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that some areas probably are 'good' and others 'not so good'. This can be used to improve the precision by stratification. In Fig. 8 the target area is mapped and categorized into two biotope types, of which one is assumed to have lower density (or, strictly, lower spatial variation) and the other higher. In Fig. 8a, sections 1-16 are the 'good' and sections 17-43 the 'bad' biotope. The target area (N := 43) is thus stratified into stratum 1 (N, = 16) and stratum 2 (N2 := 27). We found above that it would take about n = 26 to reach Class 2 in this hypothetical stream. To make judgement on how many from stratum 1 and from stratum 2, we need to know the stratum sizes Nh and Standard Deviation SDh. Further, as the cost of sampling one such unit may vary between the strata, this cost Ch is also of interest. One way to allocate the sampling effort is to choose nh proportional to SDh/~ (19) As, however, SDh seems to be proportional to the mean density '1 (see e.g. Tab. 3), and if Ch is similar in each stratum, (19) is reduced to nh proportional to Nh'1h (20) Thus, as an example, if we have reason to assume that the mean density in stratum 1 in Fig. 8a is about twice as large as in stratum 2, then from (20) we find that n, 16.2 -=-=1.19 n2 27 . 1 As n, + n2 in this case was about 26, it would be appropriate to try a sample size of 14 sections from stratum 1 and 12 from stratum 2. We now recall that the total sample size n required to reach a specific precision was calcu- lated ignoring the effect of stratification (eq. 18). In reality, a somewhat smaller sample size may be sufficient. There are methods to estimate the n value required for a given precision level in the 29 case of stratified sampling (see e.g. Cochran, 1963; p. 96), corresponding to eq. (18). However, as we seldom know very much about how the strata differ with respect to spatial variation, the crude way outlined above may be sufficient. The final question is the number of strata. As the methods of stock assessment proposed below may require both an N h value not too small and a sample size nh not too small, 2 or possibly 3 strata may be practicable. In theory, a far reaching stratification may pay if the criterion for stratifi- cation is efficient. The selection of sampling areas and methods of population estimation There are several ways of selecting the sampling areas in each stratum, and these ways may lead to different methods of population estimation. Hankin (1984) has recently treated these questions with special reference to small streams, and some of the considerations below are based on this paper. The notation is the following: N total number of areas (sections) in a stratum or target area. number of areas (sections) in a sample. population size in area i, estimated as Y i by e.g. the methods proposed in the previous section. sampling variance of Y i, estimated ^ ^ as V (y J, e.g. by the methods pro- posed in the previous section. total population size in the stratum . ^ or target area; estImate denoted Y. mean population size per area, esti- mated as n Yi V(yJ y '1 = Y /N m. I y = (f 9) /n size (usually area) of a area (section) i total size (usually area) of the stratum or target area M