# Reconstruction of Species Distribution based on poorly-sampled data

cross-posted to Signal Processing, World Building, and Biology Stack Exchange

Problem: After reading a series of fantasy novels, I noticed that the biosphere in that world made no sense. To clarify, this is a world where despite magical occurrences, the world itself is almost entirely non-magical. 'Alternate history magical realism,' perhaps. i.e., unlike, for example, Harry Potter, in which almost all plant and animal species mentioned are fictitious and magical, this series uses real flora and fauna. This allows me to extract information about the fictional world's environment based on the distribution of these animals, by assuming that similar animals will live in similar climates on Earth and in the fictional world.

Ignoring the likelihood that the original author did not put enough thought into worldbuilding to make this a necessarily reasonable endeavor, my idea for how to proceed was as follows:

As maps exist of the fictional world, and the path of the characters can be plotted, I hoped to mark every mention of a specific plant or animal in the text, along with the location of the characters when it occurred, and from this reconstruct a plausible distribution for each species. I've created a theoretical example (in photoshop), for illustration:

where the red dotted line represents the paths of various characters, the orange, green, and blue splotches represent the true distribution of the species; the stars, triangles, and circles represent the locations at which a species is mentioned; and the brown, green, and blue lines represent the reconstructed contours of the distribution.

Is there a method to do such a reconstruction? It sounds a bit like a Monte Carlo analysis, but I figured I should check... (It also sounds rather like the magical programs detective shows use to plot serial killers' locations)

Note: It should be clear from the problem statement that just because a species is not mentioned at a specific location does not mean that it does not exist there. i.e., a sample at a specific location returning only 'A' - 'Bill and Jeff saw a lemur.' - does not exclude the possibility of 'B' and 'C' also at that location, but not sampled. Just because the text may specifically say that Bill and Jeff saw a lemur, and doesn't mention any other flora or fauna doesn't mean we should assume that they are in a universe devoid of anything but the occasional lemur.

Final Thoughts: Ideally, the analysis method would further:

• take into account the coverage of the paths, and not assume that (in the example above) nothing exists in Mexico or northern Canada, just because there are no samples taken there. Remember that samples can only be taken along paths.
• take into account edges, in this case coastlines. If A, B, and C are land animals, it does not make sense that a reconstruction of their distribution would include water, even if their range surrounds a lake or something.

Sorry for the long-winded explanation. Any thoughts?

• Yes, this is presence only species distribution modelling. It is a growing field. I'll write a proper answer later. Totally awesome question. Will you have any environmental data? – timcdlucas Mar 16 '15 at 6:53
• I think the two big stumbling blocks are a) Do you have environmental data? I guess you will have latitude. Maybe some idea of altitude and broad habitat? You could go totally overboard and aim for climate modelling like this. theguardian.com/environment/blog/2013/dec/06/… b) Sample size. You need at very, very least 10 datapoints for each animal species you are interested in. 50-100 is better. How many locations do you have? Finally, what books? I'm intrigued. – timcdlucas Mar 16 '15 at 10:14

This paper is pretty relevant (pdf). The authors try to predict where various species can live, given a set of observations but no explicit information about where they weren't observed. As @timcdlucas mentioned, there's a whole subfield devoted to this kind of "presence-only" data analysis for species distribution mapping. I'll let him give a broad introduction to the field.

The wrinkle that makes the paper I linked to especially relevant to your situation is that the sampling wasn't randomly distributed across the landscape and we have some information about where the sampling took place.

In the case of the paper I linked to, most of the observations were in southern Ontario because that's where the observers were (not because that's where the species were). They suggest one approach for accounting for this sort of bias. Ideally, your method could use a similar re-weighting scheme based on the number of pages in each part of the country or the total number of species mentioned in each area.

Once you've accounted for that sort of bias, you could use a variety of techniques from the presence-only literature for mapping species' ranges.

reference: Sample selection bias and presence-only distribution models: implications for background and pseudo-absence data. Phillips et al. 2009, Ecological Applications

I've posted an answer at BioSE, but will add a brief version here as well.

The problem of how to infer species distributions from scattered species occurrences is standard in ecology, and there exists a number of methods to construct distribution maps. As a start, you should have a look at Species Distribution Models (SDMs) using regressions models or Maxent, and the paper by Elith et al (2009) is a good starting point and a standard reference. SDMs using maxent is now a very common approach, which integrates species occurrences as point data along with environmental layers (e.g. temperature, moisture and topography) to predict species distribution maps, and this can also include real absence data or "pseudo-absence" data (randomly sampled data from a region of interest). The maxent software is described and can be downloaded here: http://www.cs.princeton.edu/~schapire/maxent/

In your "Note", you get into the issue of detectability, which has received much attention recently. This problem is largest when you only have presence data, and to have real presence/absence data is preferable. Even if you don't have real absenses (the species has been searched for but not found), an estimate of sampling effort in different areas is still very useful, since this means that you can at least evaluate whether absenses is due to "real" absense or lack of sampling. The movement paths of the characters that you describe can be used to estimate the "sampling" effort in different areas. The main issue with detectability (and why it can be problematic to not take detectability into account) is if there are trends or biases in detectability, which means that apparent changes over time or space might be due to differences in detectability and not real differences between areas or over time. This could for instance be the case if observers are more likely to spot a species in one type of habitat (open savannah) then in another type of habitat (closed forest). Useful starting points for issues of detectability are Dorazio (2014) and Kery et al (2010).

• I think the movement paths are of the characters, not the species. So Mark-recapture is not appropriate unless there's more information not given by OP. – timcdlucas Mar 16 '15 at 10:12
• @timcdlucas Yes, you are most likely correct. I misunderstood the OP on this part - this is however a minor part in my answer, but I have modified this part now. – fileunderwater Mar 16 '15 at 10:14