O R I G I NA L A RT I C L E
doi:10.1111/j.1558-5646.2011.01313.x
POPULATION DIVERGENCE ALONG LINES
OF GENETIC VARIANCE AND COVARIANCE
IN THE INVASIVE PLANT LYTHRUM SALICARIA
IN EASTERN NORTH AMERICA
Robert I. Colautti1,2,3 and Spencer C. H. Barrett1
1
Department of Ecology & Evolutionary Biology, University of Toronto, 25 Willcocks St. Toronto, Ontario M5S 3B2, Canada
2
E-mail: [email protected]
Received September 28, 2010
Accepted March 28, 2011
Evolution during biological invasion may occur over contemporary timescales, but the rate of evolutionary change may be inhibited
by a lack of standing genetic variation for ecologically relevant traits and by fitness trade-offs among them. The extent to which
these genetic constraints limit the evolution of local adaptation during biological invasion has rarely been examined. To investigate
genetic constraints on life-history traits, we measured standing genetic variance and covariance in 20 populations of the invasive
plant purple loosestrife (Lythrum salicaria) sampled along a latitudinal climatic gradient in eastern North America and grown
under uniform conditions in a glasshouse. Genetic variances within and among populations were significant for all traits; however,
strong intercorrelations among measurements of seedling growth rate, time to reproductive maturity and adult size suggested
that fitness trade-offs have constrained population divergence. Evidence to support this hypothesis was obtained from the
genetic variance–covariance matrix (G) and the matrix of (co)variance among population means (D), which were 79.8% (95% C.I.
77.7–82.9%) similar. These results suggest that population divergence during invasive spread of L. salicaria in eastern North America
has been constrained by strong genetic correlations among life-history traits, despite large amounts of standing genetic variation
for individual traits.
KEY WORDS:
Fitness trade-off, G matrix, purple loosestrife, quantitative genetics.
The invasive spread of introduced species usually occurs across
heterogeneous landscapes and often along large-scale environmental gradients that correlate with latitude. Introduced species
may be aided in their spread in heterogeneous environments by
phenotypic plasticity, including general purpose genoypes (Baker
1965; Williams et al. 1995; Parker et al. 2003; Ross et al. 2009).
However, if plasticity is costly or poorly tracks environmental conditions then local adaptation may evolve (Via and Lande 1985;
Scheiner 1993; Tufto 2000), potentially increasing invasive spread
3 Current
Address: Department of Biology, Duke University, PO Box
90338, Durham, North Carolina 27708.
C
2514
(Garcı́a-Ramos and Rodriguez 2002). The extent to which local
adaptation increases fitness in invasive species confronting novel
environments will depend on the availability of standing genetic
variation within populations for ecologically relevant traits (Fisher
1930; Lande 1979; Lee 2002; Lee et al. 2007).
Evidence from neutral genetic markers indicates that bottlenecks during introduction are common in invasive species
(e.g., Barrett and Shore 1989; Barrett and Husband 1990;
Malacrida et al. 1998; Tsutsui et al. 2000; Novak and Mack
2005; Zhang et al. 2010). Nevertheless, genetic variation within
introduced populations can sometimes be greater than that occurs
in native source regions as a result of multiple introductions of
C 2011 The Society for the Study of Evolution.
2011 The Author(s). Evolution Evolution 65-9: 2514–2529
G E N E T I C C O N S T R A I N T S O N P O P U L AT I O N D I V E R G E N C E
differentiated populations followed by admixture among them
(reviewed in Lee et al. 2004; Dlugosch and Parker 2008a; see also
Keller and Taylor 2010; Verhoeven et al. 2011). However, genetic
variation inferred from neutral markers poorly predicts genetic
variation for quantitative traits (Lande 1988; Merilä and Crnokrak
2001; McKay and Latta 2002) and, consequently, determining the
potential for adaptive evolution during the geographical spread of
invasive species requires measurements of the standing genetic
variation of ecologically relevant traits sampled from across the
range.
The occurrence of genetic variation for quantitative traits
within populations may not guarantee contemporary evolution in
introduced species because fitness trade-offs have the potential
to impede local adaptation. Trade-offs among two or more lifehistory traits are often manifested as positive or negative genetic
correlations that prevent natural selection from simultaneously
improving correlated traits (Dickerson 1955; Lande 1982; Blows
et al. 2004; Roff and Fairbairn 2007). For example, the classic
life-history trade-off between age and size at maturity constrains
individuals to reproduce early at a small size, or later at a large
size. In such cases, population divergence will be constrained
along the axis of covariance between age and size (Mitchell-Olds
1996; Schluter 1996). Fitness trade-offs can therefore serve to
constrain the direction of contemporary adaptive evolution and
may influence survival and reproduction at range limits (Etterson and Shaw 2001; Etterson 2004) with consequences for the
geographical spread of invasive species.
Understanding genetic constraints on population divergence
requires the simultaneous comparison of correlations among multiple traits. The G matrix is a convenient mathematical representation of the genetic variances (diagonal cells) for a set of
quantitative traits and the covariances (off-diagonal cells) among
them (Lande 1979). However, the use of the G matrix to directly infer constraints imposed by genetic trade-offs presents
two experimental challenges. First, variance and covariance components of G (hereafter “(co)variances”) are estimated from genetic lines or families, making empirical estimates imprecise
without large sample sizes (Shaw 1991). Second, in addition to
fitness trade-offs, the covariance structure of G is also shaped
by natural selection, genetic drift, and migration (e.g., Turelli
1988; Phillips et al. 2001; Jones et al. 2003; Guillaume and
Whitlock 2007). These processes are likely to be important during
rapid range expansion by invasive species, which often includes
founder events and changes in the selective landscape. As a result, the G matrix of a randomly chosen population is likely to be
a poor predictor of constraints on adaptive evolution across the
range of a species. Therefore, both methodological (e.g., sample
size) and biological (e.g., stochastic forces) factors complicate the
identification of genetic constraints on the divergence of natural
populations.
An alternative approach for identifying genetic correlations
that may constrain population divergence is to investigate tradeoffs that are expected a priori to be of likely ecological importance (e.g., age vs. size at reproduction) and then estimate G
for these traits averaged across a sample of populations. Here,
the idiosyncratic effects of selection, migration, and drift in any
one population should be “averaged out” (see Chenoweth and
Blows 2008). For example, bottlenecks significantly changed
the (co)variance structure of G in experimental populations of
Drosophila melanogaster, yet the average G across populations
remained similar to the ancestral outbred population (Phillips
et al. 2001). Additional insight can also be obtained by investigating the primary eigenvectors (i.e., principal components) of
G because these are likely to remain more stable over time than
are particular (co)variance estimates (reviewed in Arnold et al.
2008). If the principal component eigenvectors of the “average”
G are relatively stable over time, then populations should diverge
in a predictable fashion, resulting in a correlation between the
eigenvectors of G and those of the matrix of (co)variance among
population means (D). The D matrix characterizes population divergence and is similar to G, but instead represents variances
and covariances among population means, rather than genetic
families within populations. If divergence among populations is
completely constrained by genetic variance within and covariance
among life-history traits, then G and D should be identical. Conversely, evolution that is not constrained by genetic (co)variances
within populations will result in less similarity between G and D.
Methods for comparing G and D among natural populations is
an area of active research (Shaw 1991; Phillips and Arnold 1999;
Roff et al. 1999; McGuigan et al. 2005; Chenoweth and Blows
2008; Calsbeek and Goodnight 2009; Simonsen and Stinchcombe
2010), but to our knowledge none of these approaches has yet been
used to study adaptive evolution during biological invasion. Invasive species may be well-suited for studying genetic constraints
on the evolution of natural populations because multiple introductions and admixture are likely to weaken phylogeographical
relationships and the extent of population structure that can complicate comparisons of G and D.
We investigated genetic constraints associated with lifehistory trade-offs within and among invasive populations of the
wetland plant Lythrum salicaria L. (Lythraceae) in eastern North
America. Previous work on L. salicaria identified genetically
based latitudinal clines for days to first flower and several measurements of plant size in both native European (Olsson and Ågren
2002; Olsson 2004) and introduced North American populations
(Montague et al. 2008; Colautti et al. 2010). Moreover, measurements of phenotypic selection indicate that introduced populations
of L. salicaria are under strong selection for earlier flowering
time and larger size (O’Neil 1997; Colautti and Barrett 2010). A
study of populations from eastern North America indicates that
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evolution of earlier flowering in northern populations is associated with a correlated change in vegetative size (Colautti et al.
2010). However, the extent to which multitrait genetic constraints
may limit population divergence was not previously investigated
and this is one of the main goals of this study.
Here, we evaluate constraints on population divergence during biological invasion in L. salicaria by measuring the standing
genetic variance and covariance of 12 ecologically relevant lifehistory traits. This was undertaken by sampling 20 populations
along a latitudinal gradient of 10 degrees latitude from southern Maryland (U.S.A.) to Timmins, Ontario (Canada) and conducting a quantitative genetic experiment under uniform growth
conditions in a glasshouse. The specific questions we addressed
in our study were: (1) Is there evidence for quantitative genetic
variation within and among populations for life-history traits associated with growth and reproduction? The rapid reestablishment
of latitudinal clines in North America (Montague et al. 2008) implicates the occurrence of significant standing genetic variation
within populations; however, genetic drift and founder events are
also known to play an important role in eroding diversity in introduced populations of this species (Eckert and Barrett 1992;
Eckert et al 1996). (2) Are life-history traits correlated among
populations, and among families within populations? Within populations, fitness trade-offs among traits such as seedling growth,
time to maturity, and plant size should result in significant genetic
correlations. Correlations among population means could arise
from constraints on population divergence and/or selection for
particular trait combinations. We predicted that selection for early
flowering and larger size at all latitudes should result in weaker
correlations between these traits relative to within-population genetic correlations. (3) To what extent is any correlated divergence
among population means (i.e., the D matrix) constrained by the
structure of genetic correlations among families within populations (i.e., the G matrix)? Constraints on adaptive evolution resulting from trade-offs among life-history traits should result in a
strong correlation between D and G, whereas divergence resulting
from selection for larger plants that flower sooner should not.
Methods
STUDY SYSTEM AND SAMPLING
Lythrum salicaria (purple loosestrife) is an insect-pollinated, outcrossing, autotetraploid, perennial herb native to Eurasia. During the last century it has become a successful invader of North
American wetland habitats, roadside ditches and other moist disturbed sites, particularly in eastern North America (Thompson
et al. 1987; Mal et al. 1992; Blossey et al. 2001; USDA 2009).
Herbarium records indicate initial introduction to ports along the
eastern seaboard at the end of the 18th century, with more recent
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(< 70 years) spread into central and northern Ontario, Canada
(Thompson et al. 1987). Both herbarium records and studies using
molecular markers suggest multiple introductions to North America with admixture among introduced populations (Thompson et
al. 1987; Houghton-Thompson et al. 2005; Chun et al. 2009).
Lythrum salicaria is tristylous and self-incompatible with successful mating largely between plants of different style morphs.
All shoot growth is localized within a few centimeters of the primary stem and therefore population growth occurs exclusively
through seed production (Yakimowski et al. 2005).
We used populations previously studied by Montague et al.
(2008) in which latitudinal clines for several life-history traits
were detected; details of population sampling and seed collections used in this experiment are given therein. Briefly, in autumn
2003, open-pollinated infructescences were collected from 25
populations in eastern North America. Populations were chosen
to represent a latitudinal cline from Timmins, Ontario (48◦ 48 N,
81o 30 W) to Easton, Maryland (38o 75 N, 75o 99 W). The latitude
of these populations is a strong predictor of season length (see
Montague et al. 2008). From the initial 25 populations, we chose
a subsample of 20 representing the entire latitudinal gradient.
EXPERIMENTAL DESIGN AND MEASUREMENTS
In June 2004, we planted 20 seeds from 20 families from each
of 20 populations (8000 total) into 2 cm × 2 cm plug trays filled
with Pro-MixTM “BX” peat containing vermiculite and perlite.
The position of each seed family was randomized across trays
and trays were placed on a glasshouse bench at the University
of Toronto and rotated thrice weekly to reduce position effects.
We monitored seeds daily for germination and after two weeks
we randomly selected eight seedlings from each of 17 families,
which we transplanted into 10 cm pots filled with Pro-MixTM .
The experiment involved a randomized block design with two
individuals per family per population per block (N = 4 blocks).
The final dataset contained 2623 (of 2720) individuals from 339
(of 340) seed families due to mortality. All blocks received 1.5
g/L of fertilizer (ratio 20N:20P:20K) every three weeks and were
kept partially flooded so that the lower one-fourth of each pot
was in water. To prevent aphid outbreaks, we treated plants with
Dursban 2E (chlorpyrifos) pesticide at a rate of 4 mL/L, once in
July and again in August.
Following transplant, we measured seedling height and estimated total seedling leaf area as the diameter of the largest leaf
multiplied by the largest total width of two-leaved seedlings. Two
and four weeks after transplant we measured seedling height. Onset of flowering of plants occurred from July to September 2004
and during this period we monitored plants daily. On the first
day of anthesis for a given plant, we measured stem width of the
primary stem and the height of the primary stem, divided into
two segments. The first, “vegetative size” was measured from
G E N E T I C C O N S T R A I N T S O N P O P U L AT I O N D I V E R G E N C E
the soil surface to the base of the inflorescence. The second,
“inflorescence length” was measured from the base of the inflorescence to its tip. Division of the primary stem height into
these two measures is a convenient division between resourceaccumulation structures (i.e., leaves) and resource sinks (i.e.,
flowers and fruits). Field surveys of natural populations, and a
common garden experiment, confirm that the height of the vegetative portion of the primary stem is a strong predictor of total vegetative growth (see Colautti and Barrett 2010; Colautti
et al. 2010). In October, we again measured vegetative height and
inflorescence length; we then harvested and oven-dried plants to
a constant weight to measure biomass. Similar to measurements
of stem length, we divided shoot biomass into vegetative and
inflorescence structures.
We recorded seed germination day but found it had a negligible effect on seedling growth and time to maturity because germination date was highly skewed with no seed germinating before
day 3 and 90% of seeds germinating between days 3 to 6. In
total, our analysis included 12 traits: four involving seedling
growth and development (seedling leaf area, seedling height,
Height-2wk and Height-4wk), hereafter referred to as “seedling
traits”; as well as four “adult traits” (days to first flower, stem
width, vegetative size at flowering, and inflorescence length at
flowering); and four “harvest traits” (vegetative size at harvest,
inflorescence length at harvest, vegetative biomass, and reproductive biomass).
separate 12 × 12 matrices using ReML: one from 339 seed families (G) and one from 2623 individuals (R).
To investigate genetic variation within and among populations, we compared the fraction of total phenotypic variance manifest as (1) variance among population means (Vpop ), (2) variance
among seed families within populations (Vfam ), and (3) variance
among individuals within seed families (Vres ). These variance
components represent: (1) genetic differentiation among populations (Vpop ), (2) ∼ 12 to 14 of the average standing genetic variation within populations (Vfam ), and (3) the residual phenotypic
variance (Vres ) among individuals within a seed family. Variance
among seed families represent 12 to 14 of standing genetic variation within populations because full- and half-siblings share on
average 12 or 14 of their genes, respectively.
Note that Vpop and 4 × Vfam are maximum estimates of the
additive genetic variance because they also include di-, tri-, and
tetragenic interactions, which are analogous to dominance variance in diploids but are much smaller in magnitude (Kempthorne
1955). Under random mating, with no epistasis or linkage disequilibrium, genetic covariance (σG ) between tetraploid half sibs x
and y is:
STATISTICAL ANALYSIS OF QUANTITATIVE TRAITS
which are functions of the additive genetic variance (A) as well as
interactions among two (D), three (T), or four (Q) alleles at each
locus (Kempthorne 1955; Lynch and Walsh 1998).
Differences in maternally inherited genes or in maternal provisioning to seeds can also inflate Vfam and Vpop . However, maternal provisioning is minimal as seeds of L. salicaria are very small
(200 × 400 μm) and lack endosperm (Thompson et al. 1987).
Moreover, we detected no significant maternal effects on adult
size and flowering time in experimental crosses (see supplementary material in Colautti et al. 2010).
To investigate whether there was significant genetic variation
among and within populations, we ran a separate mixed model
for each trait with populations and seed families, both as random
effects. We tested whether the variance component for Vpop or Vfam
were significantly different from zero, using a likelihood ratio test
(LRT) with one degree of freedom. We treated population as a
random effect in this analysis because it is a more conservative
test of the null hypothesis that there is no significant variation
among population means.
We tested for latitudinal trends in each phenotypic trait using
generalized linear models in R (version 2.8.1), with the standardized (BLUE) estimates of population means of each trait as
Prior to analysis we log-transformed vegetative and inflorescence
biomass to meet assumptions of multivariate normality and then
standardized the phenotypic distributions of each trait to a mean
of zero and a standard deviation of one. We performed a statistical
linear mixed model using the MIXED procedure in SAS 9.1 (SAS
Institute Inc., Cary, NC) with population as a fixed effect, seed
family nested within population as a random effect, and repeated
measurements on each individual nested within a seed family.
This model estimates the “average” (co)variance matrix among
seed family means within populations (i.e., the G matrix), and the
residual (co)variance among individuals within a seed family (R
matrix) by restricted maximum likelihood (ReML). Satterthwaite
(1946) correction was used for the degrees of freedom of the fixed
effects. We used best linear unbiased estimators (BLUEs) of population means from this model to calculate the matrix of divergence
among population means (D matrix) because (co)variance components are not estimated directly for fixed effects in a mixed model.
We used a Linux-based processor on the University of North
Carolina’s research computing cluster to run the model (20 GB
RAM; runtime ∼72 h). This was necessary due to the memory
and processing power required to simultaneously estimate two
σG (x, y) = σ2A /4 + σ2D /216
and for tetraploid full siblings is:
σG (x, y) = σ2A /2 + 2σ2D /9 + σ2T /12 + σ2Q /36
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dependent variables and latitude as the independent variable. We
fitted quadratic regression terms to allow for nonlinear relationships with latitude and used an LRT to hierarchically test the
significance of the quadratic and linear regression coefficients.
The analysis comparing the similarity between G and D (see
below) uses the first six principal component (PC) eigenvectors of
these two matrices. To determine if all six PCs should be included
in the analysis, we determined whether there was significant genetic variation in the sixth eigenvector of G using a LRT and a
factor analytical structure for G. This was particularly important
because several of the life-history traits we measured are likely
to be correlated (e.g., height measured at different stages), which
could result in nonsignificant genetic variation for higher PCs of
G. This procedure allowed us to test the significance of a statistical model with six versus five principal components (see also
McGuigan and Blows 2010).
COMPARING G AND D
The classic test for evolution along lines of genetic variance
compares gmax and dmax , which are the first principal component eigenvectors of G and D, respectively (Mitchell-Olds 1996;
Schluter 1996). The angle between gmax and dmax is calculated as
θ = cos−1 [gmax ] [dmax ] where indicates a transpose of the gmax
vector so that the two vectors can be multiplied (Schluter 1996).
The angle θ ranges from 0 (complete similarity) to 90 (orthogonal,
no similarity) and therefore provides a useful and intuitive measure of similarity (see Schluter 1996 for details). Although gmax
by definition contains the most variation of any single eigenvector,
the interpretation of θ as a measure of similarity between G and
D ignores variance in other eigenvectors of G, which may be considerable and together may account for more phenotypic variance
than gmax alone. In such cases, a more biologically informative
approach is to compare multiple eigenvectors of G and D. Therefore, we used the Krzanowski (1979) method described in Blows
et al. (2004; see also McGoey and Stinchcombe 2009), with the
exception that we were interested in potential constraints on D (the
matrix of variance–covariance among population means) instead
of γ (the matrix of nonlinear selection gradients). If population
divergence is constrained by G, then population divergence will
occur along the major eigenvectors of G, resulting in an overall
similarity between G and D. In contrast, population divergence
that is not constrained by G will not constrain eigenvectors of D,
resulting in little similarity between G and D.
The Krzanowski method for comparing the similarity between two matrices begins with a separate principal components
analysis (PCA) for each matrix. The variance–covariance matrices of G and D were standardized to the same scale (μ = 0, σ =
1) prior to the mixed model analysis and thus traits had the same
total phenotypic variance but could differ in the relative amount
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EVOLUTION SEPTEMBER 2011
of variation among populations, among seed families, or within
seed families. We then used the principal components of G and
D to generate a “matrix of similarity” (S). S is calculated as
A BB A, where A and B are matrices containing principal component eigenvectors of G and D, respectively, with each column
representing a separate eigenvector. Here again the symbol indicates matrix transposition. Technically S describes the similarity
of “subspaces” of G and D because only six of 12 eigenvectors
(i.e., principal components) from each of G and D were included.
However, this is a necessary limitation of the Krzanowski method
because including more than half of the eigenvectors of G and D
in A and B will constrain the comparison to recover angles of 0o
(see Blows et al. 2004 for details). Therefore, we included only
the first six eigenvectors of each matrix.
Interpreting the matrix of similarity (S) in biological terms is
difficult, but the principal component eigenvectors of S, denoted
ai , have two useful properties. First, the sum of their eigenvalues
represents the overall similarity between G and D, in this case
ranging from 0 to 6. For ease of discussion, we refer to this
sum as λi, or the “index of similarity.” Second, the eigenvalues
(λi ) of each ai range from 0 (orthogonal, no similarity) to 1
(complete similarity), which can be translated into angles using
√
the equation cos−1 λi (Blows et al. 2004). These angles can
be compared directly with the angle between gmax and dmax (θ),
as described above. Furthermore, Blows et al. (2004) show how
each ai can be “projected” back into the subspace of G or D,
to identify the phenotypic traits responsible for the similarity (or
dissimilarity) between G and D. Here again “subspace” refers
to the fact that this analysis uses the first six eigenvectors of G
and D represented by each ai . As in Blows et al. (2004), we
chose to project ai into the subspace G because we wanted to
identify trait variances and covariances within populations that
might constrain divergence among populations. The projection
of ai into the subspace of G results in vectors (bi ), which we
refer to as “vectors of similarity,” and are calculated as bi = Aai .
Factor coefficients of the vectors of similarity (bi ) are biologically
meaningful as they can be interpreted as coefficients describing
the loadings of each phenotypic trait on bi . This is analogous to the
coefficients of a PCA, which describe the relative “loadings” of
each phenotypic trait on each principal component eigenvector. In
this way, we could identify individual traits and trait combinations
in G with variance–covariance structure most similar to D.
We used a bootstrap method to generate 95% confidence intervals for the angle of similarity (θ) and the index of similarity
(λi ). For each iteration of the bootstrap model (10,000 iterations total), 17 standardized BLUPs of seed family means were
resampled (with replacement) within each of the 20 populations.
These data were used to generate new G and D matrices and to
recalculate both λi and θ. A second bootstrap model was used
G E N E T I C C O N S T R A I N T S O N P O P U L AT I O N D I V E R G E N C E
Table 1. The proportion of phenotypic variation of 12 traits associated with growth and phenology within and among 20 pop-
ulations of Lythrum salicaria grown under uniform glasshouse
conditions.
Trait
Vpop
Vfam
Vres
H2
Leaf area at transplant
Height at transplant
Height at week 2
Height at week 4
Days to first flower
Stem width at maturity
Vegetative size at maturity
Inflorescence length at maturity
Vegetative size at harvest
Inflorescence length at harvest
Final vegetative biomass (ln)
Final inflorescence biomass (ln)
0.178
0.242
0.257
0.184
0.383
0.427
0.542
0.103
0.513
0.253
0.377
0.197
0.088
0.109
0.069
0.068
0.129
0.100
0.111
0.044
0.104
0.060
0.070
0.057
0.734
0.649
0.674
0.747
0.488
0.473
0.347
0.853
0.383
0.686
0.553
0.745
0.428
0.575
0.371
0.334
0.836
0.698
0.969
0.196
0.854
0.322
0.449
0.284
Variance components are standardized to sum to one and were calculated
from a mixed model; they describe divergence among populations (Vpop ),
variation among seed families within populations (Vfam ), and residual variation (Vres ). Average within-population broad-sense heritabilities (H2 ) are
estimated as 4×Vfam /(Vfam +Vres ).
following Blows et al. (2004, electronic supplement), which is
more appropriate for testing the null hypothesis because it uses
an orthogonal factor rotation to force G and D into coincident
subspaces (for details see Cohn 1999 as described in Blows et al.
2004). Both bootstrap models were written and implemented in
R (version 2.8.1).
In summary, the key measurements of the similarity between
G and D are as follows. The first is θ, the angle of similarity
between gmax and dmax (Schluter 1996), which ranges from 0
(identical vectors) to 1 (orthogonal, no similarity). Second, angles
calculated from the eigenvalues of ai are analogous to θ, but allow
for multiple dimensions of G and D to be compared. Third, the
coefficients of bi show the “loadings” of each phenotypic trait
for the corresponding ai . Finally, the sum of eigenvalues of ai
represents an overall metric of similarity for the first six principal
components of G and D and ranges from 0 (no similarity) to 6
(completely identical).
Results
QUANTITATIVE GENETIC VARIATION AND
LATITUDINAL CLINES
Variance–covariance matrices among populations (D), among
seed families within populations (G), and among individuals
within seed families (R) were estimated from a single mixed
model and standardized to sum to one (Table 1). The LRT of a
factor analytic model comparing six versus five principal compo-
nents was highly significant (χ2 = 47.4, df = 7, P < 0.001), indicating significant standing genetic variation in all six eigenvectors
of G. Separate LRTs for each trait confirmed highly significant
effects of population (across all 12 traits: χ2 > 114.9, df = 1,
P < 0.001) and seed family within population (across all 12
traits: χ2 > 15.6, df = 1, P < 0.001). Adult vegetative size
and time to first flower exhibited the greatest level of divergence
among populations (i.e., Vpop ), with variance among populations
explaining 38.3% (days to first flower) to 54.2% (vegetative size
at maturity) of the total phenotypic variance (Table 1). In contrast, “populations” explained only 17.8% (leaf area at transplant)
to 25.7% (height-2wk) of the phenotypic variance in seedling
traits, and 10.3% to 25.3% of the variance in inflorescence length
and biomass (Table 1), indicating less divergence among populations for these traits relative to vegetative size and time to first
flower.
Broad-sense heritability (H 2 ), an estimate of standing genetic variation within populations (4 × Vfam /[Vfam +Vres ]), was
highest for days to flower (83.6%) and vegetative size measured
at harvest (85.4%) and at maturity (96.9%). In contrast, the lowest
H 2 estimates were for inflorescence length measured at flowering
(19.6%) and at final harvest (32.2%), as well as inflorescence
biomass (28.4%). Seedling traits had intermediate heritabilities
ranging from height-4wk (33.4%) to height at transplant (57.5%).
Nine of the 12 traits we investigated were significantly correlated with latitude (Fig. 1). Consistent with patterns of population
divergence and the relative amounts of standing genetic variation within populations, the four strongest clines involved days to
flower, stem width, vegetative size, and vegetative biomass (R2 =
0.506 to 0.709). In contrast, the weakest clines (R2 = 0.031 to
0.279) were among seedling traits, inflorescence length, and inflorescence biomass, which generally showed quadratic or nonsignificant correlations with latitude. In general, these patterns
indicate that northern plants flowered earlier at a smaller size and
also remained small in stature until the end of the experiment.
CORRELATIONS AMONG TRAITS—G AND D
To visualize potential trade-offs among life-history traits and their
influence on population divergence, we present for each pair of
traits the bivariate plots of BLUPs for family means (Fig. 2, above
diagonal) and BLUEs for population means (Fig. 2, below diagonal), which were estimated from the large mixed model. Correlations estimated from G may indicate genetic constraints among
life-history traits, whereas intercorrelations in D may arise as a
correlated response to selection or through stochastic processes
acting on genetically correlated traits. The G matrix estimated
directly from the mixed model is presented as Supporting information (Table S1, above diagonal), as well as genetic correlation
coefficients calculated from G (Table S2, above diagonal). The
variance and covariance components of the D matrix are also
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Figure 1.
Bivariate plots illustrating latitudinal clines in 12 phenotypic traits related to growth and phenology measured in 20 populations
of Lythrum salicaria grown under uniform glasshouse conditions. Measurements were made on developing seedlings (panels 1–4), on
mature individuals on the day of first flowering (panels 4–8), and on all individuals at the end of the experiment (panels 9–12). Linear
and quadratic approximations and R2 values are estimated by least-squared means regression. Phenotypic traits showing significant
quadratic relationships with latitude are indicated by curved lines; traits with significant linear but nonsignificant quadratic relationships
are indicated with straight lines. Significance of linear and quadratic terms was estimated by likelihood ratio tests using general linear
models. P-values correspond to the significance of the best-fit model based on likelihood ratio tests of a single intercept (i.e., mean) and
zero slope.
provided (Table S1, below diagonal) along with correlation coefficients (Table S2, below diagonal).
The strongest correlations in G were between time to first
flower and stem width and between vegetative size and biomass
(+0.549 < R < +0.994) (Fig. 2 and Table S2, above diago-
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nal). These traits all loaded positively on gmax , the first principal
component of the G matrix, which accounted for 45.7% of the total phenotypic variation among seed families within populations
(Table 2). Genetic correlations among seedling traits were generally weaker (+0.173 < R < +0.827) (Fig. 2 and Table S2, above
G E N E T I C C O N S T R A I N T S O N P O P U L AT I O N D I V E R G E N C E
Figure 2.
Visualization of the genetic variance–covariance matrix (G) and the variance–covariance matrix of divergence (D) among 20
populations of Lythrum salicaria grown under uniform glasshouse conditions. Above Diagonal: G estimated from standardized means
of 339 seed families, estimated as best linear unbiased predictors (BLUPs) by restricted maximum likelihood (ReML), with seed family,
nested within population as a random effect. Below Diagonal: D estimated from standardized means of 20 populations, estimated best
linear unbiased estimators (BLUEs) by ReML, with population as a fixed effect.
diagonal). The second principal component of G (g2 ), which accounted for 23.0% of the total variance among seed families, was
positively correlated with seedling traits (Table 2). Correlations
between size at transplant (i.e., transplant height and leaf area)
and adult traits were considerably weaker (−0.306 < R < +
0.279) (Fig. 2 and Table S2, above diagonal). Combinations of
these traits define other eigenvectors of G (g3 - g6 ), each of which
accounts for less than 13% of the variation among seed families
(Table 2). Thus, genetic correlations were strongest among days
to flower and adult vegetative traits, intermediate among seedling
traits, and weakest between pairs of adult and seedling traits.
Population means were highly intercorrelated for most traits
and correlations were generally stronger among population means
(i.e., D matrix) than among seed families within populations
(Fig. 2 and Table S2, below diagonal). Similar to the correlations evident in the G matrix: (1) flowering time and vegetative
size measurements exhibited the highest trait correlations among
populations (+0.698 < R < +0.999) (Fig. 2 and Table S2, below
diagonal), (2) these traits loaded primarily on dmax , which explained 67.8% of the total phenotypic variation among population
means (Table 3), and (3) seedling traits were not as strongly correlated (+0.532 < R < +0.893; below diagonal). However, unlike
G, pairwise combinations of seedling and adult traits in D varied
markedly (−0.201 < R < +0.847) (Fig. 2 and Table S2, below
diagonal) and days to first flower loaded more heavily on d2 than
dmax (Table 3). Thus, in common with genetic correlations within
populations, population divergence was highly correlated among
adult traits and less correlated for seedling traits. However, unlike
genetic correlations, population divergence was strongly correlated for a number of pairs of adult and juvenile traits, and days
to first flower was not as highly correlated with traits associated
with adult vegetative size.
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Table 2.
Factor loadings, eigenvalues, and percent variation explained by the first six eigenvectors of the average matrix of broad-sense
genetic variance–covariance (G) within 20 populations of Lythrum salicaria grown under uniform glasshouse conditions.
Trait
gmax
g2
g3
g4
g5
g6
Leaf area at transplant
Height at transplant
Height at week 2
Height at week 4
Days to first flower
Stem width at maturity
Vegetative size at maturity
Inflorescence length at maturity
Vegetative size at harvest
Inflorescence length at harvest
Final vegetative biomass (ln)
Final inflorescence biomass (ln)
Eigenvalue
Percentage of variation
Cumulative percentage of variation
−0.082
−0.189
−0.147
−0.192
0.515
0.374
0.426
0.115
0.423
−0.210
0.252
−0.110
0.474
45.7%
45.7%
0.422
0.494
0.420
0.335
−0.049
0.174
0.237
0.019
0.231
0.153
0.274
0.220
0.238
23.0%
68.7%
0.118
0.366
0.214
−0.087
0.151
−0.272
0.110
−0.299
0.083
−0.445
−0.328
−0.537
0.133
12.8%
81.6%
0.560
0.302
−0.319
−0.490
0.190
0.079
−0.259
0.267
−0.254
0.018
0.093
−0.018
0.100
9.6%
91.2%
0.339
−0.294
−0.024
0.042
−0.165
0.584
−0.122
−0.616
−0.123
−0.054
−0.026
−0.124
0.035
3.4%
94.5%
0.446
−0.403
0.002
−0.004
0.053
−0.302
0.310
0.055
0.154
0.541
−0.274
−0.231
0.026
2.5%
97.0%
Table 3.
Factor loadings, eigenvalues, and percent variation explained by the first six eigenvectors of the matrix of population divergence
(D) calculated among 20 population means of traits associated with growth and phenology in Lythrum salicaria grown under uniform
glasshouse conditions.
Trait
dmax
d2
d3
d4
d5
d6
Leaf area at transplant
Height at transplant
Height at week 2
Height at week 4
Days to first flower
Stem width at maturity
Vegetative size at maturity
Inflorescence length at maturity
Vegetative size at harvest
Inflorescence length at harvest
Final vegetative biomass (ln)
Final inflorescence biomass (ln)
Eigenvalue
Percentage of variation
Cumulative percentage of variation
0.202
0.255
0.246
0.109
0.311
0.386
0.453
0.092
0.440
−0.024
0.376
0.164
2.624
67.8%
67.8%
0.191
0.224
0.281
0.372
−0.420
−0.170
−0.125
0.239
−0.132
0.497
0.089
0.380
0.845
21.8%
89.6%
0.083
0.266
0.453
0.394
−0.152
−0.280
0.029
−0.234
0.019
−0.538
−0.118
−0.318
0.176
4.6%
94.2%
0.642
0.487
−0.191
−0.393
0.051
−0.006
−0.253
−0.132
−0.220
−0.127
0.100
0.036
0.101
2.6%
96.8%
−0.245
0.054
0.018
−0.128
0.048
−0.238
−0.147
0.665
−0.133
−0.439
0.418
0.112
0.051
1.3%
98.1%
−0.310
0.365
−0.085
−0.320
−0.030
−0.607
0.265
−0.213
0.289
0.263
0.147
−0.046
0.029
0.8%
98.9%
POPULATION DIVERGENCE ALONG GENETIC LINES
OF LEAST RESISTANCE
Quantitative estimates of G and D indicate significant similarity between the two matrices (Fig. 3). Schluter’s (1996) θ,
which measures the angle of similarity between gmax and dmax
and ranges from 0o to 90o , suggested a moderate level of similarity of ∼46o (mean = 45.78; bootstrap mean = 45.72o ;
95% CI: 39.50–51.93o ). In contrast, the index of similarity
(λi ) of the S-matrix, which compares the first six eigenvectors of G and D, was 4.8 of 6.0 (mean = 4.79; bootstrap
mean = 4.80; 95% CI: 4.66–4.97), indicating a higher level
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of similarity. Thus, while the first principal component eigenvectors of G and D were similar (θ = 45.8o /90o = 50.9%),
the first six eigenvectors of S were more so (λi = 4.8/6.0 =
80.0%), and λi was less than any of the 10,000 iterations of the
orthogonal rotation bootstrap, indicating highly significant similarity (P < 0.0001). The 10,000 bootstrap iterations of θ and λi
indicated different levels of similarity when each was scaled from
0% (orthogonal) to 100% (identical) (Fig. 3).
To investigate the trait correlations responsible for the similarity between G and D, we projected the eigenvectors of S into
the subspace defined by the first six eigenvectors of G (Table 4).
G E N E T I C C O N S T R A I N T S O N P O P U L AT I O N D I V E R G E N C E
Table 4.
Summary of the eigenvectors of the matrix of similarity (S) projected onto the eigenvectors of the genetic variance–covariance
matrix (G) of 12 life-history traits in 20 populations of Lythrum salicaria grown under uniform glasshouse conditions.
Trait
b1
b2
b3
b4
b5
b6
Leaf area at transplant
Height at transplant
Height at week 2
Height at week 4
Days to first flower
Stem width at maturity
Vegetative size at maturity
Inflorescence length at maturity
Vegetative size at harvest
Inflorescence length at harvest
Final vegetative biomass (ln)
Final inflorescence biomass (ln)
Eigenvalue
Angle
0.292
0.412
0.491
0.440
−0.094
0.070
0.305
−0.007
0.287
0.186
0.211
0.204
1.00
0.04
−0.307
−0.147
0.089
0.011
0.369
0.182
0.445
−0.202
0.440
−0.418
0.011
−0.316
1.00
1.25
0.195
0.075
−0.300
−0.308
0.353
0.425
0.059
0.419
0.097
0.034
0.457
0.261
0.989
5.99
0.594
0.358
0.019
−0.233
0.064
0.230
−0.156
−0.376
−0.156
−0.303
−0.106
−0.339
0.961
11.40
0.282
−0.640
−0.067
0.137
−0.147
0.448
0.090
−0.358
0.030
0.357
0.002
0.019
0.755
29.65
0.420
−0.132
−0.051
−0.192
0.248
−0.459
0.318
0.266
0.177
0.362
−0.258
−0.307
0.141
67.93
Angle quantifies the orientation of a principal component axis from each of D and G and ranges from 0 (aligned) to 90 (orthogonal). Factor loadings show
the contribution of each trait to the similarity between G and D. For example, the closest principal components of G and D define b1 and are largely due to
the intercorrelation of stem width, biomass, and vegetative size measured at maturity and at harvest.
The first five of six eigenvectors of this projection (b1 to b5 ) were
close to the maximum of one (eigenvalues b1 = 1.00, b2 = 1.00,
b3 = 0.989, b4 = 0.969, b4 = 0.755) with corresponding angles of
0.04o to 29.65o (Table 4). Seedling height measurements loaded
most heavily on b1 . Vegetative size at maturity and at harvest
loaded most heavily on b2 , along with inflorescence length at
harvest (Table 4). Stem width, vegetative biomass, and inflorescence length at maturity loaded primarily on b3 . Factor loadings
for days to first flowering were highest for b2 and b3 along with
measurements of adult size. The remaining eigenvectors of S (b4 b6 ) were defined by a combination of seedling and adult traits.
Discussion
The goals of this study on invasive populations of L. salicaria
from eastern North America were: (1) to estimate standing genetic variation for ecologically relevant life-history traits using
seed families grown under uniform conditions, (2) to identify genetic correlations for these traits within and among populations,
and (3) to determine to what extent divergence among populations may be constrained by the structure of genetic (co)variance
within populations. We found that despite evidence indicating that
founder events and genetic drift play an important role during the
invasion process in these populations (Eckert and Barrett 1992;
Eckert et al 1996), they maintained high levels of genetic variation
for all 12 of the quantitative traits that we examined (Table 1).
We also detected strong population differentiation for these traits,
most of which was manifested as geographical clines distributed
along latitudinal gradients in growing season length (Fig. 1).
Despite the availability of significant standing genetic variation
within and among populations, genetic correlations among traits
(Table 2, Fig. 2) appear to limit the “phenotypic space” available for populations to respond to natural selection, at least over
the short term. Evolutionary change during invasion has occurred
primarily along lines of greatest genetic (co)variance within populations resulting in a high similarity between the first five eigenvectors of G and D (Table 4; Fig. 3). Below we discuss the implications of these results and consider alternative hypotheses for
the similarity observed between G and D, particularly the possible
roles of migration and correlational selection.
GENETIC VARIATION IN LIFE-HISTORY TRAITS
There is considerable evidence for abundant genetic variation in
life-history traits within and among wild populations of plants
and animals (reviewed by Mousseau and Roff 1987; Houle 1992;
Mazer and LeBuhn 1999; Geber and Griffen 2003) although relatively few studies have measured quantitative genetic variation
in populations of invasive species (but see Rice and Mack 1991;
Chen et al. 2006; Lavergne and Molofsky 2007; Dlugosch and
Parker 2008b; Facon et al. 2008; Chun et al. 2009). Previous work
on L. salicaria reported significant amounts of additive genetic
variation for age and size at flowering in two native populations
from Sweden (Olsson 2004) and in a single introduced population from eastern North America (O’Neil 1997). Consistent with
a scenario of multiple introductions and admixture fostered by
the outcrossed mating system of L. salicaria (Thompson et al.
1987; Barrett 2000; Houghton-Thompson et al. 2005; Chun et al.
2009), we found high levels of genetic variation for vegetative and
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R . I . C O L AU T T I A N D S . C . H . BA R R E T T
northern range limit. Levels of standing genetic variation and the
strength of genetic correlations may also differ among populations
for the traits examined here. For example, stronger stabilizing selection on flowering time in northern populations may weaken
the strength of the genetic correlation between days to first flower
and vegetative size. Quantifying such changes in the variance and
covariance for genetically correlated traits is analytically difficult
and has only recently been attempted (see Hine et al. 2009). Such
an analysis was beyond the scope of the present study and instead
we examined the “average” genetic (co)variance matrix for the 20
populations we investigated.
TRAIT CORRELATIONS AS GENETIC CONSTRAINTS
Figure 3.
Bootstrap estimates of two measures of similarity be-
tween the matrix of genetic variance-covariance (G) and the matrix of covariance among population means (D) estimated from 20
populations of Lythrum salicaria grown under uniform glasshouse
conditions. (A) The angle of orientation between gmax and dmax
(θ) examines only the first principal components of G and D (see
Schluter 1996) and ranges from 0◦ (complete similarity) to 90◦ (no
similarity). (B) The index of similarity compares the first six principal components of G and D (see Blows et al. 2004) and ranges from
0 (no similarity) to 6 (complete similarity). The bootstrap models
consist of 10,000 iterations of resampling, with replacement, from
339 standardized family means to generate a bootstrap sample of
10,000 G and D matrices.
reproductive traits both within and among the 20 populations that
we investigated (Table 1). Although hybridization with native L.
alatum has been proposed as a genetic mechanism contributing
towards invasion success in L. salicaria (Ellstrand and Schierenbeck 2000; Houghton-Thompson et al. 2005), AFLP data do not
provide strong support for this hypothesis (see Fig. 2 in HoughtonThompson et al. 2005). Instead, it seems more likely that gene
flow among introduced genotypes and possibly ornamental varieties may have contributed to the high genetic diversity of invasive
populations (Houghton-Thompson et al. 2005; Chun et al. 2009).
Our previous studies revealed striking variation among populations in their overall levels of quantitative genetic variation
(Colautti et al. 2010). In particular, we reported that genetic variation for days to first flower and vegetative size declined toward the
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EVOLUTION SEPTEMBER 2011
Genetic correlations lower the “dimensionality” of available phenotypic space and can limit opportunities for local adaptation,
at least over short timescales (Dickerson 1955; Lande 1982; Orr
2000). The high intercorrelation among adult traits reported here
suggests that selection on earlier flowering in northern populations may be constrained by a trade-off with size at reproduction.
Specifically, we detected strong positive genetic intercorrelations
among days to first flower, stem width, vegetative size at flowering, vegetative size at harvest, and vegetative biomass (Fig. 2 and
Table S2). Consequently, plants that flowered earlier are likely
to suffer a cost associated with their smaller size. The smaller
vegetative size of early-flowering genotypes was fixed at the time
of first flowering and did not increase throughout the growing
season, given the strong broad-sense genetic correlation between
vegetative height at first flowering and at harvest (r = 0.994). In
native populations of L. salicaria, Olsson (2004) also found significant additive genetic correlations between time to first flower
and the number of vegetative nodes at maturity, a proxy for vegetative size. Thus, it appears that: (1) introduced populations are
subject to some of the same genetic constraints that are evident
in native populations, and (2) these trade-offs may be relatively
stable over longer timescales. Indeed, this may be a more general
phenomenon, as the evolution of earlier reproduction at higher latitudes appears to be constrained in two other species—Xanthium
strumarium (Etterson and Shaw 2001) and Chamaecrista fasciculata (Griffith and Watson 2006). Constraints on the evolution
of early flowering because of shorter growing seasons may be an
important determinant of range limits generally.
A longer term genetic constraint involving early flowering
and size in L. salicaria may be associated with the architecture
of inflorescence development. In common with several other dicotyledonous species, for example, Antirrhinum majus and Arabidopsis thaliana (reviewed in Yanofsky 1995; Ma 1998; Simpson
et al. 1999), organogenesis in L. salicaria proceeds in an acropetal
direction at the shoot apical meristem. In A. majus and A. thaliana,
maturation of the primary stem occurs in response to external
cues, particularly temperature and photoperiod, which trigger a
G E N E T I C C O N S T R A I N T S O N P O P U L AT I O N D I V E R G E N C E
developmental phase change from resource-gathering structures
(i.e., shoots and leaves) to resource sinks (i.e., flowers, nectar,
seeds). This may result in a fitness trade-off because vegetative
size correlates strongly with flower and fruit production (O’Neil
1997; Colautti et al. 2010). In the plants we investigated, genetic
variation for vegetative growth after the onset of flowering must
be negligible compared to genetic variation for size at maturity,
otherwise there would be a weaker correlation between vegetative
size measured at first flower and at the end of the experiment. This
developmental constraint may help to explain, in part, the intercorrelations among days to first flower and the measurements of
plant size (see Fig. 2).
Time to first flower and adult traits associated with vegetative size fit the model of plant development noted above, but the
results for inflorescence length and seedling traits (i.e., height at
transplant, leaf area at transplant, height-2wk, and height-4wk)
are harder to interpret. Variance–covariance components involving inflorescence length and biomass should be interpreted carefully because plants in our experiment had no opportunity to produce seeds, which require insect pollinators. Therefore, resources
available for seed production, unlike natural populations, would
not limit the length and biomass of inflorescences measured in
the glasshouse. Indeed, inflorescence measurements correlated
poorly between the glasshouse and the field, despite strong correlations between glasshouse and field measurements for flowering
time and vegetative traits (Montague et al. 2008; Colautti et al.
2010).
Overall, seedling traits were less genetically intercorrelated
within populations than adult traits, but there were a few adult
traits that were strongly correlated with seedling traits (Fig. 2 and
Table S2, above diagonal). For example, seedling height measurements were negatively correlated with days to first flower
(i.e., early-flowering plants grew faster), yet seedling height measurements were only weakly correlated with adult height measurements, despite a strong positive correlation between days to
flower and vegetative size at flowering. Thus, early-flowering
plants grow faster as seedlings but are still not able to grow as
large as later-flowering plants. This result is consistent with a
model of developmental constraint proposed by Colautti et al.
(2010) in which plants must reach a threshold size before they
begin to flower. Seedlings that grow faster are able to initiate
flowering sooner, whereas slower-growing seedlings delay flowering until they reach a threshold size.
GENETIC VARIANCE–COVARIANCE (G) AND
POPULATION DIVERGENCE (D)
If the genetic correlations illustrated in Figure 2 represent constraints on population divergence then the genetic (co)variance
matrix (G) should be a reasonable predictor of trait (co)variance
among populations (D). Indeed, this is the case as the index of
similarity (λi ) between G and D was 4.8, which is close to the
theoretical maximum (6 = identical matrices) and highly significant based on a bootstrap model with orthogonal rotation (P <
0.001). The high value of λi derives from the fact that five of the
six eigenvectors of S were close to the theoretical maximum of
one, with only the final eigenvector (b6 ) showing little similarity
between G and D (Table 4). The similarity in five of the six dimensions of comparison between G and D is consistent with strong,
multitrait genetic constraint on population divergence during the
invasion of L. salicaria in eastern North America.
Interpreting the similarity between G and D as a constraint on
population divergence assumes that our estimate of G is a reasonable approximation of the ancestral (co)variance structure of each
population (i.e., a 20-population polytomy). The genetic relationships among the 20 populations used in this study have not been
characterized using neutral genetic markers. However, introduced
populations of invasive plants often show little geographical structuring relative to native populations (Barrett and Husband 1990;
Dlugosch and Parker 2008a) and this is also true for other populations of L. salicaria in North America (Houghton-Thompson et al.
2005; Chun et al. 2009). Human-influenced gene flow in invasive
species tends to homogenize the phylogeographic relationships
among populations, which would otherwise confound interpretation of similarities between G and D as genetic constraints on
evolution. Future work combining neutral markers with measurements of natural selection at different points along the latitudinal
gradient would clarify the relative influence of genetic constraints,
natural selection, and stochastic processes on divergence of our
study populations (see methods in Chenoweth and Blows 2008;
Hohenlohe and Arnold 2008; Chenoweth et al. 2010).
The different levels of constraint suggested by θ and S are
difficult to reconcile with nonadaptive processes. The estimated
average angle (θ) between gmax and dmax was about half the theoretical minimum similarity (90o = no similarity) (Fig. 3) and
less similar than five of the six eigenvectors of S (0.04–29.65o ;
Table 4). Stochastic processes such as bottlenecks, founder events,
and genetic drift should not affect the proportional relationship
between G and D and therefore the factor loadings and eigenvalues of gmax and dmax should be similar (Lande 1979; Jones
et al. 2004; Hohenlohe and Arnold 2008). Instead, dmax explains
67.8% of the total (co)variance among populations, whereas gmax
explains only 45.7% of total genetic (co)variance within populations, demonstrating that the first principal component eigenvectors of G and D are not proportional, despite the high degree
of similarity between G and D. Therefore, stochastic processes
alone would appear to be insufficient to explain the contrasting
estimates of similarity measured by θ and λi .
In contrast to stochastic processes, strong natural selection
can result in divergence of populations away from the primary
eigenvectors of G (Lande 1979; Zeng 1988; Jones et al. 2004).
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The difference in constraint suggested by θ and λi could be
explained if: (1) selection on a few traits changed the orientation
of dmax relative to gmax , but (2) the evolutionary response to selection was still constrained by genetic correlations with other lifehistory traits. This seems likely for two reasons. First, loadings
of traits differed between gmax (Table 2) and dmax (Tables 3),
suggesting a weak constraint in the first dimensions of G and D.
Indeed, the large factor loadings for days to first flower and other
adult size traits in gmax is consistent with a strong genetic constraint, whereas the weaker loading of days to flowering in dmax is
consistent with selection that breaks apart this constraint. Second,
the eigenvalues of the first five eigenvectors of S (i.e., b1 , to b5 in
Table 4) were close to their theoretical maximum of one, suggesting a strong constraint in five of the six principal eigenvectors G
and D. Therefore, selection appears to have played an important
role in the divergence of populations for a few traits, but overall
was highly constrained along genetic lines of (co)variance among
life-history traits.
ALTERNATIVE HYPOTHESES FOR G-D SIMILARITY
We have interpreted the similarity between G and D (Fig. 3B) as
a constraint on the evolution of D imposed by the genetic variance and covariance components of G. However, theory suggests
other factors that can also orient G toward D (reviewed in Arnold
et al. 2008). One hypothesis is that correlational selection favors
combinations of traits within populations that mirror the direction of divergence among populations. For example, the genetic
correlation between stem width and vegetative size at flowering
(Fig. 2) may be a result of correlational selection, as larger plants
may need larger stems to increase transport of more resources or
as structural support. However, time to flowering and vegetative
size are positively correlated in G and D (Fig. 2) yet selection
coefficients measured in L. salicaria confirm that selection favors
both early flowering and larger size (Colautti and Barrett 2010)
without strong correlational selection (O’Neil 1997). Therefore,
correlational selection alone is an unlikely explanation for the
strong similarity between G and D.
Effects of maternal environment on offspring growth and development (i.e., maternal effects) could also result in correlations
among life-history traits resulting in similarity between G and
D. However, experimental evidence using the same populations
in this study does not support a significant influence of maternal
effects on adult traits (see Montague et al. 2008; Colautti et al.
2010). This conclusion was also supported by the weak correlations between vegetative size at harvest and seedling traits in
G and D (Fig. 2 and Table S2). Maternal effects are known to
influence seedling traits in many plant species as higher quality
seeds germinate earlier and grow faster (Roach and Wulff 1987).
However, in our experiment the opposite was true, as germination date was positively correlated with relative growth rate from
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EVOLUTION SEPTEMBER 2011
transplant to week 2 (ρ = +0.383, df = 2767 P < 0.001) and
from week 2 to week 4 (ρ = +0.278, df = 2766, P < 0.001). Our
results are therefore not consistent with the hypothesis that the
similarity between G and D results from maternal influences on
correlations among life-history traits.
A third hypothesis that predicts similarity between G and D
is that gene flow along latitudinal gradients can create latitudinal
clines like those observed in our study (Fig. 1) and orient G in
the direction of D (Guillaume and Whitlock 2007). This scenario
would require a strong pattern of isolation-by-distance (IBD),
which is unlikely for a species that has spread over 1000 km in the
past 50–100 years and shows evidence of significant long-distance
dispersal (see Houghton-Thompson et al. 2005; Chun et al. 2009).
Moreover, strong IBD alone cannot explain the lower level of
divergence of θ relative to λi (Fig. 3A) because the strength
of the covariance components of G should be proportional to
the same covariances of D, resulting in the greatest similarity
between gmax and dmax . The difference in factor loadings for days
to first flower in G (Table 2) versus D (Table 3) is contrary to
a scenario of IBD. Instead, our results are more consistent with
genetic constraints on an evolutionary response to selection on
population divergence.
CONCLUSIONS
Identifying genetic constraints on local adaptation is an important
step in understanding species’ range limits and for predicting the
rate and extent of spread in invasive species. However, identifying constraints in natural populations is complicated by variation
among populations in gene flow, natural selection, and genetic
drift because these processes can lead to idiosyncratic differences
in the magnitude and direction of genetic correlations. We have
attempted to circumvent this problem by estimating an “average
G” in 20 populations of L. salicaria from eastern North America, a method that is particularly well-suited to introduced species
that are likely to have relatively weak phylogeographical structuring as a result of human-mediated dispersal. Despite considerable standing genetic variation within populations of L. salicaria
for individual traits, genetic correlations among traits appear to
have limited the phenotypic space available for divergence among
populations, particularly for traits that display strong latitudinal
clines. The similarity in several of the genetic correlations between native and introduced populations of L. salicaria suggests
that genetic constraints on population divergence may play an
important role in the establishment of range limits in invasive
species.
ACKNOWLEDGMENTS
We thank M. Blows, J. Stinchcombe, K. Rice, A. Weis, and C. Eckert for
comments on the manuscript; L. Flagel for assistance running SAS on
University of North Carolina’s research computing cluster; the Ontario
G E N E T I C C O N S T R A I N T S O N P O P U L AT I O N D I V E R G E N C E
Government and the University of Toronto for scholarship support to RIC;
the Canada Research Chair program and an Ontario Premier’s Discovery
Award for funding to SCHB; and the Natural Sciences and Engineering
Research Council of Canada (NSERC) for a graduate scholarship to RIC
and a Discovery Grant to SCHB.
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Associate Editor: M. Blows
Supporting Information
The following supporting information is available for this article:
Table S1. Variances (diagonal) and covariances (off-diagonal) among 12 life-history traits for the G matrix (above diagonal)—the
(co)variance matrix among seed families within populations estimated by restricted maximum likelihood, and for the D matrix
(below diagonal)—the (co)variance matrix among standardized population means.
Table S2. Correlation coefficients for 12 life-history traits calculated from the G matrix (above diagonal)—the (co)variance matrix
among seed families within populations estimated by restricted maximum likelihood, and for the D matrix (below diagonal)—the
(co)variance matrix among standardized population means.
Supporting Information may be found in the online version of this article.
Please note: Wiley-Blackwell is not responsible for the content or functionality of any supporting information supplied by the
authors. Any queries (other than missing material) should be directed to the corresponding author for the article.
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