A narrow transect through a two-species population must always contain runs (or unbroken sequences) of individuals of one species alternating with runs of those of the other. If the two species are unsegregated, or if encounters w:th individuals of each species form a Markov chain, the probability distribution of the run lengths will be geometric. Two alternative distributions that might graduate the observed frequencies of these run lengths are derived; one of these fits field observations better than the geometric. The high frequencies with which runs of unit length were observed show that adjacent clumps of two species must overlap each other markedly, or else isolated individuals of each species must often grow within the clumps of the other. A close parallel exists between the distributions derived and those commonly used to graduate quadrat results from spatially aggregated one-species populations.