You can look into things like Simpson's diversity index, which weights species by abundance/rarity, and adapt it to your needs. There are several ways/functions to do this not only based on species number, but phylogenetic diversity as well.

Your question can be interpreted in at least three ways, and the answer will largely have to depend on that.  (1) By "species diversity" you actually mean "species richness", one of its two components alongside heterogeneity. That in itself does not take into account rarity, except when you are estimating "total richness" or "species density", which do. For that you need to look at rare occurrences. Richness increases with sample size (but not linearly) and therefore the number of species is dependent on that--you need to compare surveys of similar size, or to make them comparable. Rarefaction techniques accomplish that, as do total richness estimators (see Chao's indexes) based on species occurring just once or twice in samples. (2) By "diversity" you mean "diversity index". Many of them (but not all) already do account for individual species' abundances or other "impact" or "effect" attributes, as Daniel S.P. mentioned above (I tend to use biomass as well, to equalize for individual species' effects on the ecosystem). For example, aside from Simpson's indices (both 1-D and 1/D), Shannon's index and evenness indices do use relative abundances as well. (3). By "rarity" you mean species that are globally rare rather than locally rare. Diversity indices as such do not account for that, and you have to move into another turf: attributes often imported from ecosystemic levels such as irreplaceability (Brooks), uniqueness, and basically distribution models (and their parametrization) based on occurrences (see e.g. works by Rob Anderson, Town Peterson and others). HTH. A.-

There are two types...Population studies......Qualitative & Quantitative methods available....proceed Quantitative method Species diversity and IVI - (Important Value Index).... first upall any species taking (Quadrate or belt transect follwed) all species means population counting......how much area occupying species how many individiual taken.........this is the way of field survey.... and after applying.....Quantitative methods ...and following IUCN Rules criterias...........Thats all.........

Yes, you can. You can way each species with 1/#gridcells of that species; either by counting actual recorded gridcells or by modelling its distribution. By using such a weight, each species has a total weight on a global scale of 1, but a species that occurs in many cells will add to those cells little, while a species endemic to 1 cell will add its full weight. The nice thing of this method is that you can calculate for how many species your cell/area is 'vital' for survival: 1 for each endemic, 0. for each species occurring in your cell + one other area, 0.1 for a species occuring in your cell and in 9 other ones, etc.

This method is further explained in:

Wieringa, J.J. & L. Poorter, 2004. Biodiversity hotspots in West Africa; patterns and causes. In: L. Poorter, F.J.J.M. Bongers, F.N’. Kouamé & W.D. Hawthorne (eds). Biodiversity of West African Forests. An Ecological Atlas of Woody Plant Species. CABI international. pp. 61-72.

In addition to what has been already said, diversity indexes ( Shannon and Simpson) are measured in units difficult to understand and most importantly, their magnitude is not linear, that is, a site with diversity of say 3.0 is not twice as diverse as a site with diversity of 1.5, regardless whether is Shannon or Simpson. This situation makes them very hard to compare, within are among studies. This issue is addressed by using Hill numbers instead, which are directly related to diversity indexes. That is, richness, Shannon and Simpson, can be calculated using Hill numbers of order 0, 1 and 2, respectively. The calculation return values in units that are understandable (number of species in all cases, more specific effective number of species) that in addition comply with the duplication principle I mentioned above. 

You can read a much more detailed explanation in Jost, 2006. Oikos 113:363-375 and Jost & Chao. 2007. Ecology 88:2427-2439. And in Lou Jost's web page www.Jost.com.

Hope this helps.

I guess, you can separate data on endangered/endemic species from your main data, and generate stats for this subset. However, I would recommend reporting total diversity as well, as it gives complete information on diversity. 

I have written several papers on this subject including a series in Ecological Indicators. These papers show how a species a Species Conservation Value Index can be created and how these indices can be compared statistically.  They are all entered onto Research Gate but if you have any difficulty in getting the papers please let me know.

The estimation of a rarity of occurrence of a species can be carried out as follows. One chooses random areas within a biotope studied. It is important that conditions of the environment for each area have to be identical. Then one counts quantity of specimens for each area and obtains data on the frequency of species occurrence per one area. If species is rare the frequencies have to be described by Poisson's distribution. Otherwise distribution has to be binomial. The assessment of a type of statistical distribution can be carried out, for example, by means of criterion a chi-square. Besides, a characteristic sign of Poisson distribution is coincidence of average value and dispersion. The received values of average size and a standard deviation can be used for comparison with the same values of other biotopes by means of standard parametrical criteria, such as Student-test criterion, ANOVA-test and so on. If in investigated biotope specimens of investigated species occur rare and in other biotope specimens occur frequent, then most probably specimens not prefer environmental conditions and migrated there by accident. In this case there is no necessity to create the special territory for species protection.

https://www.researchgate.net/publication/318760929_My_Village_Biodiversity_Documentation_of_Western_Ghats_Biodiversity_through_Network_of_Students_and_Teachers

https://www.researchgate.net/publication/331076568_Global_Warming_Mitigation_Through_Carbon_Sequestrations_in_the_Central_Western_Ghats/stats

https://www.researchgate.net/publication/323180165_Salient_Ecological_Sensitive_Regions_of_Central_Western_Ghats_India

https://www.researchgate.net/publication/332331409_Sustainable_Management_of_Bannerghatta_National_Park_India_with_the_Insights_in_Land_Cover_Dynamics

https://www.researchgate.net/publication/301609558_Geospatial_analysis_of_forest_fragmentation_in_Uttara_Kannada_District_India

Hi, richness estimators like Chao, Jacknife, etc are used for focus on rare species.

Hello Kristy; Estimating diversity based on abundance has the effect of emphasizing the few common species. Using incidence data minimizes this effect. I have used the Chao2 estimator.

Using the Chao2 estimator (Gotelli and Colwell, 2001), Sest = Sobs + (Q1)2 / 2Q2 where Sest is the estimated number of species in the community, Sobs equals the observed number of species, Q1 is the number of species represented by a single individual, and Q2 is the number of species represented by two individuals. In this expression the rarest species in the sample are used to estimate the number of un-sampled rare species that occur in the sampled area.

Gotelli, J. J., and R. K. Colwell. 2001. Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness. Ecology Letters, 4:379-391.

A Google Scholar search for Chao2 will yield an abundance of material to study. Best regards, Jim Des Lauriers

No one index represents the QUALITY of biodiversity so use a range to show how populations differ.