Dissertation - HQ

122 Oceanography vs. behaviour
Figure 6.2 Transition matrices for the simplest parameterisation of the onedimensional
model. M 0 is the matrix associated with foraging (top), and M 1 is
the matrix associated with swimming (bottom). In each case, lines are initial states,
columns are final states, and elements of the matrix are transition probabilities
(zeros are displayed as dots for clarity). States are indexed by energy reserves
(E) and position (P)
. . . and energy resources
at recruitment
scenario, interest is in strategies which maximise the probability of
recruitment. The number of self-recruiting trajectories is potentially
infinite, so maximising self-recruitment probability means selecting the
strategues, hence trajectories along which survival is maximal. In other
words, as self-recruitment is a prerequisite, the quantity optimised along
recruiting trajectories (the gain) is, in fact, survival. As the introduction
highlighted, this criterion is meaningful in terms of natural selection.
However, more complex criteria can be specified, such as probability of
return with maximum energy, with a given energy level, etc. The gain
is then defined in terms of instantaneous gain (gain at each time step)
and final gain (gain at the last time step).
In this simple model, we focus on trajectories which optimise the
probability of recruiting with maximum energy. This translates into zero