evolvabilityMeans {evolvability}

Calculate average evolvability parameters of a G-matrix

Description

evolvabilityMeans calculates the average (unconditional) evolvability (e), respondability (r), conditional evolvability (c), autonomy (a) and integration (i) of a additive-genetic variance matrix using the approximation formulas described in Hansen and Houle (2008, 2009).

Usage

evolvabilityMeans(G, means = 1)

Arguments

G

A variance matrix (must be symmetric and positive definite).

means

An optional vector of trait means, for mean standardization.

Details

The equations for calculating the evolvability parameters are approximations, except for the minimum, maximum and unconditional evolvability which are exact. The bias of the approximations depends on the dimensionality of the G-matrix, with higher bias for few dimensions (see Hansen and Houle 2008). For low dimensional G-matrices, we recommend estimating the averages of the evolvability parameters using evolavbilityBetaMCMC over many random selection gradients ( randomBeta). The maximum and minimum evolvability, which are also the maximum and minimum respondability and conditional evolvability, equals the largest and smallest eigenvalue of the G-matrix, respectively.

Value

A vector with the following components:

e_mean				The average (unconditional) evolvability.
e_min				The minimum evolvability.
e_max				The maximum evolvability.
r_mean				The average respondability.
c_mean				The average conditional evolvability.
a_mean				The average autonomy.
i_mean				The average integration.

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.
Hansen, T. F. & Houle, D. (2009) Corrigendum. J. Evol. Biol. 22:913-915.

Examples

G <- matrix(c(1, 1, 0, 1, 2, 1, 0, 1, 2), ncol = 3)
evolvabilityMeans(G)