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24 Table 2. Coefficient of variation C % for the removal method for various values of population size y, catchability p and number of removals k. Relative precision of the removal method. y = 50 y = 100 Y = 200 y=400 P = 0.4 k=2 42 30 21 15 k=3 19 13 9 7 k=4 10 7 5 4 P = 0.6 k=2 14 10 7 5 k=3 6 4 3 2 k=4 3 2 1.5 I P = 0.8 k=2 4 3 2 1.5 k=3 1.4 I 0.7 0.5 k=4 0.6 0.4 0.3 0.2 Precision To illustrate how the precision, expressed as the coefficient of variation, depends on p, k and y, we have prepared Table 2. From this it is evident that the precision is particularily dependent on k and p, viz. the sampling fraction. For many salmonid populations, p is often in the magnitude of 0.5 or more. If3 removals are carried out in this case, the precision corresponds roughly to Class 1. Note the disastrous effect of the combination small populations, low catchability and few removals. It can also be noted that there is generally a sub- stantial gain in precision from 2 to 3 removals. A third removal may take little extra time to carry out, at least in high density biotopes. It may there- fore be worthwhile to make 3 removals in favour of2. Ifp is lower than 0.5, more removals may be required. There is an additional reason to apply 3 rather than 2 removals. For the 2-catch method, the standard error estimate seems to be of doubtful value for populations smaller than about 200, whereas the 3-catch method may tolerate popu- lations down to about 50 (Seber, 1973; Bohlin, 1982). If the population is small, there are thus two problems. The first is that the relative precision, C, will be poor, and the second that both the population size and its variance are hard to esti- mate. This is especially true for k = 2, in which case the method may fail totally. These problems, however, seem easy to overcome by using an approximately known p value, estimated from a larger population as in examples 3 and 4. If so, the precision also from very small populations may be quite good, provided that the small population is fished at least 3 times. The problem of estimating this precision remains. As will be shown be- low, however, this may not be a major draw- back. On the assumption that the catchability is reasonably constant, we recommend the use of an approximately known catchability if the popula- tion is smaller than about 50, or if the first catch yields less than about 25, or if fewer than 3 remo- vals are carried out. Accuracy The accuracy of the removal method depends on how well the basic assumptions are valid for real populations. One of the major sources of in- accuracy is probably a catchability which varies among individuals in the population. As the catches in this case are dominated by individuals with a catch ability above the population average, the result is an overestimation of p and hence an underestimation of population size. To illustrate this, consider a population in which one half is living in a biotope where the individuals are impossible to catch, and that the other half is living in a biotope in which the catch ability is 0.5. The removal method in this extreme population will yield an estimated catchability of about 0.5, although the real catchability was 0.25 in the first catch, 0.125 in the second etc. Further, the esti- mate of the population size would be half of the real number. The effect of a catchability forming a continuous distribution rather than discrete values as in the example above is similar, but the degree of underestimation of population size is heavily dependent on the shape of this distribu- tion. The most serious bias is expected when a large fraction of the population has a catchability considerably lower than the population average. It has also been shown (Seber and Whale, 1970; Bohlin and Sundstrom, 1977), that the under- estimation caused by an individually varying catchability increases with decreasing mean catchability. When evaluating estimates based on r I t .