The Importance of Time/Space in Diagnosing the Causality of Phylogenetic Events: Towards a Chronobiogeographical Paradigm?

Transcription

1 Syst. Biol. 50(3): , 2001 The Importance of Time/Space in Diagnosing the Causality of Phylogenetic Events: Towards a Chronobiogeographical Paradigm? CRAIG ANDREW HUNN AND PAUL UPCHURCH Department of Earth Sciences, University of Cambridge, Cambridge, CB2 3EQ, England, UK; cah34@esc.cam.ac.uk, pupc98@esc.cam.ac.uk Abstract. A shift from a traditional biogeographical paradigm in cladistic biogeography to a chronobiogeographical paradigm is proposed. The chronobiogeographical paradigm aims to utilize temporal data in conjunction with spatial data in the detection of discrete historical events, such as vicariance and vicariant speciation, in cladograms. The concepts of primary and secondary congruency are introduced in relation to the distinction between repeated area relationships (primary congruency) and common extrinsic causality (secondary congruency). Simple hypothetical examples demonstrate that area cladograms cannot be safely interpreted purely as representing the sequence of area fragmentation; rather, they re ect recency of biotic interaction. Temporal data are shown to have a direct and potentially profound in uence on the results of traditional cladistic biogeographical analyses, indicating the necessity of developing a chronobiogeographical approach. The implementation of the paradigm is considered rst from a theoretical viewpoint and then in the context of the type of empirical data usually available. An as yet undevised time/space algorithm is deemed necessary for the latter, and guidelines are presented for the development of such an algorithm. Finally, we argue that the most rigorous and philosophically justi ed approach to the detection of phylogenetic causal events can be found only when temporal and spatial data are considered simultaneously. Consequently, the chronobiogeographical paradigm is seen as a logical elaboration of, not a replacement for, the biogeographical paradigm. [Area cladograms; biogeography; chronobiogeography; cladistic biogeography; component analysis; phylogenetics; vicariance] Evolutionary history represents a series of events in space and time. Phylogeny results from the complex interaction of both extrinsic events (environmental change, geological activity, extra-terrestrial impacts, and so forth) and intrinsic events (mutations, behavior, dispersal, and so forth) that occur during the history of different lineages. Investigators have long recognized, therefore, that cladograms should contain certain patterns (e.g., a positive correlation between taxon age and node order). Thus, a major component of the current phylogenetics research program involves the use of temporal and spatial data, in conjunction with cladograms, to extract additional information about evolutionary history. This trend has carried research in several, sometimes contradictory, directions. With regard to temporal data, attitudes can be conveniently divided into hard and soft approaches. The hard use of temporal data characterizes stratocladistics (Wagner, 1998; Fox et al., 1999) in which stratigraphical ranges of taxa are used as characters that can directly in uence cladogram topology. The soft approach treats cladistic topologies and stratigraphical data as separate, independent, datasets. In the latter case, the congruence between cladogram structure and stratigraphical occurrence is estimated with a variety of metrics (Norell and Novacek, 1992a,b; Huelsenbeck, 1994; Benton and Hitchin, 1996, 1997; Wills, 1999); retention of the independence of temporal and cladistic data provides a cross-testing of each other s accuracy (Hitchin and Benton, 1997). The soft approach typically does not in uence cladogram structure, except where maximization of stratigraphical congruence is used as a criterion for choosing one topology from a set of equally parsimonious trees. So far, no one appears to have attempted to use the spatial distribution of organisms as characters in phylogenetic analyses. Nor have such data been widely used to test cladogram topologies. There is, however, a well-established tradition of the use of spatial distributions and cladograms in what is here termed the biogeographical paradigm. This paradigm includes various methods and approaches (e.g., vicariance and cladistic or phylogenetic biogeography) that utilize cladistic topologies and organismal distributions to detect events such as vicariance or population dispersal. Much attention has been paid to the development of these methods and the exploration of their signi cance from various perspectives (Croizat, 391

2 392 SYSTEMATIC BIOLOGY VOL ; Platnick and Nelson, 1978; Rosen, 1978; Goodman et al., 1979; Wiley, 1980, 1988; Nelson and Platnick, 1981, 1988; Platnick, 1981; Nelson, 1984; Humphries and Parenti, 1986; Zandee and Roos, 1987; Kluge, 1988; Page, 1989, 1994; Brooks, 1990; Harold and Mooi, 1994; Morrone, 1994; Morrone and Carpenter, 1994; Morrone and Crisci, 1995; Ronquist, 1997). Workers applying these techniques are usually searching for common spatial patterns that can be interpreted in terms of causality. Causality itself can be de- ned as the event or events that produced the observed pattern: the concept is justi ed by using the argument that spatial patterns, repeated across different parts of a cladogram, probably re ect the in uence of a common extrinsic factor (essentially, this is Levins principle of robustness [Levins, 1966]). Irrespective of whether extrinsic or intrinsic factors are involved, causal events have loci in space and time. Therefore, such events may be most accurately diagnosed when spatial and temporal data are considered simultaneously. In short, current biogeographical methods are potentially awed, because they do not incorporate temporal data as an additional constraint in their algorithms. The concept of time has not been totally ignored in biogeographical studies (for example, Bretsky, 1975; Wiley, 1981; Grande, 1985; Page, 1990a). These treatments have proved both interesting and insightful, ranging from conducting biogeographical analyses in discrete historical time slices to reveal ancient area relationships (Grande, 1985), to exploring component congruence with a molecular clock time-scale in gophers and their lice (Page, 1990a). None of these approaches, however, emphasized the logical and theoretical links between time, space, and causality in whichever host-associate (host-parasite, area-taxon, or organism-gene) system they considered. For purposes of discussion and clarity, therefore, we introduce the term chronobiogeographical paradigm to represent the set of approaches that utilize time/space data together to constrain interpretations of phylogenetic causality. We stress that the chronobiogeographical paradigm is essentially a soft approach, insofar as it does not advocate the use of combined time/space data as a constraint on phylogenetic relationships. Furthermore, we do not regard chronobiogeography as a direct alternative to conventional biogeography; rather, it is a logical and ultimately necessary extension of the latter approach. The goals of the following discussion include (1) exploration of the theoretical linkage between time/space and causality in host-associate systems; (2) demonstration of the impact of temporal data on the diagnosis of event causality; (3) evaluation of the theoretical and practical dif culties that currently prevent implementation of a time/space reconciliation algorithm; and (4) outline of some principles we expect will play an important part in any future chronobiogeographical methods. ESSENTIAL DIFFERENCES BETWEEN TEMPORAL AND S PATIAL DISTRIBUTIONS Discussion of the philosophical interpretation of a cladogram is not the concern of this paper, although it is useful to emphasize the foundations of any cladistic time/space method. Cladograms are usually interpreted in one of two ways: a representation of the distribution of characters from which hypotheses of monophyly can be erected (Platnick, 1979); or a character representation of evolutionary history (Hennig, 1966). Both the biogeographical and chronobiogeographical paradigms adhere to the latter interpretation; they rely on the view that cladograms, in addition to being sequences of cladogeny, also contain sequences of character transformations that exist in time/space. If cladograms are sequences of character evolution, then they must contain a temporal axis. Plesiomorphy must occur before apomorphy (by de nition) and so a plesiomorphic node is further down this temporal axis than is an apomorphic node. Due to this polarity relationship between characters, the time axis itself, therefore, is not an absolute one, but is more an indicator of temporal polarity (i.e., root to terminals). This polarity is illustrated in Figure 1. Two simple axioms derive from this reasoning: 1. A descendant node cannot be further down the temporal axis than its ancestor, and therefore, 2. An ancestral node cannot be further up the temporal axis than any of its descendants. Considerations of cladistic space are more problematic in that space is not polarized in the manner described for time. Spatial

3 2001 HUNN AND UPCHURCH CHRONOBIOGEOGRAPHICAL PARADIGM 393 FIGURE 1. (a) Cladogram showing the relationships between three taxa, A, B, and C, which live in areas X, Y, and Z respectively. The divergence times for the two nodes are t 1 and t 2 as shown. (b) Illustration of different possible ways to reconstruct temporal and spatial character state transformations. paradoxes of the type dispersal from area Y to area X cannot occur if dispersal from area X to area Y has already happened cannot exist because there is no a priori constraint on the motility vector. In other words, given a dispersal pathway, there is no reason to assume that dispersal can occur only in one particular direction or can be ordered in only one way (Fig. 1B). This implies that, when considered alone, space cannot be ordered into a sequence the way time can, a characteristic that poses a signi cant problem for the imposition of space onto cladogram nodes. For example, suppose each separate geographical area is represented by its own character state. Accurate reconstruction of the biogeographical history of organisms would depend on how the multistate area character has been constructed (ordered or unordered, branching or linear) and its polarity. Without information on the geographical histories of the areas concerned, the multistate area character can be constrained only by information obtained from the spatial distributions on the taxon cladogram. Under these conditions, the minimal number of ad hoc assumptions would be achieved when the multistate area character is unpolarized (we do not know the center of origin of the organisms) and unordered. Thus, data on organismal spatial distribution provide only a very weak constraint on biogeographical history, a constraint that decreases in power as the numbers of areas and taxa increases. The directionality of time, however, may provide some useful constraints on the construction of the spatial multistate character, in which case it will be necessary to consider time and space together. COMMENTS ON THE INTERPRETATION OF REPEATED SPATIAL PATTERNS Primary Congruence Versus Secondary Congruence The concepts of primary and secondary congruence can be demonstrated easily, for example by considering the four clades in Figure 2. Let us assume we have been able to view the cladogenetic events and therefore know the causality in each case. The two alternative histories (Figs. 2A,B) display the same topologies and area relationships. In Figure 2A, the spatial arrangement of taxa has been caused by independent dispersal events, whereas in Figure 2B a single vicariance event is responsible. Under these conditions, nodes 1 and 2 display primary congruence with each other in both Figures 2A and 2B; that is, the two nodes are identical in terms of their hierarchical and topological relationships. Nodes 1 and 2 in Figure 2A, however, do not display secondary congruence because they are actually associated with different causal events;

4 394 SYSTEMATIC BIOLOGY VOL. 50 FIGURE 2. Primary versus secondary congruence. (a, b), Relationships between the taxa A, B, C, and D, living in areas X and Y. Both (a) and (b) display primary congruence between nodes 1 and 2, but only in (b) do these nodes display secondary congruence (see text for details). only in Figure 2B, therefore, is secondary congruence observed. The terms primary and secondary congruence in this example are close analogs of the corresponding concepts of primary and secondary homology introduced by Patterson (1982) for cladistic characters. Primary homologies are a priori hypotheses of character congruence, whereas secondary homologies are synapomorphies determined with a posteriori knowledge of tree topology and character distribution. By analogy with Patterson s concepts, replicated patterns in the spatial distribution of taxa represent primary congruence because their similarity justi es the initial hypothesis that they have been produced by the same extrinsic event. The assumption of primary congruence allows the construction of an area cladogram that potentially will explain all, or most, of the replicated spatial patterns in the original organism cladogram. By analogy with synapomorphy, secondary congruence is identi ed by examining each aspect of organismal distribution in the light of the events implied by the area cladogram. This a posteriori evaluation may reveal that some parts of the spatial pattern are unlikely to have been caused by a single extrinsic event (i.e., intrinsic factors have independently created a false similarity between patterns, analogous to homoplasy creating a false impression of homology). Note, however, that Patterson s (1982) concepts are concerned only with character patterns and are not related to any notion of process ; the analogy drawn above with area data is nonetheless useful because the relationship between primary homology/congruence and secondary homology/congruence is the same in both cases: The former is an a priori interpretation, the latter an a posteriori interpretation. Repeated Spatial Patterns: Always Caused by Vicariance? Many techniques in cladistic biogeography (such as component analysis) are based on identifying primary congruence in the form of overlapping or repeated area relationships. Secondary congruence (in the form of an extrinsic event such as vicariance) is then postulated when statistically signi cant amounts of component repetition can be identi ed. This approach should provide accurate reconstructions of biogeographical history, provided vicariance is the sole, or at least the major, extrinsic factor capable of imposing a repeated spatial pattern. Conceivably, however, repetition of area-taxon relationships could re ect causes other than vicariance, for example, if groups of temporally disparate organisms exhibit similar biogeographical patterns. In that case, clearly, the coincidence in area relationships could not have been caused by the same causal events. Such coinciding spatial patterns are found in various groups of Asian and North American plants (R. Olmstead, pers. comm.). Potential vicariance-mimicking events that do occur contemporaneously (i.e., in temporally coincident groups), might include spatially

5 2001 HUNN AND UPCHURCH CHRONOBIOGEOGRAPHICAL PARADIGM 395 heterogeneous environmental changes that provoke simultaneous parapatric speciations in several clades; the appearance of a dispersal route that allows members of several different clades to simultaneously populate a new area; co-cladogenesis in hosts and their parasites; and sequential evolution, as is seen in insects and plants (Futuyma and McCafferty, 1990). For example, consider the geographical history outlined in Figure 3A. A single area, XYZ, fragments so that X separates from YZ at time t 1 and Y and Z separate at time t 2. At FIGURE 3. (a) Hypothetical fragmentation sequence for the area XYZ. (b) How the area cladogram should be at time t 2. (c) The area cladogram that could be found at time t 3. See text for details. t 3, however, dispersal allows some mixing of the organisms living in X and Z. Under these circumstances, the area cladogram that best ts the distributions of various clades will depend partly on the temporal distribution of the organisms sampled, and partly on the relative strengths of the vicariance and dispersal signals. Thus, an area cladogram reconstructed only with taxa that appeared prior to time t 3 would probably show the correct area fragmentation sequence (provided vicariance has actually occurred in the clades concerned). An area cladogram based on taxa that lived after time t 3, however, could contain no clear fragmentation signal or might even show the relationships illustrated in Figure 3C if dispersal has overwhelmed the original vicariance pattern. This point is similar to that made by Grande (1985), who argued that area coalescence and organismal dispersal cause vicariance patterns to degrade through time, making it potentially unsafe, therefore, to regard area cladograms as a pure representation of a geographical fragmentation sequence. A more realistic interpretation of the area cladogram is that it represents the recency of biotic interaction between the areas concerned. Thus it might be preferable to depict area cladograms as Venn diagrams so that the branching geometry of a dendrogram cannot convey any implicit notion of range splitting. We can model the expected forms of biotic interaction between areas, of which there are four basic types (Fig. 4): (1) dispersal from area Y to area Z; (2) dispersal from area Z to area Y; (3) dispersal from a third area into Z and Y at a time or times after Y and Z became isolated from X and each other; and (4) vicariance (i.e., Y and Z become isolated from each other after the combined YZ area separated from X). All of these causal events would produce the same area cladogram, yet only one of them incorporates the particular event we are trying to detect. Whether such biotic interactions have resulted from vicariance, or from other coherent extrinsic factors, cannot be assessed simply on the basis that an area cladogram has been found. Just as any cladistic matrix will yield a topology of some description, any spatial biotic interaction will yield an area cladogram regardless of whether interchange events have been intrinsic or extrinsic. The frequency with which non-vicariant

6 396 SYSTEMATIC BIOLOGY VOL. 50 FIGURE 4. Schematic diagram showing four models of biotic interaction between areas Y and Z: (a) dispersal from Y to Z; (b) dispersal from Z to Y; (c) dispersal from a third area, W, to Y and Z; (d) fragmentation of YZ to produce vicariance. See text for details. extrinsic factors mimic vicariance is probably low, but it is dif cult to demonstrate this without a priori knowledge of the biogeographical history of organisms. TEMPORAL DATA AND PATTERN CONGRUENCE Data on the temporal distributions of taxa seem likely to hold the key to the accurate diagnosis of event causality. Consider the taxon cladogram in Figure 5A. The seven taxa (A-G) live in four areas (W-Z). Assume that this taxon cladogram is just one of a large sample of clades, and that together these various clades have been found to support the area cladogram in Figure 5B (based on the results of, for example, a component analysis). The relationships and spatial distributions of taxa A-G are perfectly congruent with the proposed area cladogram; that is, they are maximally compatible. Implicit in this result is the interpretation that clade D-G arose after the isolation of area Z: This in turn implies that the cladogenetic events responsible for the divergence of taxa D, E, F, and G occurred either by parapatry or vicariance within area Z. Let us now suppose that we have access to information on the timing of cladogenetic and geographical events, such as the divergence time between the lineages leading to taxon C and clade D-G (t C=D G ) and the date of the appearance of the barrier between areas Y and Z (t Y=Z ). If t C=D G equals, or is slightly younger than, t Y=Z, then the original area cladogram and vicariance model are supported by the temporal data. If, however, t C=D G predates t Y=Z, then the separation of areas Y and Z cannot be causally linked to the divergence between taxon C and clade D-G. If we assume that t C=D G is earlier than t Y=Z, the area cladogram (Fig. 5B) can be reconciled with the new biogeographical history, but only at the expense of two items of error (Fig. 5C). In fact, information on the divergence times of other lineages could require even more items of error. For example, if t Y=Z is later than the divergence between taxa F and G, then ve items of error are required for complete reconciliation (Fig. 5D). Conceivably, therefore, temporal data could radically alter the results of a component analysis (or tree reconciliation analysis), producing a different area cladogram or equivocal results. TOWARDS A TIME/SPACE ALGORITHM? The evident problems outlined above stem from a biogeographical approach that excludes consideration of temporal data. These dif culties are best dealt with by using the chronobiogeographical paradigm. Because constraining the amount of time/space represented by each cladistic node maximizes the probability of secondary congruence diagnosis, a method is required for reconstructing nodal time/space in the form of some kind of algorithm that can manipulate empirical data.

7 2001 HUNN AND UPCHURCH CHRONOBIOGEOGRAPHICAL PARADIGM 397 biogeographical techniques, quite possibly as a manifestation of the taxic (pattern) cladistics philosophy (Platnick, 1979). For example, consider the assumptions and general format underlying various recent biogeographical methods: FIGURE 5. (a) Cladogram for the seven taxa A G living in the four areas W, X, Y, and Z; (b) area cladogram for the four areas established by using the taxon cladogram in (a) and a population of other clades; (c) reconciled area-taxon cladogram in which t C=D G occurs before t Y=Z (H 1 and H 2 are the hypothetical missing taxa, i.e., items of error); (d) reconciled area-taxon cladogram when the divergence between taxa F and G occurs before t Y=Z (H 1 H 5 are the required hypothetical missing taxa). Imposition of Time/Space onto Cladogram Nodes The imposition of data onto cladistic nodes is not a procedure usually featured in 1. Component analysis (Nelson and Platnick, 1981) seeks to nd a sequence of areas that is common (or could be common) to all competing area cladograms under assumptions of range relationships (the most compatible set of components). 2. Reconciliation (Page, 1990a, 1993, 1994), a form of component analysis, maximizes co-divergence and so nds the sequence of areas having the fewest items of error in terms of sorting events and paralogy. 3. Brooks parsimony analysis (Brooks, 1985, 1990) is essentially a meta-analysis (Baum and Ragan, 1993; Sanderson et al., 1997) of area cladograms. 4. Dispersal-vicariance analysis (Ronquist, 1997) nds the most-parsimonious optimization of ranges under the criterion of maximum vicariance. The last of these methods is explicitly concerned with the reconstruction of nodal terms, but only to optimize ranges and thus satisfy the assumption about the predominance of vicariance as a speciating mechanism. Effectively, the up-pass and down-pass procedures are analogous to the pre- and postorder traversals performed in standard cladistic parsimony reconstructions. Ronquist s exhaustive technique takes the distribution of two sister -taxa, considers all possible combinations of these ranges, and tries to reconstruct the range of the ancestor. As currently formulated, however, dispersal-vicariance analysis has at least two potential associated dif culties: (1) a priori maximization of vicariance (for which there is no empirical justi cation); and (2) a diagnosis of causality based on spatial data alone. Although the latter is a problem of the biogeographical paradigm in general, dispersal-vicariance analysis illustrates it best by seeking speci cally to use a spatial topology to reconstruct ancestral states and so to make statements about causal events. In other words, this approach transcends the mere detection of pattern and

8 398 SYSTEMATIC BIOLOGY VOL. 50 moves into the realm of considering ancestordescendant data. Dispersal-vicariance analysis is, therefore, a useful development of the biogeographical paradigm, in that it recognizes the importance of ancestor-descendant relations in the diagnosis of discrete historical events, but it is awed, like the other techniques, because it does not consider the natural relative of space, time. The chronobiogeographical paradigm advocates both the use of ancestor-descendant relations to diagnose discrete historical events and the conjunctive use of both spatial and temporal data. The formalization of a time/space algorithm for the reconstruction and constraining of cladistic node time/space, therefore, is a logical development in the chronobiogeographical paradigm. An Idealized Case Study At present, no algorithm available allows the combined use of temporal and spatial data to constrain biogeographical analyses. The formulation of such an algorithm is fraught with theoretical and practical dif culties, and substantial further research will be required before such a method can be fully implemented. Nevertheless, we can outline several principles that should form the foundation for such a method. Our goal is to develop a method that uses phylogenetic relationships in combination with time/space data to produce the simplest and most assumption-free estimate of biogeographical history. We start with an idealized case study in which full data are available and then modify the method by adding the complexities caused by missing data. Consider an instance of speciation in time/space, in which common ancestor A gives rise to two descendant sister species B and C (Fig. 6). The spatial and temporal distributions of A, B, and C, are completely known. The ancestor A lives in the combined area XY, whereas B and C are found only in X and Y, respectively. The ancestor A actually consists of several potentially interbreeding populations that persist through time: Together these populations, and therefore A itself, exist from their origin at t A0 to their extinction at t Aext. At time t B0, between t A0 and t Aext, one of the constituent populations of A (referred to as AB) becomes effectively separated from the rest of A and FIGURE 6. Schematic diagram showing the evolution of two daughter species (B and C) from populations belonging to their ancestor A. See text for details. gives rise to a lineage that will ultimately become taxon B; At time t B1 taxon B originates from population AB (i.e., taxon B acquires its rst autapomorphy and is therefore cladistically distinct from taxon A). A similar history is also found for taxon C, such that population AC becomes separated from other populations of A at time t C0, and C rst appears at t C1. Thus, the processes governing the origins of AB and AC are essentially those of demography and demogenetics, and only with a complete knowledge of organismal history can the separation of these populations from the rest of A be related to causal events. Species A can have a time range that overlaps those of AB, AC, B, and C, but in demographic terms AB and AC become extinct (through transformation) when B and C, respectively, appear. Note, therefore, how the existence of B and C does not automatically invoke the extinction of A, even if A is their phylogenetic ancestor. This reminds us of the importance of population sampling in the fossil record and explains why it is possible to nd apparent temporal paradoxes in fossil phylogenies, for example, when a more basal taxon (which may have originally been an ancestor for more-derived taxa) occurs at a more recent stratigraphical level than that

9 2001 HUNN AND UPCHURCH CHRONOBIOGEOGRAPHICAL PARADIGM 399 occupied by its apomorphic descendants. This consideration is relevant to some ideas that will be discussed presently. Suppose now that we have not observed the speciation event or events responsible for the appearance of B and C: The only available data relevant to the causality of these events is in the form of the spatial and temporal distributions of A, B, and C. The possible interpretations of the spatial and temporal distributions are rst considered separately and then in combination. 1. Spatial pattern. The spatial distributions of A, B and C could, in theory, be explained through an almost in nite number of potential biogeographical histories, involving differing amounts of vicariance, parapatry, dispersal, and extinction. Even considering only the simplest possible explanations for these distributions, more than one scenario is still viable. We can infer that B evolved in one part of the ancestral range (X) while C evolved in another part of that range (Y); that is, these data do not require any dispersal or extinction events in their most-parsimonious interpretation. One possibility is that vicariance has occurred (i.e., the origins of B and C are linked to a single extrinsic cause in the form of a barrier that separated populations AB and AC). Alternatively, B and C may have arisen in separate parts of the geographical range of A through the operation of parapatry. Whether vicariance or parapatry is the more probable cause of this distribution depends on knowledge of the geography of the areas concerned. If X and Y are separated from each other by a barrier, vicariance seems more probable. If no such barrier exists (i.e., if X and Y are little more than descriptive names for different parts of a continuous area), then parapatry seems more probable. Knowledge of spatial distributions can, therefore, provide some constraint on the causality of divergence, but the strength of this constraint decreases as taxon and area numbers increase (see below). 2. Temporal pattern. Unlike spatial data, which cannot be polarized, the directionality of temporal data makes it more useful in the diagnosis of causality. In particular, vicariance and parapatry make different predictions about the relative timing of taxon originations. Because vicariance represents a single extrinsic cause, the isolation of populations AB and AC should be coincident in time (i.e., t B0 D t C0 ). Parapatry, however, occurs through the operation of separate intrinsic factors, and therefore AB and AC need not appear at the same time (t B0 < t C0 or t B0 > t C0 ). Certain confounding variables might operate to obscure this pattern. For example, parapatry could occur in two separate lineages at the same time through coincidence, or because they both respond to a widespread ecological change. Similarly, two lineages may respond to the same vicariance event in different ways (because of differences in their dispersal abilities or because of some form of evolutionary lag or stabilizing selection). In the absence of other sources of data, however, the most accurate way to diagnose the speciation mechanism would be to consider vicariance decreasingly probable as t B0 and t C0 increase in temporal separation. In short, maximum common causality lies in the con guration t B0 D t C0. 3. Combined data. Spatial and temporal data, taken separately, can provide information on phylogenetic causality. Nevertheless, such constraints are relatively weak. The most powerful constraint is imposed when temporal and spatial data are considered together. For example, a vicariance explanation may be implied by the spatial distribution (B in X, C in Y), but this explanation becomes increasingly improbable as the difference between t B0 and t C0 increases. Similarly, simultaneous origination of B and C might support vicariance, but a spatial pattern (e.g., B and C still live in both X and Y) would tend to favor parapatry or necessitate some dispersal after vicariance. Extrinsic causality, therefore, can be inferred only when spatial and temporal data intersect appropriately. Several aspects of the above case study do not entirely correspond to the temporal, spatial, and phylogenetic data that are actually available to us. For example, although cladistic analysis may identify potential ancestors (in the form of metataxa), it is impossible to demonstrate that such taxa represent

10 400 SYSTEMATIC BIOLOGY VOL. 50 real ancestors. Furthermore, both temporal and spatial distributions will be affected by missing data of various types. Also, cladistics can only detect patterns that manifest at the phylogenetic level, even if their cause lies in lower-level processes. The following sections, therefore, take these issues into account and examine to what extent the temporal and spatial data provide constraints on phylogenetic causality under real conditions. Cladograms and Sister Taxa A practical and implementable chronobiogeographical method must be based on cladistic topology rather than a set of ancestor-descendent relationships. We must therefore consider how temporal and spatial data may constrain phylogenetic causality in the context of a cladogram. The temporal and spatial distributions of taxa can be represented by separate time and area cladograms (Fig. 7). Such time and space cladograms differ markedly in terms of the nature of their terminal units. Areas are typically denoted by letters or some other arbitrary notation because space is unpolarized (see above). Time, however, is meaningful only in relation to a reference, for example, the present. Let us now consider the information content of these cladograms with respect to spatial and temporal data. As mentioned above, area cladograms represent recency of biotic interaction between areas, that is, Y and Z have more recently shared biotic interaction with each other than either has with X. These biotic changes are demogenetic, not phylogenetic, processes, but they become cladistically diagnosable only after propagation in the phylogeny has occurred. The nodes cannot diagnose causality in terms of what kind of biotic interaction has occurred between the areas; it merely indicates that some form of interaction has occurred. In terms of potential cladistic expressions in three area statements, three con gurations of areas are possible: all areas different (X(Y,Z)); terminals the same, but basal area different (X(Y,Y)); and one terminal and basal area are the same, but the other terminal is different (X(Y,X)). Because we want to diagnose vicariance, not just recency of biotic interchange, we may need to consider the positions of geographical areas relative to each other (an extrinsic data source). FIGURE 7. Cladograms showing the relationships between taxa A, B, and C. (a) The three areas X, Y, and Z where A C are found; (b) the observed origination times (in arbitrary time units before the present) for taxa A C. See text for details. That is, without recourse to paleogeography, any polarizing, ordering, or directioning of space is arbitrary. In the example above, perhaps areas X, Y, and Z, are three portions of what was once a single ancestral area (XYZ), or X may represent the ancestral area that subsequently became divided into areas Y and Z. The information we need to correctly diagnose causality is as follows:

11 2001 HUNN AND UPCHURCH CHRONOBIOGEOGRAPHICAL PARADIGM 401 position of X relative to Y and Z in time; position of Y and Z relative to each other in space; and positions of Y and Z relative to X in space. These principles combine to allow us to de ne the circumstances under which the presence or absence of vicariance can be inferred: 1. If terminal area Y D terminal area Z, that is, and (Y [ Z) D (Y \ Z), (1) (Y \ Z) D 1, (2) where [ denotes union (Boolean addition) and \ denotes intersection (the subset common to both sets), then vicariance has not occurred. 2. If terminal area Y does not equal terminal area Z, that is, (Y [ Z) 6D (Y \ Z), (3) vicariance may have occurred. 3. If area X coexists with Y or Z, that is, (Y [ Z) 6D X, (4) then vicariance did not occur by X fragmenting to form Y and Z. 4. If X does not coexist with Y and Z, and towards the end of the existence of X, area Y does not equal Z, but the latter two are spatially close, then, and (Y [ Z) D X (5) (Y \ Z) D Á, (6) then ideal vicariance is diagnosed, where Á denotes the null set (Boolean equivalent of zero). If Eq. 6 is not satis ed but Eq. 5 is, then vicariance is still possible, but the descendant range intersection must be explained by invoking an event of independent dispersal. 5. If X does not coexist with Y and Z, and towards the end of the existence of X, area Y does not equal Z but the two are spatially distant, then, and (Y [ Z) 6D X (7) (Y \ Z) D Á: (8) In this case, no vicariance has occurred. In these statements, three types of information are used: (1) intrinsic biological space, (2) intrinsic biological time, and (3) extrinsic geographical space. The rst two can tell us much in themselves, but combining them with extrinsic data allows for further constraint. Now consider the information content of a cladogram from the point of view of temporal data. For fossil data, we can envisage eight kinds of three-item topologies (Fig. 8): 1. Derived sister taxa appear at the same time and occur after the appearance of the more basal taxon (Fig. 8a). 2. Derived sister taxa appear at different times but occur after the appearance time of the more basal taxon (Fig. 8b). 3. Derived sister taxa appear at different times, the older member of this pair appearing at the same time as the more basal taxon (Fig. 8c). 4. Derived sister taxa appear at the same time and before the appearance of the more basal taxon (Fig. 8d). 5. All taxa appear at the same time (Fig. 8e). 6. Derived sister taxa appear at different times, the younger of them appearing at the same time as the basal taxon (Fig. 8f). 7. Derived sister taxa appear at different times, one before and one after the basal taxon (Fig. 8g). 8. Derived sister taxa appear at different times, but both are older than the basal taxon (Fig. 8h). In these possibilities, appearance times are those observed in the stratigraphical column, not necessarily the true origination times. Patterns 1 and 2 here are temporally consistent, whereas 3 to 8 are not: That is, the latter set of patterns contain temporal paradoxes

12 402 SYSTEMATIC BIOLOGY VOL If t 2 D t 1, and t 3 < t 1, then vicariance probably did not occur. 5. If t 2 D t 1, and t 3 > t 1, then vicariance probably did not occur. FIGURE 8. Cladograms showing the eight possible alternative arrangements for observed origination times (in arbitrary time units before the present) for a threetaxon statement. See text for details. if the empirical data regarding appearance time is correct. Because we are concerned with causality and hence discrete events (vicariance), only the rst appearances of terminal entities are of any interest. Like space, however, time is meaningless by itself for our purposes, although its polarity allows us to determine which temporal statements cannot contribute information to a given study (patterns 1 and 2 can, 3 to 8 cannot). These considerations mean that, if we have a temporal cladogram with the terminal times t 1, t 2, and t 3, in the topology (t 1 (t 2, t 3 ), the following statements can be made: The rst two statements above are the criteria of internal temporal consistency for discrete historical events. These criteria stem from the existence of a polarized temporal axis. When considering phylogenies that contain mainly extant taxa, however, these arguments become simpli ed. Molecular clocks allow for the age of nodes to be estimated; that is, the timing of the cladogenetic split is obtained. This means that the eight kinds of three-item topologies outlined above do not apply. Instead, we must consider the kind of topology illustrated in Figure 9. Here, the four terminal entities occur at time t 4, the Present (taxa open to molecular analysis will nearly always be from the Present because fossil molecules are so rare). Application of a molecular clock of some kind yields cladogenesis times of t 2 and t 3 for the two terminal nodes. These gures are then used to date their ancestral node, yielding t 1. Apparent temporal paradoxes of the type seen in six of the eight possible fossil topologies, attributable to demogenetic sampling or to data missing from the stratigraphical record (patterns 3 to 8), cannot exist when clades are dated this way, because the timing of t 1 is guaranteed to be older than either 1. If t 2 D t 3, then vicariance may have occurred. 2. If t 2 < t 1, and t 3 < t 1, then vicariance may have occurred. 3. If t 2 > t 1, or t 3 > t 1, then vicariance probably did not occur. FIGURE 9. A cladogram with nodes dated by use of a molecular clock. Note how deeper nodes always have older times. See text for details.

13 2001 HUNN AND UPCHURCH CHRONOBIOGEOGRAPHICAL PARADIGM 403 of its descendants (it occurs deeper within the topology). That is, a molecular clock always gives a topology that satis es the criteria of internal temporal consistency. If the sister clades in Figure 9 have spatial distributions of ((A,B),(A,B)), then the ve statements from above are reduced and simpli ed to the following statements: 1. If t 2 D t 3, then vicariance may have occurred, and 2. If t 2 < t 3, or t 2 > t 3, then vicariance probably did not occur. Note that t 4 < t 2 /t 3 and t 2 /t 3 < t 1 for molecular clocks. These arguments are essentially the same as those for fossil phylogenies, except that times of comparison derive from nodes instead of the terminals. Once these gures are obtained by molecular analysis, they are open to the same considerations as are those for the fossils, with the potential for apparent temporal paradoxes removed by the nature of the molecular clock. Considering Area and Temporal Cladograms Together As in the idealized case study presented above, temporal and spatial data, taken separately, can provide weak constraints on the diagnosis of phylogenetic casualty. When the two data sets are considered together, however, a more powerful constraint is created. Consider again the area and temporal cladograms presented in Figure 7. We want to know the cause of the bifurcation at the terminal node. In the area cladogram, this node provides the intersection (Y, Z) which suggests the most recent common ancestor of taxa B and C could have lived in combined area YZ, or it may have lived in only one of these areas and dispersed to the other. Applying the area statements outlined above, vicariance cannot be ruled out at this stage unless extrinsic geographical information suggests otherwise. The temporal cladogram (Fig. 7B) indicates that the intersection of the terminal node is (10, 20), and therefore the minimal divergence time (MDT) for the two derived sister taxa is 20. These sister taxa may have diverged before this time (the precise date is unknowable), but not after. The MDT is the best obtainable temporal information about the common ancestor of areas Y and Z. The MDT for the basal node is 30. If we now merge the temporal and spatial data, we can make the following statements: 1. The origination times of the derived sister taxa B and C ful ll the criteria of temporal consistency. The difference between these times is 10 (i.e., they are consistent, but with a disparity value of 10). 2. Area Y does not equal area Z. 3. Because the intersection of ancestor (A,B,C) and (B,C) is (30, 20), the disparity of this basal node is 10 also. Adding extra clades to these conclusions may, or may not, widen the margins of error, fortifying/rejecting vicariance at speci c nodes. Diagnosing a historical event unequivocally, especially from the empirical data available, is not possible. We are dealing with probabilities of vicariance: the greater the margins of error, the greater the dif culty to diagnose a discrete historical event accurately. Combining time and space merely results in extra constraints on the probability that primary congruency can be correctly interpreted as secondary congruency. Finally, suppose we know that areas Y and Z have discrete and widely separated locations between times 50 and 10. This would strongly decrease the probability that vicariance had occurred due to a separation of areas Y and Z at time 20. Knowing the relations of the areas relative to each other (the extrinsic geographical source) further constrains our secondary congruence diagnosis and the probability that a discrete event was causal to a particular cladistic node. Conversely, we might know that areas Y and Z were in contact originally but separated from each other at some point between times 23 and 20. In this case, a vicariance hypothesis for the node is supported because the separation time (23 20 time units) coincides with the nodal MDT of 20. The disparity of 10 in the taxa data is then something that may have to be explained in terms of either evolutionary lag or taphonomic processes. The point is that the coincidence of intrinsic biological time with extrinsic geological time increases the

14 404 SYSTEMATIC BIOLOGY VOL. 50 probability that a discrete historical event is a causal factor. and of the biases that distort our view of it. A Note on Sampling Biases Any method that requires information on the spatial and temporal distributions of organisms will have to contend with problems caused by sampling biases. The fossil record is clearly incomplete in terms of the taxa represented and the known geographical and stratigraphical ranges of taxa. Missing taxa and incomplete information on the spatial distributions of organisms have been considered in detail by previous biogeographical studies (Nelson and Platnick, 1980, 1981, 1988; Page 1990a,b,; Nelson and Ladiges, 1991, 1996). A chronobiogeographical method must also consider biases in the estimated temporal ranges of taxa. In general, we might expect that, across many taxa in several different clades, missing data on stratigraphical distribution will be randomly distributed. This will create noise in the analysis that, if it outweighs the true signal, may lead to poorly resolved results. There may also be circumstances in which stratigraphical ranges, or more precisely origination times, display a false signal, which may lead to misleading results. This problem is most likely to occur when geological unconformity creates the false impression that many taxa have appeared at the same point in time. At rst sight, one might think this would create a false signal in favor of vicariance because many sister taxa would appear at the same time. Fortunately, one of the strengths of the chronobiogeographical method is that it considers time and space simultaneously. The simultaneous appearance of multiple taxa in several different areas could re ect several vicariance events happening in quick succession; more plausibly, however, it can be interpreted as the result of incomplete stratigraphical representation. The chronobiogeographical method is no more threatened by sampling bias than is either conventional cladistic biogeography or techniques that compare cladogram structure with stratigraphical range. Indeed, the chronobiogeographical method, by being as assumption-free as possible and by combining temporal and spatial data into a single analysis, may provide our most complete and reliable picture of evolutionary history from available empirical data FROM PARADIGM TO PRACTICE Towards Implementation Implementation of the chronobiogeographical paradigm offers many practical and methodological problems. Indeed, this may explain authors reluctance to fully utilize temporal data when constructing algorithms. In the past, the stratigraphical criterion (Hennig, 1966) has been used as an extrinsic source against which complete biogeographical hypotheses can be compared (e.g., Fortunato, 1998) despite the fact that the link between causality and time/space indicates that temporal data are not subordinate to spatial data. The chronobiogeographical paradigm suggests the most fruitful treatment of space and time will combine, rather than decouple, these data. Ideally, a practicable chronobiogeographical method would avoid, or at least minimize, assumptions about the relative predominance of vicariance, dispersal, and extinction. Without the ability to directly observe the frequency of these phenomena, the minimization of assumptions seems to be the ideal we should work toward. Indeed, one of the potential bene ts of the method would be that the frequencies of these processes could be estimated a posteriori. Although no time/space algorithm is currently available, we suggest that a chronobiogeographical method will probably utilize the following concepts and procedures: 1. Compilation of systematic and time/ space data. Forming the basis of all chronobiogeographical investigations are species-level phylogenetic hypotheses and the temporal and spatial data for terminal taxa. Phylogenetic hypotheses, ideally, would be constructed by using modern techniques such as cladistics and maximum likelihood. Time/space data can be drawn from fossils, molecular clocks (with absolute divergence times perhaps being most accurately estimated by using the fossils to calibrate molecular clocks [e.g., Cooper and Penny, 1997]), and paleogeographical maps. Evidently, the chronobiogeographical paradigm will draw on information from systematics,

15 2001 HUNN AND UPCHURCH CHRONOBIOGEOGRAPHICAL PARADIGM 405 molecular biology, paleontology, and geology. 2. Application of a time/space algorithm. 2a. The required temporal algorithm will involve the use of divergence times, estimated during step 1 above. 2b. The required spatial algorithm will be subordinate to the temporal algorithm because the latter can be used as a director for the former. That is, the temporal axis can be used to impose a polarity onto the non-polarized spatial axis. 2c. The imposition of temporal (2a) and spatial (2b) sets onto cladogram nodes, will provide constraints on the time/space represented by each node. The time/space rules and statements outlined above will be used to determine the most probable cause of phylogenetic divergence at each node. 3. Implementation of a component analysis or a reconciliation to discover a common area cladogram. Such methods, when applied after steps 2a 2c, will provide statistical support for any repeated time/space patterns in the cladograms. The additional constraint on the area cladogram provided by temporal data increases the probability of correctly diagnosing secondary congruence (see above). 4. Testing against independent data. As is already available in the biogeographical paradigm, a comparison of the biogeographical history determined from chronobiogeographical methods with independent data on the timing and nature of range fragmentation and coalescence will be desirable. The source of geographical range history will depend on the spatial and time scales of the biogeographical problem: For large time-scale historical biogeography, large amounts of data are currently available from geology and paleogeography. Such a comparison will offer independent support/rejection for hypotheses of secondary congruence. 5. The biological ideal. Postulations of speciation causality can be made by considering each instance of ancestor-descendant time/space relationships on the nal time/space cladogram in the context of their corresponding paleogeographies. From the above, it seems that most of the components of a chronobiogeographical method are already available. Steps 1 and 3 5 could be performed now, although of course many basic data (step 1) regarding evolutionary relationships and time/space ranges are yet to be collected. From a methodological viewpoint, however, it is step 2 that requires the most work to make the chronobiogeographical paradigm practicable. The required algorithms for the imposition of time/space data onto nodes need to be theoretically rigorous, as assumption-free as possible, and without a priori assertions about the dominance of a particular speciating mechanism. Once formalized, fully incorporating the algorithms into an existing biogeographical method, to complete step 3, is only a matter of technique tinkering. Similarly, step 4 is easily implemented, provided we have access to detailed paleogeographical maps, which are improving at a rapid rate. Finally, step 5 can be thought of as an aspiration of chronobiogeography in general and should be viewed as the ultimate goal of our theoretical and methodological endeavors. Conclusions The above discussion suggests several important conclusions regarding historical biogeographical methods: 1. Cladistic biogeographical methods essentially detect primary congruence between the spatial distributions of clades. Although statistically signi cant pattern repetitions will often indicate the operation of a single extrinsic factor (vicariance), such an approach does not represent the most rigorous method for accurately identifying secondary congruence. 2. An area cladogram cannot be reliably interpreted as indicating the fragmentation sequence for a set of geographical ranges. Rather, such cladogram should be more realistically viewed as representing recency of biotic interaction. 3. Data on the temporal distribution of taxa can provide an important additional constraint in biogeographical analyses. Such data may help to reinforce or overturn hypotheses of phylogenetic event causality (e.g., vicariance).