In the 1950s and 1960s equations using linear regression were developed relating morphometric and edaphic factors to fish yields in temperate lakes and reservoirs. Fish production in Canadian lakes was inversely related to mean depth (Rawson, 1952), to water chemistry (Moyle, 1956) and to physical and chemical indices (Northcote and Ryder, 1965). Ryder (1965) combined these indices to make a morpho-edaphic index (MEI) (total dissolved solids divided by mean depth) in 23 temperate lakes.
In the 1970s and early 1980s these models were applied to a selected number of African inland waters. MEI was related to yields from African tropical lakes and reservoirs (Henderson and Welcomme, 1974) and from Lake Bangweulu System (Toews and Griffith, 1979). A review on MEI was made by Schlesinger and Regier (1982). Fish yields from reservoirs were separately related to MEI by Bernacsek and Lopes (1984) and by Marshall (1984). A review of models predicting fish yields from reservoirs was made by Marshall (1984). Youngs and Heimbuch (1982) have shown that area is a powerful predictor of catch. Their Catch vs Area model was first applied to 17 African lakes and reservoirs by Marshall (1984). Other factors such as primary production (Melack, 1976; Oglesby, 1977) and total phosphorus (Hanson and Legget, 1982) could be useful predictors of fish yield, but information on these factors is only available for a very limited number of African waters.
Recently, total phosphorus and total organic nitrogen were found to be good predictors of relative fish biomass (CPUE estimated from gillnet catches) in lakes and reservoirs in Argentina (Quiros, 1990).
The most important yield models developed so far for African lakes and reservoirs are given in Table 1. Analysis of the data sets used for these models revealed that data for the lakes and reservoirs selected by Henderson and Welcomme (1974) are used in most of the models developed later. In some models catch figures were updated with data published after 1974. A list of all lakes and reservoirs used in the different models is given in Table 2. The table also indicates where catch figures are updated compared with the figures given by Henderson and Welcomme (1974). Melack (1976) used mean catch for his model and Bernacsek and Lopes (1984) used both maximum and mean catch figures for their models. The other models were based on figures given by Henderson and Welcomme (1974) which are single-year catch data.
The use of ratios in predictive models has been common in biological sciences, and in particular in aquatic and fisheries sciences. Ratios often facilitate interpretation, as they simplify interrelations and even straighten curvilinear relationships between variables. Ratios, however, have many statistical properties that compromise their use. Recently the use of ratios, specifically the use of mean depth and MEI to predict biomass, yield or production, has been criticized by Jackson et al. (1990). The statistical results based on these ratios are prone to spurious self-correlations contributing to inflated correlations and incorrect interpretation. The most important criterion for a variable used in statistical analysis is that it should be in the units in which it was originally measured. Therefore models based on ratios were not updated for this report.
This study focused on models relating total catch to morphometric and edaphic characteristics, fishing effort and differences in climate.
Characteristics which are available for most lakes and reservoirs are particularly suitable to be incorporated into the models. Therefore a number of factors related to fish yields (e.g. total phosphorus, total nitrogen, primary productivity and chlorophyll a), which are only available for a limited number of waters, were not used.
The most commonly available morphometric factor is surface area, although surface area is not given for 140 of the total of 595 African lakes and reservoirs listed in SIFRA. Another common factor for reservoirs is volume which incorporates information on surface area and mean depth, but is not available for most lakes. Conductivity is the only edaphic factor which is available or can be obtained easily for most waters. The total number of fishermen is the most common datum on effort given in SIFRA. Latitude and altitude were used as indices of climate.
Analyses of the data were made by simple and partial correlation and simple and stepwise multiple regression analyses (Weisberg, 1980). The morphoedaphic concept was tested by adding conductivity to the regression of total catch and area, as this would be more valid than the existing models based on yield (in kg/ha) and MEI.
The regression of yield of fishermen per unit of area (Bayley, 1988) was tested by using a quadratic relationship between total catch and total number of fishermen based on the catch/effort models of Schaefer (1954) and Fox (1970).
From DIFRA 46 lakes and 25 reservoirs, which were all moderately to heavily fished, were selected for updating the yield models.
Other lakes and reservoirs were excluded for the following reasons:
The following information is given for the selected water bodies (Table 3):
Pearson correlations were calculated for all characteristics (untransformed, loge transformed) of the data set of lakes and reservoirs given in Table 3. Three variables correlated highly with total catch: surface area, volume and number of fishermen.
The data set of 71 lakes and reservoirs (Data Set 1) and the data sets of lakes and reservoirs separately (Data Sets 1A and 1B) gave the following relationships between surface area and catch:
| Catch | = | 8.32 Area0.92 | (R2 = 0.93) | 71 African lakes and reservoirs |
| Catch | = | 8.93 Area0.92 | (R2 = 0.92) | 46 African lakes |
| Catch | = | 7.09 Area0.94 | (R2 = 0.94) | 25 African reservoirs |
A plot of total catch on area for the combined data set is given together with the data for Lakes Victoria, Tanganyika, Malawi and Chad in Figure 1. Confidence limits of a number of yields predicted by the model are given in Table 5. The regression lines for the three data sets are quite similar. Comparison of the equations for different subsets (based on surface area) of Data Set 1 (see Table 4) clearly revealed that selection of the lakes and reservoirs strongly determined the slope and the Y-intercept of the regression lines (Figure 2, Table 4).
As volume and total number of fishermen were highly correlated with area, they could not be used together with area in a multiple regression.
Addition of conductivity, latitude and altitude as a second independent variable next to area in a multiple regression analysis did not result in a significant reduction in the variance. Volume explained 82% of the variance of the catch, but it did not appear to be a good predictor of total catch, as the model overestimated yields in deep lakes and underestimated yields in shallow lakes.
Linear relationships between catch and number of fishermen for the combined data set and the lakes and reservoirs separately are given in Table 4. A plot of total catch against number of fishermen for the combined data set is given in Figure 3. Confidence limits on a number of yields predicted by this model are given in Table 5.
A quadratic relationship between total catch and number of fishermen based on the catch/effort models of Schaefer (1954) and Fox (1970) did not result in a reliable model.
Large errors may be expected to occur in the catch and effort data of the lakes and reservoirs used for the models. Catch figures for half of the data set are based on only a single year, and catch and effort data collection systems in many countries have worked inadequately in the last two decades. For some lakes with large adjacent swamp areas (e.g. in Uganda) fish production of the open water area could not be separated from production of the swamp area which probably resulted in an overestimation of total catch. Effort data are sparse and do not always cover the period for which catch data are given.
The Catch versus Area model explained to a large extent the variance of the catch which partly resulted from the wide range of the independent variable. As confidence limits are large, the reliability of the predicted yields is limited. Therefore, the model should be used with caution and the results interpreted with care, especially for potential yield estimates on individual water bodies. The model indicates a mean yield of 60 kg/ha for African lakes and reservoirs ranging from 40 kg/ha for the large ones to 85 kg/ha for the small ones. A more reliable model based on the morphoedaphic concept, by adding conductivity to the Catch vs Area model, could not be developed.
Total catch is evidently related to the total number of fishermen. The loge (number of fishermen) coefficients are virtually 1 in all three cases, which means that the catch is proportional to the number of fishermen to the first power and that the constant coefficient is simply the loge of the average catch per fisherman. The average catch per fisherman is 2.3 tonnes/year for the combined set as well as for the lakes, and 2.0 tonnes/year for the reservoirs.
