Can we trace biotic dispersals back in time? Introducing backward flow connectivity

Connectivity in ecology deals with the problem of how species dispersal will happen given actual landscape and species presence/absence over such landscape. Hence it can be considered a forward (ahead in time) scientific problem. I observe here that a backward theory of connectivity could be of deep interest as well: given the actual species presence/absence on the landscape, where with the highest probability such species is coming from? In other words, can we trace biotic dispersals back in time? Recently I have introduced a modelling and theoretical approach to ecological connectivity that is alternative to circuit theory and is able to fix the weak point of the "from-to" connectivity approach. The proposed approach holds also for mountain and hilly landscapes. In addition, it doesn't assume any intention for a species to go from source points to sink ones, because the expected path for the species is determined locally (pixel by pixel) by landscape features. In this paper, I introduce a new theoretical and modelling approach called "backward flow connectivity". While flow connectivity predicts future species dispersal by minimizing at each step the potential energy due to fictional gravity over a frictional landscape, backward flow connectivity does exactly the opposite, i.e. maximizes potential energy at each step sending back the species to higher levels of potential energy due to fictional gravity on the frictional landscape. Using backward flow connectivity, one has at hand a new tool to revert timeline of species dispersal, hence being able to trace backward biotic dispersals. With few modifications, the applications of backward flow connectivity can be countless, for instance tracing back-in-time not only plants and animals but also ancient human migrations and viral paths.