Dissertation - HQ

148 Oceanography vs. behaviour
makes swimming for such duration infinitely expensive energetically.
The actual immediate cost for this time step is computed as
total gain ·
time step duration
time before exhaustion
This provides an estimate that is conservative for two reasons. First,
mean relationships are used in the calibration, while best performers
could have significantly higher endurance 236 . Second, immediate costs
accumulate through time and no “recovery” (through feeding, for
example) is made possible, because no quantitative information is
available about it.
6.4.3 Complete optimisation model
Optimisation criterion
Recruitment window
Reach recruitment zones
while minimising energy
allocated to swimming
Focus is still on self-recruitment so, as in the previous model, the final
gain equals one for every larva recruiting back to the island or to
the promontory at final time, zero otherwise. But, to account for the
elasticity in the duration of the larval period, the gain is maintained
equal to one during a time window prior to the time horizon. Larvae
are assumed to recruit during this time window, so advection is not
performed in those locations either.
The optimisation criterion is still to reach the recruitment location at
final time, but immediate costs are now non-null and proportional to
swimming speed so its biological interpretation changes: in this model,
we are interested in successful trajectories along which energy consumption
is lowest. As pointed out in the introduction, maximising energetic
efficiency during the larval phase makes sense from a biological and
evolutionary point of view. Indeed, there is a trade-off between energy
allocated to swimming and energy allocated to growth. And survival
both during 237,238 and after 48,50,170 the larval phase is size dependent. So
energetic efficiency ultimately affects survival and, as a consequence,
is under strong selective pressure given the high mortality during the
larval phase 61 .
Choice of numerical parameters
Two species, from
two environments
Two fish species with contrasting swimming abilities are modelled to
study the influence of swimming behaviour in different situations. In
addition, because the relative effect of a temperature change on PLD
is much larger in cold than in warm water (Figure 6.13), one of those
species is tropical while the other is temperate. All necessary parameters
(PLD, temperature of estimation of the PLD, U crit at hatching,
U crit at settlement, time swum at 13.5 cm s -1 for settlement-stage larvae,
reproductive biology i.e. demersal or pelagic eggs) were available for
Pomacentrus amboinensis, a tropical damselfish 57,95,186,235 . No single temperate
species could be identified as a good candidate so parameters