This appendix deals with testing stem flexibility between wand and non-wand plant species in a phylogenetic indepedent contrast framework. Flexibility can be measured using strain and stress, and here we use Young’s Modulus (E; also referred to as the elastic modulus) as a measure for flexibility.

Modulus of elasticity represents a material’s resistance to being deformed, so low values mean low resistance and high values mean high resistance. In other words:

Datasets

A sample of 10 records from the WandStemFlexibilityDatabase
Spp PAIR Wand Lmm D a_mm F V EI I E Force logE logD
EURLAT EUR TRUE 100 10 50 1.5490 8.35 3864.770 490.873438 7.873252 2473.4531 2.0634712 2.302585
SYNSOR SYN FALSE 100 5 50 1.4908 15.73 1974.465 30.679590 64.357605 5054.6302 4.1644551 1.609438
HERSAL_KAB HER TRUE 100 8 50 1.5118 15.80 1993.407 201.061760 9.914402 1993.4072 2.2939885 2.079442
STRSP. STR TRUE 100 4 50 1.9652 25.61 1598.659 12.566360 127.217379 6394.6375 4.8458973 1.386294
OSTPOL OST TRUE 100 7 50 1.4982 12.62 2473.257 117.858712 20.984929 3230.3761 3.0438045 1.945910
STRSP. STR TRUE 100 3 50 2.4500 24.70 2066.464 3.976075 519.724683 14694.8568 6.2532992 1.098612
OSYCOM OSY FALSE 100 5 50 0.9852 11.87 1729.149 30.679590 56.361546 4426.6217 4.0317871 1.609438
OSYCOM OSY FALSE 100 7 50 0.9995 11.58 1798.179 117.858712 15.257076 2348.6424 2.7250434 1.945910
SYNSOR SYN FALSE 100 3 50 2.0728 19.81 2179.875 3.976075 548.248101 15501.3368 6.3067279 1.098612
ASPTER ASP TRUE 100 12 50 0.9675 11.28 1786.902 1017.875160 1.755521 794.1785 0.5627659 2.484907

Linear models of logD vs logE

Below are the linear models of (log) diameter (in mm) versus the (log) Young’s Modulus measure of flexibility.

Comparing linear models using an Analysis of Covariance

Here we compare the linear models of logD vs logE for each species. Species are the categorical variable, and logD is the continuous independent variable. An ANCOVA is able to test for differences in slopes and intercepts among regression lines.

summary(aov(logE~logD*Spp, data=dat))
##              Df Sum Sq Mean Sq   F value   Pr(>F)    
## logD          1 2045.5  2045.5 64862.152  < 2e-16 ***
## Spp          26    4.1     0.2     4.948 7.16e-14 ***
## logD:Spp     26    3.1     0.1     3.729 2.87e-09 ***
## Residuals   617   19.5     0.0                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

What we find is that there is a signicant interaction between logD and species. This means that the linear models (regression lines) have significantly different slopes across species (Fuchs 2011). Thus, the intercepts cannot be used as a unitless measure of flexibility across all diameters.

Comparing flexibility between wand and non-wand congeners

As it is not possible to use the intercept-values as an integrated unit for comparison, another approach is to do the phylogenetic independent contrast pairwise comparisons for a given diameter; and to do multiple such analyses across a range of diameter values.

The allometric relationship between logD and logE is highly significant and tightly linked (r^2 > 0.98). Thus, we can use the linear models to predict logE for any diameter and we used these predictions (along with the 0.95 confidence interval) for comparisons.

There is variation in the level of phylogenetic relatedness between wand and non-wand congeners; some combinations are between species within the same genus, while others are within the same family. Some species, we simply could not find a congener within the same family, e.g. Anginon difforme (Apiaceae — a family predominantly composed of herbs).

MAIN RESULTS

Very low levels of significantly lower wand plant flexibility for a given diameter

Analysis Diameter tt_p.less.05 wt_p.less.05
1 3 64.5 38.8
1 5 10.9 4.2
1 7 0.2 4.4
1 9 0.0 16.7
1 11 0.0 25.9
2 3 39.4 17.6
2 5 4.5 0.6
2 7 0.0 4.7
2 9 0.0 16.4
2 11 0.0 23.7
3 3 31.6 11.9
3 5 1.7 0.7
3 7 0.0 13.7
3 9 0.0 31.2
3 11 0.0 33.0