The need to have two parents caring for hatchlings appears to be the reason that many species of birds are monogamous

Question

But if the value of monogamy lies in rearing a brood successfully, why is extra-pair copulation so common among monogamous species of birds?

Answer 1

Many hypotheses have been proposed to explain the advantage of extra-pair copulations. They are not mutually exclusive, and several may operate simultaneously. Here are some examples:
Both male and female birds can benefit from certain aspects of extra-pair copulations:
• Either sex could increase the fitness of its offspring by mating with an individual of better genetic quality than the one it is paired with.
• Either sex could benefit from increasing the heterozygosity of its offspring by mating with more than one partner, as well as increasing the chance of producing genetically compatible combinations of maternal and paternal genes.
In addition, there are potential benefits of extra-pair copulations that are specific to just one sex.
For males, the advantages of extra-pair copulations are probably both genetic and practical:
• A male may be able to sire more offspring in a season by mating with multiple females than it could with a single female.
• A male benefits from the parental care provided to his offspring by the male partner of an extra-pair female with which he has mated.
• Spreading a male's reproductive investment among several nests reduces the risk of losing his entire reproductive effort if a nest is raided by a predator.
From the perspective of a female also, extra-pair copulations offer potential benefits:
• Some males are more fertile than others, and mating with several males reduces the risk that some of a female's eggs will not be fertilized.
• A female may be able to increase the fitness of her male offspring by mating with a male that has especially attractive secondary sexual characteristics. (This phenomenon is called the "sexy son" hypothesis.)
• A female may lay the egg in the nest of the male who fertilized it, thus benefiting from the parental care provided by the female that is pair-bonded to that male.