Cuckoos famously lay their eggs in other birds' nests and leave them to do the hard work of bringing up the offspring. Why then don't the other birds catch on and push the cuckoo eggs out? It seems some cuckoo species are the mafioso of the bird world, and make their hosts an offer they can't refuse.

Many cuckoo species infiltrate host birds' nests by producing eggs of identical colors and size to the host. In these cases there is also something of an arms race where the young birds develop distinctive feeding calls that enable their parents to tell them apart from cuckoo offspring, while the “brood parasites” as they are known, learn to copy.

However, by making their eggs and young too similar to a particular host species cuckoos run the risk of all specialists; if something happens to the species they target they are done for. Indeed that something could be the parasites' overburdening the hosts so that not enough young get raised to support future cuckoo generations.

The brown-headed cowbird, on the other hand, lays its eggs in the nests of 140 different species of bird's nests. As a result the egg looks nothing like that of most of its hosts (see image below) and can be easily distinguished. Why then do the hosts not throw it out, allowing them to focus their parental efforts on their own children?

In 1979 Evolutionary biologist Amotz Zahavi of Tel Aviv University proposed what he called the mafia hypothesis . He suggested that if hosts removed parasitical eggs from their nests the cuckoos would respond by coming back and destroying all the other eggs as well. Birds living in fear of such retribution would put up with a having to feed an extra mouth.

The idea has been controversial, with some biologists suggesting instead that there is an “evolutionary lag” with newly parasitized species not having caught on yet. Now however, mathematical modeling at the Max Plank Institute of Evolutionary Biology has backed-up Zahavi's theory, at least on a cyclic basis. Some birds “give their hosts no choice,” says lead author Dr Maria Abou Chakra. “If they wish to avoid retaliation, then need to keep the foreign egg.”

In Nature Chakra notes brown-headed cowbirds (Molothrus ater) and great spotted cuckoos (Clamator glandarius) have been observed to retaliate when hosts reject their eggs. To be fair the great spotted cuckoo fledgling also earn their keep by deterring predators . She says, “The mafia hypothesis works when retaliation is sufficiently costly to the host in comparison to the consequences of accepting parasitism. In particular, this assumes that the host's young are raised alongside of the parasite's young, which is the case in these examples.”

Chakra created two different models. Under the minimalistic model the cuckoo lays a single nest in a host bird's nest. A more complex model has several eggs laid, with the possibility of the host getting rid of some of them but allowing others to stay. “Biologists prefer the complex model, because it is closer to reality. But we came to the same conclusion with both models: the dynamics of the interaction between host and parasite is cyclical,” Chakra says.

Her modeling took into account the fact that the mafia birds were not the only parasites out there – other species may also be laying eggs in the hosts' nests, and it would be hard for hosts to distinguish between different parasites.

Hosts had two strategies open to them, to tolerate the parasitical eggs straight away, or to throw them out as a first resort and only raise parasitical eggs if they have been on the receiving end of a retaliation previously. The host birds normally only lay one clutch per season, but can make up to three attempts if their first effort is destroyed by vengeful mafia-birds or other forces.

Where mafia-style parasites dominate the best move is immediate toleration. Better, as it were, to learn from the real mafia and keep your children close and your enemies closer. However, if most intruder eggs come from species that don't enact retribution a bird is better off taking a chance by throwing out eggs that are not their own. However, each strategy affects the population of parasite birds. When toleration becomes dominant non-mafia species gain the benefit as well and will increase in number without having to go to the trouble of revisiting nests to see if their eggs have been thrown out. It's a sort of meta-mafia strategy, benefiting from the thuggish behavior of other birds without having to get their wings dirty. However, eventually retribution becomes so rare that host birds benefit by changing strategy, and the cycle begins again.

Rather than reaching an equilibrium, Chakra find it is more likely that swings between the two responses, and therefore the frequency of the two parasitical species, become wider and wider (see graphs below).

Unpleasant as some may find idea of birds effectively holding each others' offspring captive, the success of this strategy says a lot about the hosts' learning capacity. Chakra notes, “For retaliatory behavior to be favored, hosts need to have evolved a plastic response. On the other hand, the ability to perform such a plastic behavior is only favored if already a large fraction of parasites retaliate. So how can both behaviors emerge in the first place?” She postulates that the capacity to respond adaptively to retaliation may have other benefits in nature.