Aquatic Botany 93 (2010) 221–226
Contents lists available at ScienceDirect
Aquatic Botany
journal homepage: www.elsevier.com/locate/aquabot
Comparison of life history traits between invasive and native populations of
purple loosestrife (Lythrum salicaria) using nonlinear mixed effects model
Young Jin Chun a,∗ , Chang-Gi Kim a , Kirk A. Moloney b
a
b
Bio-Evaluation Center, Korea Research Institute of Bioscience and Biotechnology, Cheongwon 363-883, Republic of Korea
Department of Ecology, Evolution, and Organismal Biology, Iowa State University, Ames, IA 50011, USA
a r t i c l e
i n f o
Article history:
Received 10 February 2010
Received in revised form 23 August 2010
Accepted 2 September 2010
Available online 15 September 2010
Keywords:
Common garden
Environment
Invasive species
Life history
Nonlinear model
a b s t r a c t
We compared growth patterns of invasive and native populations of purple loosestrife (Lythrum salicaria) while varying water and nutrient levels. We examined three life-history traits (height, number of
branches, and the size of largest leaf) during the growth period adopting a nonlinear mixed effects model.
Invasive populations were found to be slower in shoot elongation but grew to be taller than native populations. Invasive populations produced more branches than natives only in the high water, high nutrient
treatment. Invasive populations had a similar increase in the size of the largest leaf compared to natives,
but ultimately produced a greater size of largest leaf than natives. Invasive populations were found to
display a greater vegetative expansion, but this was not strongly affected by our treatments.
© 2010 Elsevier B.V. All rights reserved.
1. Introduction
The introduction and spread of non-native species has become
a global concern, as invasive species often compete for available
resources, replace indigenous species, and ultimately may alter
ecosystem function (D’Antonio and Vitousek, 1992; Mack et al.,
2000; Lodge et al., 2006). Understanding their ecology is important to identify potential control points and effective management
plans (Simberloff, 2003). In their new ranges, invasive populations
are often assumed to exhibit higher survival, faster growth, and
greater reproduction than native populations in their original range
(Hinz and Schwarzlaender, 2004; Bossdorf et al., 2005). However,
variability in the environmental conditions and habitat quality may
also affect the success of invasive populations (Alpert et al., 2000).
Empirical studies found that the growth of invasive vs. native populations is highly dependent on morphological and physiological
traits and the biotic and abiotic conditions examined in the study
(e.g. Willis and Blossey, 1999; Kaufman and Smouse, 2001; Leger
and Rice, 2003; DeWalt et al., 2004). As successful invasion happens across a broad range of habitats, our understanding of the
characteristics predisposing an invasive species will be improved
through comprehensive biogeographical studies comparing multi-
∗ Corresponding author at: Bio-Evaluation Center, KRIBB, 685-1 Yangcheong-ri,
Ochang-eup, Cheongwon, Chungbuk 363-883, Republic of Korea.
Tel.: +82 43 240 6555; fax: +82 43 240 6549.
E-mail address: youngjinchun@gmail.com (Y.J. Chun).
0304-3770/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.aquabot.2010.09.001
ple populations from diverse environmental ranges both in native
and invasive ranges (Daehler, 2003; Bossdorf et al., 2005; Hierro et
al., 2005).
In this paper, we measured vegetative life history traits of the
perennial angiosperm purple loosestrife (Lythrum salicaria L.) under
different water and nutrient conditions throughout the first growing season, and compared performance of invasive and native
populations. Purple loosestrife is a well-known, noxious invader
in North America, introduced from Europe in the beginning of 19th
century (Stuckey, 1980). It has spread rapidly over many wetlands
and marshes in the United States and neighboring Canada, often
forming dense monospecific stands (Thompson et al., 1987). Differences in life history traits between invasive and native populations
have been reported under field (Edwards et al., 1998) or in common
garden conditions (Blossey and Nötzold, 1995; Bastlová and Květ,
2002; Bastlová et al., 2004; Chun et al., 2007). However, life history
traits have been measured usually once at the end of the growing
season. Tracing the changes in life history traits during the growth
period under different environmental conditions may reveal more
specific differences between invasive and native populations.
Nonlinear mixed models are a powerful tool for the analysis of
experiments where some response variable is observed on multiple occasions, that is, during the whole growth period (Davidian
and Giltinan, 1995). Mixed model is a general approach of accounting for the variability between individuals to estimate parameters
for both random and fixed effects (Pinheiro and Bates, 1998). Each
parameter in the model can be represented by a fixed effect that
pertains to the levels of interest (e.g. groups), and a random effect
222
Y.J. Chun et al. / Aquatic Botany 93 (2010) 221–226
that pertains to the differences between the value of the parameter
fitted for each individual and the value of the parameter fitted for
fixed effect (Davidian and Giltinan, 1995; Pinheiro and Bates, 2000).
Potvin et al. (1990) developed ANOVAR (ANOVA with repeated
measures) to test group differences of repeatedly measured physiological responses in a mixed model. However, as their method
uses a linearized model, it lacks the ability of testing for the differences in biologically meaningful parameters between groups in a
non-linear model (Peek et al., 2002).
Adopting a non-linear mixed model approach, we fitted three
life history traits during the growth of purple loosestrife in a common garden in four combinations of water and nutrient availability.
We compared the trait performance between invasive vs. native
populations in each environmental treatment by assessing the
effect of population on parameter estimation for fixed effects. Our
study addresses the following questions: (1) Do invasive populations perform better than native populations through their growth?
(2) How does environmental variation affect the differences in trait
performance between invasive and native populations?
Ohio, USA) was applied once to a pot at the beginning of the experiment (N, 2481 mg/kg soil; P, 563 mg/kg soil; K, 1320 mg/kg soil).
As a consequence, the low and high nutrient treatments were
designed to be a reasonable approximation of low and high soil
nutrient levels, respectively, which would be encountered under
natural field conditions (cf. Bridgham et al., 1996; Thormann and
Bayley, 1997; Bedford et al., 1999). Day length during the experiment ranged from 13 h 18 min to 15 h 16 min, light availability was
11.09 ± 0.40 mmol photons m−2 s−1 , and temperature ranged from
8.3 to 28.0 ◦ C.
We measured three life history traits for each experimental individual: (1) height, (2) number of branches, and (3) size of the largest
leaf. To determine (3), we chose the largest leaf from each plant
and calculated leaf area by multiplying the maximum length and
width of the leaf. Traits were measured every week for six weeks
of growth, and then finally measured after another 3 weeks when
92% of the plants initiated flowering (8, 15, 22, 29, 36, 43, 64 days).
We also recorded the date of the onset of first flowering for each
individual.
2. Methods
2.3. Fitting nonlinear models
2.1. Population sampling
All statistical analyses were conducted using the nlme package
of R 2.11.0 (R Development Core Team, 2010). The program code
for this study is provided in the Appendix. We first plotted the trait
responses for invasive vs. native populations in each environmental treatments for an exploratory analyses (Figs. 1, 2 and 3). Plant
height and size of the largest leaf appeared to show sigmoid growth,
while the number of branches followed exponential growth except
for WH NL (sigmoid growth). For sigmoid growth, we chose the
logistic model (Ricklefs, 1967) which produced the lowest Bayesian
information criterion (BIC) compared to other models (Gompertz,
Michaelis–Menten, and Weibull; P < 0.0001 from paired t-tests).
In the fall of 2002, we collected seeds from each of three
native populations in Europe (Schollener See [52◦ 39 N, 12◦ 11 E];
Strodehne [52◦ 45 N, 12◦ 11 E]; and Meißendorfer Teiche [52◦ 43 N,
9◦ 50 E]), all in Germany, and three invasive populations in North
America (Little South Storm Lake, Iowa [42◦ 38 N, 95◦ 13 W]; Shell
Rock, Minnesota [43◦ 32 N, 93◦ 15 W]; and Fayetteville, New York
[42◦ 49 N, 76◦ 49 W]). Populations were chosen to represent a range
of nutrient and water conditions found naturally in the field. We
randomly chose seeds from a bulk sample of a large number of
plants within each population. Seeds were planted in Sunshine
LC1 potting soil (Sun Gro Horticulture Canada, Seba Beach, Alberta,
Canada) on May 20, 2004 to allow germination and initial growth
for 20 days. Maternal effects were likely to be small because purple
loosestrife seeds are minute (0.5–0.6 mg; Thompson et al., 1987).
However, to restrict initial size variability of seedlings and minimize maternal effects, we selected 40 seedlings of similar size
(2–4 cm in height) from each population.
2.2. Common garden experiment
On June 9, 2004, seedlings were individually transplanted into
plastic pots (30 cm diameter × 25 cm depth). These pots contained
the same potting soil used for germination and were placed in
plastic wading pools (1.4 m diameter × 30 cm depth). We applied
a split-plot design consisting of five complete blocks, with four
wading pools within each block. Each wading pool in a block contained one of four environmental treatment combinations: (1) low
water, low nutrient (WL NL ), (2) low water, high nutrient (WL NH ),
(3) high water, low nutrient (WH NL ), and (4) high water, high nutrient (WH NH ). Two plants from each population were put in each
wading pool in each block (12 plants per pool). The total number
of experimental units for this experiment was five blocks × 4 treatment combinations = 20 units, with 6 populations × 2 plants = 12
observations per experimental unit. Pots in the high water treatments were kept at saturation, similar to the condition of lake
and pond margins. Low water treatments are comparable to drier,
upland conditions, where plants were watered every other day,
letting the soil soak for a few hours, after which the soil was
allowed to dry. In the low nutrient treatment no fertilizer was
applied, whereas in the high nutrient treatment 100 g of slowrelease 14:14:14 N:P:K Osmocote (The Scotts Company, Marysville,
Rt =
A
1 + exp[−K(t − I)]
(1)
where Rt is the response variable (height, number of branches,
and size of the largest leaf) at day t; A is the asymptote (maximum size); K is the constant proportional to the overall growth
rate; and I is the inflection point (i.e., the day at which Rt reaches
A/2). We developed a self-starting function to calculate initial values for parameters following Pinheiro and Bates (2000). The initial
estimates of parameters were:
Height =
100.16
1 + exp[−(0.13)(t − (29.49))]
Number of branched in WH NL =
Size of the largest leaf =
20.68
1 + exp[−(0.21)(t − (21.63))]
22.38
1 + exp[−(0.20)(t − (16.03))]
The exponential model employed for the number of branches in
WL NL , WL NH and WH NH was:
Rt = exp(A + K × t)
(2)
where A is related to the initial response at t = 0 and K is
related to growth rate. The initial estimates of parameters were
Rt = exp((2.11) + (0.04) × t). We included latitude as a covariate in
all models because the genetically-based difference in phenotypic
performance between invasive and native populations may be also
affected by phenotypic or genetic latitudinal clines (Colautti et al.,
2009).
Y.J. Chun et al. / Aquatic Botany 93 (2010) 221–226
223
Fig. 1. Comparison of growth pattern in height between invasive and native genotypes in (a) low water, low nutrient (WL NL ); (b) low water, high nutrient (WL NH ); (c)
high water, low nutrient (WH NL ); and (d) high water, high nutrient (WH NH ) treatments. Raw data were presented as boxplots and fitted growth curves as lines. Invasive
genotypes: gray boxes and solid lines; native genotypes: white boxes and dashed lines.
2.4. Optimization of the initial model
We improved our models arrived at as described above to satisfy the basic assumptions of nonlinear model building (Davidian
and Giltinan, 1995) that random effects are independent and normally distributed. We employed a diagonal matrix explaining the
variance–covariance structure for the three random effects using
“pdDiag” function in the nlme package of R. As our data include
observations of unequal intervals, we adapted a continuous time
autoregressive process of first order (“corCAR1” function) to the
within-individual errors. The final model was diagnosed to verify
that the standardized residuals meet the normality assumption.
Finally, there should be no heteroscedasticity. Because the initial model showed increasing variance for within group errors
(heteroscedasticity), we remedied this situation by modeling the
variance of the within-individual errors using a variance function
(i.e., a function that describes the variance of errors through covariates). This function expresses the variance as an arbitrary power of
the expected values (␯ij ) using “varPower” function.
Var(εij ) = 2 |ij |2ı
Fig. 2. Comparison of growth pattern in number of branches between invasive and native genotypes in the four treatments as in Fig. 1.
(3)
224
Y.J. Chun et al. / Aquatic Botany 93 (2010) 221–226
Fig. 3. Comparison of growth pattern in the size of largest leaf between invasive and native genotypes in the four treatments as in Fig. 1.
where ı is a vector of variance parameters. We grouped the entire
data to eight combinations of treatment × population and determined the effects of groups on the parameter estimates of three
fixed effects using maximum likelihood method.
3. Results
The estimates of the height asymptote (A) revealed that invasive populations grew significantly taller than native populations,
except for the WL NH (Table 1 and Fig. 1). The growth rate of native
populations (K) was significantly higher than that of invasive populations in all treatments. In contrast, the inflection points of native
populations (I) were significantly lower than invasive populations
in all treatments, indicating that native populations deflect earlier
from exponential increase. Together with this, we also observed
that the days from planting to the onset of flowering in native
populations (37.0 ± 0.29) were fewer than in invasive populations
(50.7 ± 0.82; P < 0.001), indicating that native populations flower
earlier than invasive populations.
In the three treatments (WL NL , WL NH , and WH NH ) where plants
showed an exponential increase in the number of branches, only
in WH NH invasive populations increased the number of branches
faster than native populations (P = 0.028), although the initial
growth was greater in native populations (P = 0.033; Table 1 and
Fig. 2). In WH NL (sigmoid growth), no difference in the final number
of branches between native and invasive populations was found.
However, native populations increased branches faster, with lower
inflection point than invasive populations.
Our estimates of the asymptote in the size of largest leaf indicate that invasive populations had significantly greater size of the
largest leaf than native populations in all treatments (Table 1 and
Fig. 3), although no difference was found in the growth rate. The
inflection point of native populations was significantly lower than
invasive populations in two treatments (WL NL and WH NH ).
4. Discussion
The pattern in shoot elongation was consistent among all treatments: native populations grew faster than invasive populations,
but reached lower asymptotes earlier than invasive populations
(Table 1 and Fig. 1). In contrast, invasive populations grew more
slowly, but reached higher asymptotes. This suggests that invasive populations have a greater ability to utilize available resources,
except for WL NH where the amount of available nutrient is limited
by water.
An interesting point in shoot elongation pattern is that native
populations reach the asymptote earlier than invasives. This may
be coupled to a difference in flowering phenology between invasive and native populations, because we frequently observed that
the flowering began at the terminal of main stem, when shoot
elongation is finished (determinate growth; Larcher, 1995). This
appears to happen earlier in native than invasive populations,
because our results also indicated that native populations flower
approximately 2 weeks before invasive populations. Consistently,
Bastlová and Květ (2002) reported that invasive populations of
purple loosestrife begin flowering approximately 10 days later
than native populations. Thus, early-flowering native populations
probably terminate shoot elongation earlier than invasive populations.
In contrast to a prolonged shoot elongation of invasive populations, this did not lead to higher branching than native populations
(Table 1 and Fig. 2). Invasive populations increased branches
faster than natives only in WH NH . The sigmoid growth in WH NL
showed contrasting patterns between invasive and native populations (Table 1 and Fig. 2), where native populations grew faster and
utilized available resources earlier than invasive populations. However, it appears that both populations used up available resources
and finally reached to a similar asymptote.
The size of largest leaf revealed another pattern of growth
(Table 1 and Fig. 3). Both invasive and native populations grew
at a similar rate, but invasive populations generally grew towards
a higher asymptote than native populations. Invasive populations
may be able to produce a greater size of the largest leaf for utilizing
more light resources than natives. However, it does not necessarily
mean that invasive populations produce larger leaves on average,
or a larger total leaf area, as we did not measure leaf area index (LAI).
In WL NL and WH NH , native populations reached the inflection point
earlier than invasives, limiting further growth.
225
Our results suggest that invasive populations generally utilize
available resources more effectively to be taller and produce a
greater size of largest leaf than native populations (Davis et al.,
2000). However, this trend was evident for the number of branches
only in the high water, high nutrient treatment, suggesting a strong
water × nutrient interaction on the number of branches. In contrast, for height and the size of largest leaf, there appears to be a
general difference between invasive and native populations, which
does not depend on water or nutrient treatments. This would suggest that invasive species may be successful by utilizing excessive
resources in disturbed habitats (Hobbs and Huenneke, 1992), but
this can be observed in certain traits only, not in all traits. Therefore, the difference in growth patterns between invasive and native
populations may vary depending on both traits and environments.
0.0101
0.0505
0.0931
0.0330
Acknowledgements
Treatments are: WL NL , low water, low nutrient; WL NH , low water, high nutrient; WH NL , high water, low nutrient; WH NH , high water, high nutrient.
This work was supported by Department of Ecology, Evolution,
and Organismal Biology at Iowa State University and a grant from
Korea Research Institute of Bioscience and Biotechnology (KRIBB)
Research Initiative Program.
a
17.303 (0.485)
14.933 (0.437)
13.964 (0.458)
15.395 (0.451)
19.051 (0.473)
16.141 (0.436)
15.014 (0.425)
16.717 (0.423)
32.931 (0.676)
27.996 (0.590)
33.806 (0.687)
31.060 (0.607)
WL NL
WL NH
WH NL
WH NH
I
29.402 (0.514)
26.238 (0.466)
29.790 (0.503)
28.114 (0.483)
<0.0001
0.0197
<0.0001
0.0002
–
–
24.431
–
–
–
19.509
–
–
–
<0.0001
–
0.6261
0.3261
0.2103
0.2692
0.183 (0.007)
0.220 (0.008)
0.210 (0.009)
0.200 (0.007)
0.178 (0.006)
0.210 (0.007)
0.224 (0.008)
0.211 (0.006)
0.1883
0.8176
<0.0001
0.0277
0.050 (0.004)
0.051 (0.004)
0.238 (0.012)
0.046 (0.002)
0.112 (0.003)
0.125 (0.003)
0.109 (0.002)
0.119 (0.003)
WL NL
WL NH
WH NL
WH NH
K
0.136 (0.003)
0.148 (0.003)
0.136 (0.003)
0.140 (0.003)
P
88.274 (2.689)
79.434 (2.360)
108.858 (3.238)
107.121 (3.130)
100.114 (3.272)
84.476 (2.620)
124.285 (4.027)
119.027 (3.671)
WL NL
WL NH
WH NL
WH NH
A
Native
<0.0001
<0.0001
<0.0001
<0.0001
0.042 (0.005)
0.050 (0.004)
0.175 (0008)
0.052 (0.002)
18.765 (1.174)
17.958 (1.164)
15.764 (1.155)
23.083 (1.193)
26.460 (1.221)
23.748 (1.196)
22.599 (1.187)
31.764 (1.245)
0.6383
0.7858
0.6893
0.0326
<0.0001
0.0006
<0.0001
<0.0001
Native
Invasive
P
1.461 (0.243)
1.427 (0.243)
21.252 (1.369)
2.537 (0.095)
Native
1.631 (0.268)
1.518 (0.231)
20.469 (1.395)
2.236 (0.103)
Invasive
Invasive
0.0053
0.1530
0.0029
0.0138
Number of branches
Height
Treatmenta
Parameter
Table 1
Fixed effect parameter estimates (±1 standard errors in parenthesis) of invasive and native populations in each experimental treatment.
Size of the largest leaf
P
Y.J. Chun et al. / Aquatic Botany 93 (2010) 221–226
Appendix A. Supplementary data
Supplementary data associated with this article can be found, in
the online version, at doi:10.1016/j.aquabot.2010.09.001.
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