In pattern–based methods, missing areas (B in fig. 1d) and redundant distributions (A in fig. 1c) are often identified in the TACs prior to the analysis and different protocols (A0, A1, and A2) are then used to determine the possible RACs. For instance, missing areas can be treated either as missing data or as observations of true absence. If treated as missing data (A1, A2), absence may be due to primitive absence, extinction, or inadequate sampling and the missing area can thus occupy any position in the RAC. If treated as true absence (A0), only primitive absence or extinction are possible explanations. For instance, if several areas are missing from the TAC, this may be taken as evidence that these areas should be grouped in the RAC (extinction) or that the non–missing areas should be grouped (primitive absence). Redundant distributions can be treated under A0, A1 (all occurrences due to ancestry, and any GAC–TAC mismatch explained by duplication and extinction) or under A2 (some of the occurrences possibly due to dispersal). In event–based methods, it is difficult to separate potential cases of incongruence that can be identified in TACs prior to analysis (observed) from missing areas and redundant distributions that are introduced during the TAC–GAC fitting process (inferred). If an area is redundant or missing in a TAC simply depends on the general area cladogram (GAC) being analyzed and on the particular events postulated by the reconstruction fitting the TAC to the GAC. The reconstruction may postulate TAC redundancy that is not apparent before analysis or change the interpretation of which areas are truly missing from the TAC. For instance, a TAC fitted to a congruent GAC will have no missing or redundant areas (figs. 3a, 3b) but if the same TAC is fitted to an incongruent GAC (fig. 3c) one must postulate that some TAC distributions are missing or redundant. A lineage (5) may have become extinct in area D and another taxon (4) may have secondarily re–colonized the same area (fig. 3c). In this reconstruction, there is both a missing area (the absence of taxon 5 in area D) and a redundant distribution (the presence of taxon 4 in area D). However, a different incongruent GAC (fig. 3d) postulates a different set of missing and redundant areas: in this case area C is both the missing area (the absence of taxon 5) and the redundant distribution (the presence of taxon 3). Therefore, a priori (observed) and a posteriori (inferred) cases of redundancy and missing areas should be treated in the same way in event–based methods; there is no need for special protocols dealing with these cases of incongruence prior to analysis. The treatment of missing areas in event–based methods is of particular interest. Event–based methods treat missing areas as true absence and explain them as due to primitive absence or extinction. If the missing data interpretation were allowed, then parsimony–based tree fitting would not work because any analysis would be swamped by low–cost solutions postulating events that left no trace in the observed TAC (RONQUIST, in press).
A simple example will illustrate the eventbased treatment of missing areas: assume that we have a “two–taxa–two–area” TAC and a four area GAC (fig. 7). GAC 1 (fig. 7a) groups the TAC areas into a monophyletic group (C–D) so a vicariance event is sufficient to explain the history of the organisms; absence of the group in areas A and B is explained as primitive absence. This could mean that the ancestor of the TAC dispersed from an area outside of the considered GAC to the area in the GAC ancestral to C and D, that the outgroups of the TAC occur in areas A and B, or some other alternative. Since we have no information about the outgroups, we cannot distinguish among the alternatives.
GAC 2 (fig. 7b) groups the TAC areas into a paraphyletic group so a vicariance and an extinction event are required to explain the history of the organisms. In GAC 3 (figs. 7c–d), the TAC areas form a polyphyletic group. The TAC can be mapped onto this GAC either by introducing a vicariance and two extinction events (fig. 7c) or one dispersal event (fig. 7d). If vicariance and duplication events are associated with a low cost and dispersal and extinction with high cost, as suggested above, GAC 1 would clearly be favored over GAC 2 and GAC 3. Thus, in searching for the optimal GAC, event–based methods favor scenarios in which the missing areas are explained as being As this example clearly demonstrates, absence data are informative in the search for the optimal GAC with event–based methods. The cost of extinction events determines the extent to which absence data influence the search for the GAC: the lower the weight of extinction, the smaller the effect of absence data. A low extinction cost downplays the importance of absence data, regardless of whether this is caused by poor sampling or true absence. Thus, an event–based method with a low extinction cost mimics the missing data treatment of true absences in pattern–based methods. This is a good argument for assigning a lower cost to extinctions than to dispersals in event– based methods of biogeographic absence.
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