Journal of Biogeography (J. Biogeogr.) (2005) 32, 755–774
SPECIAL
PAPER
PACT: an efficient and powerful
algorithm for generating area cladograms
Maggie Wojcicki and Daniel R. Brooks*
Department of Zoology, University of
Toronto, Toronto, ON, Canada
ABSTRACT
Aim To introduce and describe the functioning of a new algorithm, phylogenetic
analysis for comparing trees (PACT), for generating area cladograms that provide
accurate representation of information contained in taxon–area cladograms.
Methods PACT operates in the following steps. Convert all phylogenies to
taxon–area cladograms. Convert all taxon–area cladograms to Venn diagrams.
Choose any taxon–area cladogram from the set of taxon–area cladograms to be
analysed and determine its elements. This will be the template area cladogram.
Select a second taxon–area cladogram. Determine its elements. Document which
elements in the second tree occur in the template tree (denoted by ‘Y’) and which
do not (denoted by ‘N’). Each ‘Y’ indicates a match with previous pattern and
these are combined. Each ‘N’ is a new element and is attached to the template area
cladogram at the node where it is linked with a Y. This requires two rules: (1)
‘Y + Y ¼ Y’ (combine common elements) as long as they are connected at the
same node; and (2) ‘Y + N ¼ YN’ (add novel elements to the template area
cladogram at the node where they first appear). Once the novel elements in the
second taxon–area cladogram have been added to the template area cladogram,
see if any of them can be further combined. This requires three additional rules:
(1) ‘Y(Y) ¼ Y(Y)’ (do not combine Y’s if they are attached at different nodes on
the template area cladogram); (2) ‘Y + YN ¼ YN’ (Y is part of group YN); and
(3) ‘YN + YN ¼ YNN’ (Y is the same for each, but each N is different). Repeat
for all available taxon–area cladograms.
Results Three exemplars demonstrate that PACT provides the most accurate
area cladograms for vicariance-driven biotic diversification, dispersal-driven
biotic diversification and taxon pulse-driven biotic diversification. PACT can also
be used as an a priori method of biogeographical analysis.
Main conclusions PACT embodies all the strong points and none of the
weaknesses of previously proposed methods of historical biogeography. It is most
useful as an a posteriori method, but it is also superior to all previous a priori
methods because it does not specify costs, or weights or probabilities, or
likelihoods of particular biogeographical processes a priori and is thus sensitive to
clade-specific historical contingencies.
*Correspondence: Daniel R. Brooks,
Department of Zoology, University of Toronto,
25 Harbord Street, Toronto, ON M5S 3G5,
Canada.
E-mail: [email protected]
Keywords
Cladistic biogeography, community evolution, dispersal, evolutionary radiations, historical biogeography, phylogenetic analysis, phylogeny, speciation,
taxon pulse, vicariance.
Formal methods of historical biogeographical analysis using
phylogenetic trees began appearing more than 25 years ago
(Platnick & Nelson, 1978). Today, two classes of methods for
documenting historical biogeographical patterns exist. All
begin by converting phylogenetic trees into taxon–area
cladograms (Morrone & Carpenter, 1994; Enghoff, 1996),
ª 2005 Blackwell Publishing Ltd www.blackwellpublishing.com/jbi
doi:10.1111/j.1365-2699.2004.01148.x
INTRODUCTION
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M. Wojcicki and D. R. Brooks
replacing the name of each species with notations indicating its
geographical distribution. Cladistic biogeographical methods,
also called a priori methods (Van Veller et al., 1999, 2000,
2001, 2002; Van Veller & Brooks, 2001), produce the most
parsimonious pattern of area relationships for one or more
taxon–area cladograms, given the constraints of an a priori
model (assumptions 1 and 2 associated with various modifications of component analysis; costs associated with eventbased models such as DIVA; probabilities associated with
likelihood models such as Jungles). Phylogenetic biogeographical methods, also called a posteriori methods (Van Veller et al.,
1999, 2000, 2001, 2002; Van Veller & Brooks, 2001), utilize
simultaneous comparisons among multiple clades to generate
the most parsimonious pattern of area relationships without
reference to an a priori model. All but one of the a posteriori
methods is similar to the a priori methods in permitting each
area to occur only once.
All methods recognize three classes of biogeographical
patterns: (1) complete matching between the general pattern
and any given taxon–area cladogram, usually interpreted as
indicating vicariance, but recognized by some as possibly being
the result of sequential speciation by colonization in each clade
(Fig. 1); (2) incomplete matching, suggesting extinction in one
of the lineages (Fig. 2); and (3) duplication of all or part of the
pattern, suggesting sympatric speciation in the common
ancestor of the duplicated lineages (also known as lineage
duplication) (Fig. 3).
Three additional types of patterns have been considered
complicating factors that obscure the general area relationships. One of these is speciation by dispersal on the part of one
or more members of the co-occurring clades (peripheral
isolates allopatric speciation), introducing unique area relationships (Fig. 4). The remaining two types of patterns
represent cases in which more than one phylogenetic event
affects the same area, producing reticulated area relationships:
(1) two or more separate speciation events within a clade each
resulting in at least two non-sister species inhabiting the same
area (Fig. 5); and (2) post-speciation dispersal leading to the
occurrence of the same species in more than one area (also
known as the widespread species problem) (Fig. 6). All the
methods discussed above, except secondary BPA (Brooks et al.,
2001), treat examples of these phenomena as exceptions to a
presumed single general pattern.
Figure 1 A taxon–area cladogram showing a particular set of area
relationships involving areas A, B, C and D, stipulated to be the
general pattern (left), and a second taxon–area cladogram showing
the same area relationships as the general pattern (right). Letters ¼ areas.
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Figure 2 A taxon–area cladogram showing a particular set of area
relationships involving areas A, B, C and D, stipulated to be the
general pattern (left), and a second taxon–area cladogram showing
area relationships among areas A, C and D, interpreted as having
lost, through extinction (also known as lineage sorting) a species
occurring in area B that was the sister species of the common
ancestor of the species occurring in areas C and D (right). Letters ¼ areas.
Analysis of complex biogeographical patterns has been
hampered by the lack of an algorithm for producing area
cladograms that permits reticulated area relationships. Wiley
(1986, 1988a,b) and Zandee & Roos (1987) introduced what
they called assumption 0 to historical biogeographical studies.
Assumption 0 stipulates that all the information in each
taxon–area cladogram must be used in a biogeographical
analysis and that the area relationships depicted in the final
area cladogram must be logically consistent with the phylogenetic relationships depicted in every taxon–area cladogram
used to construct the area cladogram. Assumption 0 cannot
be fully satisfied for cases of reticulated area relationships
using any method that requires each area to appear only once
in a general area cladogram. Brooks (1990) therefore proposed
modifying one a priori method, BPA, to allow for reticulated
area relationships. Empirical studies using this modification of
BPA suggest that the historical biogeography of most biotas is
a complex and historically unique combination of most, if not
all, of the above six classes of patterns. In particular, it appears
that the majority of areas of endemism have reticulated
histories (Brooks & McLennan, 2001; Brooks et al., 2001;
Green et al., 2002; McLennan & Brooks, 2002; Spironello &
Brooks, 2003; Bouchard et al., in press; Halas et al., 2005). No
other methods of historical biogeography have been modified
to allow for reticulated area relationships. BPA can be
implemented using standard methods in phylogenetic analysis
(Brooks & McLennan, 2001, 2002), but only with laborious
manipulations of the data. All taxon–area cladograms need to
be converted into binary matrices, and each area duplication
requires that the matrix be re-formulated. This re-formulation
produces large numbers of pseudo-missing data codes representing the areas not affected by the unique events requiring
the duplication (Brooks & McLennan, 1991, 2002). Performing such an analysis for complex data sets is thus timeconsuming. In addition, because one cannot specify the
number and types of area duplications that will be needed a
priori, some have been led to believe that the duplication
convention in BPA is idiosyncratic rather than algorithmic
(e.g. Ronquist, 2002; Siddall & Perkins, 2003).
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
Phylogenetic analysis for comparing trees
Figure 3 A taxon–area cladogram showing a particular set of area
relationships involving areas A, B, C and D, stipulated to be the
general pattern (left), and a second taxon–area cladogram of two
major parts, each of which shows the same area relationships as
the first taxon–area cladogram, interpreted as having experienced
a sympatric speciation event (lineage duplication) in the common
ancestor of the clade (right). Letters ¼ areas.
Figure 4 A taxon–area cladogram showing a particular set of area
relationships involving areas A, B, C and D, stipulated to be the
general pattern (left), and a second taxon–area cladogram showing
area relationships among areas A, B, C, D and E, with the addition
in area E of a sister species of the species occurring in area B in the
second taxon–area cladogram, interpreted as an instance of peripheral isolates speciation (allopatric speciation by dispersal)
(right). Letters ¼ areas.
Figure 6 A taxon–area cladogram showing a particular set of area
relationships involving areas A, B, C, and D, stipulated to be the
general pattern (left), and a second taxon–area cladogram showing
the same area relationships as the first taxon–area cladogram,
except that the species occurring in area A also occurs in area D;
and a general area cladogram representing the area relationships
supported by both taxon–area cladograms (right). The species
occurring in areas A and D is interpreted as a case of post-speciation dispersal from area A to area D. Letters ¼ areas.
must be used, and the final area cladogram must be logically
consistent with all input taxon–area cladograms), and does
not presuppose any degree of vicariance. Unlike BPA,
however, this algorithm does not require that the taxon–area
cladograms be converted into matrices, nor does it require
two-stage analysis. The inspiration for this algorithm comes
from considering Venn diagram representations of taxon–
area cladograms as strings of hierarchically organized characters. The algorithm uses the string input to build a tree-like
data structure that can be searched for points of agreement
and disagreement with additional input taxon–area cladograms (Cormen et al., 2001). We assume that the history
of the geographical context of speciation, dispersal and
extinction for any assemblage of clades comprises a long
and complex combination of strings. We also assume that
no single clade contains the complete information, even
about its own particular history. By combining the
partial information from each of many clades, however, we
can reconstruct substantial parts of the biogeographical
record of life by integrating information from multiple
clades. As the hierarchical organization of the strings of
characters stems from phylogenetic relationships, we refer to
this algorithm as phylogenetic analysis for comparing trees
(PACT).
MECHANICS OF THE ALGORITHM
Figure 5 A taxon–area cladogram showing a particular set of area
relationships involving areas A, B, C and D, stipulated to be the
general pattern (left), and a second taxon–area cladogram showing
the same area relationships, with the addition of a species in area A
that is the sister species of the species occurring in area D, indicating that the species occurring in area A arose from two different
ancestors. Area A is thus said to have a reticulated history (right).
Letters ¼ areas.
In this contribution, we present an algorithm for deriving
area cladograms from phylogenies which, like BPA, satisfies
assumption 0 (all information in all taxon–area cladograms
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
The following exemplars represent three different biogeographical scenarios: (1) vicariance-driven diversification, (2)
dispersal-driven diversification and (3) taxon pulse-driven
diversification.
Exemplar 1: Vicariance-driven diversification
Step 1. Convert all phylogenetic trees of interest into taxon–
area cladograms. This is accomplished by replacing the names
of the species with the areas they inhabit.
Step 2. Convert the taxon–area cladograms into Venn diagrams
(Table 1). The Venn diagrams comprise two classes of
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M. Wojcicki and D. R. Brooks
elements, ‘leaves’ and ‘nodes’. A leaf is a single area, and a node
is any grouping of at least two areas. Nodes are represented by
inclusive open [‘(’] and closed [‘)’] parentheses in the Venn
diagram. When a given species inhabits more than one area, a
leaf designates each of the areas and all the areas inhabited by
that species are contained within a single node.
Step 3. Choose any taxon–area cladogram from the set of
taxon–area cladograms to be analysed and determine its
elements. We will refer to this as the template area cladogram.
Template area cladogram (taxon–area cladogram 1 in Table 1):
(A(B(CD)))
PACT reads the Venn diagram representing the second
taxon–area cladogram from left to right, element by element.
Each time a closed parenthesis [‘)’] is encountered, indicating
a grouping of at least two areas, PACT moves backwards,
until it reaches an open parenthesis [‘(’], collecting the data
for the grouping thus created. Next, PACT represents the
grouping signified by the inclusive parentheses by a node,
which is a data structure designating a grouping and which is
used in integrating the taxon–area cladogram with the
template area cladogram. In this case, the first closed
parenthesis is reached after D. PACT then reads backwards
(to the left) collecting leaves and nodes until it reaches the
open parenthesis, in this case C + D. Once the data collection
is complete a node containing the leaves CD replaces the
parentheses around C and D. If we called that node ‘X’, the
Venn diagram would now be (A(BX)). PACT continues
reading to the left, searching for the next open parenthesis.
The next open parenthesis bracket forming a node, ‘Y’,
containing the leaf B and X. The taxon–area cladogram
is now modified to (AY), a grouping that receives its own
node, ‘Z’. The template area cladogram is now represented by
four leaves and three nodes: A, B, C, D, Z[A(B(CD)))],
Y[(B(CD))] and X[(CD)].
Step 4. Select a second taxon–area cladogram. Determine its
elements as in step 1 and then compare each of them with the
template area cladogram.
Template area cladogram: (A(B(CD)))
Taxon–area cladogram 2 (Table 1): (A(B(CD)))
PACT reads the second taxon–area cladogram in the same
manner as it reads the template area cladogram. In this case,
the first closed parenthesis is reached after D. PACT then reads
to the left, collecting leaves and nodes until it reaches the open
Table 1 Nine taxon–area cladograms represented as Venn diagrams
1
2
3
4
5
6
7
8
9
(A(B(CD)))
(A(B(CD)))
(A(CD))
((A(B(CD)))(A(B(CD))))
(A((BE)(CD)))
(A(B(C(DA))))
(A(BE))
(A(CD))
(A(A(B(CD))))
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parenthesis, in this case it collects leaves C + D. Once the data
collection is complete, the parentheses around C and D are
replaced by a node containing the leaves CD. The next open
parenthesis forms a node, containing the leaf B and the node
(CD). Finally, the last open parenthesis forms a node
containing the leaf A and the node (B(CD)). The taxon–area
cladogram is now represented by four leaves and three
nodes: A, B,C, D, (A(B(CD))), (B(CD)) and (CD). The
next step is to integrate the taxon–area cladogram with the
template area cladogram. This is accomplished by maximizing
the matches between their respective leaves and nodes,
and then adding novel elements by creating novel nodes
at appropriate levels in the template area cladogram. Next,
PACT re-reads the elements of the taxon–area cladogram,
comparing them with the elements of the template area
cladogram. Each element in the input taxon–area cladogram
that also occurs in the template area cladogram is designated
with a ‘Y’; any element of the input taxon–area cladogram
that is not found in the template area cladogram is designated
with a ‘N’:
ðAðBðCDÞÞÞ Y; A Y þ ðBðCDÞÞ Y; B Yþ
ðCDÞ Y; C Y þ D Y
This produces the first and most basic rule of the algorithm,
the ‘Y + Y ¼ Y’ rule. In this case, each element of the input
taxon–area cladogram is congruent with an element in the
template area cladogram (all elements in tree 2 are Y’s), so
trees 1 and 2 can be combined completely. The general area
cladogram resulting from the combination of trees 1 and 2 is
thus (A(B(CD))) (Fig. 7).
PACT performs this search in the sequence in which groups
appear in the input taxon–area cladogram to be combined
with those in the template area cladogram. This speeds up the
process of analysing the new cladogram and making combinations and addition to the template. In the case above, for
example, PACT would have recognized that, because
(A(B(CD))) ¼ Y in the input taxon–area cladogram, all
elements in the input taxon–area cladogram corresponded to
elements in the template area cladogram, and would have
made the combination immediately.
Step 5. Add a third taxon–area cladogram (tree 3) and repeat
steps 2 and 3, comparing it with the tree resulting from the
combination of the previous steps.
Template area cladogram: (A(B(CD)))
(A(B(CD))); A + (B(CD)); B + (CD); C + D
Taxon–area cladogram 3 (Table 1): A(CD))
(A(CD)) ) N; A ) Y + (CD) ) Y; C ) Y + D ) Y
Figure 7 PACT-derived area cladogram for taxon–area cladograms 1–4 in Table 1. Letters ¼ areas.
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
Phylogenetic analysis for comparing trees
In this case, there is a mismatch between the template area
cladogram and the input taxon–area cladogram at the initial
level, indicated by N. At this point no decision can be made as
to why the mismatch occurs, so PACT does not produce any
changes and moves on. All remaining elements in taxon–area
cladogram 3 are ‘Y’, so we can combine them with the template
area cladogram. At this point we can begin to consider the
mismatch, but we discover that in this case, the entire input
taxon–area cladogram has been combined with the template
area cladogram. The ‘N’ seems to have disappeared. The reason
for this is that the template area cladogram differs from the
input taxon–area cladogram only by containing information
not found in the input taxon–area cladogram. The absence
of B in the input taxon–area cladogram does not affect
the placement of B in the template area cladogram, and
thus does not affect the topology of the area cladogram. The
general area cladogram for trees 1 + 2 + 3 is still (A(B(CD)))
(Fig. 7).
Step 6. Add the next tree (4) and repeat steps 2–3.
Template area cladogram: (A(B(CD)))
(A(B(CD))); A + (B(CD)); B + (CD); C + D
Taxon–area cladogram 4 (Table 1): (A(B(CD)))(A(B(CD))))
(A(B(CD)))(A(B(CD)))) ) N; (A(B(CD))) ) Y; A ) Y +
(B(CD)) ) Y;
B ) Y + (CD) ) Y;
C ) Y + D ) Y;
(A(B(CD))) ) Y; A ) Y + (B(CD)) ) Y; B ) Y + (CD) ) Y;
C)Y+D)Y
Once again, the only N occurs at the level of the entire input
taxon–area cladogram, and that N disappears once the lower
levels are combined with the template. In this case, the input
taxon–area cladogram appears more complex than the template, but only because it contains two identical representations of the template area cladogram. This is the diagnostic
signature of lineage duplication, sympatric speciation within an
ancestor producing two co-occurring lineages. This does not
affect the pattern of relationships among areas, so the general
area cladogram for trees 1 + 2 + 3 + 4 is still (A(B(CD)))
(Fig. 7).
Step 7. Add the next tree (5) and repeat steps 2–3.
Template area cladogram: (A(B(CD)))
(A(B(CD))); A + (B(CD)); B + (CD); C + D
Taxon–area cladogram 5: (A((BE)(CD)))
(A((BE)(CD))) ) N; A ) Y + ((BE)(CD)) ) N; (BE) ) N +
(CD) ) Y; B ) Y + E ) N; C ) Y + D ) Y
Reading from the left, PACT encounters (BE); B in the input
taxon–area cladogram is Y, and because B and BE are
connected at the same node, both B’s can be combined. E,
which is not found in the template area cladogram, is thus a
novel (‘N’) element, and added to the template area cladogram
at that point, creating a (BE) grouping (a new node) in the
template. The next closed parenthesis is encountered at (CD);
both C and D as well as the grouping CD are Y in the template
area cladogram, so there is no change at this point. The next
closed parenthesis is ((BE)(CD)). This combination already
exists in the template area cladogram due to the modification
made earlier in which E was added to the template area
cladogram. Finally, PACT encounters A, which is Y, and is
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
combined with the template. The resulting area cladogram is
(A((BE)(CD))) (Fig. 8).
Step 8. Add the next tree (6) and repeat steps 2–3, comparing it
with the tree produced by 1 + 2 + 3 + 4 + 5 (Fig. 8).
Template area cladogram: (A((BE)(CD))))
(A((BE)(CD)))); A + ((BE)(CD)); (BE) + (CD); B + E; C + D
Taxon–area cladogram 6: (A(B(C(DA))))
(A(B(C(DA)))) ) N; A ) Y* + (B(C(DA))) ) N; B ) Y +
(C(DA)) ) N; C ) Y + (DA) ) N; D ) Y + A ) Y*
This case is directly analogous to the previous one. Reading
from left to right, the algorithm initially encounters (AD),
which is not found in the template area cladogram (‘N’). The
‘A’ in (AD) is thus considered a novel element (‘N’) and the
input taxon–area cladogram is modified to
ðAðBðCðDAÞÞÞÞ N; A Y þ ðBðCðDAÞÞÞ N; B Yþ
ðCðDAÞÞ N; C Y þ ðDAÞ N; D Y þ A N
Next, PACT encounters (CD) in the template tree and
(C(DA)) in the input taxon–area cladogram tree. C is a
common element in both cladograms, and can be combined.
This leaves D in the template area cladogram and (DA) in
the input taxon–area cladogram connected at the same node.
This means that both D’s can be combined, creating a
(C(DA)) grouping (and new node) in the template area
cladogram. At the next level, we find the grouping (BE) in
the template area cladogram and the leaf B in the input
taxon–area cladogram. As in step 7, above, both B’s can be
combined, leaving the grouping (BE) in the template area
cladogram intact. At the next level, we encounter leaf A in
both cladograms, which are combined. This confirms
PACT’s initial assessment of Y for leaves A (basal most),
B, C and D. The input taxon–area cladogram contains a
novel grouping (DA) not found in the template and the
template contains a grouping (BE) not seen in the input
taxon–area cladogram. The resulting area cladogram is
(A((BE)(C(DA)))) (Fig. 9).
The situation presented by taxon–area cladograms 5 and 6,
above, represent cases of what we call the ‘Y + YN ¼ YN’ rule.
For clade 5, ‘Y’ ¼ B and ‘YN’ ¼ BE; for clade 6 ‘Y’ ¼ D and
‘YN’ ¼ DA. Next, we consider taxon–area cladograms 7 and 8
in Table 1 on their own, in order to demonstrate a final
combination rule.
Step 9. Choose one area cladogram to be the template (we
choose 7 in this case, but one could also choose 8 without
changing the results).
Taxon–area cladogram 7: (A(BE))
A(BE)); A + (BE); B + E
Figure 8 PACT-derived area cladogram for taxon–area cladograms 1–5 in Table 1. Letters ¼ areas.
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M. Wojcicki and D. R. Brooks
Figure 9 PACT-derived area cladogram for taxon–area cladograms 1–6 in Table 1. Letters ¼ areas.
Taxon–area cladogram 8: (A(CD))
(A(CD)) ) N; A ) Y + (CD) ) N; C ) N + D ) N
‘A’ is the only common element (Y) in both taxon–area
cladograms. The groups (BE) and (CD) contain no elements in
common, but each is connected at a node with A. In this case,
although many dichotomous area cladograms consistent with
the data are possible, we have no evidence supporting any
particular one. Therefore, the resultant area cladogram is
(A(BE)(CD)) (Fig. 10). This is an example of what we call the
‘YN + YN ¼ YNN’ rule, where A ¼ ‘Y’, (BE) ¼ ‘N’ and
(CD) ¼ ‘N’.
Step 10. We can now combine the area cladogram for taxon–
area cladograms 7 and 8 (Fig. 10) with the template area
cladogram (Fig. 9).
Template area cladogram for clades 1–6: (A((BE)(C(DA))))
Area cladogram for clades 7–8: (A(BE)(CD))
(A(BE)(CD)) ) N; A ) Y + (BE) ) Y + (CD) ) N; B ) Y +
E ) Y; C ) Y + D ) Y
D in the area cladogram for clades 7–8 and (DA) in the
template area cladogram is a case of the ‘Y + YN ¼ YN’ rule,
so D in the area cladogram for areas 7–8 is combined with D in
(DA) in the template area cladogram); therefore (CD) in the
area cladogram for clades 7–8 is combined with (C(DA)) in the
template. A and (BE) are both Y, so they are combined. At this
point, all elements in the area cladogram for clades 7–8
have been integrated with the template area cladogram
(A((BE)(C(DA)))) (Fig. 9).
Step 11. Finally, we add taxon–area cladogram 9 in Table 1 to
the template area cladogram.
Template area cladogram: (A((BE)(C(DA))))
(A((BE)(C(DA)))); A + ((BE)(C(DA))); (BE) + (C(DA));
C + (DA); B + E; D + A
Taxon–area cladogram 9: (A(A(B(CD))))
(A(A(B(CD)))) ) N;
A ) Y* + A(B(CD)) ) N;
A ) Y* + (B(CD)) ) N; B ) Y + (CD) ) N; C ) Y + D ) Y
Once again, reading from left to right, PACT first encounters (CD). We begin with CD in the input taxon–area
cladogram + (C(DA)) in the template area cladogram. This
is a case of the ‘Y + YN ¼ YN’ rule, so D in the taxon–area
Figure 10 PACT-derived area cladogram for taxon–area cladograms 7–8 in Table 1. Letters ¼ areas.
760
cladogram is combined with (DA) in the template area
cladogram. Next, (B(CD)) in the input taxon–area cladogram,
now considered (B(C(DA))), is connected at the same node in
the template area cladogram as ((BE)(C(DA))). (C(DA)) is the
same in both cases, so they are combined, leaving B and (BE),
another case of the ‘Y + YN ¼ YN’ rule. At the next node, the
template area cladogram and the taxon–area cladogram are
both A, so they are combined.
Finally, the input taxon–area cladogram has an additional
A, originally designated Y, because A occurs twice in the
template area cladogram and twice in the taxon–area cladogram. At this point, we have already accounted for both A’s in
the template area cladogram, so PACT must still account for
the second A in the input taxon–area cladogram. One
possibility is that the two A’s in the taxon–area cladogram
are paraphyletic because they represent an episode of sympatric speciation (lineage duplication), in which case both could
be combined. PACT does not combine these A’s, for a
methodological and a biological reason, respectively. First,
single areas are not sufficient grounds for grouping or
combining areas. PACT will not create groupings of areas in
the absence of any evidence of groupings. Secondly, sympatric
speciation is not the only possible explanation for the
paraphyletic status of the area A’s. Combining the two A’s
would be tantamount to making a choice in favour of
sympatric speciation in the face of ambiguity, rather than
waiting for additional data (more taxon–area cladograms) to
resolve the ambiguity.
This provision in PACT prevents over-combining data; we
call it the ‘Y(Y)’ ¼ ‘Y(Y)’ or ‘Y(Y) „ Y’ rule, or ‘do not
combine single common areas attached to different nodes’. All
current methods, including secondary BPA, violate this rule.
Three short exemplars underscore the importance of this final
rule. Figure 11 depicts two taxon–area cladograms, which
share only a single area (A). Because there are no area
groupings in common, PACT does not make any combinations.
The same is true for the exemplar in Fig. 12, in which each
taxon–area cladogram contains the same areas, but has no
groupings of areas in common; once again, PACT makes no
combinations.
By representing these sorts of ambiguity with duplications,
PACT differs from other methods of historical biogeography,
which may create ambiguity by over-combining data. In
matrix representation methods, including BPA, this is called
inclusive ORing, which is known to create other systemic
analytical problems (Cressey et al., 1983; Brooks & McLennan,
1991, 2002). Consider the taxon–area cladograms ((AC)B) + (A(AB)). PACT produces (A((AC)B)) for these two
taxon–area cladograms. If we combine the A’s in taxon–area
cladogram 2, the result would be ((AC)B). Now add a third
taxon–area cladogram, (A(CB)). The PACT result is still
(A((AC)B)), supporting an interpretation that all three taxon–
area cladograms are parts of a single complex pattern, one part
of which is missing in each. If we had combined the A’s in
taxon–area cladogram 2, however, the result would be an
unresolved polytomy (ACB). At this point, all methods,
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
Phylogenetic analysis for comparing trees
Figure 11 PACT does not make combinations based on single areas. ‘A’ is shared between the two taxon–area cladograms on the left, but
the other elements are unique; thus, there is no evidence to support combining the ‘A’s’. The PACT-derived area cladogram is shown on the
right. Letters ¼ areas.
Figure 12 PACT does not make combinations based on single areas. All four areas are shared between the two taxon–area cladograms on
the left, but their relative relationships are different; thus, there is no evidence supporting any combinations, producing the PACT-derived
area cladogram on the right. Letters ¼ areas.
including secondary BPA, would infer that the taxon–area
cladograms had no information in common, although cladistic
(a priori) methods could invoke various assumptions, probabilities, costs, or likelihoods to support one of the possible
resolutions of the polytomy.
PACT thus treats the basal-most A as a new element added
to the template area cladogram, which is modified to
(A(A((BE)(C(DA))))) (Fig. 13). All available taxon–area cladograms have now been incorporated, resulting in the final area
cladogram (Fig. 13; Table 2 summarizes PACT). Some may
notice at this point that either of the two basal A’s in taxon–
area cladogram 9 could be considered the same as the basal A
in the template area cladogram. We will return to this issue
later, but at this point we will note only that this ambiguity
does not affect the construction of the area cladogram, only the
mapping of particular species onto the area cladogram when
we begin to derive evolutionary inferences from the area
cladogram.
Exemplar 2: Dispersal-driven diversification
We believe that a general method for historical biogeographical
analysis should be able to distinguish biotic diversification
driven primarily by vicariance from those driven primarily by
dispersal, rather than simply searching for support for
vicariance. We next present a two-clade exemplar, in which
each clade colonized the same set of areas (B, C, D and E) from
different source areas (A and F). We explain the dispersal
scenario supported by this exemplar more fully in the
discussion.
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
Figure 13 PACT-derived area cladogram for taxon–area cladograms 1–9 in Table 1. Letters ¼ areas.
Template area cladogram (Fig. 14): (A(B(D((CE)(CD)))));
A + (B(D((CE)(CD)))); B + (D((CE)(CD))); D + ((CE)(CD));
(CE) + (CD); C + E; C + D
Taxon–area cladogram 2 (Fig. 15): (F(C(DB)((D(BE))(CD))));
F + (C(DB)((D(BE))(CD)));
C + (DB) + ((D(BE))(CD));
(D(BE)) + (CD); D + (BE); B + E; C + D
Reading taxon–area cladogram 2 from left to right, PACT
reaches the first closed parenthesis following B and reads
backwards, forming node[DB]. Taxon–area cladogram 2 is
modified to (F(C node[DB]((D(BE))(CD)))). The closest D
and B are a node apart in the template area cladogram and
they are both single areas (leaves) grouped with nodes.
Therefore D ) N, B ) N and node[DB] ) N. PACT cannot
place this node in the template area cladogram at this point,
so there is no change to the template area cladogram. The
next closed parenthesis in taxon–area cladogram 2 follows E.
Reading backwards the node[BE] is formed and taxon–area
cladogram 2 is modified to (F(C node[DB]((D node
[BE])(CD)))). The closest B and E are several nodes apart
in the template area cladogram. B is a leaf grouped with a
node and E is a leaf grouped with a leaf C. If node[BE]
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M. Wojcicki and D. R. Brooks
Table 2 Summary of the PACT algorithm
1. Convert all phylogenies to taxon–area cladograms.
2. Convert all taxon–area cladograms to Venn diagrams.
3. Choose any taxon–area cladogram from the set of taxon–area cladograms to be analysed, and determine its elements. This will be the template area
cladogram. The initial choice of a template area cladogram does not affect the final outcome (the analysis will proceed more quickly if you begin with
the most complex taxon–area cladogram).
4. Select a second taxon–area cladogram. The order in which you add taxon–area cladograms does not affect the final outcome (the analysis will
proceed more quickly if you begin with the most complex taxon–area cladograms). Determine its elements as in step 1. Then document which
elements in the second tree occur in the template tree (denoted by ‘Y’), and which do not (denoted by ‘N’). Each ‘Y’ indicates a match with previous
pattern, and these are combined. Each ‘N’ is a new element, and is attached to the template area cladogram at the node where it is linked with a Y. To
get to this point, we invoke two rules:
‘Y + Y ¼ Y’ (combine common elements) as long as they are connected at the same node
‘Y + N ¼ YN’ (add novel elements to the template area cladogram at the node where they first appear)
5. Once the novel elements in the second taxon–area cladogram have been added to the template area cladogram, see if any of them can be further
combined. At this point, we invoke three additional rules:
‘(Y(Y) ¼ (Y(Y)’ (do not combine Y’s if they are attached at different nodes on the template area cladogram)
‘Y + YN ¼ YN’ (Y is part of group YN)
‘YN + YN ¼ YNN’ (Y is the same for each, but each N is different)
6. Add the remaining taxon–area cladograms by repeating steps 4–5 for all remaining taxon–area cladograms. When novel elements (groups of more
than one area) are combined with an template area cladogram and their relationships with other groups existing in the template area cladogram are
not accounted for in the input taxon–area cladogram – they are denoted as a novel element to these unaccounted for groups which may, in fact, be
grouped together with them on a later occasion.
would be in a node with C then it would be a case of
Y + YN ¼ YN, where B is a new element. PACT reads to
the next closed parenthesis and backwards resulting in
node[D + BE], therefore the previous combination is a case
of the ‘YN + YN ¼ YNN’ rule and results in node[BCE].
The template area cladogram is modified to contain
node[BCE]. Leaf D and node[BCE] are a node apart in
the template area cladogram therefore the D grouped with
node[BCE] in taxon–area cladogram 2 is a new element and
is a case of Y + YN ¼ YN. Taxon–area cladogram 2 is
modified to (F(C node[DB](node[D + BCE](CD)))) and the
template area cladogram is also modified at node[BCE] to
node[D + BCE] and all the nodes that contained node[BCE]. The next closed parenthesis is reached after D,
forming node[CD]. C ) Y, D ) Y and node[CD] ) Y in the
template area cladogram; therefore, it is not changed and
taxon–area cladogram 2 is modified to (F(C node[DB]
(node[D + BCE] node[CD]))). The next closed parenthesis
is reached after node[CD], forming node[DBCE + CD],
node[CD] ) Y, node[D + BCE] ) Y and node[CD + DBCE] ) Y in the template area cladogram; therefore, it is
not changed and taxon–area cladogram 2 is modified to
Figure 14 Taxon–area cladogram for a group colonizing areas B,
C, D and E from area A. Letters ¼ areas.
762
Figure 15 Taxon–area cladogram for a group colonizing areas
B, C, D and E from area F. Letters ¼ areas.
(F(C node[DB] node[DBCE + CD])). Reading to the left,
the next closed parenthesis is node[C + DB + DBCECD].
C ) N, node[DB] ) N and node[DBCECD] ) Y. In the
template area cladogram, node[DBCECD] is grouped
with leaf D. These are combined, forming node
[C + DB + D + DBCECD]. The combination of node[DB] + leaf D is simplified to node[DB]; the template area
cladogram is modified at node[D + DBCECD] to node
[DB + C + DBCECD] and taxon–area cladogram 2 is
modified to (F node[DB + C + DBCECD]). The last closed
parenthesis forms node[F + DBCDBCDCD]. F ) N and
node[DB + C + DBCECD] ) Y in the template area cladogram. In the template area cladogram node[DB + C + DBCECD] is grouped with leaf B. Therefore, the combination
results in node[F + B + DBCDBCDCD]. In the template
area cladogram, node[B + DBCDBCDCD] is modified to
node[F + B + DBCDBCDCD]. PACT is finished combining
taxon–area cladogram 2 with the template, resulting in the
new template area cladogram (A(BF((DB)C((D(EBC))(DC))))))
(Fig. 16).
The BPA result for this exemplar, which also satisfies
assumption 0, is slightly different (Fig. 17). This is because
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
Phylogenetic analysis for comparing trees
BPA roots both clades at the base of the area cladogram. This
implies that both clades became associated with the areas in
which they occur at the same time. When we make that
assumption, we obtain the area cladogram shown in Fig. 17.
This result combines the basal-most B from clade 1 with the
BC grouping in clade 2, rather than combining the basal-most
C from clade 1 with the BC grouping in clade 2. While this is a
possibility, there is no direct evidence supporting such an a
priori rooting assumption, based on only two taxon–area
cladograms, so PACT produces a more conservative, and
preferable, result. BPA could produce the same result as PACT
if at least three clades were analysed, two of which showed an
unambiguous rooting with area A.
Exemplar 3: Taxon pulse-driven diversification
All a priori and a posteriori methods, including secondary
BPA, assume that general patterns are the result of
speciation resulting from the formation of geographical
barriers (vicariance) and that speciation resulting from active
dispersal across barriers does not produce general patterns,
because the ability to disperse across existing barriers and to
form founder populations should be constrained by cladespecific vagility and population biology. The exemplars
depicted in Table 1 all conform to this general expectation.
Wiley (1981) noted that some circumstances, such as
colonization of islands, might produce general distribution
patterns based on dispersal rather than vicariance, and
Endler (1982) suggested that such correlated dispersal
patterns might be common. More recently, Bouchard &
Brooks (in press) demonstrated that the evolution of
flightlessness in insects endemic to areas within the Australian Tropical Rainforest had no effect on how widespread
species were or on modes of speciation.
Erwin (1979, 1981, 1985, 1991) and Erwin & Adis (1982)
pointed out that the maximum vicariance model does not
account for common ancestors becoming widespread enough
to be affected by vicariance, or for post-vicariance dispersal
by multiple members of the same biota setting the stage for
new vicariant events. What happens, however, when a
previously existing barrier, one that produced vicariant
Figure 16 Area cladogram for taxon–area cladograms shown in
Figs 13 and 14. Letters ¼ areas.
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
Figure 17 BPA area cladogram for taxon–area cladograms shown
in Figs 13 and 14. Letters ¼ areas.
speciation among members of multiple clades, breaks down?
Erwin asserted that this should produce multiple clades
dispersing from their areas of origin, i.e. general biogeographical distribution patterns based on dispersal, or biotic
expansion, including many widespread taxa. Halas et al.
(2005) recently suggested some protocols for discerning
taxon pulse-driven diversification, or complex biotic evolution driven by biotic expansion alternating with episodes of
vicariance. In part, their protocol requires a method for
generating area cladograms that is sensitive to complex
biogeographical histories, widespread taxa, and analysis of
multiple clades. They also noted that a rigorous assessment
of the generality of taxon pulse radiations could not be
undertaken easily in the absence of an efficient algorithm for
analysing multiple clades. We next present a 17-clade
exemplar (Table 3) that embodies a taxon pulse radiation,
to demonstrate that PACT is the kind of efficient algorithm
discussed by Halas et al. In this exemplar, we use a
telegraphic version of the discussions of the first two
exemplars, to save space. For example, when we state that
an element of an input taxon–area cladogram ‘is combined’,
it should be understood that we mean ‘is combined with the
template’.
Step 1.
Template area cladogram (taxon–area cladogram 1 Table 3):
(((TH)(IS))(R(E(AL))))
Taxon–area cladogram 2 (Table 3): (((TH)(IS))(T(R(EE))))
(1) T ) Y;H ) Y; TH ) Y; I ) Y; S ) Y; IS ) Y;
TH + IS ) Y,
so
((TH)(IS))
is
combined.
(2)
E ) Y + E ) Y, so (EE) becomes E. R ) Y but (RE) ) N.
In the template area cladogram, E is grouped with AL and R
is grouped with EAL, so R and E are single areas a node
apart. PACT cannot determine if either or both are the same
as E + R in the input taxon–area cladogram, so they are
considered new areas, forming a new element RE. At this
point, we do not know where RE it fits in the template area
cladogram. (3) T ) N, so this is a new element and there is
still not enough information to place T and RE. (4) When
the PACT considers THIS + TRE, TRE can be placed at the
same node as THIS + REAL. TRE and REAL are novel
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M. Wojcicki and D. R. Brooks
Table 3 Taxon–area cladograms for 17 clades and eight areas
(called T, H, I, S, R, E, A and L), represented as Venn diagrams
Clade
Clade
Clade
Clade
Clade
Clade
Clade
Clade
Clade
Clade
Clade
Clade
Clade
Clade
Clade
Clade
Clade
1 (((TH)(IS))(R(E(AL))))
2 (((TH)(IS))(T(R(EE))))
3 (((TH)(IS))((IS)(R(E(AL)))))
4 (((TH)(IS))((IS)(T(R(EE)))))
5 (((TH)(IS))((T(HE))(T(R(EE)))))
6 (((TH)(IS))((T(HE))(R(E(AL)))))
7 (((TH)(IS))((IS)((T(HE))(R(E(AL))))))
8 ((TH)((IS)((T(HE))(T(R(EE))))))
9 ((T(HE))((R((E(AL)))(T(R(EE)))))
10 ((R(E(AL)))(T(R(EE))))
11 ((T(IS))(R(E(AL))))
12 (((TH)(IS))(T(RE)))
13 ((TH)((IS)(R(E(AL)))))
14 (H((IS)(T(R(EE)))))
15 ((T(HE))(T(R(EE))))
16 (T((IS)((HE)(T(R(EE))))))
17 ((H(IS))(T(R(EE))))
elements in relation to each other and are marked as such.
The template area cladogram is modified to (((TH)(IS))
(T(RE))(R(E(AL)))).
Step 2.
Template area cladogram: (((TH)(IS))(T(RE))(R(E(AL))))
Taxon–area cladogram 3 (Table 3): (((TH)(IS))((IS)
(R(E(AL)))))
(1) T ) Y; H ) Y; TH ) Y; I ) Y; S ) Y; IS ) Y;
TH + IS ) Y: ((TH)(IS)) is combined. I ) N; S ) N;
IS ) N; No known placement at this point. (2) A ) Y;
L ) Y; AL ) Y; E ) Y; E + AL ) Y; R ) Y; R + EAL ) Y
combined and form (R(E(AL))) in the template area cladogram. (3) IS + REAL, now IS can be placed at same node as
REAL. (4) THIS + ISREAL ) N; the information here is that
IS is grouped with REAL but not with THIS therefore THIS,
REAL and IS cannot share the same node. (5) Does TRE share
a node with IS and REAL or THIS and ISREAL? It is not
known at this point. IS and REAL are grouped together but IS
is marked as a novel element where the relationship with TRE
is unknown (i.e. it is possible that TRE may be grouped with
either IS and REAL or may remain as it is in the trichotomy of
ISREAL, TRE and THIS). The template area cladogram is thus
modified to (((TH)(IS))((T(RE))(IS)(R(E(AL))))).
Step 3.
Template area cladogram: (((TH)(IS))((IS)(T(RE))(R
(E(AL)))))
Taxon–area cladogram 4 (Table 3): (((TH)(IS))((IS)(T
(R(EE)))))
(1) T ) Y;H ) Y; TH ) Y; I ) Y; S ) Y; IS ) Y;
TH + IS ) Y: ((TH)(IS)) is combined. (2) I ) Y; S ) Y;
IS ) Y. (3) E ) Y; E ) Y; E + E ¼ E; R ) Y; R + E ) Y;
T + RE ) Y. (4) IS + TRE ) N; IS and TRE share the same
764
node, therefore IS is no longer marked as a novel element with
no relationship to TRE forming ((IS)(T(RE))(R(E(AL)))).
ISTRE is therefore represented as ISTREREAL in the template
area cladogram. (5) THIS + ISTRE-N, but ISTRE is represented by the newly formed ((IS)(T(RE))(R(E(AL)))) in the
template area cladogram; therefore, THIS + ISTREREAL ) Y.
The template area cladogram is modified to (((TH)(IS))((IS)
(T(RE))(R(E(AL))))).
Step 4.
Template area cladogram: (((TH)(IS))((IS)(T(RE))(R
(E(AL)))))
Taxon–area cladogram 5 (Table 3): (((TH)(IS))((T(HE))(T
(R(EE)))))
(1) T ) Y;H ) Y; TH ) Y; I ) Y; S ) Y; IS ) Y;
TH + IS ) Y: ((TH)(IS)) ) Y and is combined. (2) H ) N;
E ) Y; HE ) N; in the template area cladogram one E is
grouped with AL, which would immediately lead to this E
being N if these were all the Es in the template area
cladogram, but there is also E grouped with R. At this point
it is not known whether there is R in cladogram 5 therefore
no decision is made. (3) T ) Y, but T is grouped with RE,
no decision has been made as to whether R is in cladogram
5, so no decision can be made at this point. (4) E ) Y;
E ) Y; E + E ¼ E; R ) Y; R + E ) Y; and R has been found
in cladogram 5 that is also grouped with E, therefore the E
grouped with H in cladogram 5 is considered N. (5) T ) Y,
(T(RE)) ) Y; T has been found in cladogram 5 grouped
with RE as it is in the template area cladogram therefore T
grouped with HE in cladogram 5 is also set to N. (6)
(T(HE)) + (T(RE)); (T(HE)) is added to the template area
cladogram at the same node as (T(RE)). (7) THIS + THETRE ) N; THIS and THETRE are more than one level apart
and cannot be added. REAL (and all its components) are
not represented in cladogram 5, therefore the novel element
THE is marked as novel with its relationship to REAL and
IS unknown. The template area cladogram is thus modified
to (((TH)(IS))((IS)((T(HE))(T(RE)))(R(E(AL)))).
Step 5.
Template area cladogram: (((TH)(IS))((IS)(T(HE)) (T(RE))
(R(E(AL))))
Taxon–area cladogram 6 (Table 3): (((TH)(IS))((T(HE))(R
(E(AL)))))
(1) T ) Y;H ) Y; TH ) Y; I ) Y; S ) Y; IS ) Y;
TH + IS ) Y: ((TH)(IS)) ) Y and is combined. (2) H ) Y;
E ) Y;(HE) ) Y; T ) Y; (T(HE)) ) Y and is combined. (3)
R ) Y; E ) Y; A ) Y; L ) Y; (AL) ) Y; (E(AL)) ) Y;
(R(E(AL))) ) Y and is combined. (4) ((T(HE))(R(E
(AL)))) ) N, (T(HE)) shares a node with (T(RE)) in the
template area cladogram, but in cladogram 6 (T(HE)) shares a
node with (R(E(AL))). In the template area cladogram
(R(E(AL))) shares a node with (T(HE)) + (T(RE)) and THE
is no longer marked as a novel element with no known
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
Phylogenetic analysis for comparing trees
relationship to REAL. The template area cladogram is thus
modified to (((TH)(IS))((IS)((T(RE))(T(HE))((R(E(AL)))))
Step 6.
Template area cladogram: (((TH)(IS))((IS)((T(RE))(T(HE))
((R(E(AL)))))
Taxon–area
cladogram
7
(Table 3):
(((TH)(IS))((IS)((T(HE))(R(E(AL))))))
(1) T ) Y;H ) Y; TH ) Y; I ) Y; S ) Y; IS ) Y;
TH + IS ) Y: ((TH)(IS)) ) Y and is combined. (2) I ) Y;
S ) Y; (IS) ) Y and is combined. (3) H ) Y; E ) Y;
(HE) ) Y; T ) Y; (T(HE)) ) Y and is combined. (4) A ) Y;
L ) Y; (AL) ) Y;E ) Y; (E(AL)) ) Y; R ) Y; (R(E(AL))) ) Y
and is combined. (5) ((T(HE)(R(E(AL)))) ) N but
((T(HE))(R(E(AL)))(T(RE))) is in the template area cladogram; THE and REAL are not grouped together although they
are at the same level because THE is no longer a novel element
in relation to REAL (see step 5) and THEREAL is represented
as THEREALTRE in the area cladogram. ((IS)((T(HE))(R
(E(AL))))) ) N but THEREAL is represented as THEREALTRE
in the template area cladogram and therefore IS + THEREAL
is represented as IS + THEREALTRE in the template area
cladogram. (6) THIS + ISTHEREAL ) N; but ISTHEREAL is
represented as ISTHEREALTRE in the template area cladogram and THIS + ISTHEREALTRE ) Y. The template area
cladogram is unchanged.
Step 7.
Template area cladogram: (((TH)(IS))((IS)((T(RE))(T(HE))
((R(E(AL)))))
Taxon–area cladogram 8 (Table 3): ((TH)((IS)((T(HE))(T(R(EE))))))
(1) T ) Y; H ) Y; (TH) ) Y and is combined. (2) I ) Y;
S ) Y; (IS) ) Y and is combined. (3) H ) Y; E ) Y;
(HE) ) Y; T ) Y; (T(HE)) ) Y and is combined. (4) E ) Y;
E ) Y; E + E ¼ E; R ) Y; (RE) ) Y; T ) Y; (T(RE)) ) Y and
is combined. (5) ((T(HE)(T(RE))) ) N; one node apart but
neither TRE nor THE are novel in relationship to each other,
their relationship has been resolved and therefore there is
no change; THETRE is represented by THEREAL. (6)
((IS)((T(HE))(T(RE)))) is represented as ISTHEREALTRE in
the template area cladogram. (7) TH + ISTHETRE is represented in THIS + ISTHEREALTRE. The template area cladogram is unchanged.
R ) Y; (R(E(AL))) ) Y and is combined. (3) E ) Y; E ) Y;
E + E ¼ E; R ) Y; (RE) ) Y;T ) Y; (T(RE)) ) Y and is
combined. (4) ((T(RE))(R(E(AL)))) ) N; this grouping is
connected to the template area cladogram at the same node as
(T(HE) + (R(E(AL)) + (T(RE)), so (R(E(AL)) and (T(RE))
can be combined and they are no longer known as novel
elements in relation to each other as they had been marked in
step 1. The template area cladogram is modified to
(((TH)(IS)((IS)((T(HE))((R(E(AL)))(T(RE)))))).
Step 9.
Template area cladogram: (((TH)(IS)((IS)((T(HE))(R(E(AL)))(T(RE))))))
Taxon–area cladogram 10 (Table 3): ((R(E(AL)))(T(R(EE))))
(1) A ) Y; L ) Y; (AL) ) Y and is combined. (2) E ) Y
(E(AL)) ) Y; R ) Y; (R(E(AL))) ) Y and is combined. (3)
E ) Y; E ) Y; E + E ¼ E; R ) Y; (RE) ) Y;T ) Y;
(T(RE)) ) Y and is combined. (4) ((R(E(AL)))(T(R(EE))))
) Y and is combined. The template area cladogram is
unchanged.
Step 10.
Template area cladogram: (((TH)(IS)((IS)((T(HE))(R(E(AL)))(T(RE))))))
Taxon–area cladogram 11 (Table 3): ((T(IS))(R(E(AL))))
(1) I ) Y; S ) Y; (IS) ) Y; T ) Y; (T(IS)) ) N, but T
connects at the same node as (TH), making this an example of
the Y + YN ¼ YN rule, thus TIS is represented as THIS in the
template area cladogram. (2) A ) Y; L ) Y; (AL) ) Y;E ) Y;
(E(AL)) ) Y; R ) Y; (R(E(AL))) ) Y and is combined. (3)
TIS + REAL are more than one node apart and are represented
as THIS + ISTHEREALTRE in the template area cladogram.
The template area cladogram does not change.
Step 11.
Template
area
cladogram:
(((TH)(IS)((IS)((T(HE))
(R(E(AL)))(T(RE))))))
Taxon–area cladogram 12 (Table 3): (((TH)(IS))(T(RE)))
(1) T ) Y;H ) Y; (TH) ) Y; I ) Y; S ) Y; (IS) ) Y;
(TH) + (IS) ) Y: ((TH)(IS)) ) Y and is combined. (2)
T ) Y; R ) Y; E ) Y; (RE) ) Y; (T(RE)) ) Y and is combined. (3) THIS + TRE are more than one node apart in and
are represented as THIS + ISTHEREALTRE in the template
area cladogram. The template area cladogram is unchanged.
Step 8.
Template area cladogram: (((TH)(IS)((IS)((T(HE))(R(E
(AL)))(T(RE)))))
Taxon–area cladogram 9 (Table 3): ((T(HE))((R(E(AL)))
(T(R(EE)))))
(1) H ) Y; E ) Y; (HE) ) Y; T ) Y; (T(HE)) ) Y and is
combined. (2) A ) Y; L ) Y; (AL) ) Y; E ) Y; (E(AL)) ) Y;
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
Step 12.
Template
area
cladogram:
(((TH)(IS)((IS)((T(HE))
(R(E(AL)))(T(RE))))))
Taxon–area cladogram 13 (Table 3): ((TH)((IS)(R(E(AL)))))
(1) T ) Y; H ) Y; (TH) ) Y and is combined. (2) I ) Y;
S ) Y; (IS) ) Y and is combined. (3) A ) Y; L ) Y; (AL) ) Y;
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M. Wojcicki and D. R. Brooks
E ) Y; (E(AL)) ) Y; R ) Y; (R(E(AL))) ) Y and is combined.
(4) ((IS) and (R(E(AL)))) are more than one node apart in the
template and are represented by ((IS)((T(HE))((R(E(AL)))
(T(RE))))). (5) TH + ISREAL are more than one node apart in
the template and are represented by THIS + ISTHEREALTRE.
The template area cladogram is unchanged.
Step 13.
Template
area
cladogram:
(((TH)(IS)((IS)((T(HE))
(R(E(AL)))(T(RE))))))
Taxon–area cladogram 14 (Table 3): (H((IS)(T(R(EE)))))
(1) I ) Y; S ) Y; (IS) ) Y and is combined. (2) E ) Y; E ) Y;
E + E ¼ E; R ) Y; (RE) ) Y; T ) Y; (T(RE)) ) Y and is
combined. (3) IS + TRE ) N; more than one node apart and
represented in ISTHEREALTRE. (4) H ) Y; H + ISTRE ) N; if
ISTRE is represented by ISTHEREALTRE, H represented in THIS;
therefore the combination is represented in THIS + ISTHEREALTRE. The template area cladogram is unchanged.
Step 14.
Template area cladogram: (((TH)(IS)((IS)((T(HE))(R(E(AL)))(T(RE))))))
Taxon–area cladogram 15 (Table 3): ((T(HE))(T(R(EE))))
(1) H ) Y; E ) Y; (HE) ) Y; T ) Y; (T(HE)) ) Y and is
combined. (2) E ) Y; E ) Y; E + E ¼ E; R ) Y; (RE) ) Y;
T ) Y;(T(RE)) ) Y and is combined. (3) ((T(HE)(T(RE))) )
N; this combination is one node apart in the template, but the
relationship of TRE and THE is resolved (only if one of these
were novel with an unknown relationship to the other would
such a combination be made as a polytomy). The template area
cladogram is unchanged.
Step 15.
Template area cladogram: (((TH)(IS)((IS)((T(HE))(R(E(AL)))(T(RE))))))
Taxon–area cladogram 16 (Table 3): (T((IS)((HE)(T(R(EE))))))
(1) I ) Y; S ) Y; (IS) ) Y and is combined. (2) H ) Y;
E ) Y; (HE) ) Y and is combined. (3) E ) Y; E ) Y;
E + E ¼ E; R ) Y; (RE) ) Y; T ) Y;(T(RE)) ) Y and is
combined. (4) ((HE)(T(RE))) ) N; are more than one node
apart but are represented in THEREALTRE and is combined.
(5) IS + HETRE is therefore represented in IS + THEREALTRE and is combined. (6) T ) Y; T + ISHETRE is represented
in THIS + ISHETRE and is combined. The template area
cladogram is unchanged.
(1) I ) Y; S ) Y; (IS) ) Y; H ) Y; H(IS) ) N, but H + IS is
represented as TH + IS in the template area cladogram and is
combined. (2) E ) Y; E ) Y; E + E ¼ E; R ) Y; (RE) ) Y;
(T(RE)) ) Y and is combined. (3) HIS + TRE is represented
as THIS + ISTHEREALTRE in the template and is combined.
The template area cladogram is unchanged.
The area cladogram derived by PACT for the 17 taxon–area
cladograms listed in Table 3 is shown in Fig. 18.
DISCUSSION
A number of features make PACT an efficient and robust
algorithm. First, one need not convert taxon–area cladograms
into binary matrices for analysis. Secondly, at any given step,
PACT compares only two trees, the template area cladogram
and the taxon–area cladogram being integrated with the
template. Thirdly, area combinations and duplications arise
naturally from the analysis; reticulated area relationships are
neither ruled out, as in all a priori methods, primary BPA and
CCA, nor do they have to be inferred post hoc, as in secondary
BPA. Fourthly, PACT makes combinations with the template
going from the terminal levels of the input taxon–area
cladogram to the base. This feature saves time, and is the
means by which PACT is kept from assuming that all input
taxon–area cladograms were associated with each other from
the beginning. It corresponds to dual assumptions that,
whenever there is ambiguity, we should seek to make
combinations, but at the same time, we should do so beginning
with the most recently evolved taxa, because geographical
distributions of recently evolved species should, ceteris paribus, better reflect the conditions under which the species
evolved than geographical distributions of ancient species.
Finally, PACT treats four of the six classes of biogeographical patterns discussed in the introduction (depicted in Figs 2
& 4–6) as variations on a common theme called ‘partial
congruence’. For PACT, however, ‘partial congruence’ means
partial congruence with respect to a final, complex pattern of
area relationships, which may not be expressed fully by any of
the input taxon–area cladograms. None of the taxon–area
cladograms in any of the three exemplars shows the final
Step 16.
Template
area
cladogram:
(((TH)(IS)((IS)((T(HE))
(R(E(AL)))(T(RE))))))
Taxon–area cladogram 17 (Table 3): ((H(IS))(T(R(EE))))
766
Figure 18 Area cladogram derived from taxon–area cladograms
in Table 3. Letters ¼ areas.
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
Phylogenetic analysis for comparing trees
pattern in its entirety, so it would be impossible to predict the
area cladogram a priori for any of those cases. Consequently,
we believe that PACT integrates the most robust aspects of a
priori and a posteriori methods while avoiding their various
drawbacks.
Interpreting the area cladogram
Obtaining an area cladogram is a necessary, but not sufficient,
step in explaining evolutionary phenomena having a geographical context. These include speciation, dispersal and
extinction patterns for the species represented by the taxon–
area cladograms, evolutionary radiations and patterns of
community assemblage (Brooks & McLennan, 2002), including species–area relationships (Halas et al., 2005). PACT does
not invoke or prohibit any evolutionary processes. As a result,
area cladograms produced by PACT are excellent for such
comparative phylogenetic studies.
Exemplar 1
Inferring evolutionary processes from patterns depicted by
area cladograms begins with mapping each taxon–area cladogram onto the final area cladogram, giving a unique
numerical code to each of the branches (including the terminal
ones) for each taxon–area cladogram. Figs 19–27 depict the
taxon–area cladograms for exemplar 1 (Table 1) coded in this
manner. Figure 28 is the final area cladogram with the codes
for those taxa mapped onto it, and with the inferences of
speciation modes, dispersal and extinction highlighted. In this
exemplar, the area cladogram (A(B(CD))) accounts for nearly
90% (63 of 71) of the data points represented by the nine
taxon–area cladograms, strongly suggesting vicariance. The
remaining eight events involve two species occurring in area E
and two cases of reticulated histories involving area A. The
absence of clades 3 and 8 in area B and of clade 7 in areas C
and D are most parsimoniously explained as episodes of
extinction. Alternatively, the presence of species 37 and
55 occurring in area E and species 48 occurring in area A are
most parsimoniously interpreted as episodes of peripheral
isolates speciation through dispersal from area B and area D,
respectively. The occurrence of species 63 in area A may be a
peripheral isolates speciation event, part of an older vicariance
sequence, or part of a sympatric speciation event also involving
species 64 and ancestor 70; given the data at hand, we cannot
make a stronger inference.
Exemplar 2
Figures 29 and 30 depict the taxon–area cladograms for
exemplar 2 (Figs 15 and 16) coded for mapping onto the
final area cladogram. Figure 31 is the final area cladogram with
the codes for those taxa mapped onto it. In this case, each clade
occurs throughout areas B, C, D and E, but there is no single
pattern among those areas that accounts for the majority of
species occurrences. In addition, each clade appears to have
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
become associated with areas B, C, D and E from different
sources (A and F), and at slightly different times. Finally, the
two clades appear to share area relationships in less than 50%
(nine of 19) branches on the area cladogram in Fig. 31.
Consequently, this area cladogram represents a scenario of
colonization of a common set of areas by two different clades
from two different sources, which became historically linked as
a result of colonization of a common set of areas. In such cases,
it is not possible to make a parsimonious inference of
extinction, because ‘colonization + extinction’ (two events)
will always be less parsimonious than ‘never colonized’ (one
non-event).
Exemplar 3
Figures 32–48 depict the taxon–area cladograms for exemplar
3 (Table 3) coded for mapping onto the final area cladogram.
Figure 49 is the final area cladogram (Fig. 18) with the codes
for those taxa mapped onto it. In this exemplar, the area
cladogram comprises general sets of area relationships,
suggesting vicariance, but those area relationships include
eight reticulations involving 75% of the areas (two duplications each for T and E, one each for I, H, R and S), indicating
dispersal. Fourteen (82%) of the clades appear to have been
associated with each other from the beginning of the biogeographical scenario represented by the area cladogram,
suggesting vicariance, whereas clades 9, 10 and 15 became
associated with the areas at later times, again indicating
dispersal. Lastly, Fig. 50 depicts the area cladogram for
exemplar 3, with three rectangles heuristically depicting
increasing temporal scale. In this case, the shortest temporal
scale (smallest rectangle) encompasses only four areas, T, H, I
and S, two of which (I and S) exhibit reticulated relationships.
As we expand the temporal scale (medium rectangle), we add
an additional area (E), but also add reticulated relationships
for areas T and H. Finally, at the longest temporal scale (largest
rectangle), we add three additional areas, R, A and L, and also
additional area reticulations for areas E and R. This mixture of
vicariance and dispersal corresponds to a taxon pulse radiation
(Erwin, 1979; for recent phylogenetic biogeographical documentation of taxon pulse radiations, see Spironello & Brooks,
2003; Bouchard et al., in press; Halas et al., 2005).
The limits of pattern analysis
Although there is a single PACT result for any set of one or
more taxon–area cladograms, there may be more than one
equally parsimonious mapping for particular species on that
result, and thus more than one equally parsimonious inference
of processes. For example, taxon–area cladogram 9 in exemplar
1 (Table 1) has two basal A’s, dictating that the final area
cladogram has two basal A’s. The issue of which of those A’s is
part of the general pattern and which is a unique element is
ambiguous. A similar case arises in analysis of taxon–area
cladogram 14 (Table 3); PACT places ‘T(RE)’ as part of the
group T(R(EE))), but T(RE)) can be placed in three other
767
M. Wojcicki and D. R. Brooks
Figure 19–27 Taxon–area cladograms in Table 1 numbered for mapping on the area cladogram depicted in Fig. 11. Letters ¼ areas. (19)
Taxon–area cladogram 1. (20) Taxon–area cladogram 2. (21) Taxon–area cladogram 3. (22) Taxon–area cladogram 4. (23) Taxon–area
cladogram 5. (24) Taxon–area cladogram 6. (25) Taxon–area cladogram 7. (26) Taxon–area cladogram 8. (27) Taxon–area cladogram 9.
configurations on the final area cladogram without violating
assumption 0 (Fig. 51).
As we noted earlier, these ambiguities do not affect the
way in which PACT builds the area cladogram. Such
ambiguities, therefore, indicate complexities in the data, not
a shortcoming of the algorithm. That is, there are limitations on what we can robustly infer from patterns alone. For
these cases, we must have additional information, specifically
information about the ages of the speciation events not
based on biogeographical patterns (see also Brooks &
McLennan, 2002). Two additional sources of information
have been suggested, the fossil record (Lieberman, 2000,
2003a,b) and molecular clock estimates (Lieberman, 2001,
2003a,b; Donoghue & Moore, 2003), each of which has its
768
own potential drawbacks. For example, the age of a taxon
represented by a fossil is only its minimum age of origin.
Conversely, when reinforcement has played a role in
completing speciation, molecular clock estimates may overestimate the age of a speciation event due to increased rates
of divergence resulting from selection acting on potential
isolating mechanisms (Brooks & McLennan, 2001).
PACT and model-based approaches
PACT can mimic a priori methods of analysis, if the model
upon which the a priori method is based is presented in the
form of an area cladogram. That area cladogram can then be
used as the template area cladogram, and the taxon–area
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
Phylogenetic analysis for comparing trees
Figure 28 Area cladogram 1 depicted in
Fig. 11 with information derived from all
nine clades in Table 1 mapped onto it. Letters ¼ areas.
Figure 32 Taxon–area cladogram 1 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
Figure 29–31 Mapping information from taxon–area cladograms
onto the general area cladogram. (29) Taxon–area cladogram
depicted in Fig. 15 numbered for mapping on the area cladogram
depicted in Fig. 17. (30) Taxon–area cladogram depicted in Fig. 16
numbered for mapping on the area cladogram depicted in Fig. 17.
(31) Area cladogram depicted in Fig. 17 with information derived
from both clades mapped onto it. Letters ¼ areas.
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
Figure 33 Taxon–area cladogram 2 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
cladogram(s) can be compared with it using PACT as
described above. Each element of any input taxon–area
cladogram that can be combined with a template element
769
M. Wojcicki and D. R. Brooks
Figure 34 Taxon–area cladogram 3 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
Figure 35 Taxon–area cladogram 4 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
Figure 36 Taxon–area cladogram 5 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
represents a corroboration of the model, and each element
that must be added to the template represents a specific
falsification of the model. Used in this manner, PACT is
superior to all other a priori methods of biogeographical
analysis because it does not specify costs, or weights, or
probabilities, or likelihoods of particular biogeographical
770
Figure 37 Taxon–area cladogram 6 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
Figure 38 Taxon–area cladogram 7 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
Figure 39 Taxon–area cladogram 8 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
processes a priori, and is thus sensitive to clade-specific
historical contingencies.
CONCLUSIONS
If the evolution of the biosphere were the result of a single
dispersal event, followed by vicariance and extinction (lineage
sorting), there would be one species per area on this planet. If the
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
Phylogenetic analysis for comparing trees
Figure 43 Taxon–area cladogram 12 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
Figure 40 Taxon–area cladogram 9 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
Figure 41 Taxon–area cladogram 10 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
Figure 44 Taxon–area cladogram 13 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
Figure 42 Taxon–area cladogram 11 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
Figure 45 Taxon–area cladogram 14 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
evolution of the biosphere were the result of episodes of
sympatric speciation (lineage duplication), followed by a single
dispersal event, followed by vicariance and extinction (lineage
sorting), each biota would be a clade. In either case, a priori and a
posteriori methods would give the same answer, and all biotic
diversification could be represented in a simple area cladogram.
Nowhere on this planet does either of these possibilities occur,
however. Therefore, we believe that maximum vicariance is
falsified as the null hypothesis for historical biogeography. With
what do we replace it?
Biogeographers have long thought that lengthening temporal scale tends to increase spatial scale. As the temporal scale
lengthens, the spatial scale will increase through dispersal into
new areas. At the same time, there may be dispersal into areas
already inhabited by other clade members, producing reticulated area relationships (e.g. Fig. 50), making the relationship
between temporal and spatial scale complex. Such complex
area relationships are a feature of the taxon pulse radiation
hypothesis first proposed by Erwin (1979). Recent empirical
studies using BPA have documented taxon pulse radiations for
single clades (Spironello & Brooks, 2003) and multiple clades
(Bouchard et al., in press; Halas et al., 2005). The taxon pulse
hypothesis, embodying general patterns based on dispersal as
well as vicariance, would seem to be the logical replacement, at
this point in time, for the doctrine of maximum vicariance.
If area reticulations are not noise or error, but rather
information that must be documented and explained, the
methodological bases for historical biogeography become clear.
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
771
M. Wojcicki and D. R. Brooks
Figure 46 Taxon–area cladogram 15 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
Figure 48 Taxon–area cladogram 17 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
based on vicariance from those based on biotic expansion
and (3) analyse as many different clades as possible. All these
integrated tasks require an efficient and powerful algorithm
such as PACT.
ACKNOWLEDGEMENTS
Figure 47 Taxon–area cladogram 16 in Table 3 numbered for
mapping on the area cladogram depicted in Fig. 18. Letters ¼ areas.
Historical biogeographers need to (1) discover and evaluate
both general patterns and their exceptions, including reticulated area relationships, (2) distinguish general patterns
We wish to thank Patrice Bouchard (Agriculture Canada), Brian
Crother, Sarah Temple, Erica Perrer, Erik Johnson and Cathy
DiBenedetto (Southeastern Louisiana University), Ashley Dowling (University of Michigan), Eric Hoberg (US National
Parasite Collection, USDA, Beltsville, Maryland), Bruce Lieberman (University of Kansas), Deborah McLennan (University
of Toronto), Soren Nylin, Niklas Janz and Niklas Wahlberg
(Stockholm University), Marco Van Veller (Wageningen Uni-
Figure 49 Area cladogram for exemplar 3 (Fig. 18). Numbers in boldface below refer to numbers on the area cladogram; numbers following
‘¼’ refer to numbered branches from the taxon–area cladograms in Figs 32–48; numbers with an asterisk (*) represent absences of the clade
from that part of the area cladogram. 1 ¼ 1, 16, 31, 50, 69, 90, 111, 136, 193, 206, 219, 260*; 2 ¼ 2, 17, 32, 51, 70, 91, 112, 137, 207, 220, 234*,
277*; 3 ¼ 3, 18, 33, 52, 71, 92, 113, 194, 208, 278; 4 ¼ 4, 19, 34, 53, 72, 93, 114, 195, 209, 279; 5 ¼ 35, 54, 115, 138, 221, 235, 261; 6 ¼ 36, 55, 116,
139, 222, 236, 262; 7 ¼ 73, 94, 117, 140, 157, 247; 8 ¼ 74, 95, 118, 141, 158, 248, 263; 9 ¼ 75, 96, 119, 142, 159, 249, 264; 10 ¼ 20, 37, 97, 120,
160, 178, 196, 223; 11 ¼ 21, 38, 98, 121, 161, 179, 197, 224; 12 ¼ 22, 39, 99, 122, 162, 180, 198, 225; 13 ¼ 23, 40, 100, 123, 163, 181, 199,
226; 14 ¼ 5, 56, 76, 143, 164, 182, 210, 237, 250, 265, 280; 15 ¼ 6, 57, 77, 144, 165, 183, 211, 238, 251, 266, 281; 16 ¼ 7, 8, 11, 58, 59, 63, 78, 79, 84,
104, 145, 146, 148, 166, 167, 171, 184, 185, 188, 212*, 239, 240, 241, 252, 253, 255, 267, 268, 269, 282, 283, 285; 17 ¼ 9, 24, 41, 60, 81, 102, 124,
154*, 213, 231*, 234*, 260*, 277*; 18 ¼ 10, 25, 42, 61, 82, 103, 125, 202, 214, 284; 19 ¼ 80, 101, 126, 147, 168, 254, 271*; 20 ¼ 26, 44,
127, 169, 186, 200, 227; 21 ¼ 27, 45, 128, 170, 187, 201, 228; 22 ¼ 12, 64, 85, 105, 149, 172, 189, 215, 242, 256, 270, 286; 23 ¼ 14, 65, 86, 107, 151,
174, 191, 217, 244, 258, 272, 288; 24 ¼ 29, 46, 130, 173, 190, 204, 230; 25 ¼ 83, 106, 129, 150, 175, 257, 271*; 26 ¼ 42, 62, 131, 152, 229, 243, 273;
27 ¼ 13, 28, 47, 66, 133, 154*, 203, 216,231*, 234*, 260*, 287; 28 ¼ 176, 192; 29 ¼ 109, 132, 153, 177, 259, 274; 30 ¼ 48, 67, 88, 134, 155,
232, 275; 31 ¼ 15, 30, 49, 68, 89, 110, 135, 156, 205, 218, 233, 246, 276, 289. Letters ¼ areas.
772
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd
Phylogenetic analysis for comparing trees
Figure 50 Area cladogram depicted in Figs 18 and 49, with
rectangles representing an heuristic view of increasing temporal
scale associated with increasing spatial scale as well as increasing
historical reticulations of areas. The smallest rectangle indicates
five areas and two reticulations, the medium-sized rectangle
indicates eight areas and three reticulations, and the largest rectangle indicates eight areas and eight reticulations. Letters ¼ areas.
Figure 51 Area cladogram for 17 taxon–area cladograms in
Table 3 indicating possible mappings of the (T(RE)) portion of
taxon–area cladogram 14, denoted by areas in larger fonts. PACT
selects the most compact grouping possible, placing all elements of
(T(RE)) within a single clade of areas on the area cladogram, but
other placements (italicized letters) are logically consistent with
the area cladogram. This ambiguity does not affect the construction of the area cladogram. Letters ¼ areas.
versity) and Rino Zandee (Leiden University) for patient and
effective feedback during the development of PACT. We also
thank approximately 75 students in classes at the University of
Toronto and Stockholm University during the autumn of 2003,
who were the first undergraduates to be taught PACT. DRB
acknowledges funding from the Natural Sciences and Engineering research Council (NSERC) of Canada.
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BIOSKETCHES
Maggie Wojcicki is a Research Assistant in the laboratory of
Prof. D.R. Brooks, University of Toronto. She plans to begin a
doctoral program in Computer Science in the near future.
Daniel R. Brooks is Professor of Zoology, University of
Toronto, specializing in the systematics and evolution of
parasitic helminths. He is currently coordinating the inventory
of eukaryotic parasites of vertebrates, Area de Conservacion
Guanacaste, Costa Rica. He is co-author of Phylogeny, ecology
and behavior: A research programme in comparative biology
(1991), Parascript: Parasites and the language of evolution
(1993) and The nature of diversity: An evolutionary voyage of
discovery (2002).
Editor: Philip Stott
Journal of Biogeography 32, 755–774, ª 2005 Blackwell Publishing Ltd