Mathematical Model of Artificial Selection in Favour of Homozygote Dominant Gene in Inbreeding

Abstract

 The concept of inbreeding in human beings and its effect have been discussed in this research. Inbred unions are characterized by greater fertility, although they also result in higher levels of post-natal morbidity and mortality due to the expression of detrimental recessive genes inherited from a common ancestor(s). Artificial selection of the parents was used to determine the frequencies of the offspring and a five state Markov Chain model was used to determine the pattern of gene distribution. The paper is meant to reduce homozygote recessive gene which can be a carrier of any particular trait in a given population. The same model can also be applied to reduce homozygote dominant gene. The result from table 8 shows that, when genetic counseling is carried out with the various mating pattern as shown in the first column of table 5, the gene of the homozygote recessive will be eradicated within a given period of time from the population,  irrespective of the Initial Probability State Vector (IPSV). This selection model will not only reduce the gene of the homozygote recessive, but also that of the heterozygote as we can see from table 8.