Measures of diversity within populations, and distance between populations, are compared for organisms with an asexual or mixed mode of reproduction. Examples are drawn from studies of plant pathogenic fungi based on binary traits including presence/absence of DNA bands or virulence/avirulence to differential hosts. Commonly used measures of population diversity or genetic distance consider either genotype frequencies or allele frequencies. Kosman's diversity and distance measures are the most suitable for populations with an asexual or mixed mode of reproduction, because by considering genetic patterns of all individuals they take into account not just the genotype frequencies but also the genetic similarities between genotypes in the populations. The Kosman distance and diversity measures for populations can be calculated using different measures of dissimilarity between individuals (the simple mismatch, Jaccard and Dice coefficients of dissimilarity). Kosman's distances based on the simple mismatch and Jaccard dissimilarities are metrics. Comparisons of diversity indices for hypothetical examples as well as for actual data sets are presented to demonstrate that inferences from diversity analysis of populations can be driven by techniques of diversity and distance assessments and not only data driven.