Statistical Models of Chromosome Evolution

Abstract

Populations of biological organisms change with time and we can study how their genetic material is reassorted at meiosis and transmitted from one generation to the next [1]. Over longer time spans we cannot usually observe the changes in the genetic material directly but we can study the genetic properties of extant populations which we assume to have diverged from each other [2]. DNA sequencing is a direct way of characterising the genetic constitution of an individual and DNA can be recovered from bones dated by stratification in archaeological sites. Studies of fossil DNA, for example from Miocene leaves, have been reported. For the majority of extant species we are unlikely to be able to study the DNA of their antecedents. The comparative method in biology has been pursued for several hundred years on morphological criteria and for several decades on molecular criteria. The ideas of Darwinian evolution came out of a consideration of a combination of animal and plant breeding, adaptation of organism to environment, and comparative studies both morphological and biogeographical. The aim of phylogenetic inference is narrower. It attempts to elucidate the order of descent of organisms from common ancestors, most commonly on a tree. A popular example is of the three primates man, chimp and gorilla. There are three possible ways these animals could be related on a tree: (man (chimp, gorilla)); ((man, chimp) gorilla) and ((man, gorilla) chimp). Different datasets and different methods of analysis indicate different answers to the problem (a present consensus of these suggests the relationship is the second listed). If phylogenetic analysis is to be more than idle speculation then a statistical foundation to the subject is needed with explicit assumptions and testable hypotheses. Most progress has been made in this with regard to DNA sequences but other sorts of information are amenable to similar treatment. In fact the work we are doing concerns chromosomes and the orders of genes along them, but it is helpful to review other work first.