doi:10.1101/gr.4825606
published online May 15, 2006;Genome Res.
Claude W. dePamphilis
S. Soltis, John E. Carlson, Kathiravetpilla Arumuganathan, Abdelali Barakat, Victor A. Albert, Hong Ma and
Liying Cui, P. Kerr Wall, James H. Leebens-Mack, Bruce G. Lindsay, Douglas E. Soltis, Jeff J. Doyle, Pamela
flowering plants
Widespread genome duplications throughout the history of
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Widespread genome duplications throughout
the history of flowering plants
Liying Cui,1,2,3
P. Kerr Wall,1,2,3
James H. Leebens-Mack,1,2,3
Bruce G. Lindsay,5
Douglas E. Soltis,6
Jeff J. Doyle,8
Pamela S. Soltis,7
John E. Carlson,2,3,4
Kathiravetpilla Arumuganathan,9
Abdelali Barakat,1,2,3
Victor A. Albert,10
Hong Ma,1,2,3
and Claude W. dePamphilis1,2,3,11
1
Department of Biology, 2
Institute of Molecular Evolutionary Genetics, 3
Huck Institutes of the Life Sciences, 4
School of Forest
Resources, and 5
Department of Statistics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA;
6
Department of Botany and 7
Florida Museum of Natural History, University of Florida, Gainesville, Florida 32611, USA;
8
Department of Plant Biology, Cornell University, Ithaca, New York 14853, USA; 9
Virginia Mason Research Center, Benaroya
Research Institute, Seattle, Washington 98101, USA; 10
Natural History Museum, University of Oslo, NO-0318 Oslo, Norway
Genomic comparisons provide evidence for ancient genome-wide duplications in a diverse array of animals and
plants. We developed a birth­death model to identify evidence for genome duplication in EST data, and applied a
mixture model to estimate the age distribution of paralogous pairs identified in EST sets for species representing the
basal-most extant flowering plant lineages. We found evidence for episodes of ancient genome-wide duplications in
the basal angiosperm lineages including Nuphar advena (yellow water lily: Nymphaeaceae) and the magnoliids Persea
americana (avocado: Lauraceae), Liriodendron tulipifera (tulip poplar: Magnoliaceae), and Saruma henryi (Aristolochiaceae).
In addition, we detected independent genome duplications in the basal eudicot Eschscholzia californica (California
poppy: Papaveraceae) and the basal monocot Acorus americanus (Acoraceae), both of which were distinct from
duplications documented for ancestral grass (Poaceae) and core eudicot lineages. Among gymnosperms, we found
equivocal evidence for ancient polyploidy in Welwitschia mirabilis (Gnetales) and no evidence for polyploidy in pine,
although gymnosperms generally have much larger genomes than the angiosperms investigated. Cross-species
sequence divergence estimates suggest that synonymous substitution rates in the basal angiosperms are less than half
those previously reported for core eudicots and members of Poaceae. These lower substitution rates permit inference
of older duplication events. We hypothesize that evidence of an ancient duplication observed in the Nuphar data may
represent a genome duplication in the common ancestor of all or most extant angiosperms, except Amborella.
[Supplemental material is available online at www.genome.org. ]
Gene duplication has long been recognized to be a major force in
evolution (Ohno 1970). Genome doubling (polyploidy) has had
a profound influence on the evolutionary history of extant lin-
eages. Ohno proposed that whole-genome duplications occurred
in the early history of all vertebrates (Ohno 1970). While the
hypothesis of whole-genome duplication in the earliest verte-
brates has been somewhat controversial (Hughes 1999; Friedman
and Hughes 2001; Makalowski 2001; Hughes and Friedman
2003), ancient polyploidy is supported by genetic and genomic
investigations of individual gene families as well as large syntenic
chromosomal segments (Abi-Rached et al. 2002; Gu et al. 2002;
McLysaght et al. 2002; Dehal and Boore 2005). The importance
of genome duplication in the evolution of amphibians (Bogart
1979) and the yeast Saccharomyces cerevisiae has been more
widely accepted (Wolfe and Shields 1997; Friedman and Hughes
2001; Kellis et al. 2004).
Polyploidy is common in many plant lineages, particularly
angiosperms (Stebbins 1950; Grant 1981; Soltis and Soltis 1999).
The angiosperms in particular have been the subject of consid-
erable speculation regarding the frequency of polyploidy. Classic
studies estimated that 30%­50% of angiosperms are polyploids
(Müntzing 1936; Darlington 1937; Stebbins 1950), and more re-
cently most if not all extant angiosperms have been implicated as
ancient polyploids (Grant 1963; Masterson 1994; Otto and Whit-
ton 2000). Some of these inferences were based on comparisons
of nuclear DNA content (C-value) or sequenced genome size,
across a broad spectrum of species. However, the rapid reduction
of duplicate genes immediately after polyploidization can dras-
tically shrink genome size and gene content (Ohno 1970; deWet
1979; Liu and Wendel 2003). Despite the small size of the Ara-
bidopsis thaliana genome (157 Mb) (Bennett et al. 2003), recent
investigations have revealed two or more rounds of ancient ge-
nome duplications (Vision et al. 2000; Simillion et al. 2002; Bow-
ers et al. 2003). Analysis of the rice genome also suggested an-
cient polyploidy in the early history of the grass family (Poaceae)
(Paterson et al. 2004b; Yu et al. 2005). It now appears that per-
haps all major lineages of eukaryotic genomes possess consider-
able numbers of duplicate genes that may have resulted from
genome duplications (Ohno 1970; Lynch and Conery 2000).
Whole-genome duplication, tandem gene duplication, and
segmental duplication all generate paralogous gene pairs. For
species with complete genome sequences, such as Arabidopsis,
rice, and now Populus, it is possible to differentiate whole-
11
Corresponding author.
E-mail cwd3@psu.edu; fax (814) 865-9131.
Article published online before print. Article and publication date are at http://
www.genome.org/cgi/doi/10.1101/gr.4825606.
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genome duplications from segmental and tandem duplications
by mapping chromosomal locations of duplicate genes or blocks
of genes (Simillion et al. 2002; Blanc et al. 2003; Bowers et al.
2003; Cannon et al. 2004; Paterson et al. 2004b). Lynch and
Conery (2000) proposed a genomic-scale approach to estimate
the age of gene duplication events and the fate of resulting
paralogous gene pairs by evaluating the frequency distribution of
per-site synonymous divergence levels (Ks) for pairs of duplicate
genes. After gene duplication, some paralogs will be silenced and
eventually be eliminated, while many of the preserved paralogs
may be subject to changes in DNA sequence or gene expression,
leading to sub- or neofunctionalization (Force et al. 1999; Adams
et al. 2003; Wang et al. 2004b).
Synonymous substitutions are largely immune to the strong
selective pressures that greatly impact the rate of protein diver-
gence (Li and Grauer 1991; Lynch and Conery 2000), and when
corrected for multiple substitutions that occur in highly diverged
sequences, these nearly neutral substitutions in protein-coding
regions can be used as a proxy for the amount of time that has
passed since gene duplication. A genome-wide duplication event
simultaneously creates thousands of paralogous pairs. Evidence
of past genome duplications can be seen as peaks in the distri-
bution of Ks values for sampled paralogous pairs (Lynch and Con-
ery 2000; Blanc and Wolfe 2004; Schlueter et al. 2004). This
method does not depend on genomic positional information,
and can be applied to any species for which there are moderately
large EST sets. Identification of duplicated blocks of genes in
genome sequences, however, provides much stronger evidence of
ancient polyploidy, although average Ks values (or Ka) (Vision et
al. 2000) can still be used to date the origin of duplicated blocks.
Using the large number of DNA sequences generated by EST and
genome sequencing projects, Blanc and Wolfe (2004) investi-
gated 14 model plant species (mostly crop species with known
recent polyploid history) and found spikes in the distributions of
older paralogous pairs (with higher Ks values) in nine species.
Schlueter et al. (2004) advanced the analysis of Ks distributions
by applying a finite mixture model (McLachlan et al. 1999) to
sets of paralogous pairs identified in large EST databases for eight
major crop species, including soybean, Medicago, tomato, potato,
maize, Sorghum, rice, and barley, and inferred multiple indepen-
dent genome duplications in Fabaceae, Solanaceae, and Poaceae
over the last 14­60 million years. In general, this method is only
suitable for duplicated genes with similar codon usage, because
Ks is affected by codon usage bias (Bierne and Eyre-Walker 2003;
Wang et al. 2004a).
All of the plants previously investigated using Ks distribu-
tions (Blanc and Wolfe 2004; Schlueter et al. 2004) belong to
either derived monocot (a single family, the Poaceae) or eudicot
lineages. Most species examined were either crop species or close
relatives, where a predisposition to polyploidy might have in-
creased the chances of having traits important for domestication
and agriculture (but see Hilu 1993). Until recently, there has been
very little sequence data available for phylogenetically pivotal
taxa representing the basal lineages of the eudicots, monocots, or
all angiosperms, and the genome histories of these lineages are
therefore poorly understood. Here and throughout this paper we
use the term "basal" when referring to a lineage that is sister to a
larger clade containing all other members of a particular group.
An understanding of ancient genome duplication in the basal-
most angiosperm lineages is especially important in understand-
ing the role of polyploidy in the origin and early diversification
of flowering plants (e.g., Buzgo et al. 2005; De Bodt et al. 2005;
Zahn et al. 2005a,b). We use sets of 9000­10,000 ESTs generated
for species representing basal angiosperms and basal eudicot lin-
eages (Albert et al. 2005) to assess the frequency of ancient ge-
nome duplications across all major extant angiosperm lineages
(Table 1) and to evaluate whether these data can elucidate the
timing of ancient genome duplication events in early angio-
sperm history.
To facilitate the interpretation of Ks distributions, we have
modeled the gene birth-and-death process both with and with-
out genome-wide duplication events. Our model provides a pre-
dicted age distribution for any sample of duplicate genes while
accounting for empirical estimation errors in Ks. The model was
used to generate predicted Ks distributions for sets of paralogous
pairs under the null hypothesis that the given gene births and
deaths occurred at constant rates. Null distributions were mod-
eled using parameter values and error corrections estimated for
each data set (see Methods). When the null hypothesis of a con-
stant birth-and-death process was rejected, the log-transformed
Ks distribution for each taxon was analyzed using a mixture
model to identify subpopulations of paralogous pairs generated
through one or more large-scale duplication events (McLachlan
et al. 1999; Schlueter et al. 2004). Our results provide evidence of
Table 1. Genome sizes and base chromosome numbers for the angiosperm and gymnosperm species in this study
Scientific name Common name Family Group
Genome size
(Mb/1C)
Chromosome
number (2n) Source
Arabidopsis thaliana Thale cress Brassicaceae Rosid 157 10 RBG, Kew
Glycine max Soybean Fabaceae Rosid 1103 40 RBG, Kew
Solanum lycopersicum Tomato Solanaceae Asterid 1005 24 RBG, Kew
Eschscholzia californica California poppy Papaveraceae Ranunculales 502 12 This study
Acorus americanus Sweet flag Acoraceae Monocot 392 24 This study
Liriodendron tulipifera Yellow-poplar Magnoliaceae Magnoliid 1710 38 This study
Persea americana Avocado Lauraceae Magnoliid 907 24 RBG, Kew
Saruma henryi Aristolochiaceae Magnoliid 3014 52 This study
Nuphar advena Yellow water lily Nymphaeaceae Basalmost angiosperm 2772 34 This study
Amborella trichopoda Amborellaceae Basalmost angiosperm 870 26 RBG, Kew
Pinus taeda Loblolly pine Pinaceae Gymnosperm 21,658 24 RBG, Kew
Pinus pinaster Pine Pinaceae Gymnosperm 23,863 24 RBG, Kew
Welwitschia mirabilis Welwitschiaceae Gymnosperm 7056 42 RBG, Kew
The relationships among the organisms and the major lineages are indicated in Figure 6. The sources for genome size data are the Royal Botanic Gardens,
Kew Plant C-value database (RBG, Kew; http://www.rbgkew.org.uk/cval/homepage.html) and this study--the DNA content determined by flow
cytometry as described in Wang et al. (2005).
Cui et al.
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ancient polyploidy throughout the major angiosperm lineages,
and support the possibility that a genome-scale duplication
event occurred prior to the rapid diversification of flowering
plants (Darwin 1903).
Results
Model parameters and their influence on the observed age
distribution of paralogs
To add statistical rigor to the interpretation of Ks distributions for
paralogous pairs, we modeled the expected age and Ks distribu-
tions under a constant-rate birth­death model (see Methods).
Whereas recent studies have shown that evidence of paleopoly-
ploidy is often (but not always) discernible in Ks plots for paralo-
gous pairs (Blanc and Wolfe 2004; Schlueter et al. 2004; Maere et
al. 2005), the accumulation of single gene duplications, variation
in the rates of gene death, and error in Ks estimates have not been
studied quantitatively. We model the rate of gene death, the time
since gene (or genome) duplication, and the error in Ks estimates
in analyses of paralogous pairs. Our null model assumes gene
birth and death are independent events, each with a constant
rate over time. Under this model, the expected age distribution
for paralogous pairs is a declining exponential with a decay pa-
rameter corresponding to the rate of gene death. Ks distributions
derived from simulations under this model are influenced by the
random nature of nucleotide substitution and the error in Ks
estimation. To formally test for deviation from a constant-rates'
model using empirical data, we generate a null distribution for
the frequency of Ks values using parameters estimated from the
data for the rate of gene death and the error in Ks estimation.
Our model was also used to simulate Ks distributions for
paralogous pairs arising from a mixture of single gene duplica-
tions and ancient polyploidy events. Empirical estimates of varia-
tion in Ks were based on analyses of A. thaliana paralogous pairs.
Figure 1 shows Ks distributions for data simulated with different
rates of gene death and different times since a genome duplica-
tion event. These Ks distributions contain two components; the
first one is always a declining exponential distribution corre-
sponding to "background" single gene duplications, and the sec-
ond component represents paralogous pairs arising from a poly-
ploidy event. Very recent genome duplications may be obscured
by background gene duplications because the modal Ks values do
not appear as distinct peaks. Conversely, increases in the number
of gene deaths and variance in Ks with time render older genome
duplications less detectable than younger events, with no signifi-
cant duplication signal recovered for events with an expected Ks
of 1.5 (Fig. 1C,F,I). High gene death rates also eroded the impact
of genome duplications on Ks distribu-
tions (Fig. 1G,H,I). These results cor-
roborate previous evidence that ancient
genome duplication events are not al-
ways detectable in analyses of Ks distri-
butions (Blanc and Wolfe 2004; Paterson
et al. 2004a).
Evidence of genome duplications in
diverse lineages of flowering plants
Model validation: Duplications detected
in eudicots
EST sets from A. thaliana, Glycine max
(soybean), and Solanum lycopersicum (to-
mato) were used to validate our test of
the constant-birth­death-rate model.
The genome duplication histories for
these species have been elucidated in
several previous analyses (Shoemaker et
al. 1996; Blanc et al. 2000; Grant et al.
2000; Ku et al. 2000; Vision et al. 2000;
Bowers et al. 2003). To make these analy-
ses comparable to analyses of the other
EST sets in this study, we randomly
sampled sets of 6000 unigenes, or
10,000 ESTs, from a much larger set of
available ESTs for each of these taxa (see
Methods).
To determine whether inference of
genome-wide duplication events de-
pends on the method of synonymous
substitution estimation, we compared
four methods of Ks estimation, including
the original Nei-Gojobori (NG) method
(Nei and Gojobori 1986), the modified
Nei-Gojobori (modified NG) method
(Zhang et al. 1998), the Goldman and
Figure 1. Effect of gene death rate and time of genome duplication on the Ks distribution for
paralogs. A single genome duplication was simulated, where time since duplication (corresponding to
Ks = 0.5 in A, D, and G; 1.0 in B, E, and H; or 1.5 in C, F, and I) is indicated by a star. The death rate
of duplicate pairs ( ) increases from the top row to the bottom row ( = 0.67 for A, B, C, as estimated
from Arabidopsis data; 1.34 for D, E, F; and 2.68 for G, H, I). In each graph, the observed frequency of
paralogs from background gene duplication is plotted with a dashed line, while the distribution
deriving from genome duplication is plotted with a dotted line. The Ks distribution of all paralogs is
drawn with a solid line.
Genome duplication in flowering plants
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Yang maximum likelihood (ML) method (Goldman and Yang
1994), and the YN00 (YN) method (Yang and Nielsen 2000). Re-
sults were similar across all Ks estimation procedures in analyses
of the Arabidopsis data set (Fig. 2A). Analyses of replicate sub-
samples from the random Arabidopsis unigenes gave very similar
results to analyses of all paralogous pairs (Fig. 2B; Lynch and
Conery 2000; Blanc et al. 2003; Maere et al. 2005), suggesting
that 6000 unigenes are sufficient for estimating Ks distributions
for the other species in this study (Table 2).
We estimated the rate parameter for Arabidopsis data
( = 0.67) assuming a constant-birth­death model (the null
model) and tested the expected distribution against the observed
distribution using a 2
test (Fig. 2C). The null model was rejected
(P 0.0001), and the quantile­quantile plot showed obvious de-
viation from the expected distribution of Ks values (bootstrapped
Kolmogorov-Smirnov test, P 0.0001) (Fig. 2D). Next, we ap-
plied the mixture model to estimate the median age (in Ks
equivalent units) of duplicate genes from recent or older dupli-
cation events (Table 3). This analysis, using ML distances, iden-
tified two significant components, a background component
with median Ks = 0.2889, and a prominent second component
including 79% of the paralogous pairs with a median Ks = 0.7510
that corresponded to the polyploidy peak detected by Blanc and
Wolfe (2004). Similar results were obtained when the YN, NG,
and modified NG Ks estimates were used, thus only ML distance
estimates are reported for all other analyses since they are typi-
cally less biased and have lower error rates, especially for more
divergent sequences (Yang and Nielsen 2000). We obtained simi-
lar results to those reported in previous studies (Blanc and Wolfe
2004; Schlueter et al. 2004), with much smaller subsamples of
ESTs (Fig. 2B).
We next analyzed public EST sets from selected libraries of
soybean and tomato. Soybean ESTs were sampled from flower,
young seedling, root, and other vegetative tissue libraries. Mix-
ture model analysis suggests that 71% of the paralogs were likely
to have arisen from a large-scale duplication (Table 3), which
appears as a significant peak in the Ks distribution with estimated
median Ks = 0.6705 (Fig. 3A). This species is a relatively recent
tetraploid (Shoemaker et al. 1996; Blanc and Wolfe 2004;
Schlueter et al. 2004). Thus many of the duplicate pairs assigned
to the first component in the mixture model are likely derived
from polyploidization rather than background single gene dupli-
cations.
The results for tomato also suggest large-scale duplications,
which account for >90% of paralogs. Moreover, the distributions
for paralogous gene pairs sampled from two tissue sources (floral
vs. nonfloral organs) were similar (Fig. 3B,C) and in agreement
with previous analyses based on all duplicate gene pairs in this
species (median Ks = 0.277 and 0.632) (Schlueter et al. 2004).
Together, our tests found strong signals of deviation from the
null model, and as expected, mixture model analyses suggested
ancient polyploidy events in Arabidopsis, Glycine, and Solanum.
Taken together, these results suggest that unbiased Ks distribu-
tions can be obtained from as few as 6000 unigenes sampled from
complex cDNA libraries derived from developing floral organs.
Ancient polyploidy in a basal eudicot
Eschscholzia californica (California poppy, Papaveraceae) is a
member of Ranunculales, the sister lineage to all other eudicots
(Soltis et al. 2000; Zanis et al. 2002; Borsch et al. 2003). Analysis
of the Ks distribution of 178 pairs of Eschscholzia paralogs rejected
the constant birth and death model (P 0.0001), and two com-
ponents in the distribution were identified by the mixture
model. The second component dominated the distribution, with
89% of the duplicate pairs (Fig. 3D), providing the first strong
Figure 2. Ks distribution from a sample of Arabidopsis unigenes and the
diagnostic test according to the constant birth­death model (null
model). (A) Ks estimates from four methods show strong agreement. (ML)
Maximum likelihood method by Goldman and Yang; (NG) Nei-Gojobori
method; (mNG) modified Nei-Gojobori method; (YN) Yang and Nielsen
method. These sample sizes are comparable to the unigenes available for
the species sequenced in this study. (B) Ks distributions for paralogs from
four replicate unigene samples of 6000 sequences each. (C) The density
plot of observed Ks distribution and simulated data based on the null
model with parameter = 0.67. (D) The Q-Q plot of observed versus
expected Ks values shows the poor fit of the null hypothesis that gene
birth and death rates are constant (P 0.0001).
Table 2. Summary of EST data sets and paralogous pairs
identified in this study
Scientific name ESTs Unigenes
Pairs with
Ks < 2 Source
Arabidopsis thaliana 6000a
205 DbEST
Glycine max 10,046 6240 125 DbEST
Solanum lycopersicum 10,028 5303 143 DbEST
Eschscholzia californica 9079 5713 178 PGN
Acorus americanus 7484 4663 149 PGN
Liriodendron tulipifera 9531 6520 92 PGN
Persea americana 8735 6183 196 PGN
Saruma henryi 10,273 6293 184 PGN
Nuphar advena 8442 6205 138 PGN
Amborella trichopoda 8629 6099 69 PGN
Pinus taeda 6000b
276 PlantGDB
Pinus pinaster 6000c
259 PlantGDB
Welwitschia mirabilis 9776 6048 157 PGN
a
Sampled from 6369 unigenes.
b
Sampled from 52,527 unigenes.
c
Sampled from 8076 unigenes.
Cui et al.
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evidence of probable ancient genome duplication in a basal eu-
dicot. Phylogenetic analyses of duplicated AGAMOUS and AP3
homologs (Kramer et al. 1998; Kramer and Irish 1999; Zahn et al.
2005a) have suggested that this duplication event occurred after
the split between Ranunculales and core eudicots. Thus, the ge-
nome-wide duplication evident in the Eschscholzia paralogous
pairs was probably independent of the genome duplications that
have been inferred from analyses of the Arabidopsis genome (Vi-
sion et al. 2000; Bowers et al. 2003; Maere et al. 2005).
Basal monocot
Acorus americanus (Acoraceae, Acorales) represents the sister lin-
eage to all other monocots (Duvall et al. 1993; Soltis et al. 2000,
2002; Zanis et al. 2002; Borsch et al. 2003; Hilu et al. 2003). Three
components were identified in the paralogous pairs by the mix-
ture model approach. The second component, accounting for
33% of all duplicates, was shown as a sharp peak in the Ks dis-
tribution, while the third component, containing 65% of the
duplicates, appeared as a broader peak (Fig. 3E). Based on the
distinct modes observed in the raw Ks distribution, we hypoth-
esize that the second and third components estimated in the
mixture model represent two distinct large-scale duplication
events. This hypothesis will be tested in future phylogenetic
analyses of well-sampled gene families.
Magnoliids
Both shared and lineage-specific genome duplications were in-
ferred from analyses of unigenes from three magnoliid species:
Liriodendron tulipifera (Magnoliaceae, Magnoliales), Persea ameri-
cana (Lauraceae, Laurales), and Saruma henryi (Aristolochiaceae,
Piperales). A total of 92 paralogous pairs was detected in the
Liriodendron unigene set. The constant-birth­death model was
rejected (P < 0.001), and a mixture of two components was iden-
tified in the Ks distribution, with the second component being
dominant (Fig. 4A). The null birth­death model was also rejected
in the P. americana (avocado) analysis (P 0.0001) with 196
paralogous gene pairs. The optimal mixture model also included
two components very similar to those seen for Liriodendron (Fig.
4B; Table 3).
To determine whether the duplication events inferred from
the Ks distributions of Liriodendron and Persea represented events
in a common ancestor, we first computed the median Ks of pu-
tatively orthologous gene pairs (408 pairs identified as recipro-
cal best hits in BLAST searches) and compared the median Ks
for orthologs with Ks values for paralogous pairs within each
species. The Ks distribution of putative ortholog pairs showed a
single major component (median = 0.8057, variance = 0.0858)
(Fig. 4F), inferred to be slightly older than the probable ge-
nome duplication observed in Persea (median = 0.6464, vari-
ance = 0.1197; P < 0.0001, Wilcoxon test). The timing of the du-
plication event inferred from the Liriodendron Ks distribution
(median = 0.7616, variance = 0.1328) relative to the divergence
of the Persea and Liriodendron lineages was ambiguous (P = 0.35),
and direct comparison of the Persea and Liriodendron Ks distribu-
tions may have been confounded by unequal substitution rates.
To account for possible variation in synonymous substitu-
tion rates between the Persea and Liriodendron lineages, we
aligned putatively orthologous genes from Liriodendron, Persea,
and Saruma and estimated Ks values for each lineage on a phy-
Table 3. Mixture model estimates for Ks distributions in each species
Scientific name n P lnL BIC Median Variance Proportion
Arabidopsis thaliana 202 2 162.498 351.54 0.2889 0.0473 0.21
0.751 0.0777 0.79
Glycine max 123 2 147.358 318.78 0.1873 0.0398 0.29
0.6705 0.1066 0.71
Solanum lycopersicum (floral) 139 2 118.607 261.89 0.0643 0.0066 0.09
0.7894 0.1021 0.91
Solanum lycopersicum (nonfloral) 119 2 122.933 269.76 0.1857 0.0547 0.15
0.7885 0.1425 0.85
Eschscholzia californica 178 2 161.652 349.21 0.0871 0.0043 0.11
0.7098 0.087 0.89
Acorus americana 139 3 103.568 246.61 0.0118 0.001 0.01
0.455 0.0046 0.33
0.5813 0.1309 0.65
Liriodendron tulipifera 87 2 94.046 210.42 0.1005 0.0121 0.14
0.7616 0.1328 0.86
Persea americanus 186 2 196.998 420.12 0.0234 0.0004 0.07
0.6464 0.1197 0.93
Saruma henryi 146 2 162.789 350.5 0.0913 0.0168 0.2
0.7927 0.1066 0.8
Nuphar advena 134 3 159.416 358.02 0.1746 0.0461 0.37
0.4291 0.0202 0.56
1.3273 0.0084 0.07
Amborella trichopoda 49 1 80.676 169.14 0.2698 0.1147 1
Pinus taeda 227 1 405.77 822.39 0.0839 0.0147 1
Pinus pinaster 240 1 373.135 757.23 0.2499 0.0819 1
Welwitschia mirabilis 132 2 181.128 386.67 0.1139 0.0271 0.35
0.9519 0.1374 0.65
Initial tests against the null model (no genome duplication) were conducted, then a mixture analysis was applied to each species. The final mixture
model was selected according to the Bayesian Information Criterion (BIC) and restriction on the mean/variance structure for Ks (see Methods). (n)
Sample size; P, number of mixture components, lnL, log likelihood for the mixture model. For each mixture model, the proportions for each
component (subpopulation) sum to 1.
Genome duplication in flowering plants
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logeny. We examined 19 putative orthologous gene sets in the
three species with alignments of at least 400 bp for all taxa (see
Methods; Supplemental Table S2) and found that Ks on the lin-
eage leading to Liriodendron was slower on average than the rate
on the lineage leading to Persea. For example, in the tree for the
orthologous set shown in Figure 4G, the branch length (in Ks
units) for the branch leading to Persea is 1.31 times that leading
to Liriodendron. The ratio of synonymous substitutions on the
Persea branch relative to the Liriodendron branch ranged from
0.86 to 2.68, and the ratio was greater than one in 16 of 19 cases
(Supplemental Table S2). When Liriodendron paralog Ks values
were multiplied by the median branch-length ratio, 1.29, the
peak in the scaled Liriodendron Ks distributions matched an older,
but nonsignificant peak in the Persea Ks distribution (Fig. 4E).
Taken together, these analyses suggest that the prominent peak
in the Liriodendron Ks distribution (median = 0.82) represents a
duplication event in the common ancestral genome of Magno-
liales and Laurales that had not been identified as a distinct com-
ponent in the mixture model for the Persea Ks distribution. In
line with the comparison of Ks values for Persea paralogs and
putative Liriodendron­Persea orthologs, we interpret the domi-
nant peak in the Persea Ks distribution to represent a genome-
scale duplication event that occurred after the divergence of Mag-
noliales and Laurales. This hypothesis needs to be tested with
additional data.
Saruma henryi is a member of Piperales, which (with Canel-
lales) is sister to the Magnoliales/Laurales clade (Soltis et al. 2000,
2002; Zanis et al. 2002; Borsch et al. 2003). The Ks distribution of
Saruma paralogs showed a distinct peak with median Ks = 0.7927
(Fig. 4C; Table 3). This is lower than the
median Ks for 202 Saruma­Liriodendron
ortholog pairs (0.9555, P = 0.0001) and
the median Ks for 254 putative Saru-
ma­Persea ortholog pairs (1.0121,
P < 0.0001) (Fig. 4F). We therefore sur-
mise that the peak in the Ks distribution
of Saruma paralogous pairs represents a
large-scale duplication in Piperales after
divergence from the Magnoliales and
Laurales lineages.
Basal-most angiosperms
Amborella trichopoda (Amborellaceae)
and the water lilies (Nymphaeales) are
either successive sister lineages to all
other extant angiosperms, or together
form a clade that is sister to the rest of
the angiosperms (Zanis et al. 2002; Stefa-
novic et al. 2004; Leebens-Mack et al.
2005). The Ks distribution for a total of
69 Amborella paralogous pairs appeared
to follow an exponential distribution,
but the uniform birth­death process was
rejected (P < 0.01; Figure 5A). However,
the mixture model analysis identified
only one component containing all of
the gene pairs (Table 3). Nymphaeales
are represented by Nuphar advena. A to-
tal of 138 paralogous pairs was identi-
fied, and the resulting Ks distribution did
not fit the constant birth­death model
(P < 0.01). Three mixture components
were estimated from the Ks distribution. The second component,
accounting for 56% of the paralogous pairs, provided strong evi-
dence for ancient polyploidy in the history of the Nuphar ge-
nome (Fig. 5B). The third component, with a median Ks of
1.3273, may represent the oldest genome duplication to be de-
tected in analyses of angiosperm Ks distributions. The median Ks
for the third component was not distinguishable from the me-
dian Ks value for putative Amborella­Nuphar orthologs (Fig. 5C)
(median Ks[orthologs] = 1.24, variance = 0.1918, based on 113
putatively orthologous sequence pairs; P = 0.05, two-sample t-
test on the log Ks[orthologs] and log Ks[third component of
Nuphar paralogs]). Therefore, the third component in the Nuphar
Ks distribution may correspond to a polyploidy event that oc-
curred at approximately the time of divergence between the Am-
borella and Nuphar lineages (see Discussion).
Gymnosperms
We obtained 52,527 unigenes for Pinus taeda (loblolly pine) from
PlantGDB (Dong et al. 2004), and a random sample of 6000 uni-
genes was drawn to match the sample size for other species we
investigated. The Ks distribution showed a clear monotonous de-
cay of paralogs with increasing age and no detectable sign of
genome duplication in recent history (P = 0.16) (Fig. 5D). The
frequency distribution for all paralogous pairs was essentially
identical. The analysis of Pinus pinaster yielded a similar expo-
nential distribution (Table 3).
The constant-birth­death model was rejected for Wel-
witschia (P < 0.01), and a mixture analysis of the Ks distribution
Figure 3. Ks distributions of paralogs in selected angiosperm species, with fitted densities from
mixture model analysis, suggest paleopolyploidy in eudicots and monocots. Each fitted line indicates
a subpopulation in the mixture. The first (leftmost) component corresponds to paralogs from back-
ground gene duplications; other peaks indicate estimated median Ks for ancient duplications. (A)
Glycine max (soybean). (B,C) Solanum lycopersicum (tomato), data from floral tissue (B) and nonfloral
tissue (C). (D) A basal eudicot, Eschscholzia californica (California poppy). (E) A basal monocot, Acorus
americanus.
Cui et al.
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identified two components (Fig. 5E). The second component,
corresponding to the heavy right-hand tail of the distribution,
may represent one or more ancient duplication events, or a re-
duced rate of gene death for older duplicates.
Discussion
In this paper, we introduce a model-based statistical test that
accounts for estimation error in Ks values in terms of deviation
from a constant rate of gene birth and death. This represents a
refinement of previous studies using Ks distributions, which have
yielded significant insights into genome duplications (Force et al.
1999; Lynch and Conery 2000; Blanc and Wolfe 2004; Schlueter
et al. 2004). The birth­death model developed here for dupli-
cated genes is a natural extension of stochastic birth-and-death
models that have been widely used in population and phyloge-
netic approaches to studies of gene family evolution (Karev et al.
2004). Simulations based on this model have allowed us to in-
vestigate how specified death rates and duplication times result
in Ks distributions with (or without) secondary peaks or heavy
tails (e.g., Fig. 1). The model can be extended to incorporate
variable rates of gene birth or death over time, and in the ex-
treme, an instant burst of gene birth corresponding to a whole-
genome duplication. Although our results could not exclude par-
tial and segmental duplication events, the birth­death model
was validated with genomes with known
duplication histories where detection of
whole­genome events was expected.
We found that three major factors
influence the frequency and observed
divergence of paralogous pairs arising
from genome-wide duplications. The
time since the duplication event, the
rate of gene death, and the background
rate of gene birth all influence observed
Ks distributions. Very recent genome du-
plication events are associated with Ks
values for resulting paralogous pairs that
are indistinguishable from those of back-
ground single-gene duplications using
EST data. For example, polyploidy is not
clearly evident in the Ks distribution for
hexaploid wheat because there has been
little divergence among the parental or
homeologous gene copies, and the range
of divergence for allelic variants was not
distinct from that of paralogs arising
from recent gene duplications (Blanc
and Wolfe 2004). At the same time, evi-
dence of very ancient genome duplica-
tions is eroded as synonymous substitu-
tions reach saturation and variance in Ks
increases. This may be evident in Ks
plots for wheat, maize, rice, and barley,
for which evidence for a genome dupli-
cation event some 50­60 million years
ago (Mya) in the common ancestor of all
major grain lineages has been obscured
(Blanc and Wolfe 2004; Paterson et al.
2004a). Detection of very old duplica-
tion events in Ks distributions is espe-
cially difficult in species with high synonymous substitution
rates. Conversely, evidence for the oldest detectable genome-
wide duplications will be found in Ks distributions for species
with the slowest substitution rates (see below).
Concurrent expansion of a few gene families could lead to
moderate deviations from our null model. This is especially true
if ancient duplication events are overrepresented in sets of
sampled paralogous pairs, or if major adaptive radiations of in-
dividual gene families preceded or accompanied the diversifica-
tions of the organismal lineages under study. In this study, we
avoided over-counting of ancient gene duplications by con-
straining genes to be included in only one paralogous pair. Our
analysis of duplicated Arabidopsis genes verified that this ap-
proach produced Ks distributions similar to those of previous
studies that implemented more elaborate corrections for gene
family expansions (Maere et al. 2005). Moreover, sampled paralo-
gous genes were not particularly biased toward large gene fami-
lies. Whereas most sampled duplicate genes belonged to the
housekeeping functional categories, such as protein synthesis,
proteolysis, and energy metabolism (Supplemental Table S1),
none of the duplicate gene sets was dominated by a single gene
family. Several transcription factor families were also identified
in our paralog pairs, but again, no family accounted for more
than a few percent of the duplicate gene pairs.
Our results for Persea (Lauraceae) and Liriodendron (Magno-
liaceae) corroborate previous evidence of ancient polyploidy
Figure 4. Ks distributions of paralogs and orthologs among magnoliids suggest independent dupli-
cations and possibly shared genome duplication events in Laurales (Persea) and Magnoliales (Lirioden-
dron). (A,B,C) The Ks distributions for (A) Liriodendron, (B) Persea, and (C) Saruma, with fitted lines based
on the mixture model analysis. (D) The Ks distribution for Liriodendron and Persea, without scaling for
rate differences between lineages. (E) Ks distribution for paralogs in Liriodendron after rate calibration
(adj = adjusted), compared with that of Persea, suggesting recent independent duplication and older
shared genome-scale duplications. (F) Ks distribution for orthologs of two magnoliid species. (Ltu)
Liriodendron; (Pam) Persea; (She) Saruma. (G) Phylogeny of one representative orthologous gene set
used for relative rate estimates. The branch lengths show the estimated relative rates of synonymous
evolution in respective species.
Genome duplication in flowering plants
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from isozyme studies (Soltis and Soltis 1990). Soltis and Soltis
(1990) found that 25%­29% of the loci investigated were dupli-
cated in both families, and hence could have arisen via poly-
ploidy. All members of Magnoliaceae examined shared the same
isozyme duplications (PGI, TPI, 6PGD), while the species of Lau-
raceae shared a similar suite of isozyme duplications (PGM, TPI,
6PGD, GDH). These were interpreted as evidence for paleopoly-
ploid events occurring very early in the evolutionary history of
Magnoliaceae and Lauraceae. The Persea and Liriodendron paralo-
gous genes suggest polyploidy in a common ancestor at least 100
Mya (Bell et al. 2005) followed by a second round of polyploidy
in the Persea lineage (Fig. 4E), but this hypothesis must be tested
with analyses of additional gene family phylogenies. If this sce-
nario is correct, the duplicated isozyme loci observed in the Mag-
noliaceae and Lauraceae may have arisen from a polyploidy
event that predated the separation of the two families (cf.
Brysting and Borgen 2000).
Over time, nucleotide substitutions can become saturated,
and therefore lineages with slow synonymous substitution rates
will provide a deeper view into genome history relative to lin-
eages with faster substitution rates. It is estimated that the syn-
onymous substitution rate in palm (2.61 10 9
synonymous
substitutions/per year) (Gaut et al. 1996) is only about half that
reported for grasses, eudicots (Lynch and Conery 2000), and
grass­eudicot comparisons (Wolfe et al. 1987). We infer a simi-
larly slow substitution rate for other basal angiosperms based on
the Magnoliales­Laurales divergence as a calibration point. We
estimated a synonymous site divergence of Ks = 0.7 for Lirioden-
dron and Persea ortholog pairs (Fig. 4F). Using a divergence date
estimate of 116 Mya for the Magnoliales­Laurales split (Bell et
al. 2005), we estimate an average synonymous substitution rate
of 3.02 10 9
synonymous substitutions/year. The low substi-
tution rate in Liriodendron and Persea may be explained in part by
their longer generation times (these lin-
eages are trees and shrubs) relative to
model eudicot and grass species.
We found that the median for the
oldest component in the Nuphar Ks dis-
tribution is close to the median Ks for
putative Amborella­Nuphar orthologs
(median Ks = 1.24) (Fig. 5C). This level of
divergence is compatible with the syn-
onymous divergence for the very early
duplication in Arabidopsis (i.e., dupli-
cation) (Bowers et al. 2003; De Bodt et al.
2005; Maere et al. 2005). Direct dating of
the early Nuphar peak based on the Ks
data is challenging because of uncer-
tainty in the branching relationships be-
tween Amborella, Nuphar, and the rest of
the angiosperms, and the possibility of
additional rate variation as was seen for
magnoliids. We adopted two approaches
to date the earliest event in Nuphar. First,
using the median Ks Amborella­Nuphar
ortholog divergence of 1.24 and a cali-
bration range of 134­165 Mya (Leebens-
Mack et al. 2005) gives a rate of 4.66­
3.79 10 9
substitutions per silent site
per year. Therefore, Ks = 1.33 (the early
Nuphar duplication event) would predict
an age range between 143 and 173 Mya
for the split between these two lineages. An alternative calcula-
tion, using the magnoliid calibration of 3.02 10 9
substitu-
tions per silent site per year, leads to an estimate of 220 Mya for
the divergence of lineages leading to Amborella and Nuphar.
This range of age estimates supports two alternative inter-
pretations of the Nuphar and Amborella paralog Ks distributions.
The third component in the Nuphar Ks distribution may repre-
sent polyploidy in a common ancestor of all angiosperms (Fig. 6),
in agreement with recent analyses of MADS-box gene families
(Kim et al. 2004; Buzgo et al. 2005; Zahn et al. 2005a). This
scenario would require that evidence of ancient polyploidy has
been sufficiently eroded as to be undetected in analyses of EST
samples from Amborella and various other angiosperm species
owing to gene death and/or saturation of synonymous substitu-
tions as discussed above. For example, the nonsignificant peaks
around Ks = 1.5 in the Liriodendron and Persea Ks distributions
(Fig. 4A,B) may provide weak evidence of polyploidy early in
angiosperm history. Alternatively, the earliest duplication peak
detected in the Nuphar analysis may trace back to a genome du-
plication in the common ancestor of Nuphar and all extant an-
giosperm lineages other than Amborella (Fig. 6). This scenario
would be consistent with the hypothesis that Amborella is sister
to all other extant angiosperms (e.g., solid line on Fig. 6), and the
extremely low proportion of duplicate genes found in the Ambo-
rella unigene set. This scenario also would narrow the timing of
a genome duplication to 10 Myr separating the branching
points for Amborella and all other extant angiosperm lineages
(Leebens-Mack et al. 2005). As discussed above, however, there
have been instances where known genome duplication events
have not been detected in Ks distributions (Fig. 1; Blanc and
Wolfe 2004; Paterson et al. 2004b), thus lack of evidence for
ancient polyploidy in the Amborella Ks distribution does not ex-
clude the possibility of polyploidy in an ancestral genome. More
Figure 5. Ks distributions suggest possible genome duplications in basal angiosperms, and no evi-
dence for genome duplication events in Amborella and some gymnosperm species. (A) Ks distribution
in Amborella, a basal-most angiosperm. No significant large-scale duplication is detected. (B) Three
distinct components in the Ks distribution for Nuphar, also a basal-most angiosperm, suggest at least
two large-scale genome duplications. (C) Ks distribution for putative orthologs between Amborella and
Nuphar. (D) Pinus taeda (loblolly pine) paralogous pairs follow the null model (see Methods). (E) Ks
distribution for paralogs in a gymnosperm, Welwitschia.
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sequence data, and ultimately whole genome sequences, will be
needed from Amborella, water lilies, and other early branching
angiosperm species to select among these alternative scenarios
for polyploid origins of angiosperms.
While genomic sequences have revealed evidence of poly-
ploidy in Poaceae and core eudicots, the secondary peaks found
in paralog Ks distributions for representatives of virtually all ma-
jor angiosperm lineages support the notion that genome dupli-
cations are common in angiosperm history and gene birth and
death are important processes in plant evolution (Lynch and
Conery 2000). The evidence now supports the hypothesis pro-
posed initially decades ago by Stebbins (1950) that angiosperms
have experienced repeated rounds of polyploidization through-
out their evolutionary history. Many questions follow: How
many polyploidy events separate different plant lineages? What
is the typical fate of genes generated through these duplication
events? And perhaps most intriguingly, have polyploidy events
been important engines of angiosperm diversification? Genome-
scale sequencing of phylogenetically crucial angiosperm species
would provide the data necessary to directly test whether the
rapid diversification of flowering plants following their origin
(Darwin 1903) was associated with one or more polyploidy
events.
Methods
EST sequencing and assembly
EST sequences from floral cDNA libraries of seven species (Am-
borella trichopoda, yellow water lily [Nuphar advena], avocado [Per-
sea americana], yellow-poplar [Liriodendron tulipifera], wild ginger
[Saruma henryi]), sweet flag [Acorus americanus], and Cali-
fornia poppy [Eschscholzia californica]) are available through the
Plant Genome Network (http://www.pgn.cornell.edu). cDNA li-
brary construction, EST sequencing, and assembly were described
previously (Albert et al. 2005).
Public EST sets from selected libraries for Arabidopsis
thaliana, soybean (Glycine max, Williams 82), and tomato (Sola-
num lycopersicum, cultivar TA496) were downloaded from the
GenBank dbEST section, trimmed using seqclean, and assembled
using CAP3 with the percent identity parameter P = 90 and over-
lap length 40 bp. A. thaliana ESTs were from four libraries (root,
flower, green silique, and 2- to 6-wk above-ground organs). To
minimize the allelic variations in the EST sequence collection,
the unigenes were mapped to the Arabidopsis genome, and re-
dundant unigenes matching the same genomic locus were dis-
carded. Only the sequences that matched the protein-coding re-
gions were retained. From this screened unigene set, we drew
replicate samples with 6000 unigenes in each sample. The sample
size of 6000 Arabidopsis unigenes approximates the number of
unigenes from new EST data sets we analyzed. To see if library
sources influence estimates, we analyzed two samples of tomato
ESTs, one from floral cDNA libraries and one from vegetative
cDNA libraries. The soybean ESTs were sampled from cDNA li-
braries of flower, young seedling, root, and other vegetative or-
gans. Unigenes for gymnosperms Pinus taeda and Pinus pinaster
were downloaded from PlantGDB (Dong et al. 2004), which were
built with public ESTs from all libraries. For each species, we
sampled 6000 unigenes for Ks analysis.
Ks calculation for paralogs and orthologs
Paralogous pairs of sequences were identified from best reciprocal
matches in all-by-all BLASTN searches. For data sets with trace
files, we discarded bases with Phred (Ewing and Green 1998; Ew-
ing et al. 1998) quality values lower than 20. Only sequence pairs
with alignment lengths >300 bp were used for Ks calculations.
Translated sequences of unigenes generated by ESTScan (Iseli et
al. 1999) were aligned using MUSCLE v3.3 (Edgar 2004). Nucleo-
tide sequences were then forced to fit the amino acid alignments.
The Ks value for each sequence pair was calculated using the
Goldman and Yang maximum likelihood method (Goldman and
Yang 1994) implemented in codeml with the F3 4 model (Yang
1997). In order to assess whether the shape of Ks distributions
was dependent on the estimation procedure, the Nei-Gojobori
method, the modified Nei-Gojobori method, and the YN00
method (Yang and Nielsen 2000) were also applied on the Ara-
bidopsis set. The Ks frequency in each interval size of 0.05 within
the range [0, 2.0] was plotted.
The age distribution of paralogs under a constant birth­death
model (the null model)
We modeled the birth and death of paralogs formed by gene
duplications under a constant-rate birth­death model in order to
test whether an observed frequency distribution of Ks values in-
dicates deviation from this process. The duplicate genes are gen-
erated by a Poisson process at rate , and the number of duplicate
pairs decreases by age at an exponential rate . We can estimate
the age distribution of surviving paralogs (survivors), total N, by
considering the process as sampling gene birth over time [0, t],
and decide if each birth was a survivor.
The distribution for the number of survivors of age t is
N t  Po
0
t
exp s ds = Po F t ,
where = / , and F(t) = 1 exp( t), the cumulative density
function of exponential ( ). From this we deduce that the popu-
Figure 6. Phylogenetic summary of paleopolyploidy events estimated
by the mixture model approach and their distribution among angio-
sperm and gymnosperm lineages. Scaled graph in center with Xs corre-
sponding to median Ks of pairs from background gene duplications, while
small ovals indicate the median Ks of possible concentrated duplications
in the history of particular lineages. The phylogenetic tree at left shows
the likely placement of detected genome-scale duplications. Uncertainty
in phylogenetic timing of what may be a single duplication event at the
base of the angiosperms is indicated with a wide oval that covers possible
branching points compatible with the Ks evidence. Hollow ovals indicate
duplications identified in previous studies using paralogous genes or ge-
nomic data from those lineages.
Genome duplication in flowering plants
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lation size N( ) = Po( ). Furthermore, the survivors' age distribu-
tion is an empirical distribution of a sample of exponentially
distributed random variables, generated with the parameter .
To obtain an estimate of the true age, we must consider the
error of Ks with respect to the true age of paralogs. If the true age
is T, then we can calculate Ks (with error) as
Ks = T + (s|t) z,
where s|t is the standard error for Ks at T = t, and z is a standard
normal random variable. The error can be estimated from the
empirical standard error given by the PAML software.
The mean of s is expected to correlate with the time t, since
older Ks estimates have larger variances. The conditional distri-
bution of s can be approximated by exponential (2/t). The maxi-
mum likelihood estimate of the parameter from the data was
obtained using a grid-based method, and a simulated sample un-
der the null model was compared to the observed using a 2
test.
A quantile­quantile plot (Q-Q plot) was used to visualize the
difference between observed data and a simulated data set ac-
cording to the null model. A strong deviation from the 45° line in
the Q-Q plot suggests that the two distributions differ, and a
bootstrapped Kolmogorov-Smirnov test (http://sekhon.polisci.
berkeley.edu/matching/ks.boot.html) was applied to compare
the observed and expected Ks distributions. The modeling and
simulation scripts are available as Supplemental data.
Finite mixture model of genome duplications
In order to explore further how genome-wide duplication events
influence the age distribution of paralogs and Ks distributions, we
defined "background duplication" as gene duplication under the
constant-rate birth­death process, and a "genome duplication"
as an instant spike of gene birth overlaid on top of the back-
ground. We modeled changes in Ks distributions with increasing
time since a duplication event, while assuming a constant rate of
gene loss (death rate) and a constant background gene duplica-
tion rate (birth rate). Each simulation included a genome dupli-
cation (which led to new duplicates n) at time t. About 5% of
duplicates were allowed to escape the death process.
In all instances when we rejected the constant rates hypoth-
esis, we surmised that the observed Ks distributions actually re-
flect a compound distribution generated by variable birth and/or
death rates from the time of duplication. For example, a genome
duplication event would generate an immediate spike in the
birth of paralogs. Mixture models treat the distribution of inter-
est as a mixture of several component distributions in various
proportions. The EMMIX software is suitable for mixed popula-
tions, where each component can be described by a Gaussian
density (McLachlan et al. 1999) (see http://www.maths.uq.
edu.au/gjm/emmix/emmix.html for the Users' Guide). Follow-
ing Schlueter et al. (2004), we modeled the log-transformed Ks
distribution of paralogs. (The actual distribution is a mixture of
log-transformed exponentials and normals.) Observations with
Ks < 0.005 were excluded to avoid fitting a component to infinity
(Schlueter et al. 2004). This truncation might also reduce the
proportion of gene pairs attributed to background duplication.
We modeled the mixed populations with one to four compo-
nents and repeated the EM algorithm 100 times with random
starting values, as well as 10 times with k-mean start values. One
restriction imposed on the variance structure of Ks is that vari-
ance increases with the mean according to the empirical esti-
mates. The observed data could therefore often be fitted to more
than one component, with different means, variances, and mix-
ture proportions. The mixture model with the best fit was iden-
tified using the Bayesian Information Criterion (Schwarz 1978).
The mean and variance for each component (subpopulation of
log Ks values) for the selected model were back-transformed to
the original scale for plotting and interpretation.
Calibrating rate of synonymous substitution across lineages
When comparing Ks distributions among taxa, variation in the
substitution rates among lineages must be taken into account.
We used a phylogenetic approach to estimate lineage-specific
synonymous substitution rates on branches leading to the mag-
noliids L. tulipifera, P. americana, and S. henryi. Orthologous genes
from A. thaliana, rice, and the three magnoliid species were clas-
sified by InParanoid (Remm et al. 2001). Protein alignments of
Arabidopsis and rice gene models (the TIGR Arabidopsis thaliana
database, the TIGR rice database) were first constructed, then
DNA alignments were forced to protein alignments by codon
positions. A maximum likelihood tree was estimated using the
HKY model in PHYML v.2.4.3 (Guindon and Gascuel 2003) for
each putative ortholog set including at least 400 aligned nucleo-
tide positions. A per-site estimate of Ks was then made for each
magnoliid branch in gene phylogenies consistent with organis-
mal relationships ([Liriodendron, Persea] Saruma) using codeml in
the PAML package (Yang 1997). The ratio of Ks values on the
Persea branch relative to the Liriodendron branch was then esti-
mated for each gene.
Two supplemental tables and R-scripts for birth­death simu-
lations are available as Supplemental material. Teri Solow and
Lukas Muller provided the EST sequence assembly for eight spe-
cies (A. americanus, A. trichopoda, E. californica, L. tulipifera, N.
advena, P. americana, S. henryi, and Welwitschia mirabilis), now
available through the Plant Genome Network (http://pgn.
cornell.edu/).
Acknowledgments
We thank Jongmin Nam for providing code for Ks computation;
Lena Scheaffer, Yi Hu, and Shelia Plock for technical support on
cDNA library construction and sequencing; Lukas Mueller, Dan
Ilut, Teri Solow, and Steve Tanksley for the PGN Database; and
anonymous reviewers for critical comments on the manuscript.
This work was supported by NSF Plant Genome award DBI-
0115684.
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