When pairwise differences (relatedness) between species are numerically given, the average of the species differences weighted by relative frequencies can be used as a species diversity index. This paper first theoretically develops the indices of this type, then applies them to forestry data. As examples of diversity indices, this paper explores the taxonomic diversity and the newly introduced amino acid diversity, which is a modification of the nucleotide diversity in genetics. The first, mathematical part shows that both indices can be decomposed into three inner factors; evenness of relative frequencies (=the Simpson index), the simple average over species differences regardless of relative frequencies, and the taxonomic or genetic balance in relative frequencies. The taxonomic diversity has another decomposition: the sum over the Simpson indices at all the taxonomic levels. The second part examines the effects of different forest management techniques on diversity. It is shown that a thinning operation for promoting survival of specific desirable species also contributed to increasing the taxonomic diversity. If we calculated only conventional indices that do not incorporate species relatedness, we would simply conclude that the thinning did not significantly affect the diversity. The theoretical developments of the first part complement the result, leading us to a better interpretation about contrasting vegetation structures. The mathematical results also reveal that the amino acid diversity involves redundant species, which is undesirable when measuring diversity; hence, this index is used to demonstrates crucial points when we introduce species relatedness. The results suggest further possibilities of applying diversity indices incorporating species differences to a variety of ecological studies.