Trend analysis

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:

(Ct+1 + Ct)/Ct = at + b

where Ct 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.