Download Generalisation of the Hardy-Weinberg equation in the case of

University of Sri Jayewardenepura
Faculty of Graduate Studies
Department of Mathematics
Generalisation of the Hardy-Weinberg equation in the case of polygenic
inheritance in population genetics and an estimation of the number of
genes controlling human height
A Thesis
By
Valemurugan Balamurari
Submitted in partial fulfillment of the requirements for the
Postgraduate Diploma
III
Industrial Mathematics
I grant, the University of Sri Jayewardenepura, a nonexclusive right to use my work for the
university's own purposes and to make a single copy of the work available to the public on
a not- for-profit basis, if a copy is not available otherwise.
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Signature
Name
: V. Balamurari
Abstract
Most of the characteristics found in human beings are controlled by one or more genes.
There are certain characters of which we know the exact number of genes that are
involved. The variation shown by a character determined by a single gene is usually easily
distinguishable
as opposed to the variation shown by a character determined by two or
more genes. There is very little evidence of research done using statistical techniques to
determine the number of genes controlling human height. As such, the aim of my research
work is to obtain an approximate estimate of the number of genes involved.
The basic Hardy-Weinberg
equation can be used only when we wish to
calculate the allelic and genotypic frequencies for a character determined by a single gene
having two alleles. Therefore it becomes necessary to have a more general equation
relating allelic frequencies in order to perform calculations when we consider a polygenic
trait. A generalized
Hardy-Weinberg
equation for polygenic
,derived as part of my research work.
vi
inheritance
too has been
Contents
1.
2.
Declaration
v
Abstract
vi
Acknowledgements
vii
Introduction
1
1.1
Genetics
1.2
Hardy- Weinberg principle
1.3
Hardy- Weinberg equation
1.4
Applications of Hardy- Weinberg equation
1.5
Limitations of Hardy- Weinberg equation
1.6
Literature search
1.7
Objectives of the study
1.8
Limitations of the study
1.9
Organization of the report
Generalized H-W equation
2.1
H-W equation for a character determined by two genes
2.2
H-W equation for a character determined by n genes
11
Contents
3.
5.
14
Genes in human height
3.1
Background
3.2
Data collection
3.3
Chi-square test for goodness of fit
3.4
4.
IX
3.3.1
The reasons for the choice
3.3.2
Methodology
3.3.2.1
Assumptions with regard to the participating genes
3.3.2.2
Approach to the problem
A measure based on Kolmogorov-Smimov
3.4.1
The reasons for the choice
3.4.2
Approach to the problem
test for goodness of fit
20
Results
4.1
Results of Chi-square and Kolmogorov-Smimov
4.2
Discussion
tests
24
Conclusions
Glossary of terms
25
References
27
Appendices
28
A 1.
Programming code for the Chi-square test
A2.
Programming code for the Kolmogorov-Smimov
A3.
Data set ( heights of students)
28
test
33
39