טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentLevy Orr
SubjectAnalysis and Characterization of the Effects of Matching
Patterns on Models of Branching Processes:
Genetical Implications
DepartmentDepartment of Biomedical Engineering
Supervisor Professor Emeritus Isak Gath
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

The well known Galton-Watson process [1, 2] investigates the extinction of surnames which propagate from father to son. A less known propagation process from ancestor to descendants described by Zakai-Fischer is different from Galton-Watson by being dependant on both parents, and in which either the father or the mother is "tagged" as an ancestor.

The tag is propagating from the father or the mother to the offspring among the generations while the ratio between the tagged offspring to the population  is changing among generations.

In the present work we study the distribution of descendants of a known ancestor, as it propagates along generations from father or mother through any of their children where matching process is not random.

For example Endogamy is a matching pattern in which a male or a female from a certain group in a population would prefer to choose their mate within the same group rather than from the rest of the population.

A Founder mutation is a gene mutation observed with high frequency in a group that is or was geographically or culturally isolated, in which one or more of the ancestors was a carrier of the mutant gene. Among Ashkenazi Jews a number of Founder mutations lead to a high risk of cancer.

In order to examine the problem, we studied first the affect of Endogamy pattern on the propagation of a simple "tag" regardless of Biology.

The tag propagation was analyzed using simulation and has been studied numerically and analytically. The exact equation was analytically obtained and examined.

In the second part of the research we combined the biology with branching processes by changing the model and we studied how matching patterns affect the spread of the mutation.
The mutation spread was examined using a simulation model and has been studied only numerically. The results were compared to the data from an existing population in which similar matching patterns occurred.

The results showed deviation from the Hardy - Weinberg model.
For comparison with real data, we took a village with genealogical data with several common mutations that were investigated. Simulation of the population of the village and its surrounding was carried out in order to predict the number of carriers and sick people in the village under conditions of different matching patterns.

In conclusion, the study showed that matching patterns has a clear effect on the tagging process and Mutation spread among the generations.