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Appendix S1. Calculation of demographic rates and model parameterization for
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amla (Phyllanthus emblica and P. indofischeri ) populations
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Survival of seeds in the seedbank
We tested the survival of amla seeds in the seedbank by burying bags of seeds
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wrapped in nylon mesh in randomly selected corners outside each permanent plot. In
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January 2006, two bags, each containing 20 and 15 seeds for P. emblica and P.
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indofischeri respectively were buried outside each plot. Since seedlings start to germinate
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in May, one bag was dug up one year later, in May 2007, and the second bag in May
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2008. The number of seeds that were destroyed was counted and the remaining seeds
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were germinated in a soil bed in the BRT nursery.
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Germination and seedling survival
We estimated rates of amla germination and seedling survival in the field and in a
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nursery. For field germination, in January 2006 we established two adjacent 50X 50 cm
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subplots 20 m away from a randomly selected corner of each permanent plot. In one of
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the subplots we planted 15 or 20 seeds for P. indofischeri or P. emblica respectively and
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we left the other as a control. Seed germination and survival was measured monthly for
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one year. Survival of naturally germinated seedlings was also measured monthly from
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April 2005-2008 in all plots.
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In the field station nursery at BRT, we carried out annual germination
experiments from 2005 to 2008. In each of the four years, between 30-50 seeds of each
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species were planted in a bed of soil and on filter paper, and germination rates were
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recorded.
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Calculation of fruit production and harvest rates
Each year, the number of fruit per tree was counted on a subset of trees inside and
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outside the plots (N= 163 P. emblica and N= 176 P. indofischeri), in November, before
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the fruits mature. To calculate the number of fruit harvested per tree, fruit were also
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counted after harvest occurred. In 2005 we were unable to collect fruit production data
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for P. emblica and so we used the mean value over the 9 other years. By 2006 many of
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fruiting trees in the subsample had died and we counted the fruit on all adult trees in the
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plots for the remaining years.
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Estimation of frugivory rates
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To estimate the proportion of amla fruits removed by (non-human) frugivores, in
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2005 and in 2006 we used camera traps and carried out fruit removal experiments using
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paired open and enclosed bait stations. Our camera traps revealed that fruit removal was
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almost exclusively by native ungulates. To estimate the rate of predation of seeds
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dispersed by ungulates, we carried out seed removal experiments using cages that
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excluded ungulates but allowed accessed to rodents (and other small mammals). To
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estimate the rate of germination of seeds regurgitated (dispersed) by ungulates, we
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carried out germination trials of regurgitated seeds over three years for P. emblica. We
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were unable to locate enough regurgitated P. indofischeri seeds for experiments and so
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we assumed the germination rates were the same as for P. emblica.
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Parameterization of matrix models
We built 7x7 Lefkovich stage-structured transition matrices (Caswell 2001)
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directly from the annual census field data by calculating the proportion of individuals that
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moved or stayed in the same size classes. Basal area was used as a measure of size since
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some individuals had multiple stems. We built 40 annual matrices for P. emblica (4
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treatments * 10 years) and 20 for P. indofischeri (2 treatments * 10 years) (see text for an
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explanation of the treatments). When there was no movement from one transition to
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another in a given year we used the mean value for the treatment and/or the stage of
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invasion (pre invasion, moderate invasion, high invasion). If the mean was zero, we used
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a value of 0.001. When no mortality was observed in large adults we used a value of
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0.999. For P. emblica, the number of individuals 5-9 cm dbh (adult 1 category) was very
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low across all plots so we estimated transition rates from 31 individuals in experiments
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outside the plots.
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The number of seedlings produced per adult tree was calculated as:
sdl = p* f * sd* (1-h -fr) * g *s
(1)
and the number of seeds entering the seedbank produced per adult tree was calculated as:
sbk = p* f * sd* (1-h -fr) * (1-g) *sb
(2)
where p is the proportion of trees fruiting in a given year; f is the mean number of
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fruit/fruiting tree, sd is the mean number of seeds/fruit, h is the proportion of fruit
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harvested by people, fr is the proportion of fruit removed by frugivores, g is the
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proportion of seeds germinating in the field, s= the proportion of seedlings surviving
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from germination to the census time, sb is the proportion of seeds that survive in the soil
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seedbank until the next census. These estimations did not include germination of seeds
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regurgitated by frugivores since our seed germination trials from three separate years
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revealed no or very low rates of germination of regurgitated seeds and high seed
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predation. Although ungulate regurgitation of seeds likely plays an important role in
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dispersal, it contributes little to the dynamics of the populations. These equations
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produced estimates of the number of new seedlings per year close (within ± 10 seedlings)
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to what was observed in the field at each census.
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We estimated the proportion of seeds staying the seedbank from year t to year t+1
as:
s12= (s2/s1) – g1
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(3)
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Where s2= number of seeds surviving after 2 years in the seedbank, s1 = number of seeds
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surviving after 1 year in the seedbank, and g1=proportion of seeds germinating after 1
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year in the seedbank.
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Since the above experiments for frugivory, seed germination, seedling survival
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and seedbank estimates were only carried out after 2005, we used the mean values from
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our experiments in the 1999-2004 matrices. We used the same estimates for the
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proportion of fruit removed by frugivores and survival of seeds in the seedbank for all
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treatments. The rest of the parameters varied among treatments (with the exception of sd
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(mean number of seeds/fruit)).
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Calculation of λ, λs and elasticity
To calculate projected population growth rates (λ), we used the basic matrix
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population model (Caswell 2001), which projects the size and structure of populations
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over time: n(t + 1) = An(t) , where A is a 7 × 7 stage-based matrix, n(t) is a vector of the
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number of individuals in each of the stage-classes in year t, and n(t + 1) is the population
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vector in the following year t + 1. The dominant eigenvalue (λ) of the time-invariant
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matrix A is equivalent to the deterministic population growth rate and represents the rate
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at which a population would grow over the long-term under the parameterization
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conditions (Caswell 2001). All matrices were irreducible and primitive. For each matrix
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we calculated the projected population growth rate, λ, elasticity values of the matrix
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elements and determined the 95% percent confidence intervals of λ with 2000 bootstrap
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runs (Caswell 2001).
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We calculated stochastic population growth rates (λs) under pre/low invasion
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(1999-2002) and high invasion (2006-2009) contexts. To do so, we averaged successive
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growth rates over a long simulation with 50 000 iterations, which involved the random
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selection of annual transition matrices for each context (Stubben & Milligan 2007).
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Stochastic growth rates of populations in the pre/low invasion context (using 1999-2002
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matrices) were similar within both species (Fig S1). For P. emblica, λs for the 10 year
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period in control plots was 0.942 (0.933-0.950), for P. indofichceri this value was 1.013
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(1.009-1.016 CI).
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To assess the effects of fruit harvest with and without invasive species on λs, we
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simulated fruit harvest for each annual matrix during the high invasion period (2006-
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2009) for each of the four treatments. Fruit harvest rates were based on observed rates
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from 1999-2004, so that when fruit production was high, we used the mean of the years
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with high production and when fruit production was low we used the mean of the years
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with low production.
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Fig S1. Stochastic lambda values for a) P. emblica and b) P. indofischeri populations
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during pre/low invasion of mistletoe and lantana (1999-2002). Error bars represent 95%
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confidence intervals, but are so small for P. indofischeri that they are not visible.
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a)
0.95
Stochastic lambda
0.9
0.85
0.8
0.75
0.7
0.65
0.6
control
lantana mistletoe mistletoe
& lantana
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(b)
1.06
stochastic lambda
1.04
1.02
1
0.98
0.96
0.94
0.92
0.9
control
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pre-mistletoe
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Transient Dynamics
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To assess the effects fruit harvest and invasive species on indices of amla
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transient dynamics we projected the mean matrices from 2006-2009 for each treatment
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and species, with and without fruit harvest. We used the observed population structure at
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our last census (2009) as the initial population structure vector for each species and
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standardized the matrices and initial structures (Stott et al.2011). The initial structure
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included an estimated 500 seeds in the seedbank but varying this value did not change the
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trends observed. Since we were interested in understanding trends in the above-ground
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stages, we removed the seeds in the seedbank from the density calculations and scaled the
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total density of the all the above ground size classes to 1. As recommended by Stott et
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al. 2011, we calculated reactivity (population growth in the first time-step, relative to
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stable (asymptotic) growth rate), maximum amplification or attenuation (maximum short-
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term increase or decrease in population density relative to stable (asymptotic) growth
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rate) and inertia (the long-term population density relative to a population with stable
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growth and the same initial density). Since for amla it is the reproductive trees that are
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economically valuable, we also calculated inertia of trees of reproductive size only.
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Table S1. Indices of amla transient dynamics. All projections are based on standardized
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initial population structure observed in 2009 and standardized mean matrices 2006-2009.
Species
P. emblica
Index
Control
Mistletoe
Lantana
No
No
No
Frt
Frt
Frt
Mistletoe &
lantana
No
Frt
harv harv harv harv harv harv
harv harv
1.42
1.09
1.16
1.26
1.06
0.93
1.01
0.96
4.4
2.09
1.52
2.03
1.23
0.77
0.81
0.57
4.4
2.09
1.52
2.03
1.23
0.77
0.81
0.57
1.06
1.07
1.00
1.00
1.07
1.07
1.00
1.00
1.71
1.19
1.05
1.03
1.63
1.07
0.82
0.79
9.29
4.8
2.47
1.4
9.l9
3.9
0.37
0.17
8.4
4.8
2.5
1.4
9.19
3.9
0.37
0.17
Reactivity1
Max att/amp2
Inertia3
Inertia of
reproductives4
P.
Reactivity
indofischeri
Max att/amp
Inertia
Inertia of
reproductives
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1
0.71 0.77 0.22 0.13 1.15 1.16 0.68 0.68
Population growth in the first time-step, relative to stable (asymptotic) growth rate
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2
Maximum or minimum short-term increase or decrease in population density relative to
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stable (asymptotic) growth rate
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same initial density.
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dbh for P. indofischeri ) relative to a population with stable growth and the same initial
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density of adults.
The long-term population density relative to a population with stable growth and the
The long-term density of reproductive size adults (>9 cm dbh for P. emblica and >5 cm
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Reactivity indices revealed that amla populations are expected to grow faster in
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the first time-step than projected by stable (asymptotic) growth rates (Table S1). The
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exception was for populations in mistletoe&lantana plots, where the reverse was true. In
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general indices of maximum amplification or attenuation were the same as the inertia
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values, indicating that populations are projected to either consistently increase or
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consistently decrease before stabilizing. The exception was for P. indofischeri in control
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plots, where densities are expected to increase over the short-term and then decrease
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slightly before stabilizing. Trends in inertia values are discussed in the text.
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We also projected short term changes in density of amla reproductive adults.
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Projections were based on the observed population structure at the last census (initial
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structure) and mean matrices from 2006-2009. To compare trends across treatments,
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initial population structure was standardized.
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Elasticity analyses
Elasticity analyses project how λ would change in response to small changes in
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population vital rates. A small change in a vital rate with a high elasticity value will have
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a big impact on λ; a change in a vital rate with low elasticity will lead to very small
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changes in λ. Elasticities were summed by vital rate (Fig. S3), as well as per stage class.
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In the latter, the elasticity values of survival, growth and reproduction for each stage-
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class were summed.
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Fig. S2. Elasticity values (10 year mean ± 1 SD) summed by vital rate for a) Phyllanthus
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emblica and b) P. indofischeri.
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a)
1.2
survival
Elasticity
1
growth
neg.growth
0.8
reproduction
0.6
0.4
0.2
0
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low mistletoe &
lantana
high mistletoe
high lantana
high
mistletoe&lantana
b)
1.20
1.00
Elasticity
0.80
survival
0.60
growth
0.40
neg.growth
reproduction
0.20
0.00
-0.20
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low mistletoe
moderate mistletoe
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Life Table Response Experiments
We carried out fixed, one-way life table response experiments (LTRE, Caswell
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2001) among treatments and time periods within each species, and between species. We
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carried out LTREs only when differences in λ among treatments or species were high (Δλ
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> 0.05, i.e. a difference of 5% or more in projected long-term annual growth rate), and
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we used the mean matrix for each treatment or time period. We designated the year or
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treatment with λ > 1 (high lambda = λh) as the reference matrix, so that treatment effects
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on λ were measured relative to λh as:
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(h) - (l)  ∑i(aij(h) – aij(l))*( ∂λ/∂aij ) |A(m)
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where (l) is the matrix with the lower lambda value, aij are the transition coeffieicents
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in the matrices, and ∂λ/∂xj (the sensitivities) are calculated from a matrix averaging the
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two matrices being compared. Matrix elements with high LTRE contributions make the
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biggest contributions to the observed differences in λ between populations.
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References
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Caswell, H. 2001. Matrix population models – Construction, analysis, and interpretation.
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Sinauer, Sunderland. Sinauer Associates, Sunderland, Massachusetts.
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Stott, A., Townley S., & Hodgson D. J. (2011). framework for studying transient
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dynamics of population projection model. Ecology Letters 14, 959-970.
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Stubben, C., & Milligan, B. (2007) Estimating and analyzing demographic models using
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the popbio package in R. Journal of Statistical Software, 22, http://www.jstatsoft.org/.