Model Parameterization

Electronic Supplementary Material 1 for The role of drought- and disturbance-mediated competition in shaping community responses to varied environments-Napier, Mordecai, and Heckman

Model Parameterization

We set the survival rates for both species equal to a survival estimate of 11 long-lived perennials (Lauenroth and Adler 2008). To link biomass measurements from our experiment to seed production and environment-specific fitness, the model incorporates the concept of vigor, a measure of how strongly the environment is promoting growth and survival in year t. Vigor is the final mass measurement at flowering in a competition-free environment (Angertet al. 2009). This measure is not directly observable in nature, but the average mass of a plant is reflective of vigor divided by competition (Angertet al. 2009). Since this experiment was performed in a greenhouse, we used the mean biomass of each species in the absence of competition as an estimate of that plant's vigor of growth under a given environmental condition. We used the following equation to calculate vigor and the competition coefficients, α:

Bx= B0 / (1 + α)

where, for any given Species × Watering × Clipping treatment, Bx is the average biomass of an individual in competition treatment x, B0 is the average biomass of individuals in the same treatment with no competition, and α is the competition coefficient (multiplied by the density of competitors, which is 1). Here, B0 is equal to a species’ vigor in a given environment. We scaled biomass values to seedling production (λ) using an equation relating biomass in the absence of competition of our target species to seed production in the long-lived perennial grass, Boutelouagracilis(Peters 2002). These values were then scaled by species-specific germination rates(Clay 1987; Schraufet al. 1995). Parameterized in this way, the model reflects a link between environmental variation and plant vigor and between plant vigor and competition.

Model Simulations

In order to incorporate environmental variation in the model, we randomly sampled from the four different year types (i.e., the four experimental treatment combinations) each year of the simulation, and applied the corresponding λ’sand α’s to calculate population growth in that year. The simulation ran for 5000 years, with initial population sizes of 1. We compared this temporally variable model with a constant model that used the geometric mean for each parameter value across the four water and clipping treatment combinations. This model simulated the long-term dynamics if the environmental conditions were a long-term average of the four experimental treatments. To understand the effect of different environmental conditions—both temporally variable and constant—on the outcome, we also ran simulations for each of the four treatment groups held constant over time.

GRWR Calculations

To calculate the growth rate when rare (GRWR), we started with the initial conditions Ns(0) = 1, Np(0) = 0, then simulated for 10,000 years to allow Ns to equilibrate.We used the arithmetic mean of the last 20 Ns values as the resident density for S. arundinaceus. We then ran a second simulation with Ns(0) = resident density and Np(t) = 1 for all years t, allowing Nsto fluctuate around its equilibrium while Np was introduced each year at 1 and its growth into the next year was recorded. At the end of the simulation, we calculated the geometric meanof the vector recording Np(t+1)/Np(t) (equal to Np(t+1) since Np(t) = 1) to obtain the long-term average GRWR for P. dilatatum. We followed an analogous process for S. arundinaceus.All simulations were run in R version 3.0.3 (R Foundation for Statistical Computing, Vienna 2008).

Sensitivity Analysis and Results

The GRWRs in a fluctuating environment were calculated with all parameters at their usual values except the focal parameter, which was set to the lower and upper bound of its 95% confidence interval. This process was repeated for all model parameters. We then calculated the percent change in GRWR under the modified parameter value compared to the GRWR under the usual parameter values.

While the GRWR demonstrated fairly uniform sensitivity to all parameters, the largest changes were due to changes in competition parameters, suggesting that our model was more sensitive to parameters informed by our experimental data (Figure S1).

References only in ESM 1

Lauenroth WK, Adler PB (2008) Demography of perennial grassland plants: survival, life expectancy and life span. J Ecol 96:1023-1032. doi: 10.2307/20143548

Peters DP (2002) Recruitment potential of two perennial grasses with different growth forms at a semiarid-arid transition zone. Am J Bot 89:1616-1623. doi: 10.3732/ajb.89.10.1616

ESM FigureS1. Sensitivity analysis showing the percent change in growth rate when rare (GRWR) for each specieswheneach focal parameter value is set to the lower and upper bound of its 95% confidence interval. The s denotes the survival probability. The changes in competition parameters denote the effect of changes in the intra- or interspecific pressure on the target species.

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