Numerical simulations

W e estimated fishing harvest for each cell (i) and day (;') during a complete year (i.e., 2007) by com­

bining predictions of fishing effort (i.e., the B R T ) with the predictive model of Y P U E developed in Chap­

ter 6. Fishing effort estimates were provided in number of boats, whereas the Y P U E model estimated yield

(g per angler per 30-min session). Consequently, it was required to transform the number o f boat outings into number o f anglers, while considering their fishing time, expertise and bait type used. Such transfor­

mation was achieved using empirical distributions o f effective fishing time and number o f anglers per boat. Because the Y P U E model also accounted for two angling factors (i.e. angler expertise and bait type) different scenarios were considered. Bootstrap and randomization methods were used to account for uncertainty at the 95% confidence intervals. T h e following subsections provide additional details on each step o f the process.

7.2.2.7 Predicting fishing effort

W e used the hurdle model describe before (Section 7.2.1.4) to predict fishing effort (i.e., boat outings).

W e maintained the spatial offset term at the grid cell level ( i ) , but the temporal coverage was set to 100%

in order to provide an estimate o f all boats fishing at a given time period. B R T s do not provide confidence intervals in their predictions; hence we used bootstrap methods (e.g., Leathwick et al. 2006). Bootstrap was implemented by resampling (n = 1,000) the training data set with replacement. This imply that all computational steps described from Equation 7.2 to Equation 7.7 were repeated 1,000 times. Parallel threads were used to optimize computational demands (see Box 7.3). Predictions were calculated for each grid cell (/), day (;) and period o f the day (p). Boat outings predictions were provided in terms o f mean estimates ( | % ) . Therefore, the number o f boats o f each bootstrap was obtained by sampling once from a Poisson distribution with mean u.^ijp:

B^ijp ~ Poissson(^^ijp)

Then, daily predictions resulted from the sum o f the estimated values for the morning ( p = l ) and af­

ternoon (p=2) periods:

Most of the analyses performed in this thesis were executed using a regular desktop computer (e.g. Inter Core 2 Duo CPU, 2.39GHz, 4GB RAM). However, bootstrap methods required high computational de­

mands. The computing facilities of SOCIB (http://socib.es) were used to overcome such constrain. A computing server (Figure 7.8) with 2 Intel Xeon X5687 (3.60 GHz, quad-core) and 64GB RAM was used to run dif­

ferent scripts in R v.3.0.2. This configuration allowed to fit and predict multiple (up to 16 with hyper-threading technology) BRT models in parallel threads. We used the function dusterApply from the parallel

package in R to accomplish such task. In addition, the 64GB RAM al- Figure 7.8 Computing server lowed to manipulate big arrays that were generated for storing the

results of the simulations (i.e., 143 cells x 365 days x 1000 samples).

(Equation 7.2)

(Equation 7.3)

M O D E L I N G F I S H I N G E F F O R T A N D H A R V E S T

7.2.2.2 Simulating angling factors

Variability on the fishing time and the number o f anglers per boat were taken into account for esti­

mating fishing harvest. First, for each predicted boat (b) at cell (z) and day (/') we simulated its fishing time:

Sb ~ S (Equation 7.4) where Sb, the number o f 30-min time slots per boat (b), was simulated by random sampling from an empirical distribution o f effective fishing time (S) obtained from onsite interviews (n = 390, see Figure 7.9a; Morales-Nin et al. (2005)). Second, for each boat (b) we also simulated the number o f anglers:

Ab ~ A (Equation 7.5) where Ab, the number o f anglers per boat (b), was simulated by random sampling from an empirical distribution (A) obtained from the shipboard surveys. The number o f anglers per boat was found to be dependent on the business day and the season (x²(3, N = 2 5 8 1 ) = 14.13. p < 0.01), with higher number o f anglers on non-business days and warm seasons (Figure 7.9 b and c). Therefore, eight different distribu­

tions accounting for each combination o f business day (2-factors) and season (4-factors) were used.

Angler expertise (i.e., expert or non-expert) and bait type used (i.e., worm or shrimp) were found to significantly affect Y P U E (Chapter 6). W e incorporated such individual variability by:

ea ~ binom(pe) (Equation 7.6)

w^a ~ binom(p^w) (Equation 7.7)

where e„ and w^a were the expertise and bait types assigned to angler (a), respectively. Both factors were obtained by sampling two binomial distributions with probabilities o f being 'expert' (pe; the probability o f beign 'non-expert' is l-p^e) and use 'worm' {p^w; the probability o f use 'shrimp' is l-p^w). Because o f the lack

H^a^YPUE, _ijbsa (Equation 7.9)

5=1

where St is the number o f 30-min time slots o f boat (£>). Therefore, total harvest per cell (i) and day (j) can be obtained by:

(Equation 7.10)

b=l o=l

where At is the number o f anglers per boat (£>), and By is the number o f boats per cell (i) and day (;').

Finally, both fishing effort and fishing harvest were calculated with their 9 5 % confidence intervals at three levels o f aggregation: 1) on a daily basis (i.e., by summing all grid cells [143] for each day (j)); 2) at the grid cell level (i.e., by summing all days for a given cell (i)); and 3) at the entire study area per year:

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i = l j=l

(Equation 7.11) of empirical data on those probabilities, we considered five different scenarios. Four o f them consisted o f the four possible combinations assuming that the probability for each factor is 100% (e.g. 100% probabil-ity o f being 'expert' and use 'worm'). T h e fifth scenario assigned two different proportions supported by two previous independent surveys. First, the proportions o f worm (26%) and shrimp (74%) were obtained from a previous onsite survey (n = 4 1 4 , Morales-Nin et al., unpublished data), where anglers were asked about the bait type used. Second, the proportions o f expert ( 9 % ) and non-expert (91%) anglers were cal-culated from a previous survey (n = 165, Cardona et al., unpublished data). Expert anglers were defined as those anglers with more than 10 years o f expertise and with a membership in a sport club.

7.2.2.3 Predicting fishing harvest

Finally, we estimated the fishing catch for each angler (a) using the predictive model o f fishing quality developed in Chapter 6. Such model provided estimates o f Y P U E (i.e. g per angler per 30-min session) and took into account spatial (i.e. depth) and temporal (i.e. SST) information together with the two above mentioned angler factors (expertise and bait types). Bootstrapped predictions (n = 1,000) for each combi-nation o f angler factors were generated (i.e., 4 0 0 0 estimates per grid cell (¿) and day (;')). Bootstrap sam-ples were produced taking into account, not only the uncertainty in the model parameters, but also the stochastic variation considered by the random factors (i.e., cell and day) and the residual variation. This allowed incorporating model uncertainty into yield estimates:

Y P U E^{i j b s a} ~ Y P U E *^{i j w e} (Equation 7.8) where YPUEijbsa is the yield o f angler (a) per time slot (s) at boat (b), and it was sampled from boot-strapped estimates o f Y P U E (YPUE*jjW e) at cell (i) day (;') for the same expertise ( e ) and bait (w) types assigned to angler (a). Then, total harvest for angler (a) can be calculated as:

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