Evolutionarily Stable Strategies
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[edit] Introduction
In game theory, a stable strategy is a strategy such that, if everyone else follows it, it's sensible to follow it too.
In the theory of evolution, an Evolutionarily Stable Strategy, or ESS, is a trait such that if all the other members of one's species has it, it is better to have that trait too, rather than some variant on it.
The theory of evolution predicts that inherited traits or behaviors that relate to competition within a species (for food, for habitat, for nesting sites, for mates, for symbiotes, or whatever) should be evolutionarily stable strategies.
The reasoning behind this prediction is perhaps better conveyed by examples than entirely in the abstract.
[edit] Example: foraging strategies
Consider a species of bird that is capable of foraging both on the ground and in the trees, the proportion of time spent on each activity being determined by instinct --- that is, ultimately, by genetics. To make the example simple, we shall suppose that the birds are on a volcanic island which lacks carnivores, so that both strategies are equally safe.
The point where the two curves cross is the ESS. To see why this is so, consider that if the rest of the species behaved as dictated by the ESS, any variant birds which foraged more than this in the treetops would, by so doing, reduce the amount of food to go round in the treetops, while leaving more to go around on the ground, so that there would be slightly greater rewards for ground-feeding than for treetop feeding. Hence a genetic variation promoting extra foraging in trees would be selected against by natural selection; and if it nonetheless managed to spread a little among the population by genetic drift, then the further it spread through the population, the greater the rewards for ground-feeding, the less the rewards for treetop feeding, and the greater the selective pressure against the tree-loving variants. And the same reasoning applies in just the same way to variants that feed more on the ground than the proportion dictated by the ESS: by doing so, they ensure that so doing is a selective disadvantage. It follows that the only behavior which is stable is the behavior specified by the ESS, which, in this example, involves spending about 70% of the time in the trees and 30% on the ground.
We should note, by the way, that such a division of the species' time may be achieved in different ways: each bird individually may spend 70% of its time in the trees and 30% on the ground; or 70% of the species may be genetically predisposed to spend all of their time foraging in the trees and the other 30% to spend all their time ground foraging; or something between these extremes: the theory does not specify which.
Now, let us look at one other feature of this example. We have said that a stable strategy is one which is best for the individual to follow if everyone else is following it. But it is not, or not necessarily, the case that this is the best strategy for the group as a whole. It is merely the strategy which they are forced into by natural selection.
The reasoning is much as given above. What the birds need to do as a species is to show restraint in their exploitation of the treetops as a food resource. But any individual birds with genes prompting them to show such restraint, will by so doing make the payoff of foraging in the trees greater than the payoff of foraging on the ground, and so put themselves at a selective disadvantage.
To look at it another way, suppose that the strategy of the species (by some miracle) was at the optimum instead of the ESS. Then, as you can see from the graph, at the optimum the payoff for foraging in the trees is rather greater than the payoff for for foraging on the ground. This means that natural selection would favor any variation which increasing time spent foraging in trees --- driving the species' strategy towards the ESS.
It is not, we should add, an invariable rule that the rewards of the ESS are less than the optimum, but it is fairly characteristic of such situations, as we shall see in further examples.
[edit] Example: sex ratios
Consider a species of animal in which each dominant male has a harem of females which mate exclusively with him; less favored males having no real chance of reproduction. Such situations are common in mammals ranging from deer to seals. Now, it might have occurred to you to wonder what all those surplus males are for. They just stand around uselessly consuming resources which could otherwise feed pregnant and nursing mothers. In fact, from the point of view of the species, it would be much better if all the surplus males were, in fact, females.
This caught the attention of the eminent biologist Ronald Fisher, back in the 1930s, who explained this point: as you will have guessed, the explanation involves an ESS which is less than optimal.
Fisher reasoned as follows. Suppose an adult female produces an average of n offspring annually. Suppose the male to female ratio in the adult population is m:f. There are nf offspring born each year, and each has only the one father, so the average number of offspring per male per year is nf/m. This average of offspring per male per year, you will note, as Fisher noted, is the same however the males divide up the breeding females, whether monogamously or in large harems.
The ESS is, of course, the point at which the sex ratio is 50:50 and the payoff of bearing male children is the same as the payoff of bearing female children. It might be an advantage to the species if it collectively showed restraint by producing more females than males: but in such a situation, there is a greater reward to the individual who produces more male offspring, and so such a trait would be selected for until the gender imbalance was removed.
We should note that there are circumstances under which Fisher's reasoning does not apply: if, for example, producing males cost only half the investment on the part of the mother (as might happen if males were half the size) then this would tilt the balance in favor of males. In the example given above, we have kept things simple by assuming equal parental investment in both sexes: in real life, we should need to look at the data.
Another factor which tips the balance (this time towards females) is that when a species is so poor at dispersal from generation to generation that inbreeding is likely, this favors the production of female offspring: the selective pressures on a mother are different if the matings of her daughters are all going to be with her sons. In this case, having more daughters can benefit no-one but herself, and increases the number of her prospective grandchildren; hence, it is favored by natural selection.
[edit] Example: the tail of the peacock
The facts about peacocks, we suppose, are familiar to the reader: peacocks have exotic plumage, and peahens choose their mates based on the magnificence of their plumage. This too is an ESS, and we may well suppose it to be one which is disadvantageous to the species, since a better-camouflaged species would, presumably, be better able to compete against other species.
The way the ESS works is as follows. If a variation arose which made a peacock drabber (but safer from predators) then that peacock is going to lose out in the search for mates: even if he gets lucky, any male descendants that inherit the trait will be similarly handicapped in looking for mates: hence, we expect this disadvantageous trait to be removed from the gene pool by sexual selection.
But what about the peahens? What if a variant arises who prefers her mates to be drab yet safe? The problem she faces is that if she selects her mates like that, then her sons are going to be unattractive to females who do not share this gene; and those of her female descendants who inherit the trait will be likewise handicapped.
If one could wave a magic wand and change the genes of every peahen so that they did not prefer the gaudiest males, then it would no longer be advantageous for an individual peahen to do so. But as it is, they are stuck in their situation: there is no way to evolve peacocks with more sensible plumage or peahens with more sensible tastes.
[edit] Note on data
It should not have escaped your attention that in order for this sort of reasoning to be tested and applied in the real world, we need a lot of real-world data. In order to check, for example, that the foraging strategies of a particular bird species really are as described by the ESS, we need to know the actual costs and benefits of the foraging strategies.
This means that the mathematical approach that we've outlined above has to be combined by lots of measurements of, for example, how much vegetation will fit inside a moose, and the relationship between the size of a mussel and the time it takes a shore crab to break it open; it involves experimentally painting sparrows black, gluing extra tail-feathers onto birds, attaching tiny little weights to bees, and feeding hummingbirds radioactive sugar (a safe procedure, we may assure bird-lovers).
A combination of precise data with the precise logical reasoning afforded us by the theory of evolution brings this aspect of natural history --- competition within species --- as close to a hard science as natural history gets.
