Cladistic biogeography seeks to summarize information on distribution and phylogenetic relationships of organisms in area cladograms, branching diagrams that express the inter– relationships of areas based on their biotas (fig. 1a). The analysis usually starts with taxon– area cladograms (TAC) (ENGHOFF, 1993; MORRONE & CRISCI, 1995), which are constructed by replacing the terminal taxa in a phylogeny with the areas in which they occur. Comparing area cladograms of different organisms that occur in the same region may reveal common biogeographic patterns that can be represented in a general area cladogram (GAC).
If every terminal taxon is endemic to a unique area and every area harbors only one terminal taxon, the TAC represents a valid hypothesis about area relationships. However, the situation becomes more complicated when the “one–area– one–taxon” assumption is violated, in which case the TAC may be incomplete or indicate conflicting area relationships. The sources of these problems are often divided into three categories: widespread taxa (taxa present in more than one area, fig. 1b), redundant distributions (areas harboring more than one taxon, fig. 1c), and missing areas (areas of interest absent from some of the compared taxon–area cladograms, fig. 1d). The latter problem is only relevant when several TACs are analyzed simultaneously.
Problematic TACs can be converted into resolved area cladograms (RACs; that is, taxon– specific GACs), in which each area is represented by only one terminal (ENGHOFF, 1996), by applying Assumptions 0, 1, and 2 (fig. 2). These assumptions mainly differ in their treatment of widespread taxa. Assumption 0 (A0, ZANDEE & ROOS, 1987) regards the widespread distribution as the result of a failure to speciate in response to vicariance events affecting other lineages. The areas inhabited by the widespread taxon are considered to form a monophyletic clade (fig. 2: RAC1) and the widespread taxon is thus treated as a synapomorphy of the areas in which it occurs. Assumption 1 (A1, NELSON & PLATNICK, 1981) explains the widespread distribution as the result of a failure to vicariate, possibly in combination with subsequent extinction. The areas inhabited by the widespread taxon are considered to form a monophyletic or paraphyletic group of areas (fig. 2: RACs 1–3) and the widespread taxon is treated as a symplesiomorphy of areas. Assumption 2 (A2, NELSON & PLATNICK, 1981), finally, allows failure to vicariate, extinction, dispersal, or any combination of these events, in explaining the origin of widespread distributions (VAN VELLER et al., 1999). The areas inhabited by the widespread taxon are regarded as constituting a poly–, para– or monophyletic group of areas (fig. 2: RACs 1–7), and the widespread taxon is treated as a possible convergence of the areas. In practice, A2 is implemented by locking each of the areas inhabited by the widespread taxon in turn, while the other areas are allowed to “float” on the RAC (ENGHOFF, 1995; MORRONE & CRISCI, 1995). The solutions allowed under the three assumptions form inclusive sets (PAGE, 1990; VAN VELLER et al., 1999): the A0 solutions are a subset of the A1 solutions, and these in turn are a subset of the A2 solutions (fig. 2). Usually, there are also solutions that violate all three assumptions, namely those in which none of the areas of a widespread taxon occurs in the RAC in the position predicted by the place of the widespread taxon in the TAC (fig. 2: RACs 8–15). Thus, the A2 solutions are usually a small subset of the “Full Solution Set” (all possible branching arrangements of the studied areas). Redundant distributions (sympatric taxa) are essentially handled in the same way as widespread distributions. Under A0 and A1, each occurrence of the redundant area is considered as equally valid, i.e., as representing duplicated area patterns. A2 also considers the possibility that the redundant distributions are the result of dispersal, that is, each occurrence of the redundant distribution is considered separately (ENGHOFF, 1995). Missing areas are treated as missing data under A1 and A2, and explained by primitive absence (the taxon has never been in the area), extinction (the taxon went extinct in the area) or inadequate sampling. Under A0, missing areas are considered as observations of true absence and explained as due to primitive absence or extinction (ENGHOFF, 1995; MORRONE & CRISCI, 1995).
Application of these assumptions to empirical data has been controversial, as results can differ greatly when the same data set is processed under different assumptions (MORRONE & CARPENTER, 1994; ENGHOFF, 1995; DE JONG, 1998; VAN VELLER et al., 2000). A0 (and A1) has been criticized as being too restrictive and unrealistic because it does not consider the possibility of dispersal in explaining widespread distributions, which means that areas may be grouped together solely based on recent range expansion involving geographically adjacent areas (NELSON & PLATNICK, 1981; HUMPHRIES & PARENTI, 1986; PAGE, 1989, 1990; MORRONE & CARPENTER, 1994). A2, on the other hand, has been considered as uninformative or indecisive in that it allows many more solutions than the stricter A0 and A1, and therefore often gives a less resolved result (ENGHOFF, 1995; VAN VELLER et al., 1999). It has also been argued that A2 (and A1) distort the historical (phylogenetic) relationships established in the original taxon cladogram from which the area cladogram is derived (ZANDEE & ROOS, 1987; WILEY, 1988; ENGHOFF, 1996; VAN VELLER et al., 1999, 2000) but this claim seems to arise from a confusion on the meaning of the assumptions: A2 and A1 are interpretations of the relationships between areas, not between taxa (PAGE, 1989, 1990).
The problems of widespread taxa, redundancy, and missing areas have mainly been discussed within the traditional pattern–based approach to historical biogeography. Pattern–based methods search for general patterns of area relationships (general area cladograms) allegedly without making any assumptions about evolutionary processes (RONQUIST, 1997; 1998a).
Biogeographic processes, such as dispersal or extinction, are only considered a posteriori (or using ad hoc procedures) in interpreting incongruence between the general area cladogram and the taxon–area cladograms (WILEY, 1988; PAGE, 1994). However, several different combinations of events can usually explain each case of incongruence, leaving the choice of a specific set of events that could explain the observations to the investigator. Pattern–based methods may also give counter–intuitive results in some cases because they do not necessarily favor reconstructions implying likely events over those implying improbable events (RONQUIST, 1995).
Event–based methods, which are explicitly derived from models of biogeographic processes, have gained in popularity recently (RONQUIST & NYLIN, 1990; PAGE, 1995; RONQUIST, 1995, 1998a, 1998b). Unlike pattern–based methods, the event–based reconstructions directly specify the ancestral distributions and the biogeographic events responsible for those distributions, and no a posteriori interpretation is necessary. Each type of biogeographic event in the reconstruction is associated with a cost that should be inversely related to the likelihood of that event occurring in the past: the more likely the event, the lower the cost. The optimal biogeographic reconstruction is found by searching for the reconstruction that minimizes the total cost of the implied events (RONQUIST, 1998a, 1998b, in press).
The purpose of this paper is to reexamine the problems of widespread taxa, redundant distributions and missing areas in the light of the event–based approach to historical biogeography. We find that it is only widespread terminal distributions that cause problems in the event– based approach. Because the pattern–based A0, A1 and A2 only define the set of allowed solutions but not the cost of each solution nor the implied events, they cannot be applied to event–based analyses. Instead, this paper describes three event– based options that may be used to reconcile the occurrence of widespread terminals with the common assumption of each lineage being restricted to a single area at a time: the recent, ancient and free options. We give algorithms that implement these options and illustrate their properties by reexamining a classical biogeographic data set, that of ROSEN (1978).
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