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the evolving trait on one end and the optimum trait value on the other end. A weak
rubber band will provide enough slack for the trait to wiggle around the optimum
(Fig. 7.2b), whereas a strong rubber band will keep the evolving trait close to the
optimum (Fig. 7.2c). The strength of the rubber band also affects how quickly the
trait is pulled toward its optimum (Fig. 7.2b,c). The time a trait is expected to take
to get halfway to the optimum is called the phylogenetic half-life, and this is an
alternative way to think about the strength of the evolutionary pull.
Variation in traits within species, populations, and even individuals may result
from responses to environmental conditions or have a genetic basis. Until recently,
phylogenetic comparative methods largely ignored intraspecific variation and used
species means instead. Ives et al. (2007) and Felsenstein (2008) devised methods
to account for within species variation, which typically enters the model as the standard errors about the mean trait value of each species.
7.3.2 Phylogenetic Signal
Phylogenetic signal can be thought as the degree to which closely related species
resemble each other. Two different metrics have been widely used to assess phylogenetic signal: Pagel’s lambda (Pagel 1999) and Blomberg’s K (Blomberg
et al. 2003).
7.3.2.1 Pagel’s Lambda
Pagel’s lambda is a scalar for the correlation between the phylogenetic similarity
matrix and the trait matrix. It has the effect of shrinking the internal branches (as
opposed to the branches that lead to the tips) of a phylogeny, thereby reducing the
expected species correlation due to shared evolutionary history (Fig. 7.3a–d). A
lambda value of 0 indicates that trait correlations between species are independent
from evolutionary history (Fig. 7.3d), whereas a lambda of 1 suggests that trait correlations are equal to the species correlation imposed by their shared evolutionary
history (Fig. 7.3a), assuming a Brownian motion model of evolution.
7.3.2.2 Blomberg’s K
Blomberg’s K measures the degree to which trait variance lies within clades versus
among clades. Brownian motion is used as an expectation. K values greater than 1
indicate that there is more variance among clades than expected by Brownian
motion (Fig. 7.3e), while K values smaller than 1 imply that more variance is found
within clades than expected under a Brownian motion model (Fig. 7.3f).
It is important to note that both Pagel’s lambda and Blomberg’s K are treewide
metrics, meaning that they do not explicitly account for the heterogeneity in trait
values among lineages. For example, an estimate of low phylogenetic signal in fruit
J. E. Meireles et al.
the evolving trait on one end and the optimum trait value on the other end. A weak
rubber band will provide enough slack for the trait to wiggle around the optimum
(Fig. 7.2b), whereas a strong rubber band will keep the evolving trait close to the
optimum (Fig. 7.2c). The strength of the rubber band also affects how quickly the
trait is pulled toward its optimum (Fig. 7.2b,c). The time a trait is expected to take
to get halfway to the optimum is called the phylogenetic half-life, and this is an
alternative way to think about the strength of the evolutionary pull.
Variation in traits within species, populations, and even individuals may result
from responses to environmental conditions or have a genetic basis. Until recently,
phylogenetic comparative methods largely ignored intraspecific variation and used
species means instead. Ives et al. (2007) and Felsenstein (2008) devised methods
to account for within species variation, which typically enters the model as the standard errors about the mean trait value of each species.
7.3.2 Phylogenetic Signal
Phylogenetic signal can be thought as the degree to which closely related species
resemble each other. Two different metrics have been widely used to assess phylogenetic signal: Pagel’s lambda (Pagel 1999) and Blomberg’s K (Blomberg
et al. 2003).
7.3.2.1 Pagel’s Lambda
Pagel’s lambda is a scalar for the correlation between the phylogenetic similarity
matrix and the trait matrix. It has the effect of shrinking the internal branches (as
opposed to the branches that lead to the tips) of a phylogeny, thereby reducing the
expected species correlation due to shared evolutionary history (Fig. 7.3a–d). A
lambda value of 0 indicates that trait correlations between species are independent
from evolutionary history (Fig. 7.3d), whereas a lambda of 1 suggests that trait correlations are equal to the species correlation imposed by their shared evolutionary
history (Fig. 7.3a), assuming a Brownian motion model of evolution.
7.3.2.2 Blomberg’s K
Blomberg’s K measures the degree to which trait variance lies within clades versus
among clades. Brownian motion is used as an expectation. K values greater than 1
indicate that there is more variance among clades than expected by Brownian
motion (Fig. 7.3e), while K values smaller than 1 imply that more variance is found
within clades than expected under a Brownian motion model (Fig. 7.3f).
It is important to note that both Pagel’s lambda and Blomberg’s K are treewide
metrics, meaning that they do not explicitly account for the heterogeneity in trait
values among lineages. For example, an estimate of low phylogenetic signal in fruit
J. E. Meireles et al.