IDENTIFICATION OF TRAIT MARKERS USING MARKOV CHAIN PROPERTIES
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Date
2021-03
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Journal ISSN
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Publisher
UNIVERSITY OF ILORIN
Abstract
Lineage is characterized by some traits whose genetic marker is passed from any of the parents' genes to their children. Some of these traits may be physical. For example, hair, eye and/or skin colours. Laboratory tests some of which are costly and non accessible have been used for screening such traits whereas a non-laboratory Markov chain methodology which is cheaper and faster was proposed as an alternative. The study aimed at establishing a non-laboratory procedure using Markov Chain to identify useful markers to link traits. The objectives were to: (i) identify traits, the state spaces and classify them using probability transition matrix; (ii) determine the properties of the state space for each trait; (iii) determine which of the traits are the markers; and (iv) demonstrate the use of the procedure using real life data.
The process of transmitting traits from one generation to another was conceptualized as a Markov Chain. Markov chain methodology was employed to examine presence or absence of a given trait in an individual. The corresponding transition probability Matrix was studied to identify properties of the state spaces. The nature of Markov chain was examined to establish ergodicity and obtain the mean recurrence time. A test of homogeneity of the Markov chain was developed when at least three successive time points existed. These properties were used to characterize traits of Albinism as a real life example.
The findings of the study were that:
i. Markov chain concepts and techniques were successfully applied to classify various states of the available traits;
ii. all transition probability matrices were found to be recurrent with different periodicity;
iii. a best marker was identified to have the shortest period when state spaces are recurrent; and
iv. in the case of real life data involving albinism, the colour of the eye was the best marker.
The study concluded that Markov Chain is a vital tool to identify appropriate trait markers as an alternative to laboratory test. The study recommended that where information is available a Markov chain can be used to identify trait markers.
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Keywords
TRAIT MARKERS, MARKOV CHAIN PROPERTIES