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1 Appendix S1. Calculation of demographic rates and model parameterization for 2 amla (Phyllanthus emblica and P. indofischeri ) populations 3 4 5 Survival of seeds in the seedbank We tested the survival of amla seeds in the seedbank by burying bags of seeds 6 wrapped in nylon mesh in randomly selected corners outside each permanent plot. In 7 January 2006, two bags, each containing 20 and 15 seeds for P. emblica and P. 8 indofischeri respectively were buried outside each plot. Since seedlings start to germinate 9 in May, one bag was dug up one year later, in May 2007, and the second bag in May 10 2008. The number of seeds that were destroyed was counted and the remaining seeds 11 were germinated in a soil bed in the BRT nursery. 12 13 14 Germination and seedling survival We estimated rates of amla germination and seedling survival in the field and in a 15 nursery. For field germination, in January 2006 we established two adjacent 50X 50 cm 16 subplots 20 m away from a randomly selected corner of each permanent plot. In one of 17 the subplots we planted 15 or 20 seeds for P. indofischeri or P. emblica respectively and 18 we left the other as a control. Seed germination and survival was measured monthly for 19 one year. Survival of naturally germinated seedlings was also measured monthly from 20 April 2005-2008 in all plots. 21 22 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 2 23 species were planted in a bed of soil and on filter paper, and germination rates were 24 recorded. 25 26 27 Calculation of fruit production and harvest rates Each year, the number of fruit per tree was counted on a subset of trees inside and 28 outside the plots (N= 163 P. emblica and N= 176 P. indofischeri), in November, before 29 the fruits mature. To calculate the number of fruit harvested per tree, fruit were also 30 counted after harvest occurred. In 2005 we were unable to collect fruit production data 31 for P. emblica and so we used the mean value over the 9 other years. By 2006 many of 32 fruiting trees in the subsample had died and we counted the fruit on all adult trees in the 33 plots for the remaining years. 34 35 Estimation of frugivory rates 36 To estimate the proportion of amla fruits removed by (non-human) frugivores, in 37 2005 and in 2006 we used camera traps and carried out fruit removal experiments using 38 paired open and enclosed bait stations. Our camera traps revealed that fruit removal was 39 almost exclusively by native ungulates. To estimate the rate of predation of seeds 40 dispersed by ungulates, we carried out seed removal experiments using cages that 41 excluded ungulates but allowed accessed to rodents (and other small mammals). To 42 estimate the rate of germination of seeds regurgitated (dispersed) by ungulates, we 43 carried out germination trials of regurgitated seeds over three years for P. emblica. We 44 were unable to locate enough regurgitated P. indofischeri seeds for experiments and so 45 we assumed the germination rates were the same as for P. emblica. 3 46 47 Parameterization of matrix models We built 7x7 Lefkovich stage-structured transition matrices (Caswell 2001) 48 directly from the annual census field data by calculating the proportion of individuals that 49 moved or stayed in the same size classes. Basal area was used as a measure of size since 50 some individuals had multiple stems. We built 40 annual matrices for P. emblica (4 51 treatments * 10 years) and 20 for P. indofischeri (2 treatments * 10 years) (see text for an 52 explanation of the treatments). When there was no movement from one transition to 53 another in a given year we used the mean value for the treatment and/or the stage of 54 invasion (pre invasion, moderate invasion, high invasion). If the mean was zero, we used 55 a value of 0.001. When no mortality was observed in large adults we used a value of 56 0.999. For P. emblica, the number of individuals 5-9 cm dbh (adult 1 category) was very 57 low across all plots so we estimated transition rates from 31 individuals in experiments 58 outside the plots. 59 60 61 62 63 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 64 fruit/fruiting tree, sd is the mean number of seeds/fruit, h is the proportion of fruit 65 harvested by people, fr is the proportion of fruit removed by frugivores, g is the 66 proportion of seeds germinating in the field, s= the proportion of seedlings surviving 67 from germination to the census time, sb is the proportion of seeds that survive in the soil 68 seedbank until the next census. These estimations did not include germination of seeds 4 69 regurgitated by frugivores since our seed germination trials from three separate years 70 revealed no or very low rates of germination of regurgitated seeds and high seed 71 predation. Although ungulate regurgitation of seeds likely plays an important role in 72 dispersal, it contributes little to the dynamics of the populations. These equations 73 produced estimates of the number of new seedlings per year close (within ± 10 seedlings) 74 to what was observed in the field at each census. 75 76 We estimated the proportion of seeds staying the seedbank from year t to year t+1 as: s12= (s2/s1) – g1 77 (3) 78 Where s2= number of seeds surviving after 2 years in the seedbank, s1 = number of seeds 79 surviving after 1 year in the seedbank, and g1=proportion of seeds germinating after 1 80 year in the seedbank. 81 Since the above experiments for frugivory, seed germination, seedling survival 82 and seedbank estimates were only carried out after 2005, we used the mean values from 83 our experiments in the 1999-2004 matrices. We used the same estimates for the 84 proportion of fruit removed by frugivores and survival of seeds in the seedbank for all 85 treatments. The rest of the parameters varied among treatments (with the exception of sd 86 (mean number of seeds/fruit)). 87 88 89 Calculation of λ, λs and elasticity To calculate projected population growth rates (λ), we used the basic matrix 90 population model (Caswell 2001), which projects the size and structure of populations 91 over time: n(t + 1) = An(t) , where A is a 7 × 7 stage-based matrix, n(t) is a vector of the 5 92 number of individuals in each of the stage-classes in year t, and n(t + 1) is the population 93 vector in the following year t + 1. The dominant eigenvalue (λ) of the time-invariant 94 matrix A is equivalent to the deterministic population growth rate and represents the rate 95 at which a population would grow over the long-term under the parameterization 96 conditions (Caswell 2001). All matrices were irreducible and primitive. For each matrix 97 we calculated the projected population growth rate, λ, elasticity values of the matrix 98 elements and determined the 95% percent confidence intervals of λ with 2000 bootstrap 99 runs (Caswell 2001). 100 We calculated stochastic population growth rates (λs) under pre/low invasion 101 (1999-2002) and high invasion (2006-2009) contexts. To do so, we averaged successive 102 growth rates over a long simulation with 50 000 iterations, which involved the random 103 selection of annual transition matrices for each context (Stubben & Milligan 2007). 104 Stochastic growth rates of populations in the pre/low invasion context (using 1999-2002 105 matrices) were similar within both species (Fig S1). For P. emblica, λs for the 10 year 106 period in control plots was 0.942 (0.933-0.950), for P. indofichceri this value was 1.013 107 (1.009-1.016 CI). 108 To assess the effects of fruit harvest with and without invasive species on λs, we 109 simulated fruit harvest for each annual matrix during the high invasion period (2006- 110 2009) for each of the four treatments. Fruit harvest rates were based on observed rates 111 from 1999-2004, so that when fruit production was high, we used the mean of the years 112 with high production and when fruit production was low we used the mean of the years 113 with low production. 114 115 6 116 Fig S1. Stochastic lambda values for a) P. emblica and b) P. indofischeri populations 117 during pre/low invasion of mistletoe and lantana (1999-2002). Error bars represent 95% 118 confidence intervals, but are so small for P. indofischeri that they are not visible. 119 a) 0.95 Stochastic lambda 0.9 0.85 0.8 0.75 0.7 0.65 0.6 control lantana mistletoe mistletoe & lantana 120 121 (b) 1.06 stochastic lambda 1.04 1.02 1 0.98 0.96 0.94 0.92 0.9 control 122 123 124 pre-mistletoe 7 125 Transient Dynamics 126 To assess the effects fruit harvest and invasive species on indices of amla 127 transient dynamics we projected the mean matrices from 2006-2009 for each treatment 128 and species, with and without fruit harvest. We used the observed population structure at 129 our last census (2009) as the initial population structure vector for each species and 130 standardized the matrices and initial structures (Stott et al.2011). The initial structure 131 included an estimated 500 seeds in the seedbank but varying this value did not change the 132 trends observed. Since we were interested in understanding trends in the above-ground 133 stages, we removed the seeds in the seedbank from the density calculations and scaled the 134 total density of the all the above ground size classes to 1. As recommended by Stott et 135 al. 2011, we calculated reactivity (population growth in the first time-step, relative to 136 stable (asymptotic) growth rate), maximum amplification or attenuation (maximum short- 137 term increase or decrease in population density relative to stable (asymptotic) growth 138 rate) and inertia (the long-term population density relative to a population with stable 139 growth and the same initial density). Since for amla it is the reproductive trees that are 140 economically valuable, we also calculated inertia of trees of reproductive size only. 141 142 8 143 Table S1. Indices of amla transient dynamics. All projections are based on standardized 144 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 145 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 146 2 Maximum or minimum short-term increase or decrease in population density relative to 147 stable (asymptotic) growth rate 148 3 149 same initial density. 150 4 151 dbh for P. indofischeri ) relative to a population with stable growth and the same initial 152 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 9 153 Reactivity indices revealed that amla populations are expected to grow faster in 154 the first time-step than projected by stable (asymptotic) growth rates (Table S1). The 155 exception was for populations in mistletoe&lantana plots, where the reverse was true. In 156 general indices of maximum amplification or attenuation were the same as the inertia 157 values, indicating that populations are projected to either consistently increase or 158 consistently decrease before stabilizing. The exception was for P. indofischeri in control 159 plots, where densities are expected to increase over the short-term and then decrease 160 slightly before stabilizing. Trends in inertia values are discussed in the text. 161 162 We also projected short term changes in density of amla reproductive adults. 163 Projections were based on the observed population structure at the last census (initial 164 structure) and mean matrices from 2006-2009. To compare trends across treatments, 165 initial population structure was standardized. 166 10 167 Elasticity analyses Elasticity analyses project how λ would change in response to small changes in 168 169 population vital rates. A small change in a vital rate with a high elasticity value will have 170 a big impact on λ; a change in a vital rate with low elasticity will lead to very small 171 changes in λ. Elasticities were summed by vital rate (Fig. S3), as well as per stage class. 172 In the latter, the elasticity values of survival, growth and reproduction for each stage- 173 class were summed. 174 Fig. S2. Elasticity values (10 year mean ± 1 SD) summed by vital rate for a) Phyllanthus 175 emblica and b) P. indofischeri. 176 a) 1.2 survival Elasticity 1 growth neg.growth 0.8 reproduction 0.6 0.4 0.2 0 177 178 179 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 -0.20 180 181 low mistletoe moderate mistletoe 11 182 183 Life Table Response Experiments We carried out fixed, one-way life table response experiments (LTRE, Caswell 184 2001) among treatments and time periods within each species, and between species. We 185 carried out LTREs only when differences in λ among treatments or species were high (Δλ 186 > 0.05, i.e. a difference of 5% or more in projected long-term annual growth rate), and 187 we used the mean matrix for each treatment or time period. We designated the year or 188 treatment with λ > 1 (high lambda = λh) as the reference matrix, so that treatment effects 189 on λ were measured relative to λh as: 190 (h) - (l) ∑i(aij(h) – aij(l))*( ∂λ/∂aij ) |A(m) 191 where (l) is the matrix with the lower lambda value, aij are the transition coeffieicents 192 in the matrices, and ∂λ/∂xj (the sensitivities) are calculated from a matrix averaging the 193 two matrices being compared. Matrix elements with high LTRE contributions make the 194 biggest contributions to the observed differences in λ between populations. 195 196 References 197 Caswell, H. 2001. Matrix population models – Construction, analysis, and interpretation. 198 Sinauer, Sunderland. Sinauer Associates, Sunderland, Massachusetts. 199 200 Stott, A., Townley S., & Hodgson D. J. (2011). framework for studying transient 201 dynamics of population projection model. Ecology Letters 14, 959-970. 202 203 Stubben, C., & Milligan, B. (2007) Estimating and analyzing demographic models using 204 the popbio package in R. Journal of Statistical Software, 22, http://www.jstatsoft.org/.