Appendix B. A table showing mixedeffects model summaries for the effect of altitude and region on stem height and capitulum seed mass, for each of eight Asteraceae forbs separately.
TABLE B1. Mixedeffects model (residual maximumlikelihood method) summaries for the effect of altitude and region on stem height and capitulum seed mass, shown for each of eight Asteraceae forbs separately. Only denominator degrees of freedom (df) are given, since all numerator degrees of freedom are 1. When pooling across species, we found a signifcant difference between the relationship of capitulum seed mass and altitude between the native and introduced ranges (Table 2). However, this difference was not apparent at the species level. Therefore for this trait we conducted a power analysis to calculate the sample sizes (n) required to reject the null hypothesis that there were no significant differences between the observed correlations of capitulum seed mass and altitude in each region. Power was taken to be 0.8 with α = 0.05. Values of n > 100 indicate that correlation coefficients were very similar between regions.
C. arvanse 
C. vulgare 
C. intybus 
L. serriola 
C. canadensis 
E. annuus 
M. discoidea 
Solidago 

Source 
df 
F 
df 
F 
df 
F 
df 
F 
df 
F 
df 
F 
df 
F 
df 
F 

Stem height 

Region (R) 
15 
11.56** 
20 
0.24 
15 
0.09 
16 
3.36 
17 
0.45 
18 
6.32* 
18 
2.76 
17 
79.85*** 

Altitude (A) 
15 
0.68 
20 
16.64*** 
15 
0.33 
16 
25.23*** 
17 
7.88* 
18 
0.005 
18 
0.003 
17 
39.81*** 

A × R 
15 
35.93*** 
20 
0.006 
15 
0.09 
16 
9.34** 
17 
6.81* 
18 
3.55 
18 
0.13 
17 
4.20 

Capitulum seed mass 

Region (R) 
13 
3.54 
18 
0.10 
14 
6.70* 
16 
3.72 
17 
1.41 
7 
8.30* 
17 
4.10 
11 
2.68 

Altitude (A) 
13 
0.08 
18 
0.47 
14 
0.38 
16 
0.68 
17 
0.19 
7 
7.80* 
17 
16.12*** 
11 
0.37 

A × R 
13 
1.24 
18 
<0.001 
14 
0.25 
16 
0.06 
17 
0.04 
7 
1.53 
17 
0.09 
11 
1.16 

n 
26 
>100 
>100 
41 
73 
44 
>100 
29 

*P < 0.05; **P < 0.01; ***P < 0.001.