generations with a sample frequency of 2000. All
other settings were kept at default values.
In order to test our two scenarios of species
delimitation (three species vs. two species with
L. valdiviana and L. yungensis combined), we
reduced our final dataset to biallelic SNPs for the
members of L. section Uninerves, which dramatically decreased the number of SNPs to 56.
We then estimated Marginal Likelihood
(log-ML) values with SNAPP (Bryant et al.
2012) implemented in BEAST v2.3.2 (Bouckaert
et al. 2014) by conducting ten separate runs of
path sampling for each scenario using 100 steps,
a chain length of 100,000, and a preburn-in of
10,000. Priors for the Yule birth rate (k), the
population size parameter (h), and the backward
and forward mutation rates (u, v) were accepted
as given by the BEAST companion programme
BEAUTI v2.3.2. We performed some basic
statistic tests in R v3.3.3 (R Core Team 2017) to
search for a significant trend to favour one of the
species delimitation scenarios over the other
from the log-ML values. First, we tested the data
for normality using the Shapiro–Wilk normality
test, and second, the data were tested for
homoscedasticity using the Bartlett test. Since
the data showed homoscedasticity but
non-normality, we used the Kruskal–Wallis test
to test the stochastic homogeneity of the log-ML
values for the two scenarios.
11.3 Results
The GBS approach yielded between ca. 370,000
and 2.4 mio raw reads per investigated clone
(Table 11.2). The mapping rates were the highest
for members of L. section Lemna with an average
value of 49%. For members of all other sections,
the rate of reads that could be mapped to the
L. minor reference genome was noticeably lower
(Table 11.2). Nevertheless, our final dataset comprised of 2233 SNPs with an average number of
1693 SNPs per clone without missing data. The
outgroup species Spirodela polyrhiza and Landoltia punctata had the least complete SNP data
with 878 and 483 SNPs without missing data,
respectively, which indicated a high divergence of
these two species to the genus Lemna. The number
of pairwise SNP differences is shown in
Table 11.3. Each clone was represented by a
unique SNP profile. As expected, pairwise SNP
differences are bigger between clones of different
sections than between clones belonging to the
same section, that are again bigger than SNP differences between clones of the same species.
Especially, the number of SNP differences
between clones of L. minuta was relatively small.
The Bayesian majority-rule consensus tree for
the 11 clones of L. minuta, L. valdiviana, and
L. yungensis, i.e. all species of L. section Uninerves, showed a clear separation of L. minuta
from the other two species, while L. valdiviana
and L. yungensis could not be separated into distinct clades (Fig. 11.1). This is in coherence with
our species delimitation scenario B. This was also
supported by the log-ML values as estimated by
SNAPP. Scenario A had a mean log-ML value of
−315.45 (sd 23.20) and scenario B had a mean
log-ML value of −281.14 (sd 41.14). The
Kruskal-Wallis test revealed that the log-ML
value for scenario B is significantly higher than
that of scenario A (X
2 = 4.8, df = 1, P-value =
0.03), additionally supporting the synonymisation
of L. valdiviana and L. yungensis.
In order to analyse the position of L. section
Uninerves within the genus Lemna, the data were
analysed in a tree, with L. punctata and
S. polyrhiza as outgroups (Fig. 11.2). Each species was covered by only one clone outside of
L. section Uninerves, which was separated with
high posterior probability from all other clades.
The conspicuous long branch lengths confirm the
special position of this section within the genus.
Within the section, the differences between the
three species were so small that hardly any distinction in this rooted tree could be visualised
(cf. scales in Figs. 11.1 and 11.2). With one
exception (one subgroup of L. section Lemna),
all other nodes had a high posterior probability
support of 1. The main clades equal the common
categorisation in sections, i.e. besides L. section
Uninerves, the sections L. section Alatae, L.
section Biformes, and L. section Lemna.
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M. Bog et al.
other settings were kept at default values.
In order to test our two scenarios of species
delimitation (three species vs. two species with
L. valdiviana and L. yungensis combined), we
reduced our final dataset to biallelic SNPs for the
members of L. section Uninerves, which dramatically decreased the number of SNPs to 56.
We then estimated Marginal Likelihood
(log-ML) values with SNAPP (Bryant et al.
2012) implemented in BEAST v2.3.2 (Bouckaert
et al. 2014) by conducting ten separate runs of
path sampling for each scenario using 100 steps,
a chain length of 100,000, and a preburn-in of
10,000. Priors for the Yule birth rate (k), the
population size parameter (h), and the backward
and forward mutation rates (u, v) were accepted
as given by the BEAST companion programme
BEAUTI v2.3.2. We performed some basic
statistic tests in R v3.3.3 (R Core Team 2017) to
search for a significant trend to favour one of the
species delimitation scenarios over the other
from the log-ML values. First, we tested the data
for normality using the Shapiro–Wilk normality
test, and second, the data were tested for
homoscedasticity using the Bartlett test. Since
the data showed homoscedasticity but
non-normality, we used the Kruskal–Wallis test
to test the stochastic homogeneity of the log-ML
values for the two scenarios.
11.3 Results
The GBS approach yielded between ca. 370,000
and 2.4 mio raw reads per investigated clone
(Table 11.2). The mapping rates were the highest
for members of L. section Lemna with an average
value of 49%. For members of all other sections,
the rate of reads that could be mapped to the
L. minor reference genome was noticeably lower
(Table 11.2). Nevertheless, our final dataset comprised of 2233 SNPs with an average number of
1693 SNPs per clone without missing data. The
outgroup species Spirodela polyrhiza and Landoltia punctata had the least complete SNP data
with 878 and 483 SNPs without missing data,
respectively, which indicated a high divergence of
these two species to the genus Lemna. The number
of pairwise SNP differences is shown in
Table 11.3. Each clone was represented by a
unique SNP profile. As expected, pairwise SNP
differences are bigger between clones of different
sections than between clones belonging to the
same section, that are again bigger than SNP differences between clones of the same species.
Especially, the number of SNP differences
between clones of L. minuta was relatively small.
The Bayesian majority-rule consensus tree for
the 11 clones of L. minuta, L. valdiviana, and
L. yungensis, i.e. all species of L. section Uninerves, showed a clear separation of L. minuta
from the other two species, while L. valdiviana
and L. yungensis could not be separated into distinct clades (Fig. 11.1). This is in coherence with
our species delimitation scenario B. This was also
supported by the log-ML values as estimated by
SNAPP. Scenario A had a mean log-ML value of
−315.45 (sd 23.20) and scenario B had a mean
log-ML value of −281.14 (sd 41.14). The
Kruskal-Wallis test revealed that the log-ML
value for scenario B is significantly higher than
that of scenario A (X
2 = 4.8, df = 1, P-value =
0.03), additionally supporting the synonymisation
of L. valdiviana and L. yungensis.
In order to analyse the position of L. section
Uninerves within the genus Lemna, the data were
analysed in a tree, with L. punctata and
S. polyrhiza as outgroups (Fig. 11.2). Each species was covered by only one clone outside of
L. section Uninerves, which was separated with
high posterior probability from all other clades.
The conspicuous long branch lengths confirm the
special position of this section within the genus.
Within the section, the differences between the
three species were so small that hardly any distinction in this rooted tree could be visualised
(cf. scales in Figs. 11.1 and 11.2). With one
exception (one subgroup of L. section Lemna),
all other nodes had a high posterior probability
support of 1. The main clades equal the common
categorisation in sections, i.e. besides L. section
Uninerves, the sections L. section Alatae, L.
section Biformes, and L. section Lemna.
118
M. Bog et al.