Dissertation - HQ

130 Oceanography vs. behaviour
Transition matrices
are sparse
One solution in Scilab is to use linked C routines for the filling
of matrices, and to store them as sparse matrices. Sparse matrices take
advantage of the fact that transition matrices contain mostly zeros (only
two final states are reachable from any initial state) and store only
the positions and values of non-zero probabilities. The progress in
computation time is impressive: from a whole day to two seconds for a
20 × 20 × 2 × 6 state space. This is the solution used here.
Another solution, however, is to forget about the matrix aspect of
the calculation altogether, bluntly loop over all states, for each one
compute all possible outcomes for all decisions, and compute and store
the maximum mean gain and the associated optimal decision before
moving on to the next state. While very inefficient in an interpreted
language such as Scilab, which is slow at loops and only fast at vectorised
operations, this can be a viable solution in a compiled language where
vectorisation and parallelisation of loops are efficient (such as C or
Fortran). When the state and number of decisions grow too much, it
can become the only solution.
6.3.3 Comparison between contrasting biological parameters
Reproductive Reef fish larvae present very different behavioural characteristics destrategies
in fishes pending, in part, on the species’ reproductive strategy 256 .
1. Eggs can be directly dispersed in the water, thus advected as
passive particles; then larvae hatch in the ocean. The eggs are
usually small and numerous which mean larvae are small and
little developed at hatching.
2. Eggs can be demersal (i.e. laid on the substrate, within the reef).
Parents care for the eggs until they hatch. Then larvae disperse
into the ocean but are usually larger and have greater swimming
and sensory abilities than larvae hatching from pelagic eggs.
3. The larval phase is completed entirely inside a lagoon (rare).
Compare Acanthuridae
and Pomacentridae
which differ in . . .
. . . their pelagic
duration . . .
To investigate how these contrasting behavioural abilities affect dispersal
patterns, two theoretical larvae with different early life histories
are compared, namely an Acanthuridae with pelagic eggs and a Pomacentridae
with demersal eggs. The families first differ in the duration
of their larval stage: around 50 days for Acanthuridae 257 and from 14
to 35 days among Pomacentridae 246 . Pelagic larval periods of 50 and
20 days are chosen as examples. Acanthuridae disperse eggs that are
completely passive. After approximately 24 h, larvae hatch and develop
four days before the first food intake. Afterward, their swimming abilities
improve substantially, and late-stage Acanthuridae larvae have
been shown to be very good swimmers 236 . By contrast, Pomacentridae
species whose eggs are demersal disperse larvae that are active right
from the start of the pelagic period. Their swimming abilities improve
brutally around the middle of the pelagic phase 60 but stay below those