  A prey animal surveying its environment must decide whether there is a
dangerous predator present or not. If there is, it may flee. Flight has an
associated cost, so the animal should not flee if there is no danger. However,
the prey animal cannot know the state of its environment with certainty, and is
thus bound to make some errors. We formulate a probabilistic automaton model of
a prey animal's life and use it to compute the optimal escape decision
strategy, subject to the animal's uncertainty. The uncertainty is a major
factor in determining the decision strategy: only in the presence of
uncertainty do economic factors (like mating opportunities lost due to flight)
influence the decision. We performed computer simulations and found that
\emph{in silico} populations of animals subject to predation evolve to display
the strategies predicted by our model, confirming our choice of objective
function for our analytic calculations. To the best of our knowledge, this is
the first theoretical study of escape decisions to incorporate the effects of
uncertainty, and to demonstrate the correctness of the objective function used
in the model.
