evolvabilityBetaMCMC {evolvability}

Calculate posterior distribution of evolvability parameters from a set of selection gradients

Description

evolvabilityBetaMCMC calculates (unconditional) evolvability (e), respondability (r), conditional evolvability (c), autonomy (a) and integration (i) from selection gradients given the posterior distribution of an additive-genetic variance matrix. These measures and their meanings are described in Hansen and Houle (2008).

Usage

evolvabilityBetaMCMC(G_mcmc, Beta, post.dist = FALSE)

Arguments

G_mcmc

posterior distribution of a variance matrix in the form of a table. Each row in the table must be one iteration of the posterior distribution (or bootstrap distribution). Each iteration of the matrix must be on the form as given by c(x), where x is a matrix. A posterior distribution of a matrix in the slot VCV of a object of class MCMCglmm is by default on this form.

Beta

either a vector or a matrix of unit length selection gradients stacked column wise.

post.dist

logical: should the posterior distribution of the evolvability parameters be saved.

Value

An object of class 'evolvabilityBetaMCMC', which is a list with the following components:

eB				The posterior median and highest posterior density interval of evolvability for each selection gradient.
rB				The posterior median and highest posterior density interval of respondability for each selection gradient.
cB				The posterior median and highest posterior density interval of conditional evolvability for each selection gradient.
aB				The posterior median and highest posterior density interval of autonomy for each selection gradient.
iB				The posterior median and highest posterior density interval of integration for each selection gradient.
Beta				The matrix of selection gradients.
summary				The means of evolvability parameters across all selection gradients.
post.dist				The full posterior distribution.

Author(s)

Geir H. Bolstad

References

Hansen, T. F. & Houle, D. (2008) Measuring and comparing evolvability and constraint in multivariate characters. J. Evol. Biol. 21:1201-1219.

Examples

# Simulating a posterior distribution
# (or bootstrap distribution) of a G-matrix:
G <- matrix(c(1, 1, 0, 1, 4, 1, 0, 1, 2), ncol = 3)
G_mcmc <- sapply(c(G), function(x) rnorm(10, x, 0.01))
G_mcmc <- t(apply(G_mcmc, 1, function(x) {
  G <- matrix(x, ncol = sqrt(length(x)))
  G[lower.tri(G)] <- t(G)[lower.tri(G)]
  c(G)
}))

# Simulating a posterior distribution
# (or bootstrap distribution) of trait means:
means <- c(1, 1.4, 2.1)
means_mcmc <- sapply(means, function(x) rnorm(10, x, 0.01))

# Mean standardizing the G-matrix:
G_mcmc <- meanStdGMCMC(G_mcmc, means_mcmc)

# Generating selection gradients in five random directions:
Beta <- randomBeta(5, 3)

# Calculating evolvability parameters:
x <- evolvabilityBetaMCMC(G_mcmc, Beta, post.dist = TRUE)
summary(x)