For example, when we calculate tree species diversity, tree size was not included into the traditional diversity index, such as simpson, pielou, Shannon-wiener
A number of indices have been developed to evaluate in order to have a measure of functional diversity of habitats. All are based on the identification and consideration of biological traits. The number of indices proposed in the literature is already quite large: Functional Group Richness, Functional Attribute Diversity (Walker et al. 1999) Functional diversity (Petchey and Gaston 2002) Functional richness, functional evenness and functional divergence (Mason et al . 2005) Functional Regularity (Mouillot et al. 2005) ...
Petchey and Gaston (2002, 2006) proposed to calculate an index on ultrametric obtained from functional distances matrix functional traits between species. The index of functional diversity (FD) measures the dispersion of functional traits of communities. This is a transposition of phylogenetic diversity (as quadratic index Rao).
Such an index should be able to fit your case analysis.
Mason N. W. H., Mouillot D., Lee W. G. & Wilson J. B., 2005. Functional richness, functional evenness and functional divergence: the primary components of functional diversity. Oikos. 111(1), 112-118.
Mouillot D., Stubbs W., Faure M., Dumay O., Tomasini J. A., Wilson J. B. & Do Chi T., 2005. Niche overlap estimates based on quantitative functional traits: a new family of non-parametric indices. Oecologia. 145(3), 345-353.
Walker B., Kinzig A. & Langridge J., 1999. Plant attribute diversity, resilience, and ecosystem function: the nature and significance of dominant and minor species. Ecosystems. 2(2), 95-113.
Petchey O. L. & Gaston K. J., 2002. Functional diversity (FD), species richness and community composition. Ecology Letters. 5(3), 402-411.
Petchey O. & Gaston K. J., 2006. Functional diversity: back to basics and looking forward. Ecology letters. 9(6), 741-758.
the literature on the analysis of biological traits is very abundant.
Chao, A., et al. (2010). "Phylogenetic diversity measures based on Hill numbers." Philosophical Transactions of the Royal Society B-Biological Sciences 365(1558): 3599-3609
If you have density data along the time to each species in community you could plot the Ricker type competition model to N species and find the coefficienty competition to each specie, trying to adjust experimental data with model by treating the equations and manipulating the parameters. Discrete equations is much more easy to work comparing to differential equations. It will show the competiive interference.