Biology Reference
In-Depth Information
BOX 3.3 RISK AND OPTIMAL SEQUENCES OF BEHAVIOUR (HOUSTON
& MCNAMARA, 1982, 1985)
Consider a small bird in winter, which has to put on energy reserves by dusk in
order to survive the night. In the example below, the bird needs to have eight
energy units at dusk to survive.
1
0
5
6
7
8
9
10
11
Energy level at dusk (arbitrary units)
Now, imagine the bird has to choose between two foraging options:
(i) Provides one unit with probability 1.
(ii) Provides two units with probability ½, and zero units with probability ½.
So the average pay-offs are the same, but option (ii) has greater variance. If the
bird has time to make just one choice before dusk, then it is easy to see that its
best decision should vary depending on its state (current energy reserves) as
shown below.
Energy level if choosing:
State
(i)
(ii)
Best to choose
6
7
8 or 6
(ii) i.e. take risk
7
8
9 or 7
(i) i.e. play safe
Now imagine there's time for two choices before dusk. If the current state is
six units, the bird should play safe (choose (i) ) both times, so it goes to seven
units, then to eight units, and so survives the night.
This simple theoretical argument shows that the optimal choice depends on
both current state and the time available to forage. In general, hungry
individuals tend to take more risks.
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