These are the statistical parameters "Simpson Index", "Shannon Indexs", "Hill numbers" and etc.

Since Alpha estimates between species and beta between ecosystems or communities, I suggest you explore other indices like dispersal indices, diversity indices (Margalef, Shannon weiner, Pielou and Eveness e.t.c), Rao's entropy, abundance or community weighted mean and life table.

Yes, one widely used functional diversity index that accounts for species abundance is the Rao's Quadratic Entropy (Rao's Q). This index not only considers the presence and absence of species but also incorporates species abundances and the functional distances (or differences) between them. It measures the dissimilarity between species based on their traits, weighted by their relative abundance in the community.

Here’s how it works:

• Species Abundances: The index incorporates species abundance by giving more weight to species that are more abundant within the community.
• Trait Dissimilarity: It accounts for functional differences between species based on specific traits, not just their identity.

This makes Rao's Q more informative than simple presence-absence indices for functional diversity, as it reflects both how functionally different the species are and how much each contributes to the community.

Another example is the Functional Attribute Diversity (FAD), which can also include species abundances in its calculation of diversity based on functional traits.

Yes, the Rao's Quadratic Entropy index is a functional diversity measure that incorporates species abundance, not just presence or absence. It considers both the abundance and the trait differences between species, making it particularly suited to analyzing the functional diversity of communities where species abundance varies. This index reflects how species abundances and trait dissimilarities contribute to overall community diversity, offering a nuanced view that goes beyond mere species richness or presence.

Article Nestedness and turnover unveil inverse spatial patterns of c...

Beta diversity can be broken up into the components of nestedness and turnover. Which helps to explain the difference between sites. I believe you can explore this with or without including abundance for the calculations. There are R packages that can be used for the calculations. You can also find papers and packages that explore species and local contributions to beta diversity.Article Spatial patterns of site and species contributions to β dive...