Biology Reference
In-Depth Information
(a)
Pay-offs: change in fitness from a contest
Table 5.1
The
game between
Hawk and Dove
(Maynard Smith,
1982).
Winner gains, V
=
50. Loser gains 0. Injury cost, C
=
loses 100.
Assume that: (i) When a Hawk meets a Hawk, on half the occasions it wins and on half
the occasions it suffers injury. (ii) Hawks always beat Doves. (iii) Doves immediately retreat
when they meet a Hawk. (iv) When a Dove meets a Dove, they share the resource.
(b)
Pay-off matrix: pay-offs to attacker
Opponent
Attacker
Hawk
Dove
Hawk
½V
−
½C
= −
25
V
= +
50
Dove
0
½V
= +
25
fight and may injure their opponents, though in the process they risk injury themselves.
Doves
never engage in fights. These two strategies are chosen to represent the two
extremes we may see in nature. The pay-offs are explained in Table 5.1a. (The exact
values do not matter for the moment, as long as V
C, and are chosen simply because
this game is easier to explain with numbers rather than algebra.) It is important to note
that these are simply the
changes
in fitness resulting from a contest. The individual that
does not obtain the resource need not have zero overall fitness. For example, if the
resource is a territory in a good habitat, then the loser may still get to breed in a poor
habitat. So the value of winning the contest is the difference between the reproductive
success in the good and poor habitats.
We now draw up a two by two matrix, with the average pay-offs for the four possible
encounters, as explained in Table 5.1b. How would evolution proceed in this game?
Consider what would happen if all individuals in the population are Doves. Every contest
is between a Dove and another Dove and the pay-off is
<
25. In this population, any
mutant Hawk would soon spread because when a Hawk meets a Dove it gets
+
+
50.
Therefore, Dove is not an ESS.
However, Hawks would not spread to take over the entire population. In a population
of all Hawks the pay-offs per contest are
25, and any mutant Dove would do better
because it retreats immediately with a payoff of 0. (Remember that this doesn't mean
that Doves have zero fitness in a population of Hawks. It means that the fitness of a Dove
does not alter as a result of a contest with a Hawk.) Therefore, Hawk is not an ESS either.
The key point in this game is that each strategy does best when it is relatively rare: in
a population of Doves, Hawks prosper, while in a population of Hawks, Doves prosper.
This leads to frequency dependent selection; the outcome will be a stable equilibrium
where the frequencies of Hawks and Doves are such that their average pay-offs are
equal. If the population moves away from this equilibrium, then one of the strategies
will be doing better, so it will increase in frequency, suffer reduced success as a
consequence and drive the population back to the equilibrium once more. For the values
in Table 5.1, the stable mixture can be calculated as follows: Let
h
be the proportion of
−
The Hawk-Dove
game helps us to
think about the
evolutionary
stability of
contest behaviour
