Problems in Pedigrees and Phylogenies

Abstract

The footprint of genetic inheritance can be observed among both familial relationships between individuals and evolutionary relationships between species. The former can be depicted by a pedigree, whereas the latter can be depicted by a phylogeny. These two distinct objects can be viewed as analogous, in the sense that they both describe a correlation structure on the units of observation. We discuss statistical methods for various problems within both settings. We begin with heritability estimation using pedigree data, with an ordinal outcome trait. We discuss the use of the threshold model for heritability estimation, exploring the consequences of model misspecification and sample size requirements under this model. Next, we move to phylogenetic methods for the detection of recombination, or the exchange of genetic material between species. We propose a new recombination detection statistic, in which false positive detection due to convergent evolution can be avoided while detecting recombination. Finally, we conclude with an improvement to least squares phylogenetic inference, by considering a new loss function that does not use standard evolutionary distances. Instead, we use a distance measure that considers the sequence data simultaneously with substitution model parameters, the topology, and branch lengths of the phylogenetic tree.