Topological Signatures for Population Admixture

As populations with multi-linear transmission (i.e., mixing of genetic material from two parents, say) evolve over generations, the genetic transmission lines constitute complicated networks. In contrast, uni-linear transmission leads to simpler network structures (trees). The genetic exchange in multi-linear transmission is further influenced by migration, incubation, mixing and so on. The task we address in the paper is to tease apart subtle admixtures from the usual interrelationships of related populations. We present a combinatorial approach based on persistence in topology to detect admixture in populations. We show, based on controlled simulations, that topological characteristics have the potential for detecting subtle admixture in related populations. We then apply the technique successfully to a set of avocado germplasm data indicating that the approach has the potential for novel characterizations of relatedness in populations. We believe that this approach also has the potential for not only detecting but also discriminating ancient from recent admixture.