Elsa E. Cleland, Halton A. Peters, Harold A. Mooney, and Christopher B. Field. 2006. Gastropod herbivory in response to elevated CO₂ and N addition impacts plant community composition. Ecology 87:686–694.

Appendix A. Supplementary information regarding statistical analyses and outputs.

Germination

The statistical model was coded in SAS v. 9.1 using the PROC GLIMMIX procedure. This procedure uses generalized linear mixed models and allows for non-normal distributions. In this case seedlings either germinated or did not germinate, resulting in a binomial distribution of the errors associated with proportion of seedlings that germinated. The following model tests for the significance of positive events (germination) given the potential number of trials (seeds planted), and accounts for the split-split-plot nature of the experiment. The resulting table of F tests, numerator and denominator degrees or freedom, and P values is below, and is followed by the least squared means and standard errors of significant terms.

proc glimmix data=germination;

 class  co2 plot n species;

 model germinated/seeds planted = co2 n n*co2 species species*co2 

                 n*species n*species*co2 ;

 random int species n /subject=plot(co2);

 run;

Type III Tests of Fixed Effects

Least Squares Means

TABLE A1.  The following details the number of seeds of each species that were planted and subsequently germinated. Transplanted seedlings were added to plots with poor germination to make the availability of seedlings for herbivory even within and among plots and treatments. The sum of germinated and transplanted seedlings represents the total seedlings subsequently available for herbivory.

Herbivore consumption

While the germination analysis was based on the likelihood of 12 or 24 seeds germinating in each plot (both grids), the herbivory analysis was based on the likelihood that the seedlings in each grid would be consumed. The number of seedlings of each species in each grid was small – ranging between 1 and 12. In addition, frequently all or none of the seedlings of a particular species were consumed in a grid. The small sample size and severely non-normal data resulted in a lack of convergence in the algorithms used in PROC GLIMMIX. Instead, PROC CATMOD was utilized. The zero consumption of Avena barbata under elevated CO₂ and elevated CO₂ + N does not allow an effect to be tested for the CO₂*species or N*species terms, resulting in poor model fit (highly nonsignificant Likelihood ratio). Hence the saturated model was reduced to the following sparse model:

proc catmod data=herbivory order=data;

weight count;

model eat = species co2 n co2*n co2*n*species/ zero=sampling;

by open_exclosure;

run;

Chi-squared tests, degrees of freedom, P values and least squared means for the significant terms are displayed below.  Note that data for this analysis come from grids open to herbivory during the time period of Nov. 25th to Dec. 13th, 2001.

Maximum Likelihood Analysis of Variance

 Note: Least squared means estimates were obtained using the PROC GLIMMIX statements.

Species Least Squares Means

CO2*N Least Squares Means

CO2*N*Species Least Squares Means

Percent Nitrogen

Percent N was measured only on seedlings harvested within the herbivore exclosures. %N was log transformed to improve normality and was analyzed using the PROC MIXED procedure, again accounting for the split-split-plot design with the following code:

proc mixed data=percentnitrogen;

  class  co2 plot n species;

  model logpercn=co2

                 n n*co2

                 species species*co2

                 n*species n*species*co2/ solution;

 random int species n /subject=plot(co2);

 run;

Type III Tests of Fixed Effects

Least Squares Means

Growth rate

Growth rate was calculated by taking the slope of the regression line for the log seedling weights over the four harvests.  Growth rate was only calculated for the seedlings harvested within the herbivore exclosures.  The slope for each grid open to herbivory was analyzed using the same PROC MIXED statements listed in the %N analysis above.

Least Squares Means