Geometric indicators of population persistence in branching continuous-space networks.

We study population persistence in branching tree networks emulating systems such as river basins, cave systems, organisms on vegetation surfaces, and vascular networks. Population dynamics are modeled using a reaction-diffusion-advection equation on a metric graph which provides a continuous, spatially explicit model of network habitat. A metric graph, in contrast to a standard graph, allows for population dynamics to occur within edges rather than just at graph vertices, subsequently adding a significant level of realism. Within this framework, we stochastically generate branching tree networks with a variety of geometric features and explore the effects of network geometry on the persistence of a population which advects toward a lethal outflow boundary. We identify a metric (CM), the distance from the lethal outflow point at which half of the habitable volume of the network lies upstream of, as a promising indicator of population persistence. This metric outperforms other metrics such as the maximum and minimum distances from the lethal outflow to an upstream boundary and the total habitable volume of the network. The strength of CM as a predictor of persistence suggests that it is a proper "system length" for the branching networks we examine here that generalizes the concept of habitat length in the classical linear space models.