Model Selection in Estimation of Fitness Landscapes

Abstract

A solution to the problem of estimating fitness landscapes was proposed by Lande and Arnold (1983). Another solution, which avoids problematic aspects of the Lande-Arnold methodology, was proposed by Shaw, Geyer, Wagenius, Hangelbroek, and Etterson (2008), who also provided an illustrative example involving real data. An earlier technical report (Geyer and Shaw, 2008) gave an example that was simpler in some ways (the data are simulated from the aster model so there are no issues making the data fit the model one has with real data) and much more complicated in others (each individual has five measured components of fitness over four time periods, 20 variables in all) and illustrates the full richness possible in aster analysis of fitness landscapes. The one issue that technical report did not deal with is model selection. When many phenotypic variables are measured, one often does not know which to put in the model. Lande and Arnold (1983) proposed using principal components regression as a method of dimension reduction, but this method is known to have no theoretical basis. Much of late 20th century and 21st century statistics is about model selection and model averaging, and we apply some of this methodology (which does have strong theoretical basis) to estimation of fitness landscapes using another simulated data set.

All analyses are done in R (R Development Core Team, 2008) using the aster contributed package described by Geyer, Wagenius and Shaw (2007) except for analyses in the style of Lande and Arnold (1983), which use ordinary least squares regression. Furthermore, all analyses are done using the Sweave function in R, so this entire technical report and all of the analyses reported in it are completely reproducible by anyone who has R with the aster package installed and the R noweb file specifying the document.

This revision corrects major errors in the frequentist model averaging calculations (Section 8) in the first version of the technical report.