Game Theory of Bowerbird Sabotage
War is hell, and it seems that humans are not the only species that engage in competition over resources at the expense of their enemies. Since at least the 5th century BC, military scholars have been theorizing, and more recently using mathematics as well as wisdom and intuition, in order to inform decisions such as when to advance and reap the spoils of conquest, and when to remain at home and defend against similarly minded neighbours. For a male of the family Ptilonorhynchidea, colloquially known as the bowerbird, such daily strategic considerations may mean the difference between securing a copulation with another female or several wasted days. Known for constructing elaborate structures called bowers which can be seen as external secondary sex traits used for courting females, bowerbirds are known to maraud neighbouring male’s bowers, vandalizing and destroying their bowers and/or stealing decorations. In this system, females will visit several males whose bowers exist within her territory, selecting one to mate with based upon several features involved with the the elaborateness of his nest and his courtship display. After mating, the female will lay a clutch and attend to the offspring without any paternal care. As a result of this promiscuous system, a male benefits from securing as many matings as possible. It is thought that a male may benefit from marauding a neighbour’s bower by increasing the likelihood of the female selecting him as the father of her future clutch.
As a result, males daily engage in a decision process that, though superficially simple, is in fact riddled with complexities. A male must decide whether to spend time guarding his bower against intruder males (G), maurading a neighbour male’s bower and destroying it (M), stealing a neighbour’s decorations to elabourate his own bower (S), or a combined strategy of destroying and stealing from neighbours (C). So any male has four strategies to select from, and must make his decision taking into account various constraints in his environment and life history. A male only has a certain amount of time (t) in the day, and must partition this time with several factors in mind. A male must be at his bower for a female to consider him as a mate. But, as mentioned earlier, he may be able to garner an advantage should he choose strategy S, M, or C. Furthermore, the natural ecology of the species affects the benefits yielded by each strategy; in a species where decorations are not as important for mating success, S may not be as useful a strategy, and in species where bowers are difficult to destroy without an expensive investment of time and effort, M may be similarly unwise. It turns out that the male bowerbirds are engaged in an intricate game that has been investigated in detail by researchers. Below is the payoff matrix developed by the researchers to predict decisions made by males in the bower-display game. I will take apart this matrix to make it easier to digest and understand.
First, I will mention some of the variables that they dealt with, and if applicable, which ones were made into constants based upon field data averages.
R: rate at which females visit males
t: time that male can spend at his power, proportion of daylight hours, set to12h
td :travel time (round trip) required to visit neighbouring male’s bower, set to 4 min
tm: time male spends marauding neighbour’s bower or stealing decorations or interacting with resident, set to be 2 min
tt : time spent rebuilding bower, set to 4h
q: probability that female will mate with male, set to 0.5
a : change (positive or negative) in probability that female will mate with male associated in change in # of decorations, set to 0.1
p: probability that guarder’s bower will be marauded/stolen from on any given attempt
p’: probability that an intruder’s bower will be marauded and/or stolen from on any given attempt
m: average number of males on a female’s home range, set to 6 males
i: proportion of day spent displaying at bower before additional decision is made, set at 0.25
It is important to note that these constants were decided upon based on averages across species, and after the model predicted sets of dominant strategies based on various condition values, these results were compared to behaviour actually observed in nature. Three cases were examined by the model.
- Case I Marauding vs Guarding: occurring when bowers are relatively easy to destroy but decorations do not add much to the probability of a female mating (a)
- guarding is stable when:
- bower residence times are high
- travel times are high OR bower repair times are low
- marauding is stable:
- under other conditions (which correlate with actual natural conditions)
- guarding is stable when:
- Case II Stealing vs Guarding: occuring when bowers are either very sturdy (and hard to destroy) or flimsy (and easy to rebuild), but decorations add significantly to the probability of the female mating (a)
- stealing is almost always stable
- Case III All strategies combined: when there is value both to destroying neighbour’s bower and stealing decorations
- theoretically all three are stable as pure strategies
- under realistic conditions, only M, C or some combined strategy of M and C are stable
Many conditional strategies were considered by the researchers, as the males seem very dynamic in their strategic decisions based on the actions of their neighbours, as well as possibly able to remember interactions with neighbours, opening possibilities of iteration. For example, in the Satin Bowerbird, males will all guard until one is raided by a thief, at which time they adopt the S strategy, which is diagnostic of a Tit-for-Tat game. However, these are beyond the scope of what we have spoken of in class thusfar, and so it will suffice to simply say that under most natural circumstances, the stable strategy is to adopt a disruptive strategy (M or C). Males who adopt these strategies appear to gain more of a benefit than they receive in cost for being absent from their bower. So it seems that in the world of bowerbirds, in the pursuit of a mate it truly is total war, but maybe a war tinctured by morality.