The role of diversity indices in assessing sampled biological structure is complicated. Decades ago, many ecologists would have said that these indices are answers for which there are not questions. There have been many efforts to use diversity indices to assess environmental impacts.
A good introduction is in this short book:
Anne E. Magurran, 1988, Ecological Diversity and its Measurement, Springer. But, others will say as follows
Daly et al. Mathematics 2018, 6(7), 119; https://doi.org/10.3390/math6070119 (open access)
"Diversity is a concept central to ecology, and its measurement is essential for any study of ecosystem health. But summarizing this complex and multidimensional concept in a single measure is problematic."
Different indices weight abundance (or proportion) or biomass more heavily (e.g., Simpson's D) while others weight the number of taxa more (e.g. Shannon-Wiener, H) and related measures of evenness. In many cases, the lists analyzed are not "species" but some mix of species, genera, and possibly other taxonomic measures (we cannot identify all species we find). More recently, information-theory indices have been used to measure diversity from results of DNA extraction and amplification of microbes to assess microbial diversity. Diversity indices have been controversial for the past 50 years and continue to be used and criticized. A little reading will make the plusses and minuses clearer.