for selection by intelligence to have a large influence.

If you look at female secondary sex charateristics, they are the products of mind, written back onto the body by evolution. Breasts, red lips - and so on are physical projections of mental analogy-making equipment.

Of course the other classic example of the mental turning into the genetic is the Baldwin effect - where learned, acquired characteristics find their way out of the minds in which they arose and back into the gene pool.

Evolution is no stranger to the action of intelligence - indeed, without millions of intelligent choices by our ancestors, the human race as we know it today would not exist.