Population size and relatedness affect fitness
of a self-incompatible invasive plant
Diane R. Elam*, Caroline E. Ridley†, Karen Goodell‡, and Norman C. Ellstrand†§
*California/Nevada Operations Office, U.S. Fish and Wildlife Service, 2800 Cottage Way, W-2606, Sacramento, CA 95825;†Department of Botany and Plant
Sciences and Center for Conservation Biology, University of California, Riverside, CA 92521-0124; and‡Department of Evolution, Ecology, and Organismal
Biology, Ohio State University, 1179 University Drive, Newark, OH 43055
Edited by Barbara A. Schaal, Washington University, St. Louis, MO, and approved November 13, 2006 (received for review August 30, 2006)
One of the lingering paradoxes in invasion biology is how founder
populations of an introduced species are able to overcome the
limitations of small size and, in a ‘‘reversal of fortune,’’ proliferate
in a new habitat. The transition from colonist to invader is espe-
cially enigmatic for self-incompatible species, which must find a
can result in the Allee effect, a positive relationship between
individual fitness and population size or density. Theoretically, the
Allee effect should be common in founder populations of self-
incompatible colonizing species and may account for the high rate
of failed introductions, but little supporting evidence exists. We
created a field experiment to test whether the Allee effect affects
the maternal fitness of a self-incompatible invasive species, wild
radish (Raphanus sativus). We created populations of varying size
and relatedness. We measured maternal fitness in terms of both
fruit set per flower and seed number per fruit. We found that both
population size and the level of genetic relatedness among indi-
viduals influence maternal reproductive success. Our results ex-
plicitly define an ecological genetic obstacle faced by populations
of an exotic species on its way to becoming invasive. Such a
mechanistic understanding of the invasions of species that require
a mate can and should be exploited for both controlling current
outbreaks and reducing their frequency in the future.
Allee effect ? colonization ? invasiveness ? Raphanus sativus ?
of individuals and/or low density. Low density and small popu-
lation size not only increase the risk of stochastic extinction (1)
but also limit opportunities for individuals to mate effectively
(2). The latter may result in an Allee effect, a positive relation-
ship between population size and individual fitness (3). Finding
compatible mates in a small population presents a problem for
plants, which are sessile during the reproductive stage, and is
especially challenging for obligately outcrossing species, such as
those that are self-incompatible or dioecious. For example,
self-incompatibility systems both prohibit self-pollination and
significantly reduce successful cross-pollination of individuals
with shared S-alleles, (e.g., close relatives) (4). ‘‘Baker’s law’’
predicts that a self-compatible species will have a much greater
chance of establishing in a new location after a long-distance
dispersal event than a self-incompatible species because the
former can create a sexually reproducing population with a
single individual (5, 6). Nonetheless, self-incompatibility is not
rare for invasive plants. Founder populations of self-
incompatible species that become invasive must experience a
‘‘reversal of fortune.’’ That is, individuals within these small
populations overcome the limitations of small population size to
reproduce and spread successfully.
Theoretical models and a handful of empirical studies suggest
that the Allee effect is most important in very small or sparse
populations (7–10), wherein declines in individual fitness can
lead to population contraction. Mechanisms responsible for the
xotic, invasive species are a modern biological paradox.
Founder populations are characteristically small in number
Allee effect do not always depend directly on mating system. For
example, in animals they may also include reduced efficiency of
antipredator vigilance behavior in small populations (11, 12).
A paucity of empirical data has encouraged us to examine
whether the Allee effect is present in a self-incompatible,
invasive plant. Our study organism, Raphanus sativus (commonly
known as California wild radish), is an annual, sporophytically
self-incompatible plant (13, 14) pollinated largely by honey bees
and syrphid flies (15, 16). California wild radish is of hybrid
origin (5, 17); it is descended from hybrids between R. sativus
(cultivated radish) and Raphanus raphanistrum (an agricultural
weed known as jointed charlock). Since introduction of these
species ?100 years ago and their subsequent hybridization,
California wild radish has spread throughout the state of Cali-
fornia, south into Baja California and north through Oregon,
invading such diverse habitats as inland roadsides and coastal
dunes (5, 17, 18). California wild radish seeds disperse via
Like fruits of the cultivated radish progenitor parent, California
wild radish fruits generally do not break into single-seeded
segments upon maturity.
We created experimental stands of wild radish in the field to
measure the impact of the Allee effect in this invasive species
(Fig. 1). We predicted that maternal fitness (fruit and seed
production) would increase with population size (i.e., that we
would observe an Allee effect). We also expected maternal
fitness to decline as genetic relatedness increased. Because R.
sativus exhibits sporophytic self-incompatibility, we predicted
that fitness would be lowest in the smallest populations of
full-siblings, because they carry, on average, the fewest incom-
To test the effect of population size and genetic relatedness on
maternal reproductive success in California wild radish, we
constructed artificial, replicated populations of 2, 5, 10, and 20
plants in three relatedness classes (full-sibling, half-sibling, and
unrelated) in a factorial design. We counted the number of
flowers produced by each plant. At the end of flowering we
harvested all of the fruits produced by each plant. Subsequently,
the number of seeds from a random sample of five fruits from
each plant was counted.
As predicted, individual fruit set (number of fruits/number of
flowers) increased significantly with population size, with aver-
age fruit set 2.5-fold greater in populations of size 20 than those
of size 2 averaged over all relatedness classes (Fig. 2 and Table
Author contributions: D.R.E. and N.C.E. designed research; D.R.E. and K.G. performed
The authors declare no conflict of interest.
This article is a PNAS direct submission.
Freely available online through the PNAS open access option.
§To whom correspondence should be addressed. E-mail: firstname.lastname@example.org.
© 2006 by The National Academy of Sciences of the USA
January 9, 2007 ?
vol. 104 ?
no. 2 ?
1). Furthermore, we found evidence for a threshold effect of
individuals (Fig. 2 and Table 2). Increasing relatedness among
individuals reduced fruit set (Fig. 2 and Table 1). Mean contrasts
indicated little difference between full-sibling and half-sibling
populations in fruit set, but both produced significantly fewer
fruits than unrelated populations (Table 2). Contrary to our
expectations, there was no significant interaction between pop-
ulation size and relatedness (Table 1).
Mean seed production per fruit increased with population size
an average of nearly 1.5-fold from populations of size 2 to
populations of size 10 over all relatedness classes (Fig. 3 and
Table 1). Mean contrasts revealed a threshold effect of size
similar to that for fruit set; mean number of seeds per fruit
increased with population size up to populations of five plants,
above which we detected no significant increase in seed produc-
tion. Increasing relatedness negatively affected mean seed pro-
duction per fruit. Specifically, individual mean seed production
per fruit increased with decreasing relatedness from full-sibling
to half-sibling, but not from half-sibling to unrelated populations
We have demonstrated that the Allee effect has a significant
impact on maternal fitness in a self-incompatible, invasive plant.
That is, we observed that, as population size increases, so does
individual maternal fitness in experimental populations of Cal-
ifornia wild radish. Overall, mean seed production per flower
increased with population size an average of ?4-fold from
populations of size 2 to populations of size 20 over all relatedness
classes. Furthermore, we observed that the relatedness of indi-
viduals within populations can also significantly impact fitness.
Interestingly, population size did not interact synergistically with
relatedness to reduce maternal fitness more in small populations
of closely related individuals than in small populations of
Finding a mate has been receiving increased attention as a
problem in plant conservation (e.g., ref. 20). However, studies of
the Allee effect’s role in limiting the success of invasive or weedy
plants remain few. The extant relevant studies of the Allee effect
in other exotic, invasive species have produced mixed results. An
invasive population of the largely self-incompatible smooth
cordgrass Spartina alternifora was the object of a pollen supple-
mentation and exclusion experiment (21). At the low-density
leading edge of the invasion, pollen availability appears to limit
seed production to an 8-fold disadvantage relative to the max-
vine Vincetoxicum rossicum produced significantly more seeds
per individual (approximately three times more) than patches of
states that ‘‘unlike most other examples of Allee effects in plants,
the effect in V. rossicum was not due to differences in pollinator
visitation rates,’’ but she does not address possible differences in
pollen load size or pollen quality due to the availability of more
mates. In contrast, natural stands of the invasive shrub Senna
didymobotrya in South Africa display no relationship between
plant density and seed production (23). Furthermore, pollen
supplementation did not result in increased seed or fruit set. The
absence of an Allee effect in the self-compatible S. didymobotrya
is surprising, given that some individuals experience consider-
able isolation and that high-frequency vibrations of visiting
pollinators are required for successful reproduction. In our study
of California wild radish, the Allee effect in our smallest
experimental populations resulted in seed production per flower
averaging ?25% of that in the largest populations.
An Allee effect can pose a demographic challenge to any
population, invasive or not. With regard to invasiveness, an Allee
effect may reduce the likelihood of establishment. In terms of
establishment success, the total number of seeds created by the
population is more relevant than individual plant fitness. If the
total number of seeds created by a population correlates closely
with establishment success, then relative colonization success
should be calculated by comparison of total seed production. In
our study of California wild radish the relative establishment
(number of fruits/number of flowers) (see also Tables 1 and 2). Symbols
(diamonds, full-siblings; squares, half-siblings; triangles, unrelated individu-
als) represent means across populations ? SEM.
The effects of population size and genetic relatedness on fruit set
of the experiment. Magnified areas indicate how plants were arranged spa-
tially within populations of 5, 10, and 20. The shaded area shows the area
occupied by a surrounding citrus grove.
Map of our field site with the locations of the experimental popu-
www.pnas.org?cgi?doi?10.1073?pnas.0607306104Elam et al.
success of the populations of size 20 compared with that of
populations of size 2 should be the 4-fold Allee advantage times
20 individuals divided by the two individuals in the small
populations, that is, a 40-fold relative advantage to the large
For those populations that do establish with a small number
of individuals, an Allee effect is expected to increase the lag time
before the appearance of invasiveness, a period during which
populations remain small and stationary. When range expansion
occurs, an Allee effect should retard it (24). The Allee effect
adds to the paradox of exotic, invasive species, which must
overcome a suite of ecological, evolutionary, and genetic obsta-
by which successful invaders overcome demographic conse-
quences of the Allee effect include large introductions, multiple
introductions, the ability to clone or self-fertilize, the evolution
of self-compatibility, and the hybridization of introduced species
with related species and subspecies (2, 25, 26). Most of these
mechanisms would increase the number of available mates with
which an individual can reproduce.
Our results demonstrate that maternal success is determined
then have California wild radish populations become successful
invaders despite the challenge of an Allee effect? California wild
radish seeds are dispersed in multiseeded, spongy lomenta (5).
These fruits usually hold three to five seeds (19). Furthermore,
paternity analysis has demonstrated the seeds held by a single
fruit are half-siblings, sired by more than one father (27).
Therefore, if the seeds in a single fruit germinate and grow up
in isolation from conspecifics, they are likely to suffer reduced
fitness. Our results indicate the Allee effect is strongest with
founder population size ?10. Thus, if the seeds from as few as
three or four fruits set by different plants found a population, we
would expect the Allee effect to be minimal. Wild radish’s
multiseeded fruits are an apparent adaptation to overcome the
challenge of an Allee effect.
species in general. It is not uncommon for invasive species to be
dioecious (especially many animals) or self-incompatible (espe-
cially many plants). Individuals of such species will require a
mate and are likely to suffer an Allee effect in small populations
as we observed in our experiments. In the case of self-
incompatible plants, this result is exacerbated when the individ-
uals are related to one another.
Our results highlight two easily studied ecological attributes of
potentially invasive organisms, mating system and dispersal
mode, that offer powerful insights into management strategies.
When zero-tolerance eradication or containment is impossible,
but the founding colonies of species that must outcross can be
reduced to numbers that are so low that the Allee effect severely
impacts reproduction’s role in establishment, those efforts will
still be worthwhile. Furthermore, rules of thumb could be
developed for those industries that import exotic plants and
animals. For example, if vegetatively propagated, obligately
outcrossing ornamentals are restricted to a single genotype, they
are much less likely to spread by seed. Essentially, the Allee
effect can be used as a weapon against invasive species that
require a mate to reproduce.
Materials and Methods
Experimental Design. The California wild radish seeds used were
progeny of hand-crosses. The plants were germinated and grown
to flowering in the greenhouse. Flowering plants in 2-gallon pots
were used to create synthetic populations of size 2, 5, 10, and 20
represent means across populations ? SEM.
The effects of population size and genetic relatedness on the mean
Table 1. ANOVA results showing the fixed effects of population size and genetic relatedness
on two measures of individual maternal fitness, arcsine square root (fruit set) and square root
(mean number of seeds per fruit)
Fruit set (n ? 437)
Mean no. of seeds per
fruit (n ? 401)
Size ? relatedness
***, P ? 0.0001;**, P ? 0.001.
Table 2. Mean contrasts for ANOVA of arcsine square root (fruit
set) and square root (mean number seeds per fruit)
Mean no. of seeds
per fruit, F value
Size 2 vs. 5, 10, and 20
Size 2 and 5 vs. 10 and 20
Size 5 vs. 10
Size 10 vs. 20
Full-sibling vs. half-sibling
Full- and half-sibling vs.
Half-sibling vs. unrelated
0.0001;**, P ? 0.001;*, P ? 0.05.
Elam et al. PNAS ?
January 9, 2007 ?
vol. 104 ?
no. 2 ?
at the University of California, Riverside, Agricultural Experi-
ment Station. Populations of each size comprised full-siblings,
half-siblings, or unrelated plants in a factorial design. Numbers
of populations within each size-relatedness combination are
summarized in Table 3. Populations of full-siblings are expected
to have higher levels of cross-incompatibility than those of
half-siblings or unrelated individuals. Populations of half-
siblings are expected to have, on average, intermediate levels of
cross-incompatibility (14). Neighboring populations were sepa-
rated by at least 100 m, a distance that had been previously found
to substantially reduce gene flow among small populations of
R. sativus (28).
Most of the surrounding landscape was citrus orchards, avo-
cado orchards, and fallow fields. Normally, local wild radish
populations would have been flowering at the time of the
experiment. However, the winter of the experiment, 1993–1994,
was during one of California’s periodic droughts. Sufficient
rainfall for natural germination did not occur until the end of our
experiment. The few flowering resident R. sativus plants within
1 km of our experimental plants resided within the boundaries
of the Experiment Station property. Thus, they were easily
identified and eradicated to minimize external gene flow.
The entire experimental design was repeated three times for
a total of 81 populations and 450 plants. Plants within popula-
tions were placed 0.75 m from nearest neighbors. Populations
were left in the field for 16 days to allow natural insect
pollination. Only flowers open during the 16 days of the exper-
iment were considered in the analysis. After 16 days, the plants
were returned to the greenhouse, and the fruits were allowed to
mature. For each plant, we counted the total number of flowers
open during the experiment and the total number of fruits
produced from experimental flowers. Fruit set was calculated as
the number of fruits produced divided by the total number of
experimental flowers. The number of seeds produced in a
random sample of five fruits from each plant was determined for
individuals in each of the three experimental repeats.
Statistical Analyses. Separate analyses were conducted for the two
measures of individual maternal fitness, fruit set and mean
number of seeds per fruit, because the data sets differed slightly.
analysis. For this reason, multivariate tests that consider both
variables simultaneously were not possible.
Fruit set data were arcsine square root transformed and seed
production data were square root transformed to meet the
assumptions of the analyses. For both transformed versions of
fruit set and mean seed production per fruit, a mixed-model
ANOVA was conducted by using the PROC MIXED in SAS 9.1
(29). The main effects of population size and population relat-
edness and their interaction were considered fixed. Experimen-
tal repeat and population replicate were random factors. We
used the variance components covariance structure and re-
stricted maximum-likelihood estimation technique. Planned
mean contrasts were calculated to test for specific differences
between size and relatedness classes.
We thank Janet Clegg, Rebecca Sherry, and Jaime Wynn Joyner-Geiken
for assistance with the experiment. Nickolas M. Waser and Michael T.
Clegg provided input on experimental design. This project was sup-
ported, in part, by National Research Initiative–Cooperative State
Research, Education, and Extension Service–U.S. Department of Ag-
riculture Grant CA-*-BPS-7194-CG (to N.C.E.) and Environmental
Protection Agency Science to Achieve Results Fellowship U-91651901
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Table 3. Experimental design
Data shown represent the number of populations for each population size
(with a total of 27 populations and 150 individuals). The design was repeated
three times for a total of 81 populations and 450 individuals.
www.pnas.org?cgi?doi?10.1073?pnas.0607306104Elam et al.