Multivariate Aspects of Phylogenetic Comparative Methods
his thesis concerns multivariate phylogenetic comparative methods.
We investigate two aspects of them. The first is the bias caused by measurement error in regression studies of comparative data. We calculate the formula for the bias and show how to correct for it. We also study whether it is always advantageous to correct for the bias as correction can increase
the mean square error of the estimate. We propose a criterion,
which depends on the observed data, that indicates whether it is beneficial to correct or not. Accompanying the results is an R program that offers the bias correction tool.
The second topic is a multivariate model for trait evolution which is based on an Ornstein-Uhlenbeck type stochastic process, often used for studying trait adaptation, co--evolution, allometry or trade--offs. Alongside the description of the model and presentation of its most important features we present an R program estimating the model's parameters. To the best of our knowledge our program is the first program that allows for nearly all combinations of key model parameters providing the biologist with a flexible tool for studying
multiple interacting traits in the Ornstein-Uhlenbeck framework.
There are numerous packages
available that include the Ornstein-Uhlenbeck process but their multivariate capabilities seem limited.
Multivariate phylogenetic comparative method
General Linear Model
Reduced major-axis regression