6 Phylogenetic Independent Contrasts

Let’s make a digression to look at Phylogenetic Independent Contrasts (PIC). PIC were the first comparative approach proposed to deal with phylogenetic non independence (Felsenstein 1985). Although they are less flexible than PGLS, they give the same results. Let’s see how they can be used.

Phylogenetic independent contrast are estimated one trait at a time. They essentially transform the observed trait in contrasts that are not correlated with the phylogeny. This can be done in R using the pic function of the ape package.

# Estimate PIC for shade tolerance 
Shade.pic <- pic(seedplantsdata$Shade, phy=seedplantstree)
# Estimate PIC for Wood density 
Wd.pic <- pic(seedplantsdata$Wd, phy=seedplantstree)

Once this is done, the only thing to do is to fit a regression between these contrast. Note that it is important that the intercept is fixed to 0 in the model. This is done by adding - 1 to the right of the formula.

# Estimate PIC for shade tolerance
pic.results <- lm(Shade.pic ~ Wd.pic - 1)
summary(pic.results)

## 
## Call:
## lm(formula = Shade.pic ~ Wd.pic - 1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -71.943  -4.106   1.013   5.679  21.614 
## 
## Coefficients:
##        Estimate Std. Error t value Pr(>|t|)  
## Wd.pic    4.361      1.693   2.575   0.0127 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 19.21 on 55 degrees of freedom
## Multiple R-squared:  0.1076, Adjusted R-squared:  0.09139 
## F-statistic: 6.633 on 1 and 55 DF,  p-value: 0.01273

You can see that the slope estimate, 4.361, it identical to the slope estimate obtained with PGLS. Same thing for the p-value. The main retriction with PIC is that you are limited in always comparing two variables. Much more flexibility is possible with PGLS.

References

Felsenstein, Joseph. 1985. “Phylogenies and the Comparative Method.” The American Naturalist 125 (1): 1–15.