# Ecology: Indices to calculate species overlap in a community?

Experimental design: I sampled the abundances of four species for each month of the year. I did this across 6 sites. I want to calculate the temporal niche overlap for all the species at each site. Ultimately, I want to compare overlap across sites.

I want to compare the extent of overlap of species abundances in the following two secanrios. In the first scenario, species barely overlap so the index or overlap value should be zero. in the second case species fairly overlap in their abundances as shown below (Note: My data has absolute abundances not relative. The graph is only for representation).

I found Pianka's index (from Gotelli 2000) to be one such index that estimates the extent of overlap. However, on closer reading, I find that takes the resource utilization matrix as input and returns the average pairwise Pianka's niche overlap index averaged over each species pair as so:

$$O_{kl} = O_{lk} = \frac {\sum\limits_i p_{ij}p_{ik} } { \sqrt{\sum\limits_i p_{il}^2 \sum\limits_i p_{ik}^2}}$$

I am not sure if I can use it to compute the overlap of species abundance distributions alone. I am wondering are there any other indices that I can use to do a similar computation? Is there a statistical route that I can take to capture a breath of overlap?

Specific questions (in response to Ben Bolker's comments):

1. I want to calculate a single number for the overall overlap. It has to be able to deal with 0s.

2. I would be curious to know the overlap coefficient for each species pair. My guess is that I can use a alpha-diversity index like Shannon’s diversity index.

3. Would it be incorrect to use Pianka's niche overlap here? Why can't I?

• Might be handy zo.utexas.edu/courses/thoc/sppdiv.html Jun 17 at 22:56
• en.wikipedia.org/wiki/S%C3%B8rensen%E2%80%93Dice_coefficient ; can you be a little bit clearer about your experimental design? i.e., do you have a set number of observations over the course of the year (e.g. one per month)? Do you want a single number for the overall overlap, or a coefficient for every pair of species? (I'm assuming that you have "the abundances of 8 species", not "8 observations of species abundance for n species") Jun 18 at 2:01
• @BenBolker I have updated my answer based on your question. TLDR: looking for a single coefficient for all the species. I have 6 different sites, so I am trying to compute the overall overlap (across the year) at each site. The Dice/ Jacard etc calculate for two species at a time not overall. Pianka or Czekanowski niche does across all species. One of my questiosn is why can't I use pianka's index here? Jun 18 at 22:36
• I am confused now: Do you care about niche overlap or pure temporal overlap? In the former case, you obviously need to take resource consumption (and similar) into account. For example, foxes and trees can exist simultaneously while having zero niche overlap. With that being given, what’s wrong with Pianka’s overlap index? In the latter case, why do you write niche overlap in your first sentence? Jun 20 at 6:25