Probabilistic Methods for Bioinformatics

with an Introduction to Bayesian Networks

Richard E. Neapolitan

• Publisher: Morgan Kaufmann
• Year: 2009
• eBook ISBN: 9780080919362
• Topic: Biological Sciences
• Subtopic: Probability & Statistics
• Index: Biological Sciences

The Bayesian network is one of the most important architectures for representing and reasoning with multivariate probability distributions. When used in conjunction with specialized informatics, possibilities of real-world applications are achieved. Probabilistic Methods for BioInformatics explains the application of probability and statistics, in particular Bayesian networks, to genetics. This book provides background material on probability, statistics, and genetics, and then moves on to discuss Bayesian networks and applications to bioinformatics. Rather than getting bogged down in proofs and algorithms, probabilistic methods used for biological information and Bayesian networks are explained in an accessible way using applications and case studies. The many useful applications of Bayesian networks that have been developed in the past 10 years are discussed. Forming a review of all the significant work in the field that will arguably become the most prevalent method in biological data analysis. - Unique coverage of probabilistic reasoning methods applied to bioinformatics data--those methods that are likely to become the standard analysis tools for bioinformatics. - Shares insights about when and why probabilistic methods can and cannot be used effectively; - Complete review of Bayesian networks and probabilistic methods with a practical approach.

III

Bioinformatics Applications

Chapter 9 Nonmolecular Evolutionary Genetics

Evolution is the process of change in the genetic makeup of populations, Evolutionary genetics is the study of this change. In nonmolecular evolutionary genetics, we look only at the level of the allele and study how alleles might replace other alleles over time. In molecular evolutionary genetics, we investigate how nucleotide sequences change over time. In this chapter we discuss nonmolecular evolutionary genetics; in the next chapter we discuss molecular evolutionary genetics.

It is believed that the changes in genetic makeup are due to mutations. We discuss two possible means by which mutations can result in changes in alleles and allele relative frequencies in a population: namely natural selection and genetic drift. By allele relative frequency we mean the relative frequency of an allele in the population. For example, if in a diploid population a particular gene has two alleles A and a; if there are 100 individuals with genotype AA, 50 individuals with genotype Aa, and 150 individuals with genotype aa, the relative frequency of allele A is

Natural selection is the process by which organisms that have traits that better enable them to adapt to environmental pressures such as predators, changes in climate, or competition for food or mates will tend to survive and reproduce in greater numbers than other similar organisms, thereby increasing the existence of those favorable traits in future generations. So, natural selection can result in an increase in the relative frequencies of alleles that impart to the individual these favorable traits. The process of the change in allele relative frequencies due only to chance is called genetic drift.

Before discussing natural selection and genetic drift, in Section 9.1 we investigate ways in which allele relative frequencies might change if neither of them occurred. Section 9.2 presents allele relative frequency changes due to natural selection; Section 9.3 shows how genetic drift can account for changes in the relative frequencies of alleles. In Section 9.4 we present results obtained when we assume that natural selection and genetic drift are acting simultaneously. Finally, in Section 9.5 we discuss the rate of substitution, and we show that new alleles due to advantageous mutations become fixed in the population far more often than new alleles due to neutral mutations.

9.1 No Mutations, Selection, or Genetic Drift

Here we discuss allele relative frequencies if there were no mutations, no selection, and no genetic drift. First we discuss a population consisting of haploid organisms.

9.1.1 Haploid Population

Suppose we have a haploid population consisting of two strains, A and a, which produce asexually. By a strain we mean a set of organisms that have the same genotype. That is, they have the exact same genetic makeup. We assume that there are no mutations and no selection. So, the offspring are genetic duplicates of the parents. Furthermore, each member of each strain is expected to give rise to the same number of offspring. Finally, we assume that the population undergoes synchronous reproduction with nonoverlapping generations.

Define the following variables:

N_t: The total number of individuals in generation t

p_t: The relative frequency of strain A in generation t

q_t = 1 — p_t: The relative frequency of strain a in generation t

w: The expected value of the number of offspring for each individual in each strain

Then the expected value of the number of individuals in strain A in generation t + 1 is equal to (E denotes expected value)

Similarly, the expected value of the number of individuals in strain a in generation t + 1 is equal to

Owing to the law of large numbers, if we have an essentially infinite population, we can be almost certain that these expected values will be the actual values in generation t + 1. We will assume that they are. T...

Table of contents

• Cover
• Title Page
• Copyright
• Preface
• About the Author
• Table of Contents
• I: Background
• II: Bayesian Networks
• III: Bioinformatics Applications
• Bibliography
• Index
• Instructions for online access