Download INVASION DYNAMICS OF CYTISUS SCOPARIUS: A MATRIX

Ecological Applications, 10(3), 2000, pp. 726–743
䉷 2000 by the Ecological Society of America
INVASION DYNAMICS OF CYTISUS SCOPARIUS:
A MATRIX MODEL APPROACH
INGRID M. PARKER1
Department of Botany, University of Washington, Seattle, Washington 98195 USA
Abstract. It is at the level of population dynamics that an invasion either fails or
succeeds. By elucidating patterns of variation in population growth rates or demographic
rates, it is possible to forge a connection between quantitative field data and theoretical
ideas about invasiveness, invasibility, and rates of spread. Demographic models also provide
a tool to guide control strategies for invasive pests. Here I report the results of a demographic
study of Cytisus scoparius, an exotic shrub on the west coast of North America. I used
matrix population models to describe demographic patterns in six populations (three in
prairies and three in urban fields) and across advancing stages of invasion. At the edge of
the invading front, all populations showed finite rates of increase (␭) ⬎1; however, prairie
populations were increasing much more rapidly than urban ones. While many individual
vital rates differed between prairie and urban populations, Life Table Response Analysis
revealed that seedling establishment made by far the largest contribution to the difference
in growth rate between the habitats. Establishment is much higher in the prairies, which
are also less anthropogenically disturbed and show higher plant species diversity. From the
edge of the invading population to the center, ␭ generally decreased, and the elasticity
pattern changed from one evenly distributed across life history stages to one dominated
by the survivorship of large adults. Comparing the matrix model predictions to direct
estimates of invasion (change over time of various measures of density and biomass), ␭
was most closely correlated with the increase of total biomass. From a control perspective,
elasticities did not suggest one particularly sensitive life history stage (‘‘Achilles heel’’)
for this pest plant. A simulation was used to evaluate the potential efficacy of biological
control agents that attack seeds. Based on model predictions, under current conditions a
control agent would have to destroy over 99.9% of seeds in prairies, and 70% of seeds in
urban populations, to suppress the invasion of C. scoparius populations.
Key words: biological control; Cytisus scoparius; demography; density; disturbance; exotic;
legume; non-native; seed predation; shrub.
INTRODUCTION
Although biological invasions are now considered to
be one of the world’s most challenging environmental
threats (Hedgpeth 1993, Ruesink et al. 1995, Vitousek
et al. 1996), many theories in invasion ecology are still
generally untested. In a field with a rich tradition of
mostly verbal theory (Elton 1958, Baker and Stebbins
1965) and a rapidly expanding collection of detailed
case histories, what is still missing is a strong connection between quantitative field data and invasion theory. One avenue for making this connection is provided
by demographic tools. Invasion biology must ultimately address patterns at the level of population dynamics, since it is at this level that an invasion either
fails or succeeds. By elucidating patterns of variation
in population growth rates or demographic rates, it
should be possible to test theoretical ideas about invasiveness, invasibility, and rates of spread (Mack
Manuscript received 23 July 1998; revised 20 April 1999;
accepted 12 May 1999; final version received 3 June 1999.
1 Present address: Department of Biology, Earth and Marine Sciences, University of California, Santa Cruz, California
95064 USA. E-mail: [email protected]
1985). For example, Baker’s concept of the ‘‘general
purpose genotype’’ suggests that invasive species
should have high levels of phenotypic plasticity which
allow them to maintain consistently high population
growth rates in a wide range of environments (Baker
1965). In contrast, others have argued that invaders are
primarily dependent on disturbed sites and microsites
(Fox and Fox 1986, Orians 1986, Hobbs and Huenneke
1992). The role of disturbance in promoting invasion
is related to the broader concept of ‘‘biotic resistance’’:
the idea that more intact and species rich communities
should be more resistant to invasion (Simberloff 1986,
Rejmanek 1996, Parker and Reichard 1997). Demographic approaches provide us with a dynamic view of
the interactions between an invading population and
its host community (Parker et al. 1999).
The factors controlling both population growth and
density hold practical as well as theoretical interest.
The finite rate of increase of an introduced species
helps determine not only whether it will spread, but its
rate of spread (Skellam 1951, Hengeveld 1989, Andow
et al. 1990, 1993, Shigesada and Kawasaki 1997),
which is of critical interest in designing control or quarantine programs. Population fluctuations of invading
726
June 2000
INVASION DYNAMICS OF CYTISUS
pest species can have important consequences for early
detection and eradication efforts (Carey 1996). In addition, the density eventually reached by an invader
contributes to the impact of that species on the host
community. Not just the final magnitude of density, but
also the form of population response to density can be
important; for example, it has been suggested that invasive weeds may experience early inverse density dependence, creating a positive feedback loop that allows
population numbers to grow very rapidly to high levels
(Kruger et al. 1986). Little is currently known about
spatial, temporal, or density-dependent variation in
population growth rates for most plant species, let alone
comparative information for native and exotic species.
Matrix demographic analysis, now a common tool
in population biology, is well suited to understanding
how factors influencing individuals may contribute to
overall population dynamics (Caswell 1989a). Demographic analysis has been valuable in many different
contexts, including the study of natural selection and
life history evolution (Charlesworth 1980, Lande 1982,
Roff 1992), the comparison of lifetime effects of different experimental treatments (Birch 1953, Marshall
1962, Caswell 1989b), and the evaluation of ecological
risks of genetic manipulation (Crawley et al. 1993,
Parker and Kareiva 1996). In a similar vein, it has been
an important tool for conservation biologists and resource managers as a way to explore the consequences
of management options (Menges 1986, Schemske et al.
1994). By evaluating the sensitivity of population
growth to different stages of the life cycle, conservation
biologists have identified stages and biological processes critical to the viability of threatened or endangered species (Crouse et al. 1987, Menges 1990, Aplet
et al. 1994). The same analysis can be done for exotic
pest species, with the intention of identifying stages
and processes most promising for reducing the viability
of these species. The modeling effort in its more naive
form is a hopeful quest for the ‘‘Achilles heel’’ of a
pest; a more sophisticated view is that even if the model
does not reveal one critical stage of the life cycle, it
can be used to quantify the effectiveness of different
management options, particularly those, such as biological control, focused on altering the vital rates (Shea
and Kelly 1998, McEvoy and Coombs 1999).
The goal of this study was to obtain demographic
data from different populations of Cytisus scoparius,
an exotic shrub on the west coast of North America,
to characterize the variation in local invasion dynamics
of this weed and suggest possible control options. I
have performed a detailed demographic analysis of
three populations in each of two contrasting habitats,
disturbed urban fields and glacial outwash prairie remnants, and across advancing stages of invasion. One
major focus of the work is to ask whether sites with
greater anthropogenic influence are more invasible. In
contrast to other models of C. scoparius (Rees and
Paynter 1997), I focus on the invasion process in sites
727
undergoing dynamic spread of the plant, where control
is focused less on reducing equilibrium microsite occupancy rates and more on slowing the growth of patches. In addition to matrix projections of population
trends, I also examine more direct measures of biomass
and density increase, allowing a comparison of the
asymptotic measures of population growth given from
matrix theory with direct measures of population
growth over the short term. I investigate the questions:
(1) How does an invader’s population growth rate vary
temporally, spatially, and among invaded habitats? (2)
How do population dynamics change as an invasion
proceeds? and (3) Can we say anything about the potential impact of biological control strategies for this
species? This study is both descriptive in that it reports
demographic trends, and predictive in that it looks to
demographic patterns for insight into the theoretical
factors controlling invasions.
METHODS
Study plant
Cytisus scoparius (Scotch or Scot’s broom) was first
introduced into the Pacific Northwest from Europe
probably as an ornamental (Gilkey 1957); the first preserved specimen was collected from a garden in Seattle
in 1888. For the last four decades, C. scoparius has
been regarded as a noxious pest in rangelands and natural areas throughout the west coast of North America
from British Columbia to central California.
C. scoparius is a large, leguminous shrub, reaching
a height of as much as four meters in its introduced
range. It has no form of clonal growth and therefore
relies entirely on seed set for reproduction. In Washington, reproduction is strongly pollen limited, and the
frequency of visitation by pollinators varies among individuals and among sites (Parker 1997). Flowering
occurs from April through June, seeds are dispersed
from late July to September by explosive dehiscence
and secondarily by ants. Seeds begin to germinate in
early March, and some germination occurs throughout
the summer (I. M. Parker, unpublished data).
Study sites
Preliminary studies suggested that there might be
important ecological and demographic differences between populations in two major types of C. scoparius
habitat: urban fields and prairies. In 1993, I established
permanent plots at Discovery Park and Johnson Prairie
(Washington State, USA), representing these two types
of habitat. In 1994, four more populations were added
to the study: urban sites Magnuson Park and Montlake
Fill, and prairie sites Thirteenth Division Prairie and
Weir Prairie (Washington State). Two of the urban field
populations (Magnuson Park and Discovery Park) were
situated in large Seattle city parks. Both fields are in
areas that had originally been forested but were subsequently used for landfill and exhibit poorly developed
Ecological Applications
Vol. 10, No. 3
INGRID M. PARKER
728
soils. The third urban population is on the Montlake
Fill, an area reclaimed from Lake Washington by landfill. Dominant plants in these fields are primarily exotic
species such as Agrostis tenuis and Vicia villosa. While
waste areas like urban fields make up much of the
distribution of this plant across its West Coast range,
glacial outwash prairies are perhaps the most biologically interesting and sensitive ecosystem invaded by
C. scoparius. All three prairies are located within the
Fort Lewis military base ⬃80 km south of Seattle, on
gravelly outwash plains characterized by shallow,
coarse-textured soils and low levels of soil nutrients
(Franklin and Dyrness 1988). Once covering great
park-like expanses (Kruckeberg 1991), these prairies
have been reduced by development and agriculture to
a few remnants. The prairies are dominated by Festuca
idahoensis, and include small herbaceous perennials
such as Cammassia quamash and the state threatened
Aster curtis, with intervening space covered by a thick
cryptogamic layer (Lang 1961). In these same prairies,
invasion by the nitrogen-fixing shrub is associated with
an increase in total nitrogen and nitrogen availability
(K. A. Haubensak and I. M. Parker, unpublished data),
as well as an increase in the total cover of other exotic
species and a decline in native species richness in some
areas (Parker et al. 1997).
At each site (⫽ population), I chose plots representing different invasion stages; that is, different
points relative to the expanding edge and the center of
an infestation. Edge plots were at the expanding outer
extent of the population where most space was still
unoccupied by C. scoparius, intermediate plots were
behind the front but did not yet show a closed canopy,
and center plots were in areas of high C. scoparius
density in the middle of the population. To ensure consistent invasion stages across the different sites, I identified potential areas, then censused the size-specific
density of plants in each area to be sure that density
fell within a certain range for each plot type. Individual
plots were then located haphazardly within those areas.
Post hoc analysis showed that the total biomass of C.
scoparius/m2 was significantly different and nonoverlapping among plot types (Parker 1996: mean edge ⫽
386 g, intermediate ⫽ 2160 g, center ⫽ 4268 g, F2,11
⫽ 82.7, P ⫽ 0.0001). So that equivalent numbers of
plants were included in the demographic analysis for
each plot, edge plots covered a greater area (96–316
m2) than intermediate (24–60 m2) or center (20–24 m2)
plots. Discovery Park and Johnson Prairie had edge,
intermediate, and center plots, while the other four populations had only edge and intermediate plots.
Stage classification
Stages were assigned using both life history characteristics and plant size. Life history was used to delimit seed, seedling (defined as plants no larger than
the maximum size I had ever observed first-year germinants to attain), and juvenile (plants larger than the
biggest first-year germinants but ⬍5 mm diameter, the
minimum size at which plants produced fruit) stages.
Adult C. scoparius plants vary a great deal in size, and
size determines ‘‘fate,’’ especially fecundity (Parker
1996). Therefore adults were split into four size classes,
a number chosen to balance sample size per cell against
accuracy in representing the average fecundity of individuals.
Plant morphology differed significantly both among
populations and among invasion stages within populations (Parker 1996). Therefore biomass, rather than
a simple measure such as plant height, was chosen as
the most appropriate and flexible measure with which
to classify size classes. Biomass was estimated from
branch number and branch diameter, based on regression equations developed for each population on the
basis of a sample of 25–50 plants uprooted from just
outside the permanent plots (r 2 ⫽ 0.88–0.96, Parker
1996). Biomass intervals for the different adult stages
were: small (⬍100 g), medium (100–400 g), large
(400–900 g), and extra large (⬎900 g).
In order to test the correspondence of stage classification and age classification, I took circular stem samples from each of the plants used in the biomass regressions and counted rings. I used a belt sander with
220 grit sandpaper, then hand-sanded each sample to
1000-grit fineness. I then counted growth rings under
a dissecting microscope. I regressed diameter and biomass on age (N ⫽ 168) and also compared the distribution of ages in each stage.
Demographic analysis: transition rules
Over the course of the three years of this study, I
marked, mapped, and followed the fate of ⬎3000
plants. Other than fecundity, matrix elements were determined from the probability of passing from one stage
to each of the other stages. Because C. scoparius is a
shrub, its diameter increases monotonically; however,
because stages were based on biomass, plants could
occasionally shrink by losing branches. In a few cases,
sample sizes were too small to observe a transition that
biological intuition dictated must occur. For example,
of the 37 extra large plants in Johnson Prairie’s Intermediate plot in 1993, none died, although obviously
the true global mortality rate is not zero. Rather than
choosing an arbitrary value, I dealt with these ‘‘problem transitions’’ in the following manner. Sampling
from a binomial distribution, I calculated the transition
probability that would yield a zero value (i.e., no dead
plants) 50% of the time, given the sample size. Thus,
the survival probability P in the above example would
be obtained as the solution to the binomial probability:
0.5 ⫽ P0(1 ⫺ P)37.
This protocol took advantage of the information provided by the sample size itself. There were 21 of these
problem transitions out of a total of 413.
Fecundity.—The calculation of fecundities depends
June 2000
INVASION DYNAMICS OF CYTISUS
on the timing of the census (Caswell 1989a). Censuses
were done at the end of fruit production (late summer);
conceptually, the time step can be thought of as occurring immediately after dispersal, with ‘‘newborn’’
seeds showing up as individuals in the matrix, and
fecundities estimated as the contribution to next year’s
seed for a plant in a particular stage. Therefore juveniles had a nonzero entry. I calculated fecundity as
follows: The average number of fruits per plant at the
t ⫹ 1 census was found for each stage at time t. That
number was then multiplied by the average number of
seeds per fruit in that population. That is, mean fecundity for small adults for the 1993–1994 matrix was the
mean number of seeds produced in 1994 by a plant
that was a small adult in 1993. This calculation took
into account plants that died between the censuses (having zero fecundity) as well as those that grew or shrank
into different stages in the following year.
Establishment.—Establishment rate was calculated
as the number of new seedlings appearing in a plot
divided by the number of seeds produced in the previous year. While this approximation neglects dormant
seeds, it was probably reasonable for the edge plots
(which had never previously been occupied by adult
plants), but overestimated germination rates for the
plots at later stages of invasion. The seed bank density
was determined by invasion history at each site and
not by an equilibrium process and therefore could not
be back calculated analytically. However, because both
the establishment rates themselves and their elasticities
are extremely low in the later invasion-stage plots, the
effect of this approximation should be minimal.
Seed dormancy.—What is defined in the matrix models as a single seed stage is in fact made up of many
age cohorts. C. scoparius seeds can be very long lived
under controlled laboratory conditions (Youngman
1951), although the long-term behavior of seeds in the
field is poorly known. Seed age could affect dormancy
both by changes in characteristics of the seed coat over
time and by random variation among seed cohorts (Kalisz and McPeek 1992, McPeek and Kalisz 1993). The
time scale of this study set limits on my ability to
estimate long-term dormancy rates. I quantified dormancy probabilities for three cohort–year combinations: (1) seeds produced in 1993 and analyzed at the
1994 census (1993 0-yr-olds), (2) seeds produced in
1993 and analyzed at the 1995 census (1994 1-yr-olds),
and (3) seeds produced in 1994 and analyzed at the
1995 census (1994 0-yr-olds).
In the fall of 1993, I collected fresh seeds from a
mix of many donors at each site and distributed them
in mesh envelopes; each envelope contained 50 seeds
and a tablespoon of autoclaved soil collected from that
site. Seed envelopes (N ⫽ 16) were placed at 1m intervals along transects adjacent to each of the three
demography plots at Discovery Park, Magnuson Park,
Johnson Prairie, and 13th Division Prairie. I removed
whatever litter or surface material was present, attached
729
the envelope to the soil surface, and replaced the surface material to simulate the microenvironment experienced by seeds lying on the soil at each location. At
each annual census, eight envelopes from each transect
were collected from the field, and the remaining seeds
were counted and tested for viability using tetrazolium
(Moore 1973). Because there were no consistent differences in dormancy rates among plots at different
stages of invasion, I lumped information from all transects.
In the fall of 1994, again seeds were set out in envelopes, but these were set into stainless steel insect
exclosures. Each 0.25 ⫻ 0.5 m exclosure was sunk 3
cm into the ground and extended 10 cm above the
ground, with a beveled edge pointing inward and coated
with ‘‘Tanglefoot’’ (Tanglefoot Company, Grand Rapids, Michigan, USA) to discourage ants or seed predators such as carabid beetles from removing the seeds.
Into one half of the exclosure I set envelopes of seeds,
and, to test for whether the envelopes introduced a
systematic bias, into the other half I scattered the same
number of seeds directly onto the surface. There was
no significant difference between treatments in the
number of germinated seeds (paired Wilcoxon Signed
Rank Test, N ⫽ 11, Z ⫽ 1.6, P ⫽ 0.11). Each population
had three exclosures, and at the time of the 1995 census,
450 seeds per population (three envelopes per exclosure) were collected and tested for viability.
The dormancy (seed to seed) matrix element was a
mean of the estimates from these three seed cohorts.
Using matrix analysis, I explored the consequence of
choosing different dormancy estimates and found that
the range of values from the three cohorts made little
difference to the outcome of the analysis. However,
these estimates of seed viability do not include postdispersal seed predation; it was not possible to obtain
direct estimates of seed predation because predation
could not be distinguished from local dispersal by ants,
which move high proportions of seeds in these habitats
(B. Semsrott and I. Parker, unpublished data). Therefore the dormancy rates presented here constitute an
upper limit. I again explored the consequences of this
omission and found that even a 90% reduction of the
matrix entry for dormancy (biologically possible, based
on observations from the exclosures) made little difference except to (1) reduce ␭ by 1–8% and (2) reduce
the elasticity for dormancy.
Demographic analysis: analytical methods
The life cycle of C. scoparius is represented in Fig.
1. Transitions between stages of the life cycle were
summarized in a projection matrix model of the form
n(t ⫹ 1) ⫽ A·n(t)
where n(t) is a vector of stage abundances at time t,
and A is a matrix of aij’s that describes how each stage
contributes to the number of individuals in all other
stages at the next time step. The dominant eigenvalue
INGRID M. PARKER
730
Ecological Applications
Vol. 10, No. 3
FIG. 1. Life cycle graph of C. scoparius, showing all possible transitions (those with nonzero matrix entries in at least
one plot and year). Dotted lines represent transitions that were only seen in one or two plot ⫻ year combinations.
␭ of A represents the asymptotic finite rate of increase
at the stable stage distribution.
I used projection matrices to calculate the finite rate
of increase for each combination of year, population,
and invasion stage. Because of the disparate sources
for different elements in the matrix, I could not use
bootstrap methods to generate estimates of variance
(Caswell 1989a). Therefore standard errors for ␭ were
generated analytically using the first-order approximation
V(␭) 艐
冘 (⳵␭ /⳵a ) V(a )
ij
2
ij
(Lande 1988). It should be noted that this approach
assumes independence among the matrix elements and
small variances, both of which are violated in this
study; therefore, confidence intervals are presented as
approximate values only.
Discovery Park and Johnson Prairie were censused
three times yielding two matrices each, and the other
four populations were censused twice yielding one matrix. Using analysis of variance with plots as replicates,
I tested for significant temporal variation in ␭ for Discovery Park and Johnson Prairie. I also tested for a
significant effect on ␭ of habitat type (urban, prairie)
and stage of invasion (edge, intermediate, center) in
1994–1995.
As a measure of the relative contribution of each
matrix element to ␭, I calculated its elasticity, where
elasticity is defined as aij /␭ ⫻ ⳵␭/⳵aij (Caswell 1989a).
To present the elasticity structure in a simple way, I
summed elasticities for each column, excluding seed
production, generating total elasticities for the fate of
seedlings, juveniles, and small, medium, large, and extra-large adults. I also generated a summary elasticity
for fecundity.
Because newly invading populations are not expected to conform to a stable stage distribution, and,
in fact, these populations do not (Parker 1996), it is
not clear how accurately analytical results such as ␭
can represent population dynamics in this system.
Therefore I also ran simulations of the transient dynamics of edge plots. I started with 10 seeds and calculated the number of years required to reach saturation, using the density of extra-large plants in center
plots as a measure of full occupancy (1.5/m2, Parker
1996). Spearman rank correlations were used to compare ␭ values with years to saturation for each site/year
combination (N ⫽ 8).
Given a difference in growth rate between the invading edges of urban and prairie populations, an interesting issue is what ecological or life history factors
are most responsible for this difference. Life Table Response Analysis was designed to answer this question
(Levin et al. 1987, Caswell 1989b). Life Table Response Analysis decomposes the effect of an experimental treatment, a life history strategy, or as in this
case, an environmental factor such as habitat type, into
the contribution cij of each vital rate to that effect. To
calculate the effect of habitat type, I first generated two
composite (mean) matrices, one for urban fields and
June 2000
INVASION DYNAMICS OF CYTISUS
731
one for prairies, weighting the matrix elements for each
site by their sample size (Horvitz and Schemske 1995).
I then took the difference between the mean urban and
mean prairie value for each matrix element. I also generated a matrix midway between these two matrices.
Finally, the effect of habitat type on ␭ was decomposed
into the contribution of each vital rate to the difference
in ␭ using the equation
cij ⫽ (aij(urban) ⫺ a(prairie)
) (⳵␭/⳵aij)
ij
where ⳵␭/⳵aij was evaluated at the matrix midway between urban and prairie matrices.
Biomass, density, and direct measures of invasion
I documented the progression of C. scoparius invasion directly using (1) measurements of biomass accumulation and (2) measurements of plant density. I
calculated plant biomass per square meter by summing
the estimated biomass of all plants in the plot. Using
ANOVA and the post hoc Bonferroni-Dunn test, I compared edge, intermediate, and center plots for biomass,
total number of vegetative plants, number of adult
plants, and number of extra large adults, per square
meter.
I followed the increase of biomass in each plot over
time, and calculated the proportional increase in biomass by dividing all values by the initial (1993 or 1994)
biomass in the plot. I took the difference of the logs
of biomass (log[1995] ⫺ log[1994]) as one estimate of
the speed at which C. scoparius fills up space and increases its draw on the local resources (⫽ invasion
rate). I then correlated this change in biomass with
initial biomass using Spearman rank correlations. The
14 plots served as replicates. I did the same set of
analyses for the three numerical density measures. I
then asked how well each of the four measures of invasion rate (change in biomass or density) could be
explained by each of the measures of current occupancy
(biomass, density), again using Spearman rank correlations. Finally I tested for a correspondence between
␭ and each of the direct measures of invasion, and I
generated correlations between ␭ and each of the four
measures of current occupancy.
The impact of biological control
A variety of insect species have been either introduced or considered for introduction as control agents
for C. scoparius both in the United States and in other
regions where the plant is a pest species (Andres et al.
1967, Harman 1992, Syrett and Harman 1995, Hosking
1996, Hosking et al. 1996). One useful application of
the matrix models is to determine a priori what level
of damage would be required if a biological control
agent were to have a significant impact on the growth
of C. scoparius populations in Washington State. Focusing on the activity of seed-eating insects, I constructed matrices for the fastest and the slowest growing edge plots among my populations, and reduced fe-
FIG. 2. Box plot of the distribution of ages in each stage.
Boxes surround the central 50% of the data, with the middle
line representing the median, and outer lines at 10% and 90%.
Sample sizes (N) are presented for each stage.
cundity values by differing proportions of damaged
seeds, recalculating the matrices to find the point at
which population growth fell below 1.
RESULTS
Age, stage, and demographic traits
Several factors support the use of stage-based (Lefkovitch matrix) rather than age-based (Leslie matrix)
demography for this plant species. Using estimates of
plant age from growth rings, I first inspected the relationship between age and size/stage. Diameter and
biomass both increased significantly with age (diameter
vs. age, N ⫽ 168, r 2 ⫽ 0.48, P ⬍ 0.0001; biomass vs.
age, N ⫽ 168, r 2 ⫽ 0.33, P ⬍ 0.0001), but the low r 2
values show that age is a poor predictor of size. In
addition, each life stage comprises a large range of ages
(Fig. 2). Because the relationship between size and age
is likely to be sensitive to environmental quality, a sizebased classification was central to allowing comparison
among habitats. The stage classification used did successfully capture the biology of C. scoparius, in that
different stages showed different demographic rates
(Figs. 3 and 4).
Inspecting the pattern of individual vital rates provides some insight into the life history of C. scoparius,
as well as into what is driving differences in population
dynamics among habitats and as intraspecific density
increases (Appendix). In general, mortality declined
from the younger to the older stages, with seedlings
and juveniles showing greater mortality than adult stages (Fig. 3). The most dramatic differences were seen
in the center plots, where mean seedling mortality was
as high as 80%, while mortality for large and extra
large adults was ⬍20%. Invasion stage had a dramatic
effect on overall patterns of mortality, with much lower
survivorship in the center of the population than at the
edge. Mean fruit production (and variance in fruit pro-
732
INGRID M. PARKER
Ecological Applications
Vol. 10, No. 3
FIG. 3. Mean mortality rates of plants of different life
history stages, for prairie populations (circles) and urban populations (squares), and across stages of invasion (edge, intermediate, center). Means are for three populations, with two
separate transition years for Johnson Prairie and Discovery
Park. Bars represent ⫾1 SE.
duction) increased dramatically with plant size, with
fruit number increasing over two orders of magnitude
from small adults to extra large adults (Fig. 4a). The
effect of invasion stage on fecundity was of a smaller
magnitude than the effect of plant size, and trends
among edge, intermediate, and center plots were not
as consistent for fecundity as for mortality. However,
germination rate, like mortality, declined consistently
from the edge to the center of populations (Fig. 5).
The vital rates in urban populations differed from
those in prairie populations. Mortality was almost always higher for individuals of the same stage in urban
populations than it was in prairie populations (Fig. 3).
Germination rates were much lower in urban than prairie habitats (Fig. 5). Patterns of fecundity in the different populations reflected a balance between the low
level of pollinator visitation in prairie sites (Parker
1997), and the increased vigor and growth of plants in
those same populations. This is seen by comparing
mean fruit production within the same year (year t), to
fecundity values used in the matrix (fruit production
in year t ⫹ 1) which incorporate growth and survival
(Fig. 4a vs. 4b). The first measure primarily reflects
the pollination environment, and in almost every case,
plants in urban populations had higher fecundity than
those in prairie populations. The second measure reflects the fact that plants growing on the edge of prairie
populations were more likely to grow into larger, more
fecund plants in the next year. The relative importance
of pollination vs. conditions for growth determines
FIG. 4. Mean fruit production (⫾1 SE) for plants of different life history stages, in prairie populations (circles) and
urban populations (squares), across three stages of invasion
(edge, intermediate, center). Two types of fecundity are presented: (a) the mean current (1994) reproduction of plants
within a given stage in 1994, and (b) the mean reproduction
in the following year (1995) of plants within a given stage
in 1994. The second measure was used in the projection matrices and incorporates mortality and growth between years.
whether prairie or urban plants show higher fecundity
in the following year, and this varies from the edge to
the center and for different life history stages (Fig. 4b).
Analytical results of the demographic model
All populations were increasing at the invasion front
over both transition years; that is, the finite rate of
increase (␭) was greater than one for all edge plots
(Fig. 6). However, the 95% confidence intervals (approximated by two standard errors, Lande 1988) are
wide and suggest that population growth was not significantly greater than one for urban populations except
for Magnuson Park. For the 20 projection matrices including intermediate and center plots, ␭ varied from
0.88 to 1.93. In six of eight cases, ␭ decreased with
June 2000
INVASION DYNAMICS OF CYTISUS
733
TABLE 1. Test for significant effects of invasion stage (edge,
intermediate, center) and habitat (prairie vs. urban field)
on ␭ generated from the 1994–1995 projection matrices.
Source
df
Sum of
squares
Mean
square
Invasion stage
Habitat
Stage ⫻ habitat
Residual
2
1
2
8
0.447
0.200
0.212
0.215
0.224
0.200
0.106
0.027
F
P
8.32
7.45
3.95
0.011
0.026
0.064
Note: Data from 1993–1994 were not used in this analysis.
FIG. 5. Mean germination rates (seedlings per seed) in
prairie populations (circles) and urban populations (squares),
across three stages of invasion (edge, intermediate, center).
Bars represent ⫾1 SE. Note logarithmic scale.
advancing stage of invasion, although large confidence
intervals resulted in considerable overlap (Fig. 6). ANOVA using ␭’s from each population as replicates revealed a significant effect of invasion stage (Table 1).
C. scoparius showed higher rates of population
growth in prairies than in urban fields (Table 1). The
difference between habitats was strongest in the edge
plots, and the interaction between habitat and invasion
stage was marginally significant (Table 1). In the center
plots, where intraspecific density was very high, prairie
and urban sites were nearly indistinguishable (Fig. 6).
Stochastic year-to-year variation did not have a large
effect on population growth over the short time scale
of this study. The two populations that had two sets of
matrices showed no significant temporal variation in ␭
FIG. 6. Finite rate of increase (⫹ 2 SE ) for
six populations of C. scoparius in two habitats:
glacial outwash prairies (Johnson Prairie, Thirteenth Division Prairie, and Weir Prairie) and
disturbed urban fields (Discovery Park, Magnuson Park, and Montlake Fill). Johnson Prairie
and Discovery Park were represented by separate estimates for 1993–1994 and 1994–1995
and contained plots at three stages of invasion:
the edge of the advancing front, intermediate,
and the center of the infestation. Four other populations were censused only in 1994–1995, with
edge and intermediate plots only. Rates of increase were estimated as the dominant eigenvalue of a seven-stage matrix model; standard
errors were estimated analytically by the firstorder approximation (Lande 1988).
(Paired t, df ⫽ 5, t ⫽ 1.26, P ⫽ 0.26). In addition to
the seven-stage model presented here, an alternative,
four-stage model using only one adult stage was also
explored and produced similar results (Parker 1996).
The elasticity structure was quite consistent over different years and populations, but differed among stages
of invasion (Fig. 7). Edge plots showed comparable
elasticities across all life history transitions, but center
plots were completely dominated by the fate of extra
large plants. Interestingly, intermediate plots differed
in their elasticity structure depending on whether they
were in urban or prairie habitats. In prairies, the elasticities for intermediate plots were more like edge plots,
while in urban fields, the elasticity of extra large individuals was dominant for intermediate plots, like center plots.
Simulations of the transient dynamics of edge plots
showed the same patterns as the analytical results. The
number of years to go from 10 seeds to the density of
plants in center plots was tightly correlated with ␭
(Spearman rank correlation ␳ ⫽ 0.98, P ⫽ 0.01). Prairie
populations took from 11 to 18 years to fill in, while
urban populations took from 46 to 178 yr.
734
INGRID M. PARKER
Ecological Applications
Vol. 10, No. 3
corresponding elements in two matrices by their sensitivity, reveals that the matrix elements exhibiting the
largest difference in magnitude between habitats are
not the most important. In terms of the difference in
rate of increase between urban and prairie populations,
establishment (seed to seedling) made by far the greatest contribution (Fig. 8). In a similar reversal, the contribution of fecundity of medium adults outweighed the
contribution of large adults.
Direct estimates of invasion (change over time)
and density dependence
FIG. 7. Combined elasticities for fecundity and the fate
of each stage for 1993–1994 in Johnson Prairie and Discovery
Park and 1994–1995 in all six populations. Different symbols
represent edge plots (circles), intermediate plots (squares),
and center plots (triangles) for each population. Elasticities
were combined by summing each column, excluding fecundities. Abbreviations are: fec ⫽ fecundity, sd ⫽ seed, sdl ⫽
seedling, juv ⫽ juvenile, sa ⫽ small adult, ma ⫽ medium
adult, la ⫽ large adult, and xl ⫽ extra-large adult.
Analysis of the mean matrices provided some unique
insights into the biological processes driving differences between prairie and urban habitats (Fig. 8). Looking simply at the difference matrix for prairie vs. urban
populations, the largest contrasts were for dormancy
(greater for the urban matrix), growth of small and
medium adults to the next size class (greater for the
prairie matrix), and stasis of small and medium adults
(greater for the urban matrix). For fecundities, large
adults showed the greatest difference between urban
and prairie values. However, the differences between
the matrix elements themselves do not describe the
contribution these make to overall difference in population growth rate. Life Table Response Analysis (Caswell 1989b), which weights the differences between
In addition to estimating parameters for the matrix
model, I used the demography plots to directly quantify
the change in plant occupancy (⫽invasion) over time.
Estimated biomass increased in all plots between the
first and last years of the study (Table 2). Both center
plots rose in biomass between 1993 and 1994, but lost
biomass between 1994 and 1995. These were the only
cases in which biomass did not increase monotonically.
Numbers of individuals showed a much less consistent
pattern over time (Table 3), and three different estimates of density provide different impressions of population change from 1994 to 1995. First, the total plant
density (minus seeds) increased in ten of fourteen plots,
but decreased in four of the urban plots (Discovery
Park intermediate and center, Magnuson Park edge, and
Montlake Fill intermediate). Considering adult plants
only (excluding seedlings and juveniles), density increased in nine of fourteen plots, and decreased in a
slightly different set of plots (Johnson Prairie center,
Montlake Fill intermediate, and all Discovery Park
plots). In contrast, when only extra large plants are
counted, density increased in eleven plots and stayed
nearly constant in the remainder. The change over time
for each of these density measures was calculated as
the difference in the logs, and there were no significant
correlations among the three measures (Table 4). However, change in biomass was significantly correlated
with the change in extra-large plants and in adult plants
(Table 4). In comparisons with direct measures of invasion, ␭ was significantly correlated with the change
in biomass over time and with change in the density
of adults (Table 4), but was not correlated with either
change in total plant density or change in the density
of extra-large plants.
The different measures also provide different views
of density-dependence. All four direct estimates of invasion were uncorrelated with either total density or
adult density (Table 5). In contrast, three of the four
showed significant negative correlations with biomass
and the density of extra-large plants. Biomass and extra-large plants were also negatively correlated with ␭.
One can ask whether C. scoparius shows a consistent
maximum occupancy (or carrying capacity) among different habitats. The answer depends on which measurement is used. In 1995, center plots at Discovery
Park and Johnson Prairie were nearly identical for bio-
INVASION DYNAMICS OF CYTISUS
June 2000
735
FIG. 8. Differences between elements in the mean prairie matrix vs. the mean urban matrix (top), and the contributions
of these individual differences to the difference in population growth rate (bottom), for life history transitions (regression,
stasis, and growth for each stage) and fecundities. Abbreviations are: sd ⫽ seed, sdl ⫽ seedling, juv ⫽ juvenile, sa ⫽ small
adult, ma ⫽ medium adult, la ⫽ large adult, and xl ⫽ extra-large adult.
mass (4110 vs. 4212 g/m2), while they varied widely
in terms of plant density (3.5 vs. 22.2/m2). In 1994
biomass was again consistent between habitats (4213
vs. 4324 g/m2), but so was density (4.2 vs. 5.8/m2).
Evaluating biological control
To assess the possible impact of seed-eating insects
introduced for biological control on plant population
TABLE 2. Biomass per square meter in 1994 and 1995, estimated for six populations and in plots at different stages of
invasion.
Edge
Intermediate
Center
Plot
1994
1995
1994
1995
1994
1995
Prairie
Johnson Prairie
13th Division Prairie
Weir Prairie
464
297
230
602
409
297
2364
1748
1902
2572
2297
2185
4324
4212
Urban
Discovery Park
Magnuson Park
Montlake Fill
499
547
280
574
708
320
1789
1950
3207
1854
2218
3572
4213
4110
Ecological Applications
Vol. 10, No. 3
INGRID M. PARKER
736
TABLE 3. Density (individuals/m2) of C. scoparius individuals in 1994 and 1995, calculated for six populations and in plots
at different stages of invasion.
Total plants/m2
Intermediate
Edge
Plot
Adult plants/m2
Center
Intermediate
Edge
Extra-large adults/m2
Center
Edge
Intermediate
Center
1994 1995 1994 1995 1994 1995 1994 1995 1994 1995 1994 1995 1994 1995 1994 1995 1994 1995
Prairie
Johnson Prairie
13th Division
Prairie
Weir Prairie
Urban
Discovery Park
Magnuson Park
Montlake Fill
6.1 9.7
3.6 5.8
14.6 25.9
9.5 11.2
2.0 2.5
8.8 16.8
1.3 1.5
2.3 2.2
1.6 1.7
3.7 2.2
10.5 21.0
6.0 5.5
5.8 22.2
4.2
3.5
0.4 0.5
0.7 1.0
1.5 1.7
5.2 5.5
0.5 0.8
4.4 4.7
0.9 0.9
0.8 1.0
0.7 0.8
3.5 2.2
4.4 5.0
4.0 4.0
4.0 2.8
0.17 0.20 0.68 0.68 1.50 1.55
0.08 0.12 0.33 0.58
0.04 0.06 0.54 0.54
3.7 2.5
0.14 0.20 0.44 0.58 1.42 1.42
0.14 0.20 0.42 0.50
0.04 0.05 1.08 1.21
Notes: ‘‘Total plants’’ are all vegetative individuals including seedlings, ‘‘Adult plants’’ are all individuals larger than
100 g (estimated); ‘‘extra-large adults’’ are all individuals larger than 900 g (estimated).
growth and spread, I manipulated fecundity values and
generated a hypothetical ␭ for two expanding edge
plots. For the slowest-growing population (Montlake
Fill 1994–1995), ␭ remained ⬎1 until over 70% of
seeds were destroyed. For the fastest-growing population (Johnson Prairie 1994–1995), ␭ did not fall below one until over 99.9% of seeds were destroyed (Fig.
9). The relationship between ␭ and attack rate was an
accelerating decline.
DISCUSSION
Demography of invasion
Rates of population growth integrate the entire life
history of an organism within the context of its environment, and therefore are uniquely useful for studying
patterns of invasiveness and invasibility. At the advancing edge of C. scoparius invasions, all sites studied
showed positive growth rates, but prairie populations
grew much more rapidly than urban ones. The pattern
is unambiguous whether one considers asymptotic rates
of increase or simulations of transient dynamics.
Spatial or habitat-based variation in population
TABLE 4. Spearman rank correlation coefficients (and P values) for correlations among ␭ (the finite rate of increase)
and four direct measures of invasion: change in (log10) biomass, total density of vegetative plants, density of adult
plants, and density of extra-large plants.
Variable
␭
⌬
Biomass
⌬
Total
␭
⌬ Biomass
1
0.83
(0.003)
1
⌬ Total plants
0.41
(0.14)
0.11
(0.70)
1
⌬ Adult plants
0.73
(0.01)
0.60
(0.03)
0.33
(0.24)
⌬ Extra-large
0.34
(0.22)
0.64 ⫺0.29
(0.02) (0.30)
⌬
⌬
ExtraAdults large
1
0.17
(0.53)
1
growth rate is common in plants (Werner and Caswell
1977, Horvitz and Schemske 1986, Menges 1990, Boeken and Canham 1995). However, the pattern seen here
is particularly interesting in light of theoretical predictions from invasion biology. First, the wide variability in population growth does not provide support
for the idea that successful invaders should be buffered,
either through phenotypic plasticity or genetic variation, against demographic variation across environments (Baker 1965).
A second expectation is that more diverse systems
are less invasible (Elton 1958, Case 1991, Morton et
al. 1996), and therefore an invasive species should be
least successful in habitats with high species richness.
However, Johnson Prairie, where C. scoparius reached
its highest rate of population growth, contains the highest diversity of native plant species of all these sites,
as well as the highest total plant diversity (Parker et
al. 1997). It is also often stated that exotic species are
tightly linked to disturbed habitats and habitats dominated by anthropogenic influences (Orians 1986,
Hobbs and Huenneke 1992), and much of C. scoparius
habitat falls into this category: urban fields, highway
rights-of-way, abandoned lots, landfills, etc. However,
the most rapid rates of spread occurred in the most
pristine habitats. It appears as if ‘‘biotic resistance’’
(Elton 1958, Simberloff 1986) in the way it is classically defined, is not a factor limiting the spread of this
particular invader.
Differences between urban and prairie habitats were
evident throughout the life cycle of the plant. Dormancy/seed persistence was the only life history transition in which urban sites showed an advantage over
prairies. Even though seed production for plants of similar size was higher in urban fields due to patterns of
pollinator visitation (Parker 1997), the contribution of
plants to next year’s seeds (the fecundity row in the
matrix) was greater in prairies, because plant growth
in the intervening year was fast enough to overcome
INVASION DYNAMICS OF CYTISUS
June 2000
737
TABLE 5. Spearman rank correlations (and P values) between five measures of invasion (change in [log10] estimated biomass,
change in [log10] total plant density, change in [log10] adult plant density, change in [log10] extra-large plant density, and
[finite rate of increase]) and four measures of occupancy.
Measure of
occupancy
Measure of invasion
⌬ Biomass
⌬ Total
⌬ Adults
⌬ Extra large
␭
Biomass
⫺0.75
(0.007)
0.11
(0.70)
⫺0.61
(0.028)
⫺0.61
(0.028)
⫺0.62
(0.026)
Total plants
⫺0.16
(0.56)
0.47
(0.09)
⫺0.31
(0.76)
⫺0.48
(0.08)
0.19
(0.49)
Adult plants
⫺0.38
(0.16)
0.18
(0.52)
⫺0.52
(0.06)
⫺0.20
(0.46)
⫺0.40
(0.15)
Extra large plants
⫺0.74
(0.008)
0.11
(0.70)
⫺0.67
(0.016)
⫺0.67
(0.016)
⫺0.58
(0.037)
Note: Invasion measures were estimated between 1994 and 1995; occupancy was based on plant numbers in 1994.
the reproductive advantage experienced by plants in
urban sites.
While there were many differences between the habitats, Life Table Response Analysis (Caswell 1989b)
revealed that the higher overall rate of increase in prairies was overwhelmingly controlled by seedling establishment. This result illustrates that the vital rates most
responsive to environmental conditions (or experimental treatments) may not be the same as those most responsible for fitness differences, or invasibility differences, among environments. The central importance of
seedling establishment is also interesting in light of
experimental work on the importance of a guild of moss
and lichen species in the prairies. These cryptogams
make up a large proportion of the total cover, and a
removal experiment demonstrated that disturbing the
cryptogam layer by fire or scraping resulted in a dramatic reduction in C. scoparius establishment (Parker
1996). In the same prairies, Hartway and Steinberg
(1997) found fewer C. scoparius seedlings on gopher
mounds than in nearby undisturbed prairie. Therefore
the fact that western Washington prairie remnants seem
to be remarkably hospitable sites for invasion of this
pest plant may be explained, not by disturbance, but
rather by the beneficial influence of a guild of native
species.
Not all habitats invaded by C. scoparius behave in
this way, however. In California, Bossard (1991) found
that disturbance increased establishment of the shrub
in two communities of mixed annual grasses and forbs.
Urban sites in this study, which are dominated by exotic
annual grasses, may be more similar to these California
sites in terms of the role disturbance plays. Paynter et
al. (1998) also found that disturbance (removal of
shrubs followed by cultivation) promoted germination
and survival of seedlings in densely occupied C. scoparius stands in France. In mature, high density stands
of C. scoparius in Washington as well, linking establishment to disturbance is probably correct and may
explain why ␭’s for the center plots projected a decline.
Small understory individuals seem to require the removal of a large dominant plant in order to grow into
a large size class.
In contrast to variation between habitats, there was
surprisingly little temporal variation shown by the two
populations with replicate matrices, though clearly one
can not generalize from such a short time scale. Limited
demographic data from 1996 suggest that ␭‘s in prairies
may be lower in some years than those observed in
this study.
The biology of density dependence
FIG. 9. Finite rate of increase as a function of the proportion of seeds destroyed by a hypothetical biological control agent. Results are given for two scenarios: the most rapidly increasing population (Johnson Prairie, circles) and the
slowest growing population (Montlake Fill, squares), using
1994–1995 projection matrices.
The invasion of C. scoparius involves a dramatic
increase in plant density, from scattered individuals to
a near monoculture involving several kilograms of
plant material per square meter. Such a range in density
is characteristic of many noxious invasive pests, and
the final densities reached in part determine the ecological impact of a weed (Parker et al. 1999). In addition to defining the demographic character of the invasion process, the increase in density over time within
738
INGRID M. PARKER
single populations provides an excellent system with
which to examine mechanisms of density dependence.
Different measures of occupancy produce different
representations of change over time. Total density of
vegetative plants and density of adult (flowering) plants
actually peaked in plots that were at the intermediate
stage of invasion, whereas the density of extra-large
plants increased from edge to intermediate to center
plots. In general, the different measures of invasion
rate (change over time of biomass, total density, adult
density, and extra-large adult density) and ␭ were not
well correlated with each other, nor did they always
show negative correlations with measures of density.
Of particular interest is the fact that total plant numbers,
which is the traditional density measure in population
biology, was entirely uncorrelated with all other measures of occupancy, and with all estimates of invasion
rate, including ␭.
Total biomass, on the other hand, increased monotonically with invasion stage and showed much more
predictable behavior. Biomass increased from year to
year in all plots except for high density plots from
1994–1995. The magnitude of the change in biomass
was negatively correlated with biomass itself, as was
␭. Similarly, change in biomass was the direct measure
of invasion most closely correlated with ␭. Unlike total
numbers, biomass reflects size structure, and size structure has an obvious and important effect on ␭. Surprisingly few other studies have compared short-term
population trends with matrix predictions (Croxall et
al. 1990, Brault and Caswell 1993), and even fewer
have made this comparison for plants. As more studies
accumulate, it will be interesting to see if ␭ always
approximates change in biomass better than change in
total numbers for plant species. Because it integrates
the relative ability of each plant to deplete local resources (soil nutrients, water, light, etc.), biomass may
also be a more relevant measure than numerical density
for assessing the impact of C. scoparius on the host
community and ecosystem.
The decoupling of numerical density and total biomass is consistent with the well-studied phenomenon
of self thinning and compensatory growth in plants
(Yoda et al. 1963, Weller 1987). As shown in many
experimental plantings as well as natural populations,
as a stand matures, density declines while biomass per
individual continues to increase, resulting in a biomass/
density relationship with slope ⫺3/2 (White 1980,
1985). Simple geometrical explanations for this pattern
have emphasized that biomass scales with volume (linear dimension l3) while density (or leaf area) scales
with area (l2) (Yoda et al. 1963, Lonsdale 1990). Westoby (1984) presents the concept of ‘‘crowding capacity’’ in place of carrying capacity for species, including
most plants, in which regulation depends on both density and biomass. Therefore it is perhaps not surprising
that in C. scoparius it was biomass, and not simple
Ecological Applications
Vol. 10, No. 3
numbers, that generated the demographic responses we
expect from density dependence.
There was little evidence for positive density dependence in this invasive species. In contrast, Taylor
and Walker (1984) found that recruitment rate was positively correlated with population density in the invasive exotic Cereus peruvianus, and Richardson obtained similar results for three other invasive species
(Kruger et al. 1986). If positive density dependence is
only evident at very low densities, however, such an
effect would not have been observable in this study.
The elasticity structure changed dramatically as the
invasion progressed. In the center plots, elasticity was
overwhelmingly dominated by the survival/stasis of
extra-large plants. In these very dense stands of plants,
many seeds were produced and considerable numbers
of seedlings germinated, but none grew into adults unless there was a local mortality within the largest stage.
From a management perspective, one should be cautious in interpreting such an elasticity pattern; cutting
down the extra-large adults in center plots would not
magically eliminate the weed problem. This illustration
underscores the well known concept that matrix models
only describe a single set of conditions under which
the matrix was built and should not be interpreted as
predictions.
Evaluating the potential for biological control
Elasticity analysis for the edge plots did not yield
any suggestions for an Achilles heel for C. scoparius;
that is, no life stage or transition overwhelmingly dominated ␭ in rapidly invading populations. Rather, elasticity was fairly uniformly distributed throughout the
life cycle at the expanding edge. Although the matrix
analysis does not suggest an easy management strategy
for this species, it does provide some insight into the
potential for biological control. For example, a seedeating insect would need to reduce reproduction by as
much as 99.9% in the fastest growing population to
halt the expansion, and would need to reduce reproduction by 70% to stop even the slowest growing population.
While these levels of damage sound very high, control may be possible in some areas. The seed weevil
Apion fuscirostre was introduced to the United States
to combat C. scoparius (Andres et al. 1967) and has
been actively spread in the Pacific Northwest by the
Oregon Department of Agriculture and others (D.
Isaacson, personal communication). When this study
was initiated in 1993, A. fuscirostre was not present in
any of the six populations, but by 1995 it was found
occasionally in Johnson Prairie. A census of seed damage on 22 August, 1997, revealed 97% damaged fruits,
with over 50% damaged seeds (N ⫽ 54). These numbers are consistent with damage estimates of up to 48%
of seeds at Eldorado National Forest in California (Bossard and Rejmanek 1994), and 49–72% of seeds over
seven years in an Oregon population (D. Isaacson, per-
June 2000
INVASION DYNAMICS OF CYTISUS
sonal communication). However, it is still unrealistic
to expect that Apion fuscirostre alone will control the
invasion of C. Scoparius in most places, especially
prairie remnants. As more information becomes available on the potential demographic effects of other biological control agents for this plant, such as the twigmining moth Leucoptera spartifoliella, matrix simulations can be used to evaluate the likelihood of successful control with suites of these agents acting in
concert.
Others have also used matrix models to investigate
the potential value of biological control strategies for
noxious weeds. McEvoy and Coombs (1999), by combining matrix modeling with detailed factorial experiments (McEvoy et al. 1993), were able to quantify the
relative importance of different control agents in the
suppression of tansy ragwort (Senecio jacobaea)
through their individual effects on different stages of
the life cycle. This analysis revealed that the ragwort
flea beetle (Longitarsus jacobaeae) was the most effective control agent due to both its impact on several
different life history transitions and its large effect on
the transitions most important to population growth.
As in the case of C. scoparius, Shea and Kelly (1998)
concluded that Carduus nutans was unlikely to be exterminated by Rhinocyllus conicus, a seed weevil introduced for biological control in New Zealand. However, while the invasion was not reversed by the control
agent, in this case population growth rate could be
reduced considerably with a moderate reduction in seed
production. When grazing was incorporated in the form
of variable germination, results suggested that an integrative pest management strategy reducing grazing
as well as promoting seed weevils could effectively
control populations of C. nutans (Shea and Kelly 1998).
Noble and Weiss (1989) produced similar results with
a more complex model tracking vertical seed movement in Chrysanthemoides monilifera. They found that
while an effective seed predator acting alone would
have to damage ⬎95% of seeds, the use of fire dramatically increased the success of the control agent. In
an approach similar to that of Rees and Paynter (1997),
Lonsdale et al. (1995) combined experiments with a
model to predict the reduction in equilibrium density
of Sida acuta caused by the defoliator Calligrapha
pantherina. In an elegant test of the model, the actual
reduction observed in their experiments conformed
nicely to model predictions.
In conclusion, this study revealed some expected patterns for invading populations, such as the decrease in
␭ as an invasion proceeds and the greater importance
of early life history stages in the most rapidly colonizing plots (Lewontin 1965). However, using a demographic approach, I have also discovered some unexpected aspects of the biology of C. scoparius in western Washington. First, its rates of increase are greatest
in the most undisturbed open habitats, and it is not
dependent on agents of disturbance for its success. Sec-
739
ond, while differences between prairie and urban habitats were evident throughout the life cycle, the contribution of one stage dominated the overall difference
in ␭. Third, although vital rates and population growth
are strongly influenced by stage of invasion and standing biomass, these are not closely correlated with simple numerical density. Fourth, biological control seed
predators will have to be very effective to halt the
invasion of even slow growing populations. While they
are yet to be proven in a predictive manner, the usefulness of matrix models as a management tool for
exotic species shows great potential. By applying the
models to assess current and projected control efforts,
one can define the degree of efficacy required to have
a lasting impact on invasive populations.
ACKNOWLEDGMENTS
I am deeply grateful for field assistance from many friends,
especially K. Ward, H. Bonifield, J. Banks, D. Dionne, S.
Madsen, B. Best, G. Parker, M. Groom, K. Koprowicz, J.
Ruesink, D. Bigger, and S. Reichard. As part of my dissertation work, all aspects of this research benefited greatly from
the guidance and inspiration of my mentors and colleagues
at the University of Washington, especially D. Schemske and
P. Kareiva. Helpful comments on the manuscript were provided by K. Rice, H. Caswell, G. Aplet, J. Maron, R. T. Paine,
K. Shea, P. McEvoy, and K. Haubensak. This research was
supported by the Hardman Foundation, a Sigma Xi grant-inaid-of-research, NSF dissertation improvement grant DEB9411702, and NSF training grant BIR-9256532 in Mathematical Biology.
LITERATURE CITED
Andow, D. A., P. M. Kareiva, S. A. Levin, and A. Okubo.
1993. Spread of invading organisms: patterns of spread.
Pages 219–242 in K. Kim and B. A. McPheron, editors.
Evolution of insect pests: patterns of variation. John Wiley
and Sons, New York, New York, USA.
Andow, D., P. Kareiva, and A. Okubo. 1990. Spread of invading organisms. Landscape Ecology 4:177–188.
Andres, L., R. Hawkes, and R. Rizza. 1967. Apion seed weevil introduced for biological control of Scotch broom. California Agriculture 10:13–14.
Aplet, G., R. D. Laven, and R. B. Shaw. 1994. Application
of projection matrix models to the recovery of the rare
Hawaiian shrub, Tetramolopium arenarium (Asteraceae).
Natural Areas Journal 14:99–106.
Baker, H. G. 1965. Characteristics and modes of origin of
weeds. Pages 147–168 in H. G. Baker and G. L. Stebbins,
editors. The genetics of colonizing species. Academic
Press, New York, New York, USA.
Baker, H. G., and G. L. Stebbins. 1965. The genetics of
colonizing species. Academic Press, New York, New York,
USA.
Birch, L. C. 1953. Experimental background to the study of
the distribution and abundance of insects. Ecology 34:698–
711.
Boeken, B., and C. D. Canham. 1995. Biotic and abiotic
control of the dynamics of gray dogwood (Cornus racemosa Lam.) shrub thickets. Journal of Ecology 83:569–
580.
Bossard, C. C. 1991. The role of habitat disturbance, seed
predation and ant dispersal on establishment of the exotic
shrub Cytisus scoparius in California. American Midland
Naturalist 126:1–13.
Bossard, C. C., and N. Rejmanek. 1994. Herbivory, growth,
seed production, and resprouting of an exotic invasive
740
INGRID M. PARKER
shrub Cytisus scoparius. Biological Conservation 67:193–
200.
Brault, S., and H. Caswell. 1993. Pod-specific demography
of killer whales Orcinus-Orca. Ecology 74:1444–1454.
Carey, J. R. 1996. The future of the Mediterranean fruit fly
Ceratitis capitata invasion of California: a predictive
framework. Biological Conservation 78:35–50.
Case, T. J. 1991. Invasion resistance, species build-up and
community collapse in metapopulation models with interspecies competition. Biological Journal of the Linnean Society 42:239–266.
Caswell, H . 1989a. Matrix population models. Sinauer, Sunderland, Massachusetts, USA.
Caswell, H. 1989b. Analysis of life table response experiments: I. Decomposition of effects on population growth
rate. Ecological Modelling 46:221–238.
Charlesworth, B. 1980. Evolution in age-structured populations. Cambridge studies in mathematical Biology. Cambridge University Press, Cambridge, UK.
Crawley, M. J., R. S. Hails, M. Rees, D. Kohn, and J. Buxton.
1993. Ecology of transgenic oilseed rape in natural habitats. Nature 363:620–623.
Crouse, D. T., L. B. Crowder, and H. Caswell. 1987. A stage
based population model for loggerhead sea turtles and implications for conservation. Ecology 68:1412–1423.
Croxall, J. P., P. Rothery, S. P. C. Pickering, and P. A. Prince.
1990. Reproductive performance, recruitment and survival
of wandering albatrosses Diomedea exulans at Bird Island,
South Georgia. Journal of Animal Ecology 59:775–796.
Elton, C. S. 1958. The ecology of invasions by animals and
plants. Methuen, London, UK.
Fox, M. D., and B. J. Fox. 1986. The susceptibility of natural
communities to invasion. Pages 57–66 in R. H. Groves and
J. J. Burdon, editors. Ecology of biological invasions: An
Australian perspective. Australian Academy of Sciences,
Canberra, Australia.
Franklin, J. F., and C. T. Dyrness. 1988. Natural vegetation
of Oregon and Washington. Oregon State University Press,
Corvallis, Oregon, USA.
Gilkey, H. M. 1957. Weeds of the Pacific Northwest. Oregon
State College, Corvallis, Oregon, USA.
Harman, H. M. 1992. The suitability of a stem-mining weevil,
Apion immune (Coleoptera: Apionidae), for biological control of broom (Cytisus scoparius) in New Zealand. Page 41
in E. S. Delfosse and R. R. Scott, editors. Biological control
of weeds. VIII International Symposium (Canterbury, New
Zealand, February 2–7, 1992). Commonwealth Scientific
and Industrial Research Organization Publications, East
Melbourne, Victoria, Australia.
Hartway, C., and E. K. Steinberg. 1997. The influence of
pocket gopher disturbance on the distribution and diversity
of plants in western Washington prairies. Pages 131–139
in P.V. Dunn, and K. Ewing, editors. Ecology and conservation of the South Puget Sound prairie landscape. The
Nature Conservancy, Seattle, Washington, USA.
Hedgpeth, J. 1993. Foreign invaders. Science 261:34–35.
Hengeveld, R. 1989. Dynamics of biological invasions. Cambridge University Press, Cambridge, UK.
Hobbs, R. J., and L. F. Huenneke. 1992. Disturbance, diversity, and invasion: implications for conservation. Conservation Biology 6:324–337.
Horvitz, C. C., and D. W. Schemske. 1986. Seed dispersal
and environmental heterogeneity in a neotropical herb: a
model of population and patch dynamics. Pages 169–186
in A. Estrada and T. H. Fleming, editors. Frugivores and
seed dispersal. Dr. W. Junk, The Hague, The Netherlands.
Horvitz, C. C., and D. W. Schemske. 1995. Spatiotemporal
variation in demographic transitions of a tropical understory herb: projection matrix analysis. Ecological Monographs 65:155–192.
Ecological Applications
Vol. 10, No. 3
Hosking, J. R. 1996. The impact of seed- and pod-feeding
insects on Cytisus scoparius. Pages 45–51, in E. S. Delfosse
and R. R. Scott. Biological control of weeds; VIII International Symposium (Canterbury, New Zealand, February
2–7, 1992). Commonwealth Scientific and Industrial Research Organization Publications, East Melbourne, Victoria, Australia.
Hosking, J. R., J. M. B. Smith, A. W. Sheppard. 1996. The
biology Australian weeds: 28. Cytisus scoparius (L.) Link
subsp. scoparius. Plant Protection Quarterly 11:102–108.
Kalisz, S., and M. A. McPeek. 1992. Demography of an agestructured annual: resampled projection matrices, elasticity
analyses, and seed bank effects. Ecology 73:1082–1093.
Kruckeberg, A. R. 1991. The natural history of Puget Sound
Country. University of Washington Press, Seattle, Washington, USA.
Kruger, F. J., D. M. Richardson, and B. W. van Wilgen. 1986.
Processes of invasion by alien plants. Pages 145–155 in I.
A. W. MacDonald, F. J. Kruger, and A. A. Ferrar, editors.
The ecology and management of biological invasions in
Southern Africa. Oxford University Press, Oxford, UK.
Lande, R. 1982. A quantitative genetic theory of life history
evolution. Ecology 63:607–615.
Lande, R. 1988. Demographic models of the northern spotted
owl (Strix occidentalis caurina). Oecologia 75:601–607.
Lang, F. A. 1961. A study of the vegetation change in the
gravelly prairies of Pierce and Thurston Counties, western
Washington. Thesis. University of Washington, Seattle,
Washington, USA.
Levin, L. A., H. Caswell, K. D. DePatra, and E. L. Creed.
1987. Demographic consequences of larval development
mode: planktotrophy vs. lecithotrophy in Streblospio benedicti. Ecology 68:1877–1886.
Lewontin, R. C. 1965. Selection for colonizing ability. Page
588 in H. G. Baker and G. L. Stebbins, editors. The genetics
of colonizing species. Academic Press, New York, New
York, USA.
Lonsdale, W. M. 1990. The self-thinning rule: dead or alive?
Ecology 71:1373–1388.
Lonsdale, W. M., G. Farrell, and C. G. Wilson. 1995. Biological control of a tropical weed: a population model and
experiment for Sida acuta. Journal of Applied Ecology 32:
391–399.
Mack, R. N. 1985. Invading plants: their potential contribution to population biology. Pages 127–142 in J. White,
editor. Studies on plant demography: A festschrift for John
L. Harper. Academic Press, London, UK.
Marshall, J. S. 1962. The effects of continuous gamma radiation on the intrinsic rate of natural increase on Daphnia
pulex. Ecology 43:598–607.
McEvoy, P. B., and E. M. Coombs. 1999. A parsimonious
approach to biological control of plant invaders. Ecological
Applications 9:387–401.
McEvoy, P., N. T. Rudd, C. S. Cox, and M. Huso. 1993.
Disturbance, competition, and herbivory effects on ragwort
Senecio jacobaea populations. Ecological Monographs 63:
55–75.
McPeek, M. A., and S. Kalisz. 1993. Population sampling
and bootstrapping in complex designs: demographic analysis. Pages 232–252 in S. M. Scheiner and J. Gurevitch,
editors. Design and analysis of ecological experiments.
Chapman & Hall, New York, New York, USA.
Menges, E. S. 1986. Predicting the future of rare plant populations: demographic monitoring and modeling. Natural
Areas Journal 6:13–25.
Menges, E. S. 1990. Population viability analysis for an endangered plant. Conservation Biology 4:52–62.
Moore, R. P. 1973. Tetrazolium staining for assessing seed
quality. Pages 347–366 in W. Heydecker, editor. Seed ecology. Butterworths, London, UK.
June 2000
INVASION DYNAMICS OF CYTISUS
Morton, R. D., R. Law, S. L. Pimm, and J. A. Drake. 1996.
On models for assembling ecological communities. Oikos
75:493–499.
Noble, I. R., and P. W. Weiss. 1989. Movement and modelling
of buried seed of the invasive perennial Chrysanthemoides
monilifera in coastal dunes and biological control. Australian Journal of Ecology 14:55–64.
Orians, G. H. 1986. Site characteristics favoring invasions.
Pages 133–148 in H. A. Mooney and J. A. Drake, editors.
Ecology of biological invasions of North America and Hawaii. Springer-Verlag, New York, New York, USA.
Parker, I. M. 1996. Ecological factors affecting rates of population growth and spread in Cytisus scoparius, an invasive
exotic shrub. Dissertation. University of Washington, Seattle, Washington, USA.
Parker, I. M. 1997. Pollinator limitation of Cytisus scoparius,
an invasive exotic shrub. Ecology 78:1457–1470.
Parker, I. M., W. S. Harpole, and D. Dionne. 1997. Plant
community diversity and invasion of the exotic shrub Cytisus scoparius: Testing hypotheses of invasibility and impact. Pages 149–162 in P. V. Dunn and K. Ewing, editors.
Ecology and conservation of the South Puget Sound prairie
landscape. The Nature Conservancy, Seattle, Washington,
USA.
Parker, I. M., and P. Kareiva. 1996. Assessing the risks of
genetically engineered organisms: acceptable evidence and
reasonable doubt. Biological Conservation 78:193–203.
Parker, I. M., and S. H. Reichard. 1997. Critical issues in
invasion biology for conservation science. Pages 283–305
in P. Fiedler and P. Kareiva, editors. Conservation biology.
Second edition. Chapman Hall, New York, New York,
USA.
Parker, I. M., D. Simberloff, W. M. Lonsdale, K. Goodell,
M. Wonham, P. M. Kareiva, M. H. Williamson, B. Von
Holle, P. B. Moyle, J. E. Byers, and L. Goldwasser. 1999.
Impact: toward a framework for understanding the ecological effects of invaders. Biological Invasions 1:(1)3–19.
Paynter, Q., S. V. Fowler, J. Memmott and A. W. Sheppard.
1998. Factors affecting the establishment of Cytisus scoparius in southern France: Implications for managing both
native and exotic populations. Journal of Applied Ecology
35:582–595.
Rees, M., and Q. Paynter. 1997. Biological control of Scotch
broom: modelling the determinants of abundance and the
potential impact of introduced insect herbivores. Journal
of Applied Ecology 34:1203–1221.
Rejmanek, M. 1996. Species richness and resistance to invasions. Pages 153–172 in G. H. Orians, R. Dirzo, and J.
H. Cushman, editors. Biodiversity and ecosystem processes
in tropical forests. Springer-Verlag, Berlin, Germany.
741
Roff, D. A. 1992. The evolution of life histories: theory and
analysis. Chapman & Hall, New York, New York, USA.
Ruesink, J., I. M. Parker, M. J. Groom, and P. Kareiva. 1995.
Reducing the risks of nonindigenous species introductions:
guilty until proven innocent. BioScience 45:465–477.
Schemske, D. W., B. C. Husband, M. H. Ruckelshaus, C.
Goodwillie, I. M. Parker, and J. Bishop. 1994. Evaluating
approaches to the conservation of rare and endangered
plants. Ecology 75:584–606.
Shea, K., and D. Kelly. 1998. Estimating biocontrol agent
impact with matrix models: Carduus nutans in New Zealand. Ecological Applications 8:824–832.
Shigesada, N., and K. Kawasaki. 1997. Biological invasions:
theory and practice. Oxford University Press, Oxford, UK.
Simberloff, D. 1986. Introduced insects: a biogeographic and
systematic perspective. Pages 3–26 in H. A. Mooney and
J. A. Drake, editors. Ecology of biological invasions of
North American and Hawaii. Springer-Verlag, Berlin, Germany.
Skellam, J. 1951. Random dispersal in theoretical populations. Biometrika 38:196–218.
Syrett, P., and H. M. Harman. 1995. Leucoptera spartifoliella
Hubner as a biological control agent for broom in New
Zealand. Plant Protection Quarterly 10:75–78.
Taylor, S. E., and B. H. Walker. 1984. Autecology of an
invading population of the cactus Cereus peruvianus
(Queen of the Night) in the central Transvaal. South African
Journal of Botany 3:387–396.
Vitousek, P. M., C. M. D’Antonio, L. L. Loope, and R. Westbrooks. 1996. Biological invasions as global environmental change. American Scientist 84:468–478.
Weller, D. E. 1987. A re-evaluation of the ⫺3/2 power rule
of plant self-thinning. Ecological Monographs 57:23–43.
Werner, P. A., and H. Caswell. 1977. Population growth rates
and age vs. stage distribution models for teasel (Dispsacus
sylvestris Huds.). Ecology 58:1103–1111.
Westoby, M. 1984. The self-thinning rule. Advances in Ecological Research 14:167–225.
White, J. 1980. Demographic factors in populations of plants.
Pages 21–48 in O. T. Solbrig, editor. Demography and evolution in plant populations. Blackwell, Oxford, UK.
White, J. 1985. The thinning rule and its application to mixtures of plant populations. Pages 291–309 in J. White, editor. Studies on plant demography. Academic Press, New
York, New York, USA.
Yoda, K., T. Kira, H. Ogawa, and K. Hozumi. 1963. Selfthinning in overcrowded pure stands under cultivated and
natural conditions. Journal of Biology, Osaka City University 14:107–129.
Youngman, B. J. 1951. Germination of old seeds. Kew Bulletin 23:423–426.
Ecological Applications
Vol. 10, No. 3
INGRID M. PARKER
742
APPENDIX
Projection matrices: Individual matrix elements for plots representing different stages of invasion (edge, intermediate,
center) in six populations: Johnson Prairie and Discovery Park (1993–1994 and 1994–1995), plus Thirteenth Division Prairie,
Weir Prairie, Magnuson Park, and Montlake Fill (1994–1995 only). For ‘‘problem transitions’’ (see Methods: Demographic
analysis: transition rules), the original value is given in square brackets.
Johnson Prairie
1993–1994
Johnson Prairie
1994–1995
Discovery Park
1993–1994
Edge
Intermediate
Center
InterEdge mediate Center
InterEdge mediate
Seed–Seed
Seed–Seedling
Seedling–Seedling
Seedling–Juvenile
Seedling–Small adult
0.45
0.014
0.11
0.50
0.056
0.45
0.0081
0.36
0.52
···
0.45
0.0011
0.065
0.009
···
0.45 0.45
0.031 0.028
0.47 0.61
0.17 0.16
···
···
0.45
0.0086
0.19
0.032
···
0.74
0.74
0.74
0.001 0.00001 1.9 ⫻ 10⫺5
0.21
0.31
0.11
0.14
0.35
0.056
···
0.038
···
Juvenile–Seed
Juvenile–Juvenile
Juvenile–Small adult
Juvenile–Medium adult
Juvenile–Large adult
Juvenile–Extra-large adult
19.0
0.15
0.35
0.32
0.075
0.025
7.2
0.32
0.28
0.26
0.04
0.02
···
0.40
0.10
···
···
···
12.6
0.18
0.41
0.18
0.029
···
0.74
0.62
0.22
0.14
···
···
···
0.20
0.13 [0]
···
···
···
3.4
0.31
0.29
0.069
···
···
3.2
0.12
0.29
···
···
···
···
0.38
0.19
···
···
···
Small
Small
Small
Small
Small
Small
161.2
21.0
···
···
0.091 0.24 [0.25]
0.61
0.75
···
0.15
···
0.03
36.5
···
0.58
0.083
···
···
162.0
···
0.20
0.65
0.05
···
10.8
9.1
47.1
···
···
0.024
0.40
0.20
0.39
0.47 0.067 [0] 0.44
···
···
···
···
···
···
27.7
···
0.63
0.30
···
···
19.2
···
0.55
0.10
···
···
461.4
0.06
0.29
0.24
0.35
117.8
0.034
0.52
0.21
···
1043
0.025
0.32
0.52
0.075
21.0
···
0.78
0.17
···
52.8
···
0.30
0.25
···
108.7
···
0.32
0.44
0.029
97.0
0.022
0.53
0.31
0.022
201.6
···
0.48
0.27
···
483.4
313.2
611.5
0.038
···
···
··· 0.071 [0.08] 0.15
0.36
0.50
0.58
0.59
0.42
0.15
1655
···
0.048
0.33
0.57
57.0
···
···
0.40
020
159.6
···
0.095
0.43
0.19
1120
···
···
0.53
0.40
396
···
···
0.55
0.30
548.8
···
0.05
0.60
0.25
1094
877.2
1058
3956 559.2
··· 0.015 [0.03]
···
0.037 0.007
···
0.054
···
0.037 0.049
0.84
0.92
0.97 [1] 0.89 0.93
605.7
···
0.067
0.90
3339
0.091
0.091
0.73
1284
···
0.091
0.82
2173
···
0.032
0.94
Life Stage
adult–Seed
adult–Juvenile
adult–Small adult
adult–Medium adult
adult–Large adult
adult–Extra-large adult
Medium
Medium
Medium
Medium
Medium
Large
Large
Large
Large
Large
adult–Seed
adult–Small adult
adult–Medium adult
adult–Large adult
adult–Extra-large adult
adult–Seed
adult–Small adult
adult–Medium adult
adult–Large adult
adult–Extra-large adult
Extra-large
Extra-large
Extra-large
Extra-large
adult–Seed
adult–Medium adult
adult–Large adult
adult–Extra-large adult
57.6
···
0.13 [0]
0.69 [0.8]
0.17 [0.2]
Center
INVASION DYNAMICS OF CYTISUS
June 2000
743
APPENDIX. Extended.
13th Division
Prairie
1994–1995
Discovery Park
1994–1995
Edge
Intermediate
Center
0.74
0.0013
0.048 [0]
0.36
···
0.74
0.00007
0.21 [0]
0.21 [0]
···
3.3
0.20
0.52
···
···
···
Weir Prairie
1994–1995
Magnuson Park
1994–1995
Montlake Fill
1994–1995
InterEdge mediate
Edge
Intermediate
Edge
Intermediate
Edge
Intermediate
0.74
0.00029
0.16 [0]
0.16 [0]
···
0.40
0.052
0.16
0.79
0.017
0.40
0.008
0.34
0.46
···
0.42
0.069
0.52
0.38
···
0.42
0.017
0.52
0.077
···
0.72
0.00058
0.12
0.66
···
0.72
0.0016
0.46
0.30
···
0.73
0.0069
0.52
0.14
···
0.73
0.00002
0.54
0.17
···
···
0.16 [0]
0.16 [0]
···
···
···
···
0.08 [0]
0.12
···
···
···
5.5
0.75
0.20
0.028
···
···
2.6
0.50
0.29
···
···
···
0.21
0.61
0.23
0.056
···
···
11.2
0.65
0.12
0.05
···
···
0.4
0.428
0.33
0.055
···
···
1.6
0.62
0.25
0.04
···
···
2.4
0.70
0.25
0.016
···
···
6.4
0.64
0.27
···
···
···
19.8
···
0.60
0.13
···
···
19.2
···
0.25
0.20
···
···
16.8
···
0.43
0.07
···
···
36.4
···
0.30
0.69
···
···
29.5
···
0.48
0.42
···
···
3.1
···
0.60
0.38
···
···
36.3
···
0.78
0.19
···
···
41.8
···
0.30
0.55
0.05
···
87.1
···
0.65
0.26
···
···
51.6
0.038
0.77
0.15
···
···
95.7
···
0.66
0.19
···
···
76.8
0.031
0.56
0.28
···
147.8
···
0.44
0.24
···
121.6
···
0.37
0.053
···
134.4
···
0.54
0.46
···
195.0
···
0.77
0.21
···
82.2
···
0.73
0.23
···
146.5
0.014 [0.026]
0.87
0.10
···
112.3
···
0.50
0.32
···
620.2
0.03
0.67
0.23
···
277.8
···
0.84
0.08
···
274.0
···
0.64
0.32
···
57.8
···
···
0.54
0.38
267.6
···
···
0.42
0.25
353.6
···
···
0.45
0.18
403.3
···
···
0.71
0.29
639.2
···
···
0.73
0.25
147.2
···
0.15 [0.18]
0.54
0.27
329.3
···
0.06
0.82
0.06
563.0
···
···
0.29
0.35
2977
···
···
0.74
0.22
716.3
···
0.07
0.64
0.14
447.2
···
···
0.64
0.31
2510
···
···
0.87
2271
···
···
0.94
2189
···
···
0.88
472.5
···
0.070
0.92
1675
···
···
0.98
401.3
···
···
0.97 [1.0]
1030
···
0.044 [0.056]
0.94
3728
···
···
0.95 [1]
8177
···
···
0.96
1993
···
···
0.86
4074
···
···
0.96