To calculate the trend of each time series of landings and of total landings, the following simple linear regression model was used:
Y = aX + b
where Y = rate of increase, X = number of years and a and b are the slope and the intercept of the regression line. The rate of increase (Y) is calculated from the equation:
(C_{t+1} + C_{t})/C_{t} = at + b
where C_{t} is the catch in the year t. Before the calculations were made, the trends of each of the time series of landings were standardized and smoothed by three-year running means. The theoretical maximum production was then calculated when the rate of increase statistically reaches zero (the mean of the standarized series). Taking into account the fact that most of the Cuban fisheries developed during the 1960s, the trends of all time series of landings were calculated for the last 21 years (1975 to 1995). The results of these calculations, as well as the coefficients of determination (r2), are shown in Table 2. When the value of the slope (b) is positive, the general trend is of increasing catches while, when it is negative, the catch trend is decreasing. As can be appreciated from the last row of Table 2, the trend of total landings is negative but not significantly so. The significantly negative correlation for Nassau grouper, mullets, gray snappers, land crab and stone crab landings is particularly noteworthy. Less important, but also significant, are the negative trends in the landings of sharks, grunts and mangrove oysters.
TABLE 2
Parameters of the regression lines fitted to relative rates of landing increases (1975 to 1995) | |||||
Species or species group |
a |
b |
r2 |
Potential maximum production(1) |
Year of full exploitation |
Nassau grouper |
+0.3709 |
-0.0907 |
0.9510* |
630 |
1979 |
Stone crab |
+0.8011 |
-0.1213 |
0.8269* |
119 |
1982 |
Mullets |
+0.9795 |
-0.1286 |
0.9030* |
519 |
1983 |
Scaled sardines |
+0.4222 |
-0.0556 |
0.1418 ns |
877 |
1983 |
Gray snappers |
+2.2721 |
-0.1820 |
0.8413* |
674 |
1987 |
Land crab |
+1.4714 |
-0.1092 |
0.6586* |
876 |
1988 |
Lane snapper |
+0.5889 |
-0.0417 |
0.2998* |
1 981 |
1989 |
Sharks |
+1.2861 |
-0.0871 |
0.5412* |
2 079 |
1990 |
Shrimps |
+0.2741 |
-0.0177 |
0.0242 ns |
4 295 |
1991 |
Spanish mackerel |
+0.9620 |
-0.0621 |
0.2985* |
520 |
1991 |
Small tunas |
+1.2532 |
-0.0779 |
0.6991* |
1 890 |
1991 |
Mangrove oyster |
+1.0094 |
-0.0445 |
0.4556* |
2 439 |
1993 |
Grunts |
+0.7854 |
-0.0434 |
0.4723* |
1 951 |
1993 |
Yellowtail snapper |
+0.6264 |
-0.0226 |
0.0513 ns |
740 |
2003 |
Mutton snapper |
+0.9948 |
-0.0239 |
0.0222 ns |
1 007 |
2017 |
Jacks |
+1.0860 |
+0.0494 |
0.1196 ns |
381 |
(2) |
Mojarras |
-0.9478 |
+0.1483 |
0.9428* |
930 |
(2) |
Turkey wing clam |
-0.6587 |
+0.0927 |
0.2680* |
1 414 |
(2) |
Porgies |
-0.1805 |
+0.0762 |
0.3363* |
340 |
(2) |
Spiny lobster |
+1.0513 |
-0.0043 |
0.0077 ns |
10 769 |
(?) |
Thread herring |
+1.3743 |
-0.0048 |
0.0045 ns |
1 919 |
(?) |
All species |
+1.5716 |
-0.0196 |
0.1212 ns |
56 961 |
(?) |
Notes: * = statistically significant (P < 0.05);
ns = not significant (P > 0.05);
(1) calculated when the rate of increase statistically reaches 0 (the mean of the
standardized series);
(2) positive slope, catch trend still growing;
(?) very low value of the slope, statistically not significant, it indicates a
very slow decrease and, therefore, the estimate of the potential is not reliable.
The potential maximum production according to the generalized fishery model would be about 57 000 tonnes, a value that is 87 percent higher than the 1995 landings of the same species and groups of species.