Dispersal routes reconstruction and the minimum cost arborescence problem

We show that the dispersal routes reconstruction problem can be stated as an instance of a graph theoretical problem known as the minimum cost arborescence problem, for which there exist efficient algorithms. Furthermore, we derive some theoretical results, in a simplified setting, on the possible optimal values that can be obtained for this problem. With this, we place the dispersal routes reconstruction problem on solid theoretical grounds, establishing it as a tractable problem that also lends itself to formal mathematical and computational analysis. Finally, we present an insightful example of how this framework can be applied to real data. We propose that our computational method can be used to define the most parsimonious dispersal (or invasion) scenarios, which can then be tested using complementary methods such as genetic analysis.

► Formal proof that dispersal reconstruction is a minimum cost arborescence problem.
► Reduces to minimum cost spanning tree problem when first occurrence times are unique.
► Derivation of analytical expressions for optimal value of simplified problem version.
► Placing the dispersal routes reconstruction problem on solid theoretical grounds.