Conceptual and statistical problems with the DEC plus J model of founder-event speciation and its comparison with DEC via model selection

Phylogenetic studies of geographic range evolution are increasingly using statistical model selection methods to choose among variants of the dispersal-extinction-cladogenesis (DEC) model, especially between DEC and DEC+J, a variant that emphasizes jump dispersal, or founder-event speciation, as a type of cladogenetic range inheritance scenario. Unfortunately, DEC+J is a poor model of founder-event speciation, and statistical comparisons of its likelihood with DEC are inappropriate. DEC and DEC+J share a conceptual flaw: cladogenetic events of range inheritance at ancestral nodes, unlike anagenetic events of dispersal and local extinction along branches, are not modelled as being probabilistic with respect to time. Ignoring this probability factor artificially inflates the contribution of cladogenetic events to the likelihood, and leads to underestimates of anagenetic, time-dependent range evolution. The flaw is exacerbated in DEC+J because not only is jump dispersal allowed, expanding the set of cladogenetic events, its probability relative to non-jump events is assigned a free parameter, j, that when maximized precludes the possibility of non-jump events at ancestral nodes. DEC+J thus parameterizes the mode of speciation, but like DEC, it does not parameterize the rate of speciation. This inconsistency has undesirable consequences, such as a greater tendency towards degenerate inferences in which the data are explained entirely by cladogenetic events (at which point branch lengths become irrelevant, with estimated anagenetic rates of 0). Inferences with DEC+J can in some cases depart dramatically from intuition, e.g. when highly unparsimonious numbers of jump dispersal events are required solely because j is maximized. Statistical comparison with DEC is inappropriate because a higher DEC+J likelihood does not reflect a more close approximation of the true model of range evolution, which surely must include time-dependent processes; instead, it is simply due to more weight being allocated (via j) to jump dispersal events whose time-dependent probabilities are ignored. In testing hypotheses about the geographic mode of speciation, jump dispersal can and should instead be modelled using existing frameworks for state-dependent lineage diversification in continuous time, taking appropriate cautions against Type I errors associated with such methods. For simple inference of ancestral ranges on a fixed phylogeny, a DEC-based model may be defensible if statistical model selection is not used to justify the choice, and it is understood that inferences about cladogenetic range inheritance lack any relation to time, normally a fundamental axis of evolutionary models.