Determining the most recent common ancestor in a finite linear habitat with asymmetric dispersal

Many species that are birthed in one location and become reproductive in another location can be treated as if in a one-dimensional habitat where dispersal is biased downstream. One example of such is planktonic larvae that disperse in coastal oceans, rivers, and streams. In these habitats, the dynamics of the dispersal are dominated by the movement of offspring in one direction and the distance between parents and offspring in the other direction does not matter. We study an idealized species with non-overlapping generations in a finite linear habitat that has no larval input from outside of the habitat and is therefore isolated from other populations. The most non-realistic assumption that we make is that there are non-overlapping generations, and this is an assumption to be considered in future work. We find that a biased dispersal in the habitat reduces the average time to the most recent common ancestor and causes the average location of the most recent common ancestor to move from the center of the habitat to the upstream edge of the habitat. Due to the decrease in the time to the most recent common ancestor and the shift of the average location to the upstream edge, the effective population size (N${}_e$) no longer depends on the census size and is dependent on the dispersal statistics. We determine the average time and location of the most recent common ancestor as a function of the larval dispersal statistics. The location of the most recent common ancestor becomes independent of the length of the habitat and is only dependent on the location of the upstream edge and the larval dispersal statistics.