# Linking species distribution models (SDM) and phylogenies When using phylogenies in spatial conservation prioritisation, we need to link the phylogeny with distribution data. Increasingly, distribution data is used to predict where species occur across the landscape using a species distribution model (SDM). SDMs are currently underused in conservation, but have great potential for a variety of applications from threatened species management to conservation planning. Our recent paper shows how to use SDMs with a phylogeny in spatial conservation planning (this method could also be used for a variety of applications linking phylogenies and SDMs).

An SDM models the response of a species to a set of predictor variables (usually environmental variables). The model can be extended across a landscape with a probability of occurrence of species in grid cells**. The external branches (tips) of the phylogeny correspond to a particular taxon (let’s assume we have a species-level tree). Therefore, each external branch can simply be the probability of that species occurring in each cell (a,b,c,e,f in figure above). Now, for the internal branches. The probability of each branch occurring is the probability that any of that branches descendent species occur. Remembering back to that stats lecture long ago on Venn Diagrams, we add the probability of each event (species) happening, but then need to subtract the intersection (both events happen). Or, it is computationally easier to calculate the probability that the species doesn’t occur.

And, in equation form: Bi,j is the probability of an internal branch (i) occurring in cell j,

m is the number of descendent species downstream of this branch

Pn,j is the probability of descendent species n occurring in cell j.

**because this is essentially ‘stacking’ species layers, one would need to ensure either you are working with probabilities (i.e. from presence-absence data). If using presence-only or presence-background data, you would want to be confident that 0.5 for species 1 equals 0.5 for species 2 to have a sensible internal probability.. I’m not sure how sensitive branches would be to this, and this wouldn’t be as much of a concern if using Zonation, which standardises distributions by using the proportion remaining for each unit during each iteration, but it’s a good thing to keep in mind.