Variation in pollen limitation and floral parasitism

Annals of Botany 115: 315–326, 2015
doi:10.1093/aob/mcu243, available online at www.aob.oxfordjournals.org
Variation in pollen limitation and floral parasitism across a mating system
transition in a Pacific coastal dune plant: evolutionary causes or
ecological consequences?
Sara Dart and Christopher G. Eckert*
Department of Biology, Queen’s University, Kingston, Ontario, K7L 3N6 Canada
* For correspondence. E-mail [email protected]
Received: 25 June 2014 Returned for revision: 25 July 2014 Accepted: 24 October 2014 Published electronically: 22 December 2014
Background and Aims Evolutionary transitions from outcrossing to self-fertilization are thought to occur
because selfing provides reproductive assurance when pollinators or mates are scarce, but they could also occur via
selection to reduce floral vulnerability to herbivores. This study investigated geographic covariation between floral
morphology, fruit set, pollen limitation and florivory across the geographic range of Camissoniopsis cheiranthifolia,
a Pacific coastal dune endemic that varies strikingly in flower size and mating system.
Methods Fruit set was quantified in 75 populations, and in 41 of these floral herbivory by larvae of a specialized
moth (Mompha sp.) that consumes anthers in developing buds was also quantified. Experimental pollen supplementation was performed to quantify pollen limitation in three large-flowered, outcrossing and two small-flowered, selfing populations. These parameters were also compared between large- and small-flowered phenotypes within three
mixed populations.
Key Results Fruit set was much lower in large-flowered populations, and also much lower among large- than
small-flowered plants within populations. Pollen supplementation increased per flower seed production in largeflowered but not small-flowered populations, but fruit set was not pollen limited. Hence inadequate pollination
cannot account for the low fruit set of large-flowered plants. Floral herbivory was much more frequent in largeflowered populations and correlated negatively with fruit set. However, florivores did not preferentially attack
large-flowered plants in three large-flowered populations or in two of three mixed populations.
Conclusions Selfing alleviated pollen limitation of seeds per fruit, but florivory better explains the marked variation in fruit set. Although florivory was more frequent in large-flowered populations, large-flowered individuals
were not generally more vulnerable within populations. Rather than a causative selective factor, reduced florivory
in small-flowered, selfing populations is probably an ecological consequence of mating system differentiation, with
potentially significant effects on population demography and biotic interactions.
Key words: Beach evening primrose, Camissoniopsis cheiranthifolia, coastal dunes, floral herbivory, fruit set, geographic variation, mating system variation, microlepidoptera, parasitism, pollen limitation, reproductive assurance,
self-fertilization.
INTRODUCTION
The evolutionary transition from large, showy, outcrossing
flowers to small, less conspicuous, self-fertilizing flowers has
occurred thousands of times (Stebbins, 1974), and generated
sustained interest in the ecological and evolutionary causes and
consequences. The most widely invoked adaptive explanation
is that selfing provides reproductive assurance when pollinators
and/or mates are scarce (Eckert et al., 2006). Selfing taxa occur
in geographically or ecologically marginal habitats where outcross pollination may be unreliable (Baker, 1955; Jain, 1976;
Lloyd, 1980; Busch, 2005) and are over-represented among invasive plants that may often experience Allee effects (Rambuda
and Johnson, 2004; van Kleunen et al., 2008). Pollen limitation,
which is common and often severe (Burd, 1994; Ashman et al.,
2004; Knight et al., 2005), may be alleviated by traits enabling
selfing (Larson and Barrett, 2000).
Selection on floral traits may also arise from herbivory
(Ashman, 2002; Eckert et al., 2006; Strauss and Whittall,
2006). Florivory is common and can affect fitness directly
though consumption of pollen, ovules and seeds, or indirectly
through consumption of attractive structures and rewards that
alter pollinator visitation and foraging (Krupnick et al., 1999;
McCall and Irwin, 2006; Steets et al., 2007b). Floral traits that
attract pollinators can also attract herbivores (Adler and
Bronstien, 2004; Teixido et al., 2011; Theis and Adler, 2012),
and larger flowers may provide more resources for herbivores,
resulting in indirect selection on traits that correlate with overall
size. Hence, florivory may select for smaller, less conspicuous
flowers (Hanley et al., 2009), indirectly promoting the evolution of selfing (Penet et al., 2009). Although herbivoremediated selection on floral traits that influence the mating
system is not mutually exclusive of selection for reproductive
assurance via pollen limitation, the evolutionary scenarios are
fundamentally different (Eckert et al., 2006). Selection for reproductive assurance favours floral modifications that increase
self-pollination (e.g. reduced herkogamy and dichogamy) and
C The Author 2014. Published by Oxford University Press on behalf of the Annals of Botany Company. All rights reserved.
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Dart & Eckert — Pollen limitation, florivory and mating system variation
self-fertilization (weaker self-incompatibility), with reductions
in attractive and reward traits and overall flower size
favoured only after selfing predominates. Selection to reduce
florivory would act directly on attractive/reward traits and
flower size, with higher selfing occurring as a secondary
consequence.
Key floral traits can vary strikingly among populations
within species (Jain, 1976). This facilitates investigation of mating system evolution, as it reduces the likelihood that variation
in ecological and genetic factors that cause (or at least maintain) mating system differentiation is confounded with major
differences in life history and ecology. Variation among plants
within populations is additionally useful, because the effect of
floral variation on pollination, florivory and mating can be evaluated more directly. Such intraspecific variation has enabled
analyses of covariation between key floral traits and mating (reviewed in Button et al., 2012; Dart et al., 2012), and between
selfing and inbreeding depression, the main selective factor opposing selfing (Husband and Schemske, 1996; Winn et al.,
2011). However, the pollination ecology of small-flowered selfing and large-flowered outcrossing populations within species
(Inoue et al., 1996; Fausto et al., 2001) or phenotypes within
populations (Piper et al., 1986) has rarely been studied, leaving
fundamental predictions with equivocal support. For instance,
the prediction that self-compatibility increases fruit or seed set
has been supported in some species (Lyons and Antonovics,
1991; Busch, 2005) but not in others (Barrett et al., 1989;
Hererra et al., 2001; Schueller, 2004). The prediction that
selfing alleviates pollen limitation is also weakly supported
(Lyons and Antonovics, 1991; Hererra et al., 2001; Schueller,
2004; Kennedy and Elle, 2008; Moeller et al., 2012). Whether
variation in floral morphology and mating system affects
floral antagonists or vice versa has rarely been studied. It is
not known, for instance, whether smaller, less conspicuous
flowers experience lower rates of florivory than larger, showier
flowers.
We combine multi-year surveys of fruit set and florivory
with experimental pollen supplementation to investigate the
causes and consequences of mating system differentiation in
Camissoniopsis cheiranthifolia (Onagraceae). This is a shortlived perennial endemic to Pacific coastal dunes of western
North America (Samis and Eckert, 2007) that varies widely in
floral traits and mating system across its geographic range
(Dart et al., 2012). Raven (1969) divided the species into two
subspecies: large-flowered, often self-incompatible and putatively outcrossing ssp. suffruticosa, distributed from Point
Conception, California to the southern range limit in northern
Baja California, Mexico; and small-flowered, highly
autogamous and putatively selfing ssp. cheiranthifolia,
distributed from Point Conception to the northern range limit in
southern Oregon and on the Channel Islands. Linsley et al.
(1973) observed that visitation by the principle pollinators,
small oligolectic Andrena bees, was much lower in smallflowered than large-flowered populations, and hypothesized
that heavy morning fog typical north of Point Conception
reduces bee activity, thereby selecting for selfing (and consequently small flowers) to provide reproductive assurance.
Dart et al. (2012) revealed greater complexity. Flower size
did vary discontinuously, such that populations could readily be
categorized as large- (LF, mean corolla width approx. 29 mm)
or small-flowered (SF, mean approx. 16 mm), and common
garden experiments confirmed a strong genetic basis to this.
As expected, plants from SF populations (ssp. cheiranthifolia)
are self-compatible and can achieve full seed set via autonomous self-pollination within buds before anthesis (Dart and
Eckert, 2013). Plants from LF populations (ssp. suffruticosa) in
San Diego County California are self-incompatible (SI).
However, LF populations just to the north are self-compatible
(SC) and can set considerable seed by autonomously selfing
when flowers close, although the contribution of delayed
selfing to seed production in natural populations is unclear
(Dart and Eckert, 2013). Populations in Baja California,
classified by Raven (1969) as ssp. suffruticosa, turned out to be
SF, SC, highly autogamous and very similar to ssp.
cheiranthifolia.
Further, all populations engage in some self-fertilization
(Dart et al., 2012). The mean proportion of seeds self-fertilized
ranged from 018 in LF–SI populations and 036 in LF–SC populations to 067 in SF–SC populations north of Point
Conception and 084 in SF–SC populations on the Channel
Islands and Baja California. Strong geographic differentiation
in floral traits but weaker differentiation in self-compatibility,
autonomous selfing and mating system suggests that selective
factors other than or in addition to reproductive assurance have
promoted floral differentiation in C. cheiranthifolia.
Interactions with herbivores might have influenced floral
evolution in C. cheiranthiolia. Developing flowers are exploited by a specialist microlepidopteran herbivore that consumes anthers within buds, causing flowers to abscise before
anthesis. Because buds are not consumed outright, we refer to
this as bud parasitism. DNA barcoding of >200 larvae
identified the parasite as a single undescribed Mompha species
(Coleophoridae; Emery et al., 2009), within a genus known
for species-specific associations with the Onagraceae.
Large-flowered plants may be more heavily parasitized if adult
moths are attracted to larger flowers, or if LF plants produce larger buds that provide more resources for larval
development.
We investigate the roles of pollen limitation and florivory in
the differentiation of floral morphology and mating system in
C. cheiranthifolia by addressing the following predictions. (1)
Fruit set will be higher in SF than in LF populations due to
some combination of high autonomous selfing and lower floral
parasitism. (2) Because fruit set in LF populations depends on
the abundance and activity of specialist pollinators and
florivores, which may vary in time and space, fruit set will vary
more among populations and between years within populations
in LF than in SF populations. (3) A higher proportion of buds
will be parasitized in LF than in SF populations. (4) Mompha
may parasitize LF plants more frequently because they
have larger, more attractive flowers and/or larger buds.
Hence, within populations, plants with larger flowers will be
parasitized more than those with smaller flowers. (5) An important assumption of prediction (4) is that larger flowers arise
from relatively larger buds. (6) Selfing could have been favoured via reproductive assurance if LF phenotypes experienced chronic pollen limitation, hence outcross pollen
limitation of fruit set and seed production will be greater for LF
than for SF populations and for LF than for SF plants within
mixed populations.
Dart & Eckert — Pollen limitation, florivory and mating system variation
Geographic covariation between flower size, fruit set and bud
parasitism
We tested whether the capacity for selfing increases fruit set
by comparing 15 LF and 60 SF populations from across
the geographic range from May to July 2002–2005
(Supplementary Data 1). Populations were classified as LF or
SF following Dart et al. (2012) based on a large sample of
flowers measured for corolla width (measured from the tip of a
randomly selected petal to the tip of the opposing petal;
Fig. 1A; data from Dart et al., 2012) and herkogamy (distance
from the base of the stigma to the closest dehiscing anther;
Dart et al., 2012). Populations were visited near the end of
the flowering season so that plants had produced many flowers
that were unambiguously either aborted or developing
into fruit. We randomly selected a single lateral branch
on 10–51 randomly selected plants per population (mean ¼ 25,
total n ¼ 1851 branches) and counted the mature, maturing and aborted fruits, and calculated fruit set as the number
of mature or maturing fruits divided by the total number
of ovaries.
We tested the prediction that bud parasitism was more frequent in LF than in SF populations, by estimating the frequency
of parasitism for 41 populations (16 LF, 25 SF) across the range
(Supplementary Data 1) by sampling a single bud just before
opening from 20–98 plants per population (mean ¼ 42) visited
once during peak flowering from May to July 2005–2010 (25
populations sampled in 2005, 11 in 2007, two in 2009, three in
2010, n ¼ 1706 buds total). We measured the length of each
bud (to 001 mm), dissected it and scored it as parasitized if it
contained a moth larva, larval frass or characteristic damage to
40
35
30
25
20
15
10
1·0
LF−SI
LF−SC
VAR
SF−SC
0·8
Mean
fruit set
Camissoniopsis cheiranthifolia (Hornem. ex Spreng.)
W.L. Wagner & Hoch produces actinomorphic flowers with
four green, reflexed sepals, four bright yellow petals, a shallow
hypanthium, eight stamens in two whorls and a large globular
stigma presented adjacent to or 9 mm above the anthers.
Flowers are produced singly in leaf axils, mostly along lateral
stems extending from a central rosette. Flowers open at sunrise
and close in the late afternoon or early evening. The duration of
opening within a day and the consecutive days that flowers reopen are much lower in SF than in LF populations (Dart et al.,
2012). Peak flowering occurs during May–July in all populations studied here (S. Dart and C.G. Eckert, unpubl. data).
Mature fruits and undeveloped ovaries remain attached to
stems, allowing retrospective measurement of fruit set.
Because LF and SF populations are geographically segregated (Dart et al., 2012), differences in fruit and seed set, bud
parasitism and pollen limitation might arise from geographic
variation in the abundance and activity of mutualists and parasites in addition to or instead of variation in floral morphology.
Although geographic surveys alone cannot verify a causative
influence of floral morphology, LF and SF phenotypes co-occur
within three populations, allowing more direct tests of associations between floral morphology, fruit set, pollen limitation and
bud parasitism.
0·6
0·4
0·2
0
1·0
Proportion
parasitized
Study species
Corolla
width (mm)
MATERIALS AND METHODS
317
0·8
0·6
0·4
0·2
0
30
32
34
36
38
40
42
44
Latitude (°N)
FIG. 1. Geographic variation in flower size (corolla width), fruit set and the proportion of buds parasitized among natural populations of Camissoniopsis cheiranthifolia across its geographic range. The dotted vertical lines indicate the
locations of the Mexico–USA border (325 N) and Point Conception (345 N).
Filled triangles are large-flowered self-incompatible populations (LF–SI); filled
circles are large-flowered self-compatible populations (LF–SC); open circles are
small-flowered self-compatible populations (SF–SC); and diamonds indicate the
three phenotypically mixed populations just north of Point Conception (VAR).
In subsequent figures and all analyses, LF–SI and LF–SC are pooled as LF populations. Note the two clusters of SF–SC populations south of Point Conception:
one on the Channel Islands (33–34 N) and the other in northern Baja California
(30–31 N). The flower size data are from Dart et al. (2012).
floral organs. In analyses below, the frequency of bud parasitism varies both within and among flowering seasons, hence
there is undoubtedly uncontrolled temporal variation in parasitism among the populations in our survey that may obscure the
difference between LF and SF populations.
Generalized linear mixed models (GLMMs) evaluated
whether fruit set or bud parasitism differed between LF and SF
populations, with fruit set (number of flowers setting fruit or
not) and bud parasitism (bud parasitized or not) as binomial responses, population flower size as a fixed categorical predictor
and population as a random effect nested within flower size.
Models using the logit link function were fit using the glmer
command in the package lme4 (version 1.0-5, http://cran.
r-project.org/package ¼ lme4, accessed 13 November 2013)
for the R statistical computing environment (version 3.0.2; R
Core Team, 2013). Fruit set data were overdispersed, so we
fit models using quasi-likelihood estimation (Zuur et al.,
2013). A mixed-effects linear model implemented using the
lmer command (lme4 package) tested the prediction that
buds were longer in LF than in SF populations, with population flower size as a fixed predictor and population as a
nested random effect. For all analyses, likelihood ratio tests
evaluated the significance of potential predictors.
318
Dart & Eckert — Pollen limitation, florivory and mating system variation
We tested whether fruit set and bud parasitism are more variable among LF than among SF populations using Levene’s test
(Schultz, 1985; leveneTest command, car package, version
2.0-19, http://cran.r-project.org/web/packages/car/index.html,
accessed 13 November 2013). Given that fruit set and the proportion of buds parasitized are both binomial variables, their
statistical variance should be highest when mean ¼ 05. More
variation among LF than among SF populations would be expected if, as predicted, the grand mean of LF populations was
closer to 05 than that of SF populations. Simulations were used
to determine whether Levene’s test detected additional variation among LF populations due to stochasticity of pollination or
parasitism (above and beyond differences in binomial sampling
error) (Supplementary Data 2). Absolute year to year differences in fruit set and bud parasitism were also compared
between LF and SF populations (Supplementary Data 3).
To supplement categorical comparisons of fruit set, parasitism frequency and bud length between LF and SF populations,
generalized linear models (GLMs; glm command in R) analysed the regression between these response variables and corolla width as a continuous predictor, with fruit set and
proportion parasitized as binomial responses (logit link) and
bud length as a Gaussian response (identity link). Each analysis
was done for all populations and for LF and SF populations
separately to determine if the large-scale regressions were observed within population flower size groups. At the population
level, fruit set was represented by the total sampled flowers setting fruit vs. not setting fruit. Similarly, the proportion of buds
parasitized was represented by the number of sampled buds parasitized vs. not parasitized. GLMs also analysed regressions between proportion parasitized and fruit set (binomial response)
and bud length and proportion parasitized (binomial response).
Data for the response variables fruit set and proportion parasitized were overdispersed, so we used quasi-likelihood estimation. For each analysis, we report the regression coefficients
back-transformed to the original scale of the data using the
predict function in R (Zuur et al., 2009, p. 250).
Covariation between flower size, fruit set and bud parasitism
within populations
For a more direct test of the prediction that smaller flowers
and higher selfing are associated with increased fruit set, we
compared LF and SF phenotypes within three phenotypically
mixed populations (CGN1C, CSP1C and CMN1C). In 2005,
plants in each population were classified as LF (corolla width
>20 mm) or SF (20 mm) following Dart et al. (2012). We estimated fruit set on 30 plants per phenotype (total n ¼ 263
plants). A GLM with quasi-likelihood estimation modelled fruit
set as a binomial response (logit link), with population, floral
phenotype (LF vs. SF) and their interaction as potential predictors. Levene’s test with simulations evaluated whether fruit set
was less variable among SF than among LF plants
(Supplementary Data 2).
We tested the prediction of higher parasitism on plants with
larger flowers in two ways. In 2005, we sampled the most mature bud from LF and SF plants within each mixed population
(n ¼ 230 buds), measured its length and scored it as parasitized
or not. We compared LF vs. SF plants for bud length using
linear models, and for frequency of parasitism (binomial
response) using GLM (logit link), with population, floral
phenotype and their interaction as potential predictors. GLM
(logit link) evaluated the association between parasitism and
bud size with population and bud length as predictors.
Secondly, we sampled a single flower and the most mature
adjacent bud for a large sample of plants in three LF populations (CCO1C, CIV1C and CBV1C) during 2007. We randomly sampled 60 plants on each of five occasions at CCO1C,
two at CIV1C and one at CBV1C. The corolla width of the
sampled flower was measured and the adjacent bud was measured and scored as parasitized or not. For each population,
GLM modelled parasitism as a binomial response (logit link),
with corolla width (or bud length) and sampling date as
predictors.
Pollen supplementation experiment
To test the prediction that small flower size and consequent
selfing reduces pollen limitation (PL), supplemental pollinatatuion was provided to flowers in three LF and two SF populations in 2004 and 2006 (Supplementary Data 1). We randomly
selected 34–115 plants per population, each with at least one
open flower, and randomly assigned 16–63 plants to each of
two treatments: cross-pollen supplementation (þX) or open
pollination (OP). Pollen limitation is usually quantified by comparing naturally pollinated and cross-supplemented flowers,
whereas the extent to which selfing might alleviate PL must be
determined by comparing naturally pollinated flowers with
those supplemented with self pollen (Eckert et al., 2010); therefore, we added a self-supplemented treatment (þS) in 2006.
For each supplemented plant, we hand-pollinated every open
flower (mean approx. 3, range ¼ 1–10) on a single day during
peak flowering by brushing pollen from three anthers across the
stigma, using one anther from each of three donor plants located 3 m away for þ X flowers and three anthers from another flower on the same plant for þ S flowers. We randomly
selected a single treated flower on each plant as the focal
flower, marked it with acrylic paint on the ovary, recorded
whether it matured a fruit and counted the filled seeds within.
To avoid confounding effects of flower position and phenology
(Wesselingh, 2007), all focal flowers were centrally located on
their stems and open during peak flowering.
Because the number of seeds produced per focal flower
is the product of a Bernoulli variable (fruit set) and a zerotruncated Poisson variable (seeds per mature fruit), we modelled the effect of pollination treatment, population flower size
and their interaction using the ASTER model in R (Shaw et al.,
2008; version 0.8-27, http://cran.r-project.org/web/packages/aster/index.html, accessed 13 November 2013). We followed
Geyer et al. (2007) to estimate the expectation and 95 % confidence intervals of seeds per focal flower. Population could not
be included as a nested random effect because too few populations within flower size classes were used to estimate its random variance accurately. Supplementary analysis substituting
population for flower size revealed no heterogeneity among
populations within size categories that would complicate interpretation. Data for 2004 and 2006 were analysed separately
because different populations were used.
Dart & Eckert — Pollen limitation, florivory and mating system variation
To determine whether PL might cause the lower fruit
set observed in LF than in SF populations in our geographic
survey (see the Results), GLM (logit link) analysed the fruit set
component of seed per flower, with pollination treatment, population flower size and their interaction as predictors.
Pollen limitation was compared between LF and SF
phenotypes within two mixed populations (CGN1C and
CSP1C). As above, randomly chosen plants were randomly
assigned to þX or OP treatments in 2004, and þX, OP and
þS treatments in 2006. ASTER and GLM evaluated the effect
of population (CGN1C vs. CSP1C), pollination treatment,
flower size and their interactions on seeds per flower and
fruit set.
Providing supplemental pollination to only a sample of flowers on individual plants and comparing these with flowers on
open-pollinated plants may overestimate PL (Knight et al.,
2006) because preferential allocation of resources to supplemented flowers may elevate their fruit and seed set at the expense of unsupplemented flowers. We evaluated this bias
experimentally and found no evidence that seed set of supplemented flowers was boosted by resource reallocation in any
population (Supplementary Data 4).
Depression of fruit set by bud parasitism alone
Comparing the fruit set of flowers that had been potentially
exposed to parasitism vs. those that had not estimated how
much bud parasitism alone depresses fruit set. Elimination of
parasitism by pesticide application was not permitted in our
study populations, so we adopted the following approach.
First, we retrospectively estimated fruit set for all flowers on
the focal stem on all plants selected for the 2004 pollen supplementation experiment before experimental treatments were applied. These ‘retrospective’ flowers were exposed to natural
pollination and bud parasitism, with fruit set potentially depressed by resource limitation, pollen limitation and/or parasitism. The open-pollinated ‘focal’ flowers used in the
supplementation experiment were exposed to natural pollination, but not bud parasitism (parasitism causes abscission before
opening). The difference in fruit set between ‘retrospective’
and ‘focal’ flowers estimates fruit set lost to bud parasitism.
This assumes that background fruit abortion does not vary temporally, because retrospective flowers tended to open earlier
than focal flowers. The increase in abortion during the flowering sequence typical of many plants (Diggle, 1995) would
cause the effect of bud parasitism to be underestimated.
However, our surveys suggest extremely infrequent parasitism
in SF populations, which should reveal any temporal reduction
in fruit set alone.
We monitored fruit set of retrospective and focal flowers on
360 plants in three LF (COR1C, CBV1C and CCO1C) and two
SF populations (CGN3C and CMS1C). Directly comparing
fruit set of retrospective vs. focal flowers was not possible because, for each plant, the former involved a sample of flowers,
whereas the latter involved a single flower. Instead, we calculated and compared maximum likelihood estimates of the expected value and 95 % confidence intervals for fruit set
(binomial response) of each type of flower for each population
using a GLM (logit link).
319
RESULTS
Geographic covariation between flower size, fruit set and bud
parasitism
The mean proportion of flowers setting fruit (fruit set) ranged
from 023 to 100 among 75 populations surveyed (n ¼ 1851
plants; Fig. 1) and was, as predicted, lower for 15 LF populations (mean 6 s.e. ¼ 053 6 0045) than for 60 SF populations
(097 6 0009; likelihood ratio v2 ¼ 6782, d.f. ¼ 1, P < 0001).
Mean fruit set varied more among LF than among SF populations (Levene’s test F1,73 ¼ 1919, P < 0001). The difference
in variance was not quite significantly larger than that expected
from differences in binomial sampling variance alone (Psim
approx. 0057) (Supplementary Data 2). Between-year difference in fruit set was not greater within the nine LF than within
the 31 SF populations surveyed in > 1 year (Supplementary
Data 3).
Overall, 23 % of the 1706 buds were parasitized, ranging
from 000 to 090 among 41 populations surveyed (Fig. 1) and,
as predicted, this was higher for 16 LF (041 6 0056) than for
25 SF populations (005 6 0013; v2 ¼ 3438, d.f. ¼ 1,
P < 0001). The proportion of buds parasitized varied more
among LF than among SF populations (F1,73 ¼ 1274,
P < 0001) but not more than expected based on binomial sampling variances (Psim approx. 012) (Supplementary Data 2).
Between-year differences in parasitism were higher for seven
LF than for six SF populations (Supplementary Data 3). Bud
length ranged from 266 to 1535 mm (n ¼ 1293 buds) and was
40 % shorter in 25 SF (617 6 012 mm) than in ten LF populations (1068 6 027 mm; v2 ¼ 8313, d.f. ¼ 1, P < 0001).
Across all populations, increasing corolla width was associated with decreasing fruit set, increasing proportion parasitized
and increasing bud length (Fig. 2A, B, C, respectively;
Table 1). However, none of these regressions was significant
among LF or SF populations analysed separately (Table 1).
Similarly, fruit set covaried negatively with proportion parasitized (n ¼ 35 populations; Fig. 2D) but only the regression
among SF populations neared significance. Proportion parasitized covaried positively with bud length (n ¼ 35) but not within
flower size categories (Table 1).
Covariation between flower size, fruit set and bud parasitism
within populations
In three mixed populations, fruit set ranged from 017 to 10
(mean ¼ 082, n ¼ 263 plants; Fig. 3A) and varied significantly
among populations (likelihood ratio v2 ¼ 1010, d.f. ¼ 2,
P ¼ 00064). As predicted, fruit set was lower for LF than for
SF phenotypes (v2 ¼ 12532, d.f. ¼ 1, P < 0001; no interaction
v2 ¼ 299, d.f. ¼ 2, P ¼ 022). Within each population, fruit set
varied more among LF than among SF plants (Levene’s test:
CGN1C F1,91 ¼ 2191, P < 0001; CMN1C F1,58 ¼ 946,
P ¼ 00032; CSP1C F1,108 ¼ 3901, P < 0001). However, the
difference in variance exceeded that expected from binomial
sampling variance in CGN1C (Psim approx. 0044) and CSP1C
(Psim approx. 00072) but not in CMN1C (Psim approx. 026)
(Supplementary Data 2). Overall, 19 % of 230 buds were parasitized, and parasitism varied among populations (v2 ¼ 857,
d.f. ¼ 2, P ¼ 0014), and was higher for LF than for SF plants
Dart & Eckert — Pollen limitation, florivory and mating system variation
320
(v2 ¼ 399, d.f. ¼ 1, P ¼ 0046). Although the interaction was
not quite significant (v2 ¼ 496, d.f. ¼ 2, P ¼ 0084), the difference between floral phenotypes was only evident in one of
three populations (Fig. 3B). Bud length did not vary among
populations (v2 ¼ 088, d.f. ¼ 2, P ¼ 064) but was 40 % shorter
on SF than on LF plants (v2 ¼ 57462, d.f. ¼ 1, P < 0001), and
this difference varied in magnitude but not in direction among
populations (v2 ¼ 2481, d.f. ¼ 2, P < 0001), being somewhat
smaller in CSP1C (31 %) than in CGN1C (42 %) or CMN1C
(47 %). There was no association between bud length and parasitism across these populations (v2 ¼ 0049, d.f. ¼ 1, P ¼ 082).
In the three LF populations where bud parasitism and bud
length were measured along with corolla width of the adjacent
flower, 38 % of 458 buds were parasitized. Bud length covaried
positively with corolla width (range of r among populations
and sampling dates ¼ 037–059, all P < 001, mean
r ¼ þ 048). Although parasitism varied among populations and
sampling dates, parasitism did not vary with corolla width in
any populations (Table 2). Similarly, bud length and parasitism
did not correlate within populations (CCO1C v2 ¼ 140,
d.f. ¼ 1, P ¼ 023; CIV1C v2 ¼ 112, P ¼ 029; CBV1C
v2 ¼ 083, P ¼ 036).
A
1·0
Mean fruit set
0·8
0·6
0·4
0·2
Large-flowered
Small-flowered
0
B
Proportion parasitized
1·0
0·8
0·6
0·4
0·2
Pollen supplementation experiment
0
C
Bud length (mm)
12·5
10·5
8·5
6·5
4·5
10
20
30
Corolla width (mm)
40
0·2
0·4
0·6
0·8
Proportion parasitized
1·0
D
1·0
Mean fruit set
0·8
0·6
0·4
0·2
0
0
FIG. 2. Relationships of fruit set, bud parasitism and bud length to corolla width
(A–C) and of fruit set to bud parasitism (D) among natural populations of
Camissoniopsis cheiranthifolia. Open circles are small-flowered populations,
and filled circles are large-flowered populations. Analysis based on these data is
given in Table 1.
In both 2004 and 2006, supplemental pollination increased
the seeds produced per flower more in LF than in SF populations (Fig. 4), although the interaction between population
flower size and pollination treatment was not quite significant
in 2004 (Supplementary Data 5). For both years, the effect of
pollination treatment was significant for LF populations (2004,
v2 ¼ 5304, d.f. ¼ 1, P < 0001; 2006, v2 ¼ 4052, d.f. ¼ 1,
P < 0001) but not SF populations (2004, v2 ¼ 015, d.f. ¼ 1,
P ¼ 070; 2006, v2 ¼ 262, d.f. ¼ 1, P ¼ 027). Cross-pollination
did not increase seeds per flower more than self-pollination in
2006. In fact, the trend was in the opposite direction (Fig. 4B),
though not quite significant (v2 ¼ 378, d.f. ¼ 1, P ¼ 0052).
Supplemental pollination increased seeds per flower in LF
populations primarily by increasing seeds per fruit rather than
fruit set. Fruit set was generally high in both years (2004 ¼
893 %; 2006 ¼ 870 %). Although fruit set was higher in SF
than in LF populations (2004, LF ¼ 823 %, SF ¼ 963 %;
2006, LF ¼ 766 %, SF ¼ 979 %), supplemental pollination did
not increase fruit set, nor did the effect of pollination treatment
and population flower size interact (Supplementary Data 5).
Effects of supplemental pollination in the two mixed populations were complex (Fig. 5). In 2004, the effects of population,
flower size and pollination treatment interacted (Supplementary
Data 6) but not in a way that indicated consistently stronger
pollination effects for LF than for SF plants. Instead, supplemental cross-pollination increased seed production of SF but
not LF plants in population CGN1C and decreased seed production of SF but not LF plants in CSP1C. For instance, population
and pollination treatment interacted for SF (v2 ¼ 1039, d.f. ¼ 1,
P ¼ 00013), but not LF plants (v2 ¼ 008, d.f. ¼ 1, P ¼ 078).
In 2006, all two-way interactions but not the three-way interaction were significant (Supplementary Data 6) but, again, not in
a way that indicated stronger effects of pollination for LF
plants. Instead, the interactions seem to arise from the
Dart & Eckert — Pollen limitation, florivory and mating system variation
321
TABLE 1. Associations among flower size (as measured by corolla width), bud length, fruit set and the proportion of buds parasitized
by Mompha among populations of Camissoniopsis cheiranthifolia
Response (distribution)
Predictor
Fruit set (binomial)
Corolla width
Proportion parasitized (binomial)
Corolla width
Bud length (Gaussian)
Corolla width
Fruit set (binomial)
Proportion parasitized
Proportion parasitized (binomial)
Bud length
All populations
LF populations only
SF populations only
0031 (43)
1561 (P < 0001)
0034 (24)
273 (P < 0001)
0293 (19)
1215 (P < 0001)
076 (35)
281 (P < 0001)
0056 (35)
323 (P < 0001
0028 (11)
32 (P ¼ 0074)
00048 (11)
0040 (P ¼ 084)
0074 (6)
037 (P ¼ 054)
0011 (14)
035 (P ¼ 055)
00069 (10)
064 (P ¼ 042)
00021 (32)
003 (P ¼ 057)
00094 (13)
0059 (P ¼ 044)
016 (13)
226 (P ¼ 013)
034 (21)
381 (P ¼ 0051)
00031 (25)
167 (P ¼ 020)
Responses were modelled as binomial variables except for bud length, which was considered Gaussian. Analyses were conducted for all populations and for
large-flowered (LF) and small-flowered (SF) populations separately.
The upper level of each cell contains the back-transformed regression slope (change in the response per unit change in the predictor) with the number of populations sampled in parentheses. The lower level contains the v2 value from a likelihood ratio test (with the P-value).
Plots of the first four relationships are given in Fig. 2.
1·0
A
Fruit set
0·9
0·8
Large-flowered
0·7
and the effects of population and pollination interacted
(v2 ¼ 1141, d.f. ¼ 2, P ¼ 00033). In contrast, for SF plants,
only the interaction was marginally significant (v2 ¼ 654,
d.f. ¼ 2, P ¼ 0038) and the effect of pollination was not
(v2 ¼ 479, d.f. ¼ 2, P ¼ 0091).
Variation in treatment effects among floral phenotypes in
these mixed populations resulted from variation in seeds per
fruit rather than fruit set. Fruit set was high for all treatments in
both 2004 (935 %, n ¼ 387) and 2006 (920 %, n ¼ 138). The
GLM detected only a difference in fruit set between populations
and only in 2004 (Supplementary Data 6).
Small-flowered
63
0·6
30
80
30
30
30
B
For all three LF populations, retrospective flowers exposed
to bud parasitism set fewer fruit than focal flowers for which
losses could not have involved parasitism, and in two populations there was no overlap in the 95 % confidence intervals
(Fig. 6). In contrast, fruit set was consistently very high
(>90 %) in both SF populations and did not differ between retrospective and focal flowers.
0·4
Proportion buds parasitized
Depression of fruit set by bud parasitism alone
0·3
0·2
0·1
DISCUSSION
0
Covariation between the mating system and pollen limitation
49
19
CGN1C
64
34
CSP1C
34
30
CMN1C
Population
FIG. 3. Comparison of mean (6 95 % confidence interval) fruit set (A) and the
proportion of buds parasitized (B) between large-flowered (LF) and smallflowered (SF) phenotypes within three mixed populations of Camissoniopsis
cheiranthifolia. The numbers of plants sampled for each combination of population and flower size phenotype are indicated.
difference between self-supplementation vs. both natural pollination and cross-supplementation, being somewhat larger for
LF than for SF plants. Analysing LF plants alone, the effect of
pollination was significant (v2 ¼ 1052, d.f. ¼ 2, P ¼ 00052)
Reproductive assurance is the most widely accepted adaptive explanation for the evolution of self-fertilization
(Cheptou, 2004; Morgan et al., 2005), yet some of its most fundamental predictions have rarely been tested, and the few existing studies produced mixed results. The prediction of higher
fruit or seed set in selfing vs. outcrossing populations is supported in some species (Primula vulgaris, Piper et al., 1986;
Helleborus foetidus, Herrera et al., 2001; Leavenworthia spp.,
Lyons and Antonovics, 1991; Busch, 2005) but not others
(Eichhornia paniculata, Barrett et al., 1989; Nicotiana glauca,
Schueller, 2004). At face value, our results lend additional support to this prediction. Fruit set was much higher, though not
biologically less variable, in SF vs. LF C. cheiranthifolia populations. Although LF and SF populations are geographically
Dart & Eckert — Pollen limitation, florivory and mating system variation
322
TABLE 2. Analysis testing for an association between flower size, bud length and bud parasitism among plants within three largeflowered populations of Camissoniopsis cheiranthifolia
Population
CCO1C
CIV1C
CBV1C
Summary statistics
Generalized linear model
(binomial response ¼ parasitized)
Generalized linear model
(Gaussian response ¼ bud length)
Proportion of buds
parasitized
Corolla
width (mm)
Bud
length (mm)
Date (D)
Corolla
width (C)
DC
Date (D)
Corolla
width (C)
DC
0431
(028–066)
0287
(028–029)
0300
(NA)
3500
(2113–4592)
3337
(2181–4396)
3487
(2128–4396)
1119
(410–1918)
1150
(740–1506)
1169
(708–1498)
2141 (4)
<0001
00019 (1)
096
NA
013 (1)
072
068 (1)
041
002 (1)
090
362 (4)
046
225 (1)
013
NA
1246 (4)
0014
340 (1)
0067
NA
8913 (1)
<0001
2581 (1)
<0001
1649 (1)
<0001
518 (4)
027
035 (1)
055
NA
Summary statistics cells contain mean and range (in parentheses) among sampling dates for parasitism among flowers measured for corolla width and among
buds measured for bud length.
Results of generalized linear models include the likelihood ratio v2 values (above), P-values (below) and degrees of freedom (in parentheses).
Population CCO1C was sampled five times, CIV1C twice and CBV1C only once (hence variation among sampling dates was not analysed; NA).
separated, the difference in fruit set is probably not due to confounding geographic variation in abiotic factors (e.g. temperature or precipitation), as we consistently observed high fruit set
in all three geographically disjunct groups of SF populations:
north of Point Conception, Baja California and the Channel
Islands. Moreover, SF plants set more fruit than LF plants
within three mixed populations where divergent phenotypes
experience similar environments.
Our results also support the prediction that selfing increases
seed production because it alleviates outcross pollen limitation.
Again, results from previous pollen supplementation experiments are mixed, with lower pollen limitation observed in selfing than in outcrossing populations of Primula vulgaris, but not
of Leavenworthia crassa (Lyons and Antonovics, 1991),
Helleborus foetidus (Herrera et al., 2001), Nicotiana glauca
(Schueller, 2004) or Collinsia parviflora (Kennedy and Elle,
2008; see also Goodwillie, 2001). This disparity may partially
reflect the fact that selfing is not the only evolutionary response
to pollen limitation. Outcrossing populations might evolve
other compensating mechanisms, such as increased floral attraction, reward or longevity, depending on the ecological conditions affecting the strength of pollen limitation and other
selective factors such as inbreeding depression (Eckert et al.,
2010). Although stronger pollen limitation in outcrossing vs.
selfing populations may linger after mating system differentiation, implicating pollen limitation as a causal selective force (as
may be the case in C. cheiranthifolia), selfing and outcrossing
populations might diverge in multiple compensating mechanisms, yielding low pollen limitation and high fruit set regardless of the mating system.
Higher pollen limitation in LF than in SF populations is consistent with the conjecture of Linsley et al. (1973) that selfing
(and consequentially smaller flowers) evolved in C. cheiranthifolia to provide reproductive assurance. If pollen limitation is
common in LF populations south of Point Conception, as seems
the case, decreased pollinator visitation in the colder and foggier environment to the north could tip the selective balance to
favour higher selfing. However, we recognize two caveats: first,
pollen limitation cannot explain the much lower fruit set in LF
vs. SF populations north and south of Point Conception, as
pollen supplementation only increased seeds per fruit (not fruit
set) in LF populations. Instead, the lower fruit set in LF populations is probably caused by differential Mompha parasitism (see
below).
Secondly, verifying that pollen limitation of LF phenotypes
would be higher north of Point Conception requires experimental transplants (e.g. Geber and Eckhart, 2005; Moeller and
Geber, 2005), for which we could not obtain permits. The
mixed LF/SF populations north of Point Conception provided a
‘natural experiment’ but, contrary to expectations, pollen limitation was not higher for LF than for SF phenotypes. However,
naturally mixed populations are an imperfect analogue of transplant experiments, as they may experience conditions (e.g. frequent pollinator visitation) that permit the persistence of LF
phenotypes (indeed, LF plants have probably existed in these
populations for at least 45 years; Raven, 1969, p. 266). Thus LF
phenotypes could suffer much stronger pollen limitation if
transplanted into pure SF populations north of Point
Conception.
Mompha parasitism as a selective force on floral morphology,
development and the mating system
By directly interfering with reproduction, florivory is a
strong potential selective force (Hanley et al., 2009), but only if
florivory induces covariation between fitness and floral traits.
Mompha larvae can reduce fruit set dramatically by causing
C. cheiranthifolia flowers to abscise before opening, although
we could not estimate this effect directly since experimental
florivore exclusion (e.g. Galen, 1999; Herrera et al., 2002) was
not permitted. Mixed populations provided equivocal results, as
lower parasitism was associated with higher fruit set in only
one of three populations, although this might be because parasitism was measured only once per flowering season whereas
fruit set integrates reproductive success across the season.
Florivore effects on fitness were more clearly revealed by lower
fruit set of retrospective flowers exposed to both pre- and
post-anthesis losses compared with focal flowers exposed to
post-anthesis losses only (Fig. 6). The negligible difference in
Dart & Eckert — Pollen limitation, florivory and mating system variation
60
A 2004
80
323
A 2004
Natural
Selfed
Crossed
Seeds per flower
70
Seeds per flower
50
40
50
40
30
Natural
30
Selfed
Crossed
60
102
90
98
93
B 2006
50
20
48 46
80
B 2006
20 25
80 66
58 64
7 10 8
16 15 16
14 15 14
Large
Small
70
Seeds per flower
20
Seeds per flower
60
60
50
40
30
40
20
7 7 9
Large
30
Small
CGN1C
CSP1C
Population and flower size
20
82
84
Large
82
79
78
79
Small
Population flower size
FIG. 4. Comparisons of mean (6 95 % confidence interval) seeds per flower
between open-pollinated (open circles), cross-pollinated (filled circles) and
self-pollinated (filled triangles; 2006 only) flowers in large-flowered (LF) and
small-flowered (SF) populations of Camissoniopsis cheiranthifolia in 2004 (A)
and 2006 (B). The numbers of plants sampled for each combination of treatment
and population are indicated.
fruit set between retrospective and focal flowers in SF populations confirms that Mompha parasitism is the only appreciable
cause of pre-anthesis fruit abortion.
Lack of experimental proof notwithstanding, we conclude that
Mompha parasitism reduces fruit set, contributing strongly to the
much lower fruit set in LF than in SF populations. Evidence that
Mompha florivory favours smaller, less conspicuous flowers is
weaker. The positive correlation between flower size and parasitism among populations was not evident among LF or SF populations analysed separately, and LF plants suffered more frequent
parasitism in only one of three mixed populations. Flower size
and parasitism also did not correlate in any of the three LF
FIG. 5. Comparisons of mean (6 95 % confidence interval) seeds per flower
between open-pollinated (open circles), cross-pollinated (filled circles) and
self-pollinated (filled triangles; 2006 only) flowers on large-flowered (LF) and
small-flowered (SF) phenotypes in two mixed populations of Camissoniopsis
cheiranthifolia in 2004 (A) and 2006 (B). The numbers of plants sampled for
each combination of treatment, phenotype and population are indicated.
populations analysed. Female Mompha may not preferentially
oviposit on larger flowers if there is no benefit to doing so or little opportunity to distinguish flower size. The more abundant
nectar in large flowers may not attract females if their feeding
proboscises are not functional (Emery et al., 2009), and floral
traits may not cue oviposition if Mompha adults are strictly nocturnal, when C. cheiranthifolia flowers are closed (Dart et al.,
2012). As we could not reliably observe the oviposition behaviour of these nocturnal microlepidopterans (see also Artz et al.,
2010), it remains uncertain whether plants with less conspicuous
flowers would avoid parasitism.
Alternatively, higher florivory in LF populations may arise if
they support larger Mompha populations. Individual larva may
require >1 bud for development (C.G. Eckert, unpubl. data),
and LF buds are 40 % larger than SF buds, providing more resources. If moving among buds exposes larvae to predation or
parasitism, larger buds could increase survival by reducing bud
to bud movements. Higher mitochondrial DNA haplotype diversity in Mompha populations south of Point Conception
Dart & Eckert — Pollen limitation, florivory and mating system variation
324
1·0
0·9
Fruit set
0·8
0·7
0·6
0·5
Retrospective
0·4
0·3
Focal
27
40
COR1C
CBV1C
114
97
82
CCO1C
CGN3C
CMS1C
Population
FIG. 6. Comparison of mean (6 95 % confidence interval) fruit set in flowers exposed to bud parasitism (retrospective flowers: pre- and post-anthesis losses) vs.
flowers in the pollen supplementation experiment not exposed to bud parasitism
(focal flowers only post-anthesis losses) in five populations of Camissoniopsis
cheiranthifolia. Retrospective and focal flowers were on the same set of plants.
Populations COR1C, CBV1C and CCO1C are large flowered. Populations
CGN3C and CMS1C are small flowered. The numbers of plants sampled in
each population are indicated.
(Emery et al., 2009) also suggests that LF C. cheiranthifolia
populations maintain larger Mompha populations. This proposed causal link between flower size and parasite abundance
would explain their geographic association, which is unlikely to
reflect a coincidental match in latitudinal trends because
Mompha abundance was low in geographically disjunct groups
of SF populations. Although we cannot rule out the possibility
that Mompha abundance reflects unmeasured environmental
factors that also correlate with C. cheiranthifolia flower size,
abrupt, parallel shifts in flower size and parasitism make a
causal role for flower size (or closely correlated trait) a more
parsimonious explanation.
CONCLUSIONS
This study provides a rare example of the reduced pollen limitation in selfing vs. outcrossing populations generally predicted
by theoretical models and broad interspecific comparative analyses. Our results are consistent with a role for reproductive
assurance in the transition from outcrossing to selfing, a hypothesis that requires further testing with transplant experiments. Large flowers and other traits promoting outcrossing
correlate strongly with florivory by the larvae of a microlepidopteran Mompha species, which appears to account more directly than pollen limitation for the much lower fruit set in
large-flowered populations of C. cheiranthifolia. However, the
available evidence suggests that differential floral parasitism is
probably a consequence, rather than a cause, of mating system
evolution.
The evolution of selfing may fundamentally change the
ecology of plant species by influencing key demographic
parameters (Lloyd, 1980; Cheptou, 2004). In particular, selfing
may allow species to colonize marginal habitats and persist under low-density conditions in the absence of pollinators (Baker,
1955; Morgan et al., 2005; Eckert et al., 2006). Further, plants
in small, isolated populations may avoid herbivory (e.g. Kery
et al., 2001), resulting in an indirect association between selfing
and reduced herbivory. In C. cheiranthifolia, however, SF populations are not smaller than LF populations (Samis and Eckert,
2007), suggesting a more direct effect of floral variation on herbivory that may commonly occur in flowering plants.
Evolutionary shifts to selfing are associated with reduced floral
and display size (Goodwillie et al., 2010) and hence resources
for florivores. Reduced florivore fitness and, in turn, abundance
may increase the ecological success of nascent selfing lineages.
For instance, SF C. cheiranthifolia populations outnumber and
are more widely distributed than LF populations (Samis and
Eckert, 2007; Dart et al., 2012). This ‘release from florivory’
hypothesis could be evaluated with demographic analysis
(Steets et al., 2007a). Reduced florivory may, in turn, select
upon the types, levels and deployment (constitutive vs. inducible) of plant chemical defences, a possibility for which there is
evidence at both micro- and macro-evolutionary scales
(Campbell and Kessler, 2013). These speculations highlight the
potential for relatively unexplored evolutionary feedbacks
between pollination and herbivory (Hanley et al., 2009).
Although Mompha florivory may not have caused the evolution of higher selfing in C. cheiranthifolia, it may still influence
the mating system, especially in LF populations (e.g. Penet
et al., 2009). High Mompha-induced flower loss might strongly
reduce mate availability and pollinator visitation (Krupnick
et al., 1999), and thus outcrossing opportunities. This may contribute to the substantial variation in outcrossing observed
among LF populations, which remains unexplained by floral
morphology (Dart et al., 2012), and might ultimately influence
the maintenance of mixed selfing and outcrossing in largeflowered populations (Steets et al., 2007b).
SUPPLEMENTARY DATA
Supplementary data are available online at www.aob.oxfordjournals.org and consist of the following. 1: list of study populations,
their locations and the type of data collected from each. 2: simulation analysis of variation in fruit set and bud parasitism. 3: analysis of between-year variation in fruit set and floral parasitism.
4: analysis testing for resource reallocation between flowers
within plants following pollen supplementation. 5: analysis
of pollen supplementation’s effect on fruit set and seed production among large- and small-flowered populations. 6: analysis of
pollen supplementation’s effect on fruit set and seed production
among large- and small-flowered phenotypes in two mixed
populations.
ACKNOWLEDGEMENTS
We thank Karen Samis, Emily Austen, Sarah Yakimowski,
Colleen Inglis and Kyle Lauersen for help in the field; Alisa
Yokum, Virginia Emery, Jeffrey Lam, Johanna McGlaughlin,
Adam Kwok and William Mi for help in the lab; Peter Raven,
Peter Hoch, Dave Hubbard and Jenny Dugan for logistic
Dart & Eckert — Pollen limitation, florivory and mating system variation
support and advice; Anna Hargreaves and Mick Hanley for
comments on the manuscript; and the United States National
Park Service, California State Parks and Oregon State Parks
for research permits and logistic support. This work was supported by an Ontario Graduate Scholarships to S.D. and the
Natural Sciences and Engineering Research Council of
Canada through a Discovery Grant to C.G.E.
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