全 文 ：Journal of Systematics and Evolution 46 (2): 130–141 (2008) doi: 10.3724/SP.J.1002.2008.07165
(formerly Acta Phytotaxonomica Sinica) http://www.plantsystematics.com

Inference of phylogenetic relationships among key angiosperm lineages
using a compatibility method on a molecular data set
Yin-Long QIU* George F. ESTABROOK*
(Department of Ecology & Evolutionary Biology, The University of Michigan, Ann Arbor, MI 48109-1048, USA)
Abstract Phylogenetic relationships among the five key angiosperm lineages, Ceratophyllum, Chloranthaceae,
eudicots, magnoliids, and monocots, have resisted resolution despite several large-scale analyses sampling taxa
and characters extensively and using various analytical methods. Meanwhile, compatibility methods, which were
explored together with parsimony and likelihood methods during the early development stage of phylogenetics,
have been greatly under-appreciated and not been used to analyze the massive amount of sequence data to recon-
struct the basal angiosperm phylogeny. In this study, we used a compatibility method on a data set of eight genes
(mitochondrial atp1, matR, and nad5, plastid atpB, matK, rbcL, and rpoC2, and nuclear 18S rDNA) gathered in an
earlier study. We selected two sets of characters that are compatible with more of the other characters than a
random character would be with at probabilities of pM<0.1 and pM<0.5 respectively. The resulting data matrices were
subjected to parsimony and likelihood bootstrap analyses. Our unrooted parsimony analyses showed that Cerato-
phyllum was immediately related to eudicots, this larger lineage was immediately related to magnoliids, and
monocots were closely related to Chloranthaceae. All these relationships received 76%–96% bootstrap support. A
likelihood analysis of the 8 gene pM<0.5 compatible site matrix recovered the same topology but with low support.
Likelihood analyses of other compatible site matrices produced different topologies that were all weakly sup-
ported. The topology reconstructed in the parsimony analyses agrees with the one recovered in the previous study
using both parsimony and likelihood methods when no character was eliminated. Parts of this topology have also
been recovered in several earlier studies. Hence, this topology plausibly reflects the true relationships among the
five key angiosperm lineages.
Key words angiosperm, Ceratophyllum, character analysis, Chloranthaceae, compatibility, eudicots, magnoliids,
monocots, phylogenetic method, phylogeny.
Relationships among five key angiosperm lin-
eages (Ceratophyllum, Chloranthaceae, eudicots,
magnoliids, and monocots) near the base of the an-
giosperm phylogeny remain unresolved despite sev-
eral recent studies that sample a large number of taxa
and characters and use various analytical methods
(Chase et al., 1993; Qiu et al., 1999, 2005, 2006a;
Doyle & Endress, 2000; Graham & Olmstead, 2000;
Soltis et al., 2000; Hilu et al., 2003; Moore et al.
2007). A number of factors might be responsible for
this phylogenetic conundrum: rapid radiation, extinc-
tion, evolutionary rate heterogeneity among different
characters and different lineages, character state
paucity in DNA sequence evolution that causes a
disproportionately large number of back mutations,
and lack of extensive fossil evidence. While it can
certainly be hoped that with more genes sequenced
this problem may be solved eventually, it is also worth
exploring more analytical methods to untangle these
difficult nodes in the angiosperm phylogeny. In this
study, we use a compatibility-based method on a data
set that was analyzed recently to attempt to resolve
relationships among basal angiosperms (Qiu et al.,
2006a). Our goals are to resolve relationships among
these angiosperm lineages and to evaluate the useful-
ness of this compatibility-based method to this diffi-
cult phylogenetic problem.
Compatibility-based methods have not been used
widely in recent phylogenetic studies. Hence we
present a brief review of their history here. In the
middle of the last century, a few systematic biologists
began to include explicit phylogenetic concepts to
compare characters, with an understanding that not all
characters are equally useful for inferring evolutionary
relationships among organisms. Wilson (1965) and
Camin & Sokal (1965) each proposed related but
distinct operational tests for the phylogenetic com-
patibility of a pair of characters based on the pattern of
their character states within a group of related taxa.
Hennig (1966) was among the first to advocate the use
of compatibility to recognize characters that were
phylogenetically in conflict so as to resolve them

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Received: 13 December 2007 Accepted: 18 February 2008
* Authors for correspondence. Tel.: 1-734-764-8279 (YLQ), 1-734-764-6219
(GFE); Fax: 1-734-763-0544; E-mail: .
QIU & ESTABROOK: A compatibility analysis of key angiosperm relationships


131
explicitly. Le Quesne (1969) used the test of Wilson
(1965) together with a heuristic algorithm to select
characters estimated to be phylogenetically most
reliable. Estabrook (1972a, b) reviewed these and
other concepts of that time, and incorporated evolu-
tionary history into the evaluation of characters.
Through the 1970’s and early 1980’s many systema-
tists applied compatibility concepts to evaluate char-
acters and estimate phylogenetic relationships (e.g.,
Estabrook et al., 1977; Estabrook & Anderson, 1978;
Meacham, 1980; Wiley, 1981). Wilson’s (1965)
concept of character compatibility was generalized,
and the mathematical soundness of related concepts,
with algorithms to implement them in practice, was
established by Estabrook and his collaborators in
several studies (Estabrook et al., 1975, 1976a, b;
Estabrook & McMorris, 1977, 1980; Estabrook &
Meacham, 1980; Meacham, 1983). Estabrook (1983),
Meacham (1984), and Meacham & Estabrook (1985)
reviewed the use of character compatibility analysis at
a somewhat later time, and Estabrook (1997, 2008)
gave a more recent review of compatibility-related
concepts and questions. An early attempt to use
character compatibility analysis with molecular data
was made by Boulter et al. (1979). They used con-
cepts, presented by Fitch (1975), Estabrook &
Landrum (1975), and Sneath et al. (1975), to general-
ize compatibility concepts applicable to molecular
data, and devised an algorithm to apply them to amino
acid sequences to estimate relationships among 10
families of flowering plants. More recently, Pisani
(2004) and Gupta & Sneath (2007) have used com-
patibility-based methods to investigate phylogenetic
relationships in arthropods and bacteria, respectively.
1 Methods
To understand and evaluate the concepts and
methods that we apply here, it is important to have an
explicit definition of character compatibility. For a
collection S of species or other evolutionary units
(EUs), a qualitative character is a partition of S into
character states of EUs that share a common property
with respect to some basis for comparison. Two
qualitative characters for S are defined to be compati-
ble if there exists a tree with the EUs in S at all the
branch tips (and perhaps some of the interior nodes)
on which the states of both characters could evolve
without homoplasy. Although we may not know
which is the historically true phylogenetic tree for S,
conceptually we define a true qualitative character to
be one whose states can evolve on this true tree with-
out homoplasy. Note that all true characters will be
compatible with each other, and for any pair of in-
compatible characters at least one of them is false, i.e.,
suggesting a relationship that is phylogenetically false.
In our view, there are three categories of charac-
ters for any group of organisms: (1) those that accu-
rately reflect relationships among lineages within the
group and exhibit no homoplasy on the true phyloge-
netic tree for those lineages, (2) those that have ex-
perienced parallel, convergent or reversed evolution,
and (3) those that contain human error, whether in the
form of poor character definition or inaccurate coding
of morphological characters, or in the form of poor
alignment in molecular sequences. Characters in the
first category are always compatible with each other,
and they will make a group of mutually compatible
characters. From such a group of characters, an accu-
rate, if not completely resolved, representation of
evolutionary relationships can be made. In the second
category of characters, some could also be compatible
with one another if they have experienced similar
selection pressure resulting in parallel, convergent or
reversed evolution. For example, the floral characters
whose states reflect the wind pollination syndrome of
species in the now defunct angiosperm subclass
Hamamelidae are so often compatible with one an-
other that they have misled botanists for nearly a
century to incorrectly recognize that taxon (see Cron-
quist, 1981; Qiu et al., 1998). Similarly, genes in the
mitochondrial genomes of the angiosperm genera
Plantago and Pelargonium seem to have experienced
accelerated evolution in comparison to those of other
angiosperms, and in most phylogenetic analyses this
phenomenon would lead to mis-placement of these
two taxa because of random compatibility generated
by the limited character states of DNA sequence
evolution (Cho et al., 2004; Parkinson et al., 2005).
However, we believe that true causes of the compati-
bility among characters of this kind are more likely to
be brought to light if more characters of the entire
organism are investigated carefully. Finally, charac-
ters in the third category are compatible among them-
selves in unpredictable ways.
In a real phylogenetic study, we do not know
which characters belong to which category. However,
because characters in the first category are compatible
among themselves and should form a core group of
compatible characters, they may appear among a
surprisingly large number of characters with which a
given character may be compatible. We here introduce
a character concept that has been previously proposed
by Meacham (1994), the COSLAC, which is a
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132
Character that is cOmpatible with a Surprisingly
LArge number of other Characters. The first category
of characters should be COSLACs. Fewer second
category characters should be among COSLACs, and
very few third category characters should belong to
COSLACs. Thus we select characters that qualify as
COSLACs for further analysis, because among such
characters should be relatively more first category
characters and relatively fewer second and third
category characters.
To discover which characters are COSLACs, we
use the criterion of Estabrook and Landrum (1975),
Fitch (1975), and Sneath et al. (1975) to test the
compatibility of a pair of characters, as shown in Fig.
1. Notice that this algorithm does not require the
construction of any phylogenetic tree. For each char-
acter (or position in the aligned sequences), we com-
pare it with every other character, counting the Num-
ber of other Characters with which it is Compatible
(NCC hereafter).
One might naively think that the characters com-
patible with the most other characters would be more
likely to be COSLACs. However, Meacham (1981)
showed that, depending on the number of character
states and the distribution of taxa through those states,
some characters are more likely than others to be
compatible at random with other characters. For this
reason it is important to know whether a given char-
acter is compatible with many other characters as
much as we would expect of a random character. To
address this issue, we need to calculate the probability
that a random character would be compatible with at
least as many other characters as was a given charac-
ter. It would, however, be an impossibly complicated
problem to calculate such a probability using the
closed procedures of Meacham (1981) for each char-
acter in a large data set, such as the one we analyze
here. To avoid this problem, Meacham (1994) esti-
mated very close approximations to these probabilities
using simulation. We will use his approach here.
To estimate this probability for a given character,
we replace it with one chosen at random equiprobably
from all possible characters with the same number of
states and the same number of EUs in each state
(distribution of the states among the EUs will be
almost always different in the random character than
in the given character). We then compare this random
character to each of the other observed characters in
the data set, and count the number of them with which
it is compatible. We repeat this process 10000 times.
The probability that a random character would be
compatible with at least as many other characters as
was the given character (NCC) can now be estimated
as: the number of simulated characters that were
compatible with NCC or more other characters di-
vided by the number of simulated characters, in our
case 10000. Note that the other characters that are
compatible with the random character may or may not
be the same as those compatible with the given char-
acter, and only the number may be equal or larger.
This probability, termed pMANY here, can be construed
as the realized significance of NCC for the given
character. An NCC equal to the expected number of
other characters with which a random character would
be compatible would have a significance of p = 0.5. A
character with a realized significance of NCC substan-
tially less than pMANY = 0.5 would be compatible with
surprisingly many other characters, i.e., less likely to
be a random character and thus qualified as a
COSLAC. This could be grounds for including such a
character in the data set used subsequently for further
phylogenetic analysis.
A computer program called MEACHAM (avail-
able at www-Personal.umich.edu/~gfe/) was devel-
oped based on the fast algorithm of Estabrook and
McMorris (1977) and was used here to identify
COSLACs in the 8-gene matrix used in an earlier
study (Qiu et al., 2006a). The eight genes used in that
study were: mitochondrial atp1, matR, and nad5,
plastid atpB, matK, rbcL, and rpoC2, and nuclear 18S
rRNA gene. Because highly divergent taxa in the data
set present problems for proper identification of
COSLACs, the gymnosperms, Amborella, Nym-
phaeales, and Austrobaileyales used in the original
data set were excluded from the analyses here. As a
result, 144 taxa representing Ceratophyllum, Chlor-
anthaceae, eudicots, magnoliids, and monocots were
used in this study. Removal of Amborella, Nym-
phaeales, Austrobaileyales and gymnosperms prevents
them from influencing resolution of relationships
among the five key angiosperm lineages, and previous
studies have demonstrated that these five lineages
make a strongly supported monophyletic group (Qiu
et al., 1999, 2005, 2006a; Hilu et al., 2003).
Each of the eight genes was analyzed individu-
ally using the program MEACHAM to identify
COSLACs. To illustrate the output file from analyses,
we present a sample from the nuclear 18S rRNA gene
in Table 1, which shows a list of selected sites, the
number of other compatible characters with a given
site (NCC), and realized significance of NCC for the
site. We provide the following explanation to help
interpret this output file. For example, site 34 is
compatible with 297 of the other informative sites of
QIU & ESTABROOK: A compatibility analysis of key angiosperm relationships


133



Fig. 1. An example to demonstrate tests of potential compatibility for three qualitative characters (I, II, and III) in a study of seven evolutionary
units (a – g). A shows a matrix of character state distribution of three characters in seven evolutionary units. B and C illustrate two tests of character
compatibility. In each test, states of one character label the row and those of the other label the column; each evolutionary unit is placed in the cell
whose row and column labels indicate the states that it manifests. Moving only from one occupied cell to another in a straight line horizontally or
vertically but never retracing a path already taken, if you can return to an occupied cell you have already visited then the two characters are incom-
patible, as for I and III in test 2. Otherwise, the two characters are compatible, as for I and II in test 1. D presents a realized tree from two compatible
characters, I and II.

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134
Table 1 A sample of output file of compatible analysis of the nuclear 18S rRNA gene*
Site NCC pMANY pFEW Site NCC pMANY pFEW
25 289 0.705 0.324 144 9 0.572 0.463
34 297 0.452 0.575 146 276 0.045 0.962
36 111 0.081 0.928 150 168 0.972 0.034
39 28 0.888 0.123 154 252 0.872 0.142
42 201 0.171 0.846 160 147 0.072 0.938
96 57 0.016 0.988 162 302 0.331 0.691
101 18 0.909 0.097 169 201 0.988 0.014
102 99 0.023 0.981 170 127 0.291 0.735
* NCC indicates number of other compatible characters for a selected site; pMANY and pFEW represent respectively the probabilities that at least as
MANY and at most as FEW other informative sites would be potentially compatible with a random site with the same frequency of EU’s among its
states as observed, estimated by 10000 simulations per site.

the gene. A random site was chosen 10000 times
equiprobably from all possible sites with the same
number of EUs exhibiting each nucleotide as for site
34. For 4520 of these random sites (pMANY = 0.452),
the number of other informative sites of 18S with
which these random sites were compatible was greater
than or equal to 297; for 5750 of these random sites
(pFEW = 0.575), the number of other informative sites
of 18S with which these random sites were compatible
was less than or equal to 297. Thus site 34 is compati-
ble with about as many other sites as would be ex-
pected of a random site.
Site 96 is compatible with 57 of the other infor-
mative sites of 18S. Of 10000 random sites, only 160
were compatible with 57 or more of the other infor-
mative sites of 18S (pMANY = 0.016), and 9880 (nearly
all) were compatible with 57 or fewer other informa-
tive sites of 18S (pFEW = 0.988). Site 96 has too many
other sites (even though NCC = 57) compatible with it
to seem like a random site, because only very few
random sites were compatible with 57 or more other
sites. Thus, site 96 is significantly non-random (pMANY
= 0.016) and qualifies as a COSLAC.
When NCC has been calculated for each site of a
gene and the probability p that a random character will
be compatible with at least NCC other sites has been
estimated by simulation, two subsets of sites are
chosen for further phylogenetic analysis: sites with
pMANY≤0.1, which are compatible with surprisingly
many other sites; and sites with pMANY≤0.5, which
are compatible with at least as many other sites as
would be expected of a random character. Basically,
two categories of COSLACs are identified according
to different levels of realized significance (i.e., prob-
abilities that the characters selected for further analy-
sis are better than random characters).
The resulting matrices were analyzed using both
parsimony (Swofford, 2003) and maximum likelihood
(Posada & Crandall, 1998; Guindon & Gascuel, 2003)
bootstrap (Felsenstein, 1985) methods to investigate
phylogenetic relationships among Ceratophyllum,
Chloranthaceae, eudicots, magnoliids, and monocots.
The search details are available upon request.
2 Results and Discussion
2.1 Character compatibility in the eight genes of
the five angiosperm lineages
The numbers of sites in each of the eight genes
with various levels of realized significance are pre-
sented in Table 2. The sites with realized significance
pMANY≤0.1 and pMANY≤0.5 of at least as MANY
other compatible characters as NCC represents really
high and high quality COSLACs, respectively; their
numbers are listed under NoM<0.1 and NoM<0.5 in Table
2. These sites were used in the parsimony and maxi-
mum likelihood bootstrap analyses to reconstruct
phylogenetic relationships among the five key angio-
sperm lineages.
The levels of compatibility shown in Table 2 are
strikingly low. Day et al. (1998) used the compatibil-
ity criterion described here to measure the phyloge-
netic randomness of 102 published data sets, of which
only 7 had comparably low levels of compatibility.
Only about half of the informative sites are compatible
with more other sites than would be expected of a
random site (see NR in Table 2); this is what we
would expect if all the sites were random. On the
other hand, the data are clearly non-random, which is
shown by the observed number of sites with realized
significance pMANY≤0.1 of at least as MANY other
compatible characters as NCC being far greater than
the expected number of such sites for the random data
(see NoM<0.1 in Table 2).
Less than half of the sites in plastid atpB and
QIU & ESTABROOK: A compatibility analysis of key angiosperm relationships


135
Table 2 The results of compatible analyses of the eight genes*
Gene NoT NoI NoM<0.1 NoM<0.5 NoF>0.2 NoF>0.4 NR
Nuclear
18S 1755 350 95 (35) 167 (175) 248 153 0.48
Mitochondrial
atp1 1330 373 97 (37) 144 (187) 235 215 0.39
matR 2153 709 202 (71) 366 (355) 539 292 0.52
nad5 1248 218 65 (22) 114 (109) 169 81 0.52
Total 4731 1300 364 (130) 624 (651) 943 588 0.48
Plastid
atpB 1506 568 95 (57) 228 (284) 367 296 0.40
matK 1851 1222 395 (122) 733 (611) 995 494 0.60
rbcL 1043 561 180 (56) 339 (281) 447 188 0.60
rpoC2 3173 1864 534 (186) 1004 (932) 1363 749 0.54
Total 7573 4215 1204 (421) 2304 (2108) 3174 1727 0.54
Grand total 14059 5865 1663 (586) 3095 (2933) 4365 2468 0.52
* NoT = number of total sites; NoI = number of informative sites; NoM<0.1 and NoM<0.5 represent respectively numbers of sites with realized significance
pMANY≤0.1 and pMANY≤0.5 of at least as MANY other compatible characters as NCC (the numbers in parentheses represent the expected number of
sites if the data were random); NoF>0.2 and NF>0.4 represent respectively numbers of sites with realized significance p≥0.2 and p≥0.4 of at most as
FEW other compatible characters as NCC; NR = NM<0.5/NoI, i.e., the fraction of informative sites more compatible than expected of a random site.

mitochondrial atp1 are compatible with more other
sites than would be expected of a random character.
Of the remaining genes, the chloroplast genes have
slightly more sites that are compatible with one an-
other, although levels are still low. These low levels of
compatibility might have been caused by several
factors mentioned at the beginning of the paper: rapid
radiation, extinction, evolutionary rate heterogeneity
among different characters and different lineages, and
character state paucity in DNA sequence evolution
that causes a disproportionately large number of back
mutations. They are consistent with the difficulty that
has been experienced in several earlier studies at-
tempting to elucidate relationships among these
angiosperm lineages using molecular data (Chase et
al., 1993; Qiu et al., 1999, 2005, 2006a; Graham &
Olmstead, 2000; Soltis et al., 2000; Hilu et al., 2003).
Previous studies have also detected high levels of
homoplasy in morphological characters among key
basal angiosperm lineages (Donoghue & Doyle, 1989;
Doyle & Endress, 2000). Hence, these observations
highlight the need of conducting phylogenetic analysis
using refined character sets to resolve relationships
among the key angiosperm lineages.
2.2 Phylogenetic relationships among the key
angiosperm lineages inferred from COSLACs in
the eight genes
Figure 2 shows the bootstrap consensus tree from
an unrooted parsimony analysis of the 8 gene matrix
composed of pM<0.1 sites (COSLACs at the pMANY≤
0.1 level of significance). In this tree, eudicots are
immediately related to Ceratophyllum with 96%
bootstrap support; this lineage is in turn immediately
related to magnoliids with 83% bootstrap support. The
latter value can also be interpreted as support for a
close relationship between monocots and Chlorantha-
ceae as the tree is an unrooted network. In all trees
shown here, Chloranthaceae are placed at the bottom
being sister to all other taxa because some phyloge-
netic analyses have indicated that they may represent
the lineage splitting from other angiosperms right after
Austrobaileyales (Doyle & Endress, 2000; Qiu et al.,
2006a), and because this family also has the oldest
fossil record among all angiosperms (Friis et al., 1986,
1999; Eklund et al., 2004). We use this topology
merely for the convenience of presentation.
In parsimony bootstrap analyses of three other
matrices, one made of the 8 gene pM<0.5 sites and two
consisted of the 4 plastid gene pM<0.1 and pM<0.5 sites
respectively, topologies of the bootstrap consensus
trees are all identical to the one shown in Fig. 2 in
terms of relationships among the key lineages, and
topologies within the key lineages are all similar to
those shown in Fig. 2. Thus, we will not present those
trees here and instead provide only bootstrap values
for the important nodes in Fig. 2. In all three analyses,
the relationships among the five key angiosperm
lineages receive moderate (75%–90%) to strong
(>90%) bootstrap support. No parsimony bootstrap
analysis was performed on the matrices composed of
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QIU & ESTABROOK: A compatibility analysis of key angiosperm relationships


137
either mitochondrial or nuclear gene COSLAC sites
because some search replicates found a huge number
of equally parsimonious trees and the analyses could
not be finished within a reasonable amount of time.
In a maximum likelihood bootstrap analysis of
the 8 gene pM<0.5 site matrix, we obtained a consensus
tree with a topology virtually identical to that shown
in Fig. 2, but with only 54% and 26% bootstrap values
for the close relationships between eudicots and
Ceratophyllum and between this larger lineage and
magnoliids, respectively. These results are again
shown in Fig. 2 to save space. Our maximum likeli-
hood bootstrap analyses of five other matrices pro-
duced four topologies that differed from the one
shown in Fig. 2 in terms of relationships among these
key angiosperm lineages. In consideration of space
limitation and presentation conciseness, we provide
only schematic diagrams of these trees that depict
relationships among the lineages with bootstrap values
indicated on the important nodes. These matrices and
the resulting trees are: (1) the 8 gene pM<0.1 site matrix
and Fig. 3A, (2) the 3 mitochondrial gene pM<0.1 site
matrix and Fig. 3B, (3) the 3 mitochondrial gene
pM<0.5 site matrix and Fig. 3C, and (4) the 4 plastid
gene pM<0.1 and pM<0.5 site matrices and Fig. 3D. In
contrast to the parsimony bootstrap analyses, likeli-
hood bootstrap analyses of all six matrices recovered
very low bootstrap values for relationships among
these lineages, whether the topologies were identical
to or different from the one shown in Fig. 2.
The moderate to strong bootstrap support for
relationships among Ceratophyllum, Chloranthaceae,
eudicots, magnoliids, and monocots, recovered in the
parsimony analyses shown above gives some indica-
tion that these relationships may be resolved soon.
Though complete resolution of a difficult phylogenetic
problem should receive consistent internal support
within the data of a study and also have external
corroboration from evidence of other studies, a high
bootstrap value is an indication of strong internal
support and can usually be taken as an early sign that
the problem may be near resolution (Nei et al., 1998;
Qiu et al., 2006a). In this case, the moderately to
strongly supported relationships among the five key
angiosperm lineages are also recovered in a maximum
likelihood bootstrap analysis of one matrix (Fig. 2),
albeit with low support. Moreover, in maximum
likelihood bootstrap analyses of the 3 mitochondrial
gene pM<0.1 and pM<0.5 site matrices (Fig. 3: B, C), the
overall topology of both trees would be identical to
that in Fig. 2 if Chloranthaceae were attached to
monocots. The mitochondrial genes exhibited acceler-
ated evolution in Acorus and alismatids and were
excluded from the data set (Qiu et al., 2006a). This
data removal might have been responsible for the
different placement of monocots in these two analyses.
Hence, it is likely that the topology in Fig. 2 reflects
the true underlying evolutionary relationships among
these five angiosperm lineages. Still, we would cau-
tion that this result should serve only as a hypothesis
for further test in future studies.
The results of maximum likelihood analyses are
puzzling in several aspects: (1) they differ by data
sets, (2) the bootstrap values are uniformly low, and
(3) they are different from those obtained by the
parsimony analyses. When such sharply different
results are obtained from likelihood and parsimony
analyses, one may be inclined to think that the parsi-
mony analyses have probably suffered from the
systematic errors present in the data due to the par-
ticular character and taxon distribution shaped by
extinction, evolutionary rate heterogeneity among
different characters and different lineages, and sam-
pling error in the study design (Felsenstein, 1978).
While this possibility cannot be excluded, it is worth
pointing out that the phylogenetic pattern recovered
by the parsimony analyses is also present in some of
the likelihood analysis results (Fig. 2; Fig. 3: B, C).
Perhaps in this case likelihood analyses have failed to
detect the true historical pattern due to over-parame-
terization. It should also be realized that likelihood
analysis computer programs are at an early stage of
development. Further, maximum likelihood methods
can become strongly biased and statistically inconsis-
tent when sequence evolutionary rates change
non-identically over time (Kolaczkowski & Thornton,
2004). Therefore, we are not particularly concerned by
the poor results of the likelihood analyses in this study
even though they certainly caution us to be careful in
interpreting the results generated by the compatibility

←
Fig. 2. Results of bootstrap analyses of various compatible site matrices and one matrix with all sites. The tree shown is the parsimony bootstrap
consensus tree from the 8 gene pM<0.1 site matrix. For other matrices, only bootstrap values (all from parsimony analyses except indicated) for the
nodes under investigation in this study are provided and they are shown in boldface and large font, in the following order: above the branch, 8 gene
pM<0.1 site matrix / 8 gene pM<0.5 site matrix / 4 plastid gene pM<0.1 site matrix; below the branch, 4 plastid gene pM<0.5 matrix / 8 gene pM<0.5 site matrix
with maximum likelihood analysis / 8 gene all site matrix (without editing sites) with parsimony analysis. Bootstrap values from analyses of all these
matrices are also provided for monophyly of, and relationships within, magnoliids. Abbreviations: Acorus cal, Acorus calamus; Acorus gra, Acorus
gramineus; Ceratophyllum dem, Ceratophyllum demersum; Ceratophyllum sub, Ceratophyllum submersum; CHL, Chloranthaceae.
Journal of Systematics and Evolution Vol. 46 No. 2 2008

138


Fig. 3. Schematic presentation of maximum likelihood bootstrap consensus trees of various compatible site matrices. A, 8 gene pM<0.1 site matrix.
B, 3 mitochondrial gene pM<0.1 site matrix. C, 3 mitochondrial gene pM<0.5 site matrix. D, 4 plastid gene pM<0.1 / pM<0.5 site matrices. Bootstrap values
from analyses of all these matrices are also provided for monophyly of, and relationships within, magnoliids.
Abbreviations: CAN, Canellales; CER, Ceratophyllum; CHL, Chloranthaceae; EUD, eudicots; LAU, Laurales; MAG, Magnoliales; MON, monocots;
PIP, Piperales.

method we used here.
Because compatibility and parsimony methods
are more closely related to each other than either is to
likelihood methods (Felsenstein, 2004), it is fair to ask
whether uniform increase of bootstrap values on
relationships among the key angiosperm lineages in
the parsimony analyses, but not the likelihood analy-
ses we performed on the refined data sets, is caused by
this factor. On the other hand, parsimony methods
have been shown to be robust in analysis of most real
world as well as simulated data sets (Hillis et al.,
1994; Kolaczkowski & Thornton, 2004). Hence, we
will leave it for future studies to determine whether
the increase of bootstrap values in these analyses is
due to the superior capability conferred by the com-
bined use of the compatibility and parsimony methods
to detect the true phylogenetic signal, or the long
branch attraction problem of the parsimony method
worsened by its closely related cousin.
Some of the relationships reconstructed here have
also been obtained earlier by other studies. The close
relationship between Ceratophyllum and eudicots was
seen in three analyses with large data sets (Soltis et al.,
2000; Hilu et al., 2003; Qiu et al., 2005), but all with
low bootstrap support. Magnoliids were placed as
sister to eudicots (not including Ceratophyllum) in
another study with a large data set, but again with low
bootstrap support (Zanis et al., 2002). Chloranthaceae
were shown to be sister to monocots with 74%–81%
jackknife values (Hilu et al., 2003). Finally, all the
relationships reconstructed among the five angiosperm
lineages in this study were recovered by both parsi-
mony and likelihood analyses of the 8 gene matrix and
most of its various partitions when all characters were
included in an earlier study, but all with <50% boot-
strap support (Qiu et al., 2006a). It is difficult to
assess at present whether agreement of these results
from the earlier studies with the ones obtained here
can serve as evidence to support a conclusion that the
true phylogenetic relationships among the five key
angiosperm lineages are correctly reconstructed.
Recently, Moore et al. (2007) reported moder-
ately supported relationships among Ceratophyllum,
Chloranthaceae, eudicots, magnoliids, and monocots,
with a maximum likelihood analysis of 61 plastid
genes from 45 seed plants. Eudicots were shown to be
sister to Ceratophyllum, and this larger lineage was
then sister to monocots. The clade of these three
lineages was then sister to a clade composed of
Chloranthus and magnoliids. The parsimony analyses
QIU & ESTABROOK: A compatibility analysis of key angiosperm relationships


139
performed in that study consistently failed to recover
these relationships. Two factors should be kept in
mind when we examine these results. One is that
phylogenomic analyses are extremely sensitive to
taxon sampling (Stefanovic et al., 2004; Lee-
bens-Mack et al., 2005; Wolf et al., 2005; Qiu et al.,
2006b; Lemieux et al., 2007). The other is that all of
the genes used in Moore et al. (2007) were from a
single organellar genome. It remains to be seen
whether these two factors are responsible for the
different results obtained in that study and ours here.
2.3 Usefulness of the compatibility method
Did eliminating less compatible characters help
reconstruct phylogenetic relationships among the key
angiosperm lineages? The answer is largely a positive
one in our opinion, as there is a consistent phyloge-
netic pattern emerging from all performed parsimony
analyses and some likelihood analyses (Figs. 2; Fig. 3:
B, C), which not only agrees with the one recovered
before when no character was eliminated (Qiu et al.,
2006a) but also is more strongly supported. Neverthe-
less, the likelihood analysis results of some matrices
are not congruent with this pattern, and the underlying
causes of these differences remain to be determined.
The compatibility method we used here adopts a
very strict criterion in detecting historical signals for
phylogenetic reconstruction. Even though it is related
to parsimony methods (Felsenstein, 2004), it is suffi-
ciently different that it deserves to be explored for its
usefulness for solving difficult phylogenetic problems,
especially when it can help maximize phylogenetic
signal retrieval from existing data. Today, molecular
systematic studies do have the luxury of gathering a
large amount of data because of rapid progress in
sequencing technology. However, building large data
sets without careful evaluation of the quality of data
unnecessarily lowers the efficiency of research, and
thus delays resolution of difficult phylogenetic prob-
lems. Many large data sets gathered for difficult
phylogenetic problems have high levels of homoplasy
(e.g., Chase et al., 1993; Qiu et al., 1999, 2005, 2006a,
b; Doyle & Endress, 2000; Graham & Olmstead,
2000; Soltis et al., 2000; Hilu et al., 2003; Stefanovic
et al., 2004; Leebens-Mack et al., 2005; Wolf et al.,
2005; Lemieux et al., 2007). This seems to be where
compatibility methods can make a contribution to the
solution of difficult phylogenetic problems.
In this study, we specifically examined increase
of bootstrap values for the two key nodes, i.e., the
close relationships between Ceratophyllum and eudi-
cots, and between this larger lineage and magnoliids.
These relationships were reconstructed before, when
all characters of the 8 genes were analyzed by both
parsimony and likelihood methods, but the bootstrap
support was low: 49% and 31% respectively (both
from a parsimony analysis) (Qiu et al., 2006a). Be-
cause the analysis in Qiu et al. (2006a) differed from
the ones conducted here in having gymnosperms,
Amborella, Nymphaeales and Austrobaileyales in the
data set, we removed these taxa to generate a data set
with identical taxon sampling to the 8 gene pM<0.1 and
pM<0.5 site matrices so that the contribution of both
taxon and character removal to the increase of boot-
strap values could be partitioned. A parsimony boot-
strap analysis of the resulting data set increased
bootstrap values from 49% and 31% to 69% and 56%
for these two nodes (Fig. 2). Hence, removal of the
distantly related taxa did increase bootstrap values, but
not to the extent as observed in the compatibility
analyses performed in this study. Comparisons of
bootstrap values at these two nodes from analyses of
the matrix with all characters and the matrices with
only COSLACs show that elimination of less com-
patible characters increases bootstrap values at least
by16%–20%, and often more. Therefore, these analy-
ses demonstrate that exclusion of distantly related taxa
and elimination of less compatible characters can help
increase confidence levels on resolution of difficult
phylogenetic problems.
Recently, several other authors have also ex-
perimented with identifying and eliminating problem-
atic characters to optimize performance of phyloge-
netic methods on difficult problems (Brinkmann &
Philippe, 1999; Philippe et al., 2000; Burleigh &
Mathews, 2004; Pisani, 2004; Gupta & Sneath, 2007).
While it may be too early to generalize the usefulness
of compatibility methods to help solve difficult phy-
logenetic problems, the results from this study are
certainly encouraging. Hence, we suggest that they
should be explored and added to the toolbox of phy-
logeneticists in the effort to reconstruct the tree of life.
Acknowledgements We thank Bin WANG for help
with some analyses and James A. DOYLE for sugges-
tions. YLQ was supported by an Early Career Award
(DEB 0332298) and an ATOL grant (DEB 0431239)
from the National Science Foundation, USA.
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