lnL.M {lmf}

Maximum likelihood function for temporal coefficients of selection

Description

lnL.M calculates the loglikelihood of the maximum likelihood function for temporal coefficients of selection from Engen et al. 2012. Returns the estimate of alpha for a given temporal variance-covariance matrix (M) if desired.

Usage

lnL.M(D, At, at, npar, ret.alphas = FALSE)

Arguments

D

a vector with the non-zero elements of the upper triangular matrix of the Cholesky decomposition of a temporal variance-covariance matrix M.

At

a list containing the named yearly variance-covariance matrices. Sorted by year.

at

a list containing the named yearly vectors of the estimated selection coefficients. Sorted by year.

npar

the number of parameters in the model for the estimates selection coefficients.

ret.alphas

logical. If TRUE the function returns the vector with the estimates of the temporal mean selection coefficients (alpha) for the given temporal variance-covariance matrix M. FALSE (default) makes the function return the loglikelihood for the given M.

Details

The function was developed for internal use in fs, but can be applied as a standalone.

The upper triangular matrix (D) of the Cholesky decomposition of M is defined as M = t(D)%*%D.

Details of the method is provided in Engen et al. 2012.

Value

lnL.M returns the loglikelihood estimate (for ret.alpha = FALSE) or the temporal mean selection coefficients (for ret.alpha = TRUE) for a given temporal variance-covariance matrix M.

Author(s)

Thomas Kvalnes

References

Engen, S., Saether, B.-E., Kvalnes, T. and Jensen, H. 2012. Estimating fluctuating selection in age-structured populations. Journal of Evolutionary Biology, 25, 1487-1499.

See Also

lmf, fs, chol

Examples

#Data set from Engen et al. 2012
data(sparrowdata)
#Fit model
lmf.1 <- lmf(formula = cbind(recruits, survival) ~ weight + tars,
               age = age, year = year, data = sparrowdata)
#Extract At and at
At <- lmf.1$At
at <- lmf.1$at
#Estimate D
D <- as.vector(chol((Reduce('+', At) / length(At))))
D <- D[D != 0]
#Estimate loglikelihood
lnL.M(D = D, At = At, at = at, npar = 3, ret.alphas = FALSE)
#Estimate temporal mean selection coefficients
lnL.M(D = D, At = At, at = at, npar = 3, ret.alphas = TRUE)