Most of us assume that babies cry during the night because they want to nurse, or perhaps because they just want to be held.
The idea: babies cry at night to delay the birth of another sibling
Delaying the birth of a sibling certainly wouldn't be a conscious decision on the part of the babies, just a result of the fact that throughout the many years of our species' evolutionary history, babies that had more time before the birth of another sibling tended to survive more often. (This is probably because of the increased amount of time, attention, and resources given to babies spaced further apart.)
Why would crying at night delay the birth of a sibling? It's not because frustrated parents would be interrupted having sex. Instead, it's because mothers don't ovulate while they're nursing, so the longer they nurse for, the longer it'll be until they can have another baby. Nursing at night and on demand (rather than on a schedule) seems to be especially important for delaying the return of ovulation after a baby.
The evidence for
Haig presents a few lines of evidence for this idea. One is the timing of nighttime waking: studies show that in general, babies tend to sleep through the night more often during their first six months (when mothers aren't ovulating either way), then wake more often from 6 to 12 months (when mothers might start ovulating if they're not nursing a lot at night). After 12 months, they tend to start sleeping through the night again — because at this point, a spacing of nearly two years has been established, enough to establish a greater chance of survival.
He also points to the fact that, on the whole, babies fed from bottles wake up less often during the night than breastfed infants. If waking up doesn't delay their mothers' fertility (because it doesn't actually involve breastfeeding), the argument goes, these babies are better off just sleeping.
The last line of evidence is a bit more complex, and involves a subtle split in the genes a baby gets from a mother and a father. For a mother, having a baby with a genetic predisposition to waking at night is evolutionarily costly — even though it makes that baby more likely to survive, the greater spacing lowers the amount of babies she can have overall. For a father, this is less of a problem — he can always reproduce with other women. This would predict that genes inherited from a father would promote waking more than those from mothers, and at least in some cases, this has found to be true: babies with Angelman syndrome (in which a small set of maternal genes are randomly deleted) tend to wake up particularly often, while those with Prader-Willi syndrome (in which the same set of paternal genes are deleted) tend to sleep excessively.
The evidence against
The study generated a number of responses from experts in infant sleeping patterns, lactation, and human social evolution, and on the whole, most were intrigued by the idea, if not fully convinced by it.
The main problem with it is that we have existing explanations for why babies wake during the night. For one, there's the most obvious reason: babies want maternal contact and reassurance. But there's also the fact that more frequent suckling increases milk production. In general, a baby's nutritional demands begin to outstrip a mother's milk production at six months of age, providing another reason why nighttime waking increases at this time.
Additionally, some infant sleep researchers have observed that babies tend to wake most often when they're having difficulty breathing — a habit that would also provide an evolutionary benefit (reducing the chance of a life-threatening apnea, or perhaps sudden infant death syndrome).
These alternate explanations don't rule out Haig's idea, and may in fact complement it — babies could wake up to avoid suffocating, to get their mothers to produce more milk, and to keep her from ovulating.