Parsimony Analysis of Endemism and similar

Quiiiite some time ago now I started a little series on the uses of parsimony in systematics, evolutionary biology and biogeography, and then kind of dropped the ball before coming to the biogeography part. Having recently read a few more papers on methods in biogeography, this seems like an opportune time to pick the thread up again.

Specifically, I came across an approach that was apparently very popular in the early noughties but then seems to have disappeared again: Parsimony Analysis of Endemicity (PAE; e.g. Nihei, 2006) and its variant Cladistic Analysis of Distributions and Endemism (CADE; e.g. Porzecanski & Cracraft, 2005).

But before I consider if PAE is worth trying out, it would be interesting to know what it is supposed to be good for, and for that let's consider...

What is biogeography about?

This is actually not an easy question to answer. I mean, it is very simple for phylogenetics (inferring relationships between species) or taxonomy (naming and classifying groups of organisms), but certain other fields like ecology or evolutionary biology are much more complex, broad and fuzzy. And biogeography is one of them, at least in my eyes.

At a minimum, biogeography as a discipline seems to encompass all of the following:

Describing the distribution of taxa, that is groups of related organisms (in plants called floristics).

Explaining the distribution of taxa through biogeographic processes such as vicariance or long distance dispersal, closely connected with the inference of ancestral areas. Alternatively, explaining the distribution of taxa from environmental conditions, as a kind of ecological biogeography.

Predicting the distribution of taxa where they have not yet been collected, where recently introduced invasive species may still be able to spread, or where species would have occurred or will occur under past and future climatic conditions (species distribution modelling).

Describing patterns of diversity across the landscape in spatial studies, for example to identify hotspots of endemism that should become priorities for conservation under triage conditions.

Describing and classifying biota, that is groups of species occurring together (bioregionalisation). This allows us to distinguish, say, the arid interior of Australia, the south-eastern temperate zone or the Monsoonal Tropics not as climatic zones but as vegetation zones, and the borders may not always be exactly the same or as sharp as the climatic ones.

Inferring the historical relationships of biota - area cladograms - under the assumptions of vicariance biogeography.

Where does PAE fit and how does it work?

As one can see from the above, there are taxon-focused subdisciplines of biogeography (the first three) and biome- or area-focused subdisciplines (especially the last two). PAE is definitely area-focused. The method is really simple:

Areas are defined. For each area, the species occurring in it are scored as 1 and the ones not occurring in it are scored as 0, resulting in a 0/1 matrix of areas by species. This matrix is then used for a parsimony analysis, as if it were a matrix of species by morphological or genetic characters.

The result is an area cladogram that shows all the areas in the analysis in nested relationships. Where clades on a parsimony tree of species are supported by shared characters called synapomorphies, area clades are here supported by shared (endemic) species called "synendemic taxa".

Okay, what is it good for and does it make sense?

That was apparently already the bit point of contention in the noughties, and it depended on the interpretation. My reservation here is the same as the one I expressed recently regarding Nelson & Ladiges (2001): To interpret an area cladogram in the sense of a historical relationship between areas, we first need to assume that there is very little movement between areas. And that seems like a rather tough sell, especially at smaller geographic scales like in the Porzecanski & Cracraft paper.

This leaves us essentially only the use of this method for bioregionalisation, as an alternative to several clustering methods using similarity metrics like S2 or Jaccard and implemented for example in the Biodiverse software. However, there are a few issues even here.

First, this may just be a case where similarity clustering is the more appropriate method. We use parsimony for phylogenetic inferences because the assumption of a minimum number of character changes along the phylogenetic tree makes a lot of sense. For example, all else being equal one would expect that four-legged lizards are descended from four-legged ancestors as opposed to from snakes, because that would add the additional step of re-evolving the legs. But we would not use the same logic within a species, to understand population structure, because the individuals of the same (sexual) species do not have a tree-like but a network-like relationship with each other.

So here is the thing: if we are making an area cladogram, where does even just the assumption that there is a tree structure to the data come from? Also, just out of curiosity I recently tried PAE with a dataset that gives fairly meaningful looking results with clustering, and the PAE results did not turn out to be very useful: massive polytomies everywhere, no bootstrap support for any grouping, and several extremely unconvincing "relationships".

Second: Admittedly I have not read very many of the relevant papers so far, but what I have read kind of skirts around the issue of rooting the area cladogram. And without rooting it is impossible to even figure out what is a clade and what isn't, because the true root could be inside any 'clade' that we find appealing. Here clustering has the clear advantage that one can use a method on the lines of UPGMA that produces an ultrametric tree that is rooted automatically. Admittedly we could try to midpoint root an area cladogram, but again I would not know how to justify that theoretically.

So really I find neither the theory nor the interpretation of PAE convincing at this stage. I have a soft spot for parsimony, be it for gene trees, species trees, super-trees or ancestral character reconstruction, and am regularly whinging about the shortcomings of Bayesian or likelihood methods. But I also think one should be a methodological pragmatist and use whatever is most appropriate in any given case.

Some of these publications from the noughties discussing PAE and related methods read a bit as if people were so impressed with parsimony analysis in phylogenetics that they just wanted to use it for other things. They had a shiny new hammer, so distribution data suddenly looked a lot like a nail. But there are cases where you want a hammer, and there are cases where you want, say, a shovel. Bioregionalisation may just not be a good fit for parsimony.

References

Nihei SS, 2006. Misconceptions about parsimony analysis of endemicity. Journal of Biogeography 33: 2099-2106.

Porzecanski AL, Cracraft J, 2005. Cladistic analysis of distributions and endemism (CADE): using raw distribution of birds to unravel the biogeography of the South American Aridlands. Journal of Biogeography 32: 261-275.