evolvabilityBetaMCMC2 {evolvability}

Calculate posterior distribution of evolvability parameters from a selection gradient estimated with uncertainty

Description

evolvabilityBetaMCMC2 calculates (unconditional) evolvability (e), respondability (r), conditional evolvability (c), autonomy (a) and integration (i) along a selection gradient estimate with uncertainty.

Usage

evolvabilityBetaMCMC2(G_mcmc, Beta_mcmc, post.dist = FALSE)

Arguments

G_mcmc

A 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_mcmc

A posterior distribution of a unit length selection gradient where iterations are given row wise.

post.dist

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

Beta.median				posterior median and highest posterior density interval of the selection gradient.
summary				The posterior median and highest posterior density interval of evolvability parameters.
post.dist				The full posterior distributions of the evolvability parameters.

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)

  # Simulating a posterior distribution (or bootstrap distribution)
  # of a unit length selection gradient:
  Beta <- randomBeta(1, 3)
  Beta.mcmc <- sapply(c(Beta), function(x) rnorm(10, x, 0.01))
  Beta.mcmc <- t(apply(Beta.mcmc, 1, function(x) x / sqrt(sum(x^2))))

  # Running the model:
  evolvabilityBetaMCMC2(G_mcmc, Beta_mcmc = Beta.mcmc, post.dist = TRUE)
}