10 Phylogenetic Comparative Methods (PCM)
This is part of the UHH MSc Biology Course EvoSys 2023 (9/11)
Used to infer evolutionary process and history through comparing species character data in a phylogenetic context. Many standard statistical methods assume that data are independent, BUT, phylogenetic tree terminals cannot be treated as independent data.
Therefore Phylogenetic Independent Contrasts (PIC): a statistical transformation that creates independent data points from trees, can be used to test for evolutionary correlations between characters.
10.1 Models for Character Evolution
10.1.1 Continuous traits
10.1.1.1 Brownian Motion
“Evolution proceeds with random changes.”
- A “random walk” model of evolution of continuous characters, describes motion that results from a large number of weak, independent forces
- Genetic drift, random change, weak selection (especially given timeframe) \[ \sigma ^2=\frac{\Sigma S_i}{n-1} \]
- \(\sigma ^2\) is related to standarized contrasts from PIC, affects the range of the motion.
10.1.1.2 Brownian Motion with a Trend (Trend)
BM with a directional trend.
10.1.1.3 Ornstein-Uhlenbeck Process
“Evolution bounded around median value - equilibrium”
10.1.1.4 Early Burst (EB)
“Rate of evolution decreases through time.”
10.1.1.5 Late Burst (LB)
“Rate of evolution increases through time.”
10.1.2 Discrete traits
10.1.2.1 MK model
- Most widely used.
- Uses “Q” matrix of instantaneous transition rates between states:
- Equal rates (ER)
- Symmetric rates (SYM) - forward and reverse are equal
- All rates different (ARD)
10.2 A note on working with continuous characters
10.2.1 Log transformation
When working with continuous characters, we should always consider log-transforming our data before conducting analysis.
- Log-transformation result in a ratio scale between data points
- In biology, percentage change rather than absolute change is often what matters
- Log-transformation often result in distribution closer to normal