The Random Amplified Polymorphic DNA (RAPD) technique can potentially provide hundreds of polymorphic markers for use by ecologists studying mating systems in natural populations. We consider here the implications of the dominance displayed by RAPD markers for deterministic paternity assignment. Our goal was to provide a means for assessing the costs associated with such a study for ecologists who might be considering the use of RAPD markers for paternity analysis. The theoretical expected proportion of offspring for which all males except the true father can be exlucded (P(ET)) is calculated for both dominant and codominant marker systems. The ability to assign paternity unambiguously generally increases with the number of loci and the frequency of the recessive allele (but only up to a point), and decreases with increasing sample size (number of individuals surveyed). The gain in P(ET) with decreasing sample size is unexpectedly slight. Not surprisingly, the performance of dominant markers at paternity exclusion is, in general, greatly exceeded by codominant markers, with the exception of the case in which the frequency of the recessive allele is high at all loci. In this case, codominant markers perform only slightly better than do dominant markers. Thus, a researcher should expect to score more than 50 RAPD loci for each offspring for most applications of paternity exclusion analysis.(ABSTRACT TRUNCATED AT 250 WORDS)