Estimation of species range fragmentation

Question

While discussing species distribution patterns along spatial, temporal or functional gradients one often finds a hump shaped species richness pattern. This is well documented in many taxa and spatial scales and known as the mid-domain-effect (e.g. Colwell & Lees 2000 ).

These patterns also arise stochastically (depending on the species range frequency distribution). So random distribution of species ranges midpoints are used as null models to test for these mid-domain-effects.

However, these models assume unfragmented species ranges. With a highly fragmented species range the pattern would look quite dissimilar.

So I don't want to start a discussion on the validity of this concept but rather ask:

Given a gradient and known species occurences on that gradient. Has anyone read an article about (or has an idea) what would be a good/unbiased* estimator for species range fragmentation?

Thanks

*e.g: One that doesn't over- or underestimate fragmentation for rare or abundant species

Answer 1

Very interesting question +1. I don't know the literature on the subject very well but I did not find much by looking for it. I know that a number of methods exist when you have genetic data (STRUCTURE or some of the work of J. Novembre probably).

Here are two possible solutions

Fitting $x$ distributions

You could be fitting 1, 2, 3, ...., n normal (or uniform) distributions to the observed data. Each time, compare their maximum likelihood (for which you might need a MCMC with 2⋅x parameters, where $0≤x≤n$ is the number of distributions you're fitting) and select the "best" model with some information criterion such as AIC or BIC.

The number of fragments is just the $x$ value associated with the lowest AIC.

Logistic regression

Another (faster and simpler) solution would be to fit a logistic regression to your data.

Iteratively fit a logistic regression of degree 1,2,3,...n and then again use some information criteria to select the 'best'.

To find the number of fragments, you can then either use the number of degrees in the model or even better use some threshold on the the probability of getting a zero (which you could compute with the package effects in R).

Notes

It will probably takes you a day or so if you're at ease with these methods and have intro knowledge in programming.

You might want to get opinions from stats.SE as well.