Measuring diversity: from individuals to populations

Making inferences about variation within and among various operational units may depend on the ability of a selected approach to diversity analysis to utilize correctly all information available in the raw data. Frequency-based genotypic and gene diversity parameters, methods of 'true diversity' and functional diversity, as well as two types of dissimilarity based approaches (by means of averaging pairwise dissimilarities, and solution of the assignment problem) are comprehensively discussed. The dissimilarity based approaches need a suitable assessment of dissimilarity between individual operational units (individuals, communities, populations, clusters, functions, phylogenetic trees etc.). Many commonly used diversity parameters can be derived in terms of the average based measures. The assignment based methods are able to address some limitations and shortcomings of the commonly used measures of population diversity, and they are preferable in the case of possible association between traits. They are always mathematically valid, whereas validity of the average based methods depends on the selected dissimilarity measure. The dissimilarity based methods actually assess functional diversity in the space of the selected traits, and they allow measuring complex diversity and assessment of total gamma-diversity as the sum of the independent components of alpha- and beta-diversity with descriptors of different types. The dissimilarity based method for diversity analysis can be consistently employed together with other approaches to data analysis (e.g. clustering). In particular, they may provide valid diversity estimates and replace Nei's diversity measures, which are often inconsistently used with binary molecular marker data.