Rare species are very common; a significant proportion of every community is made up of species with small populations (e.g. Morse et al. 1988). Such species pose a real problem for ecologists studying diversity, species composition and turnover. The chief problem is: when is a rare species not there? Clearly this can only be determined absolutely by an exhaustive, 100% efficient, search of the entire habitat. This is usually impractical. If the search is incomplete, say by sampling the habitat, the absence of the species from the sample may be because the species is truly absent or because the worker did not look hard enough. Only a probabilistic statement is possible; the more complete the search, the firmer the statement can be. There is a relationship between the number of sampling units taken from the habitat, the rarity of the species, and the probability it will be detected in the sample. Let N be the number of sampling units taken randomly from the habitat, p be the probability of the species appearing in a single sampling unit, and a is the probability or confidence that the species will be detected in the sample of N units. For rare species p would usually be less than 0.05; that is, the species would be expected to appear in less than 5 out of every 100 sampling units. The relationship can be described by a simple application of probability theory (though the same result can be derived via the binomial or even the negative binomial distribution). (l-p) is the probability of the species not appearing in a sampling unit, so (l-p)N is the probability of the sample not detecting that species. Thus the probability of the species appearing in the sample is