Coherent and incoherent inference in phylogeography and human evolution
Abstract
A hypothesis is nested within a more general hypothesis when it is a special case of the more general hypothesis. Composite hypotheses consist of more than one component, and in many cases different composite hypotheses can share some but not all of these components and hence are overlapping. In statistics, coherent measures of fit of nested and overlapping composite hypotheses are technically those measures that are consistent with the constraints of formal logic. For example, the probability of the nested special case must be less than or equal to the probability of the general model within which the special case is nested. Any statistic that assigns greater probability to the special case is said to be incoherent. An example of incoherence is shown in human evolution, for which the approximate Bayesian computation (ABC) method assigned a probability to a model of human evolution that was a thousandfold larger than a more general model within which the first model was fully nested. Possible causes of this incoherence are identified, and corrections and restrictions are suggested to make ABC and similar methods coherent. Another coalescentbased method, nested clade phylogeographic analysis, is coherent and also allows the testing of individual components of composite hypotheses, another attribute lacking in ABC and other coalescentsimulation approaches. Incoherence is a highly undesirable property because it means that the inference is mathematically incorrect and formally illogical, and the published incoherent inferences on human evolution that favor the outofAfrica replacement hypothesis have no statistical or logical validity.
 Publication:

Proceedings of the National Academy of Science
 Pub Date:
 April 2010
 DOI:
 10.1073/pnas.0910647107
 Bibcode:
 2010PNAS..107.6376T