This article from Discovery News compares two recent studies that try to understand the evolution of The first one from Opie, et al. at University College in London looked at the primate family tree and used statistical models to show that appearance of monogamy coincided frequently with the appearance of infanticide. In this case, infanticide refers to the practice of males who kill the offspring of females that they have not mated with. This strategy evolved because females of many species will immediately become fertile if the young they are caring for are killed. Thus, the males create a mating opportunity for themselves and eliminate the offspring of a rival male. Of course a male that engages in infanticide runs the risk of losing his own offspring to another male, so monogamy may have evolved as a way for fathers to protect their children from other males.
The second study by Lukas and Clutton-Brock from the University of Cambridge is similar but it looked at monogamy across all mammalian species. But they did not find a correlation between monogamy and infanticide. Instead, their analysis suggested that monogamy evolved as a consequence of females living in solitary territories. Males in this situation have to defend a large area if they want to mate with multiple females and prevent other males from mating with their partners. Presumably then monogamy evolved because it was more efficient to only defend one female against rival suitors.
Monogamy is an interesting puzzle in evolutionary biology, because on the surface it seems like a bad idea. If the name of the game is to get your genes copied into the next generation then you would want to mate with as many partners as possible. This only applies to males though because females are usually limited by the number of eggs they can produce or the number of offspring they can gestate at one time in the case of mammals. Many hypotheses have been proposed over the years to try explain the phenomenon. For example, it was once assumed that monogamy evolved for the benefit of the offspring. Having two adults looking after you has obvious benefits for survival over just one. However, even though these two studies do not agree on what was the original function of monogamy, they both failed to support the paternal care hypothesis. They showed that fathers started actively caring for their offspring after monogamy evolved which suggests that paternal care may have appeared as a side benefit of a strategy that originally only benefited the fathers.