Quantifying diversity of bird species I’m wondering if anyone could recommend a diversity index to look at the differences in breeding bird territories between two sites. These are my data - the numbers represent the number of breeding pairs of each species:
c(4L, 3L, 14L, 1L, 4L, 11L, 2L, 1L, 2L, 7L, 1L, 5L, 7L, 3L, 1L, 2L, 1L, 1L, 4L, 1L, 1L, 4L, 2L, 4L, 3L, 3L, 1L, 1L, 1L, 14L, 3L, 14L) -> site1

c(27L, 25L, 21L, 23L, 1L, 2L, 26L, 3L, 1L, 16L, 3L, 12L, 29L, 2L, 5L, 1L, 17L, 2L, 6L, 19L, 6L, 3L, 3L, 5L, 1L, 1L, 8L, 7L, 1L, 2L, 5L, 2L, 6L, 2L, 8L, 1L, 5L, 1L, 25L, 1L, 1L, 4L, 1L, 26L, 7L, 1L, 1L, 13L, 1L, 30L, 34L, 13L, 2L) -> site2

I’ve tried Simpson’s index in R:
library(vegan)

diversity(site1, index = "simpson")
diversity(site2, index = "simpson")

But the diversity index is very similar for both sites (0.94 and 0.96 respectively) and I would say site2 is considerably more diverse than site1.
Are there any functions that are more sensitive when quantifying diversity?

Firstly, I assume that you are talking about alpha-diversity (although the existence of multiple sites where the data were taken suggests that beta-diversity could be also relevant).
The simplest diversity indices (but see also here - Wikipedia has two complementary articles on the subject) are:

*

*Species richness : the number of species present, $R$.

*Shannon entropy : $H=-\sum_{i=1}^R p_i\log_2 p_i$

*Simpson index : $\lambda=\sum_{i=1}^R p_i^2$
where $p_i$ is the proportional abundance of species of type $i$ (i.e., the fraction of these species in respect to the size of the sample).
Shannon entropy and Simpson index differ from simple richness in that they give less weight to rare species, and thus less subject to fluctuations from site to site and less dependent on the sampling depth (total number of individuals sampled).
More general measures are Hill numbers
$$
^qD=\left(\sum_{i=1}^Rp_i^q\right)^{\frac{1}{q-1}},
$$
which for $q=0,1,2$ are related to the diversity indices mentioned above. Hill numbers with $q>0$ can be interpreted as effective number of species.
As a crash course about quantifying alpha-diversity, I could recommend Measuring and Estimating Species Richness, Species Diversity, and Biotic Similarity from Sampling Data by Gotelli and Chao. This also contains information on estimating the true diversity, as well as such important tools as rarefaction curves.
Finally, relative species abundance, presented by Fisher plot or Whittaker plot can be also of interest here.
Remark: As I am more a python person than an R person, I could recommend using scikit-bio, which contains library skbio.diversity, with functions for calculating alpha- and beta-diversity. Note however that most alpha-diversity metrics are easily implemented by hand.
