for Doug (and others):
There is ample historical evidence to document the incredible propensity of parents to murder their children under an assortment of stressful situations. In nineteenth century England, for example, infanticide was so rampant throughout the country that a debate over how to correct the problem was carried out in both the lay and medical press. An editorial in the respected medical journal Lancet noted that "to the shame of civilization it must be avowed that not a State has yet advanced to the degree of progress under which child-murder may be said to be a very uncommon crime.
more to read here: History of infanticide.
Obviously common throughout societies. If a child is murdered the probability that it was one of the parents is much higher than the probability that it was a stranger. The younger the child is the higher is the probability that it is murdered by the mother.