Six rainbows across Norway (link).
While rainbows are often associated with magic and pots of gold, they are actually caused by refraction and reflection. An analogy occurs in population sampling, where diverged and remerged sub populations can cause the effect of seeing "ghosts", or images, in a sampled population. This can cause several artefacts. One possible artefact is the appearance of migration between nonadjacent populations. Another artefact can be that the apparent level of migration can be more than two orders of magnitude smaller than the actual level, depending on the number of waves of migration allowed by the model.
Seeing ghosts: the effect of unsampled populations on
migration rates estimated for sampled populations
Department of Integrative Biology, University of California, Berkeley, CA 94720–3140, USA
29 September 2004
In 2004, the term ‘ghost population’ was introduced to summarize the effect of unsampled subpopulations that exchange migrants with other subpopulations that have been sampled. Estimated long-term migration rates among populations sampled will be affected by ghost populations. Although it would be convenient to be able to define an apparent migration matrix among sampled populations that incorporate the exchange of migrants with ghost populations, no such matrix can be defined in a way that predicts all features of the coalescent process for the true migration matrix. This paper shows that if the underlying migration matrix is symmetric, it is possible to define an apparent migration matrix among sampled subpopulations that predicts the same within-population and between-population homozygosities among sampled populations as is predicted by the true migration matrix. Application of this method shows that there is no simple relationship between true and apparent migration rates, nor is there a way to place an upper bound on the effect of ghost populations. In general, ghost populations can create the appearance of migration between subpopulations that do not actually exchange migrants. Comparison with published results from the application of the program, MIGRATE, shows that the apparent migration rates inferred with that program in a three subpopulation model differ from those based on pairwise homozygosities. The apparent migration matrix determined by the method described in this paper probably represents the upper bound on the effect of ghost populations.migrate, shows that the apparent migration rates inferred with that program in a three- subpopulation model differ from those based on pairwise homozygosities. The apparent migration matrix determined by the method described in this paper probably represents the upper bound on the effect of ghost populations.