M_stat: Calculate M statistic

Description

M_stat calculates the value of M statistic as a measurement of the strength of the phylogenetic signal for the trait(s). The trait(s) could be continuous, discrete, or multi-variable. Blomberg and Garland (2002) provided a widely accepted statistical definition of the phylogenetic signal, which is the "tendency for related species to resemble each other more than they resemble species drawn at random from the tree". The M statistic strictly adheres to the definition of phylogenetic signal, formulating an index and developing a method of testing in strict accordance with the definition, instead of relying on correlation analysis or evolutionary models. The novel method equivalently expressed the textual definition of the phylogenetic signal as an inequality equation of the phylogenetic and trait distances and constructed the M statistic. The M statistic implemented in this package is based on the methodology described in Yao and Yuan (2025) doi:10.1002/ece3.71106. If you use this method in your research, please cite the paper.

Usage

M_stat(trait_dist = NULL, phy = NULL, auto_multi2di = TRUE)

Value

A value that lies between 0 and 1, inclusive.

Arguments

trait_dist: A distance object of class matrix or dist. Its row and column names should match the tip labels of the phylogenetic tree (phy). The functions gower_dist() and cluster::daisy() can be used to calculate distances using trait data.
phy: A phylogenetic tree of class phylo.
auto_multi2di: A logical switch, TRUE or FALSE. Default is TRUE, then function ape::multi2di() in ape package will be called to make the phylogeney (tree) be dichotomous if the tree (phy) contains some polytomies.

References

Blomberg, S.P. & Garland, T., Jr (2002) Tempo and mode in evolution: phylogenetic inertia, adaptation and comparative methods. Journal of Evolutionary Biology, 15(6): 899-910.

Yao, L. and Yuan, Y. (2025), A Unified Method for Detecting Phylogenetic Signals in Continuous, Discrete, and Multiple Trait Combinations. Ecology and Evolution, 15: e71106.

Examples

Run this code

data("turtles")
# Continuous trait
trait_df <- data.frame(M1 = turtles$traits$M1, row.names = turtles$traits$specie)
trait_dist <- gower_dist(x = trait_df)
M_stat(trait_dist, turtles$phylo)

# Nominal discrete trait
trait_df <- data.frame(B1 = turtles$traits$B1, row.names = turtles$traits$specie)
trait_dist <- gower_dist(x = trait_df, type = list(factor = 1))
M_stat(trait_dist, turtles$phylo)

# Ordinal discrete trait
trait_df <- data.frame(CS1 = turtles$traits$CS1, row.names = turtles$traits$specie)
trait_dist <- gower_dist(x = trait_df, type = list(ordered = 1))
M_stat(trait_dist, turtles$phylo)

# Multi-trait Combinations
trait_df <- data.frame(turtles$traits[, c("M1", "M2", "M3", "M4", "M5")],
                       row.names = turtles$traits$specie)
trait_dist <- gower_dist(x = trait_df, type = list(factor = c("M4", "M5")))
M_stat(trait_dist, turtles$phylo)