OBTAINING SPECIES - SAMPLE-SIZE CONSIDERATIONS

Suppose fish are to be sampled from a stream. A fisheries biologist mi ght ask one of the following three questions: 'How many fish do I need to catch in order to see all of the species?', 'How many fish do I ne ed to catch in order to see all species whose relative frequency is mo re than 5%?', or 'How many fish do I need to catch in order to see a m ember from each of the species A, B, and C?'. This paper offers a prac tical solution to such questions by setting a target sample size desig ned to achieve desired results with known probability. We present thre e sample size methods, one we call 'exact' and the others approximate. Each method is derived under assumed multinomial sampling, and requir es (at least approximate) independence of draws and (usually) a large population. The minimum information needed to compute one of the appro ximate methods is the estimated relative frequency of the rarest speci es of interest. Total number of species is not needed. Choice of a sam ple size method depends largely on available computer resources. One a pproximation (called the 'Monte Carlo approximation') gets within 16 u nits of exact sample size, but usually requires 20-30 minutes of compu ter time to compute. The second approximation (called the 'ratio appro ximation') can be computed manually and has relative error under 5% wh en all species are desired, but can be as much as 50% or more too high when exact sample size is small. Statistically, this problem is an ap plication of the 'sequential occupancy problem'. Three examples are gi ven which illustrate the calculations so that a reader not interested in technical details can apply our results.