*Ecological Archives* E096-213-A1

Jayne L. Jonas, Deborah A. Buhl, and Amy J. Symstad. 2015. Impacts of weather on long-term patterns of plant richness and diversity vary with location and management. *Ecology* 96:2417–2432. http://dx.doi.org/10.1890/14-1989.1

Appendix A. Detailed description of the methods.

*Plant data sets and variables*

We downloaded datas ets (1982–2003) from the Cedar Creek website (e001 data set, http://www.cedarcreek.umn.edu/). We did not use data from the first three years of the experiment (1982 – 1984) to avoid issues associated with rapid changes in plant composition due to initiation of fertilization. Data for 1984 – 2011 were downloaded from the Konza Prairie website (pvc02 dataset, http://www.konza.ksu.edu/). Data for 1992 – 2008 for the Shortgrass Steppe (SGS) site (GZTX, Study 32 dataset from ungrazed pastures) were acquired directly from the SGS data manager with permission from the dataset originator (D. Milchunas). We accessed data collected from 1934 – 1972 at College Pasture through Ecological Archives E088-161-D1 (Adler et al. 2007).

We error-checked all data sets to the greatest extent possible; data managers of the respective data sets were contacted for clarification as necessary. We classified species as native or exotic according to the United States Department of Agriculture Plants Database (http://plants.usda.gov/) or *Flora of the Great Plains* (Great Plains Flora Association 1986). We calculated total, native, and exotic species richness (S) and Shannon diversity (H') for each year in each plot (Shortgrass Steppe, Cedar Creek and College Pasture) or transect (Konza) in each data set (Magurran 2004).

*Weather data sets and variables*

We obtained weather data for two of the LTER sites from the Cedar Creek e080 data set and Konza data set AWE012 (URLs given above). Data were downloaded for data set cr21x from the LTER ClimDB website (http://climhy.lternet.edu/) for station 12 (SGS). Generally, this dataset contained weather data for 1991 – 2008, however there were various time periods when data were missing. Weather data for the same period were also downloaded from the High Plains Regional Climate Center (HPRCC) at the University of Nebraska (Lincoln, NE) for National Weather Service (NWS) weather stations near SGS (Ft Collins. ID# 053005; Ft Collins 4E, ID# 053006; and Nunn, ID# 056023). In cases of missing data points in the SGS LTER weather data set, weather values were averaged across available NWS weather data sets then scaled for departure from the SGS weather dataset based on periods when data were available for all data sets (SGS LTER and NWS). Weather data for College Pasture came from an NWS weather station (Hays 1S, ID# c143527) and was acquired through the HPRCC.

From daily weather data, we calculated average maximum temperature (oC), coefficient of variation (CV) of maximum temperatures, total precipitation (mm), and CV of precipitation for each of four seasons in each location for each year. We also calculated winter average minimum temperature and CV of minimum temperature in our weather matrices as these values may correspond to dormant-season freeze-thaw cycles. However, due to collinearity, these variables (winter minimum temperature and CV winter minimum temperature) were removed from the set of weather variables prior to model development. For each site, we defined seasons based on long-term average maximum temperatures to account for latitudinal variation among sites [spring: 10°C–20°C (early months), summer: >20°C, fall: 10°C–20°C (late months), winter: <10°C]. We chose these temperature ranges to approximate the dormant season (prior winter), peak growing season for cool-season species (spring and prior fall), and peak growing season for warm-season species (summer) using a water-year approach (i.e., for a given plant sampling year (*t*), seasonal weather encompassed fall_{t-1}, winter_{t-1}, spring* _{t}*, and summer

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*Data analysis*

Richness and diversity values were not directly comparable among datasets due to differences in temporal extent, experimental manipulation and data collection methodologies among locations, so we analyzed each data set separately. All response variables satisfied the assumptions of normality and homogeneity of variances. All plots/transects surveyed within a site each year will have the same values for the weather variables, but different values of the response variables (i.e., native, exotic, and total species richness and diversity). Therefore, we used a two-stage process that first computed an average response across all plots/transects for each year, and second examined the relationship between the average response and the weather variables.

In the first stage of the analysis, we used a repeated measures analysis of variance to model each response variable as a function of focal experimental treatments (nitrogen fertilization at Cedar Creek; fire frequency, grazing, and season of burn at Konza; major plant assemblage at College Pasture; none at Shortgrass Steppe), secondary treatments (none in SGS, Cedar Creek, or College Pasture datasets; soil type in the Konza FRI and season of burn datasets; soil type and FRI in the Konza grazing dataset), and year, while accounting for the design of the original study. Year was modeled as a repeated measure using two different covariance structures: compound symmetry and first-order auto-regressive (Littell et al. 2006). Akaike’s Information Criterion corrected for small sample size (AICC) (Burnham and Anderson 2002) was used to determine which covariance structure was a better fit. Because there were significant focal treatment × year interactions on all response variables but focal treatment × secondary treatment × year interactions were rare (Supplement 12), we estimated the least squares means of each response variable for each year × focal treatment combination, while averaging across secondary treatments using the model with best fit (i.e., lowest AICC value). We analyzed weather effects for each focal treatment separately using these estimated least squares means in the next stage of the analysis.

In the second stage of the analysis, we used autoregressive error models (Dickey 1998) to relate the estimated least squares means to the weather variables. With time series data, the ordinary regression residuals are usually correlated over time; therefore, we used autoregressive models to account for this autocorrelation of the errors. Only first-order autoregressive models were considered because samples sizes were too small to accommodate more parameters. Weather variables were checked for collinearity prior to analyses.

We used information-theoretic (IT) techniques (Burnham and Anderson 2002) to assess relative importance of *a priori* hypothesis models for relationships between interannual variability in weather and plant species richness or diversity. The set of *a priori* models consisted of all weather variables singly and some two-variable models (Table 1; Supplement 3). The candidate set also included a null model (i.e., no weather variables). We constructedthese models based on plant biology and climate change predictions for the Great Plains region using 28 weather variables (Table 1). We included previous (*t*-1) spring and summer weather variables in some models to assess potential lagged effects of weather on plant communities. In order to calculate relative importance values of each variable without bias, we included each weather variable in the same number of models.

The IT method we employed used Akaike’s Information Criterion corrected for small sample size (AICC) based on maximum likelihood estimates to rank models relative to one another: the smaller the AICC, the more likely the model (Burnham and Anderson 2002). To assess overall fit of each model, we computed the regression *R*², a measure of the fit of the weather variable(s) after adjusting for the autocorrelation, and the total *R*², a measure of predictability using the weather variable(s) and the past values of the residuals. All models with DAICC<2, where DAICC is the difference between the AICC of a given model and that of the model with the lowest AICC, were considered equally plausible (Burnham and Anderson 2002). However, we consider only those models where the weather variable(s) accounted for at least 30% of the variability in a given response variable (regression *R*²≥0.30) and have DAICC<2 to be ecologically meaningful models (EMM). In addition, if the null model was among the set of plausible models (DAICC<2), then we concluded that none of the weather variables were related to the response variable. We calculated relative importance values (RIV) for each explanatory variable by summing Akaike weights of all models containing that variable. Akaike weights (*wi*) provide a measure of the relative likelihood of model *i* being the single best model compared to all others in the set of candidate models. We consider those variables with either A) RIV > 0.4 or B) RIV between 0.2 and 0.4 and appearing in an EMM to be ecologically meaningful variables (EMV), except in cases where RIV of a given variable was greater than 0.20 because it was included in a 2-variable model with a highly important partner variable (RIV>0.35). These instances were identified by comparing the weight of that 2-variable model to the weight of the 1-variable model of the partner variable; if the weight of the 2-variable model was lower than the weight of the model containing only the partner variable (i.e., adding the given variable decreased the weight of models containing the partner variable), then the given variable was not considered to be an EMV. All statistical analyses were conducted in SAS (SAS Institute Inc., Cary, NC).

Literature Cited

Magurran, A. E. 2004. Measuring biological diversity. Blackwell Publishing, Oxford, UK.