I sampled several plots in an area and would like to spatially extrapolate the species richness. I planned to use these presence data to make species distribution models which can then be stacked to provide a measure of species richness per pixel.
However, the rarefaction curve of the total number of individuals sampled does not reach an asymptote, indicating that not all species were detected. This means that the S SDM will always underestimate the 'true' number of species. Is there a way to correct for this?
As each SDM gives a measure for habitat suitability per pixel, I guess I cannot use it as an input for rarefaction.
First you should preserve your original data-set completely untouched. Remember this is your uncut data, keep it pure.
Second there is no limit to the kinds and numbers of adjustments you can perform on your individual data-pixels/sample spaces.. If the adjustment leads to some redundancy so what? Just keep the columns representing various treatments to the data separate one from another. There is no "one" best adjustment method that you can use (beyond counting/measuring on the ground). Remote data acquisition leads to an enrichment of what you observe via grounded sampling protocols. Use as many modes of integration and estimation as you can in order to approach a degree of absolute knowledge about the assembly you are studying. In the end everything (including) your direct on-ground measurements) amounts to estimates of what is "truly" there. Just keep the adjustment components separate as you go along so that you can play mix & match with your data-set in order to present the clearest picture possible. You are the observer, you decide on the best way to present the data.
The easiest adjustment that comes to mind is to build your own species-area curves by successive addition of "sampled-space". See if you can fit a curve/line to the successive assemblage then extrapolate to a sensible space-maximum. Use the variance around the line to get max/min estimates.
Reported presence in an overall given area is a kind of data but keep this in a separate column of your data-matrix. You can do this as a maximum (aggregate) &/or observer-wise. The same would be true for co-lateral physical and biological variables (temperature, % ground cover etc etc)., You may have to use a probability function the report species likelihood presence pixel-wise. ie a species-probability array.
All pixels present as "blurs" in the end. (I have been doing a lot of remote sensing - ecological "truthing" lately) so you are in effect calculating what should be, might possibly be, inside that blur based on a variety of seemingly independent factors which you are seeing fit to combine in one way or another.
Please, read this paper by Comte & Grenouillet (Species distribution modelling and imperfect detection: comparing occupancy versus consensus methods) that can be useful in your case....
All the best,
Federico
Hi Federico, in the scenario you depicted isn't it possible that rarefaction curves are not valid method for correcting species richness? Basically, rarefaction curves correct for sampling effort, but I am not sure if it is reasonable to use them to account for the species detectability. Maybe bias corrected Chao-1 estimator would be more reasonable as this has lower number of unrealistic assumptions (which rarefaction curves have).
hi
i can't really give you advice on this topic, because i have only read about rare faction curves and have quite limited experience of SDM specifically. But i do work with other kinds of spatial ecological modelling, and i've been working some with geostatistical methods, in which the toolbox of interpolation methods is very refined. Presence/absence data is obviously categorical, and many geo-statistic interpolation methods do not work well (or not at all) with categorical data. However, there are several traits of species occupancy data that could benefit from geostatistcal methods, e.g. patterns of autocorrelation and direction, clustering and hot/coldspots etc. specifically when it comes to interpolation of probable occurence/habitat suitability i belive the Kriging family could be interesting (but it would require data to be in e.g. ratios instead of categorical presence/absence of course).
To my knowledge it has not been tested...
But well, it wouldn' really tell about the expected no. of species, but it would probably produce good predictions of occurence/pixel in your raster.
Just sharing my thoughts=)
/Mårten, Sweden.
As a matter of fact, as long as you have presence/absence data, you can use a community occurrence model with data augmentation to estimate detection probabilities and account for undetected species to get an enhanced estimate of species richness. The method is clearly laid out by Royle and Dorazio (2008) (http://www.mbr-pwrc.usgs.gov/pubanalysis/roylebook/ ) and Zipkin et al. (2010) (http://www.sciencedirect.com/science/article/pii/S0006320709004819) with R code and everything. It would be a small step to add habitat variables as predictors of species richness.
Maybe Dorazio`s paper can provide some guideline. Accounting for imperfect detection and survey bias in statistical analysis of presence-only data. http://onlinelibrary.wiley.com/doi/10.1111/geb.12216/abstract
Cheers,
Diego
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