On rare mutation, chaos and Darwin’s theory

According to the Holy Quran, the evolution of life is the result of divine will and divine guidance. One of the key elements of natural selection is that offspring sometimes vary from their parents. For instance, a yellow buttery may have a black offspring. This kind of variation and mutation, thoug...

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Main Authors:	Ganikhodjaev, Nasir, Saburov, Mansoor
Format:	Article
Language:	English
Published:	Revelation and Science, IIUM 2014
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/37168/ http://irep.iium.edu.my/37168/ http://irep.iium.edu.my/37168/1/Paper_Rev.4%281%292014.pdf

id	iium-37168
recordtype	eprints
spelling	iium-371682018-06-12T07:55:19Z http://irep.iium.edu.my/37168/ On rare mutation, chaos and Darwin’s theory Ganikhodjaev, Nasir Saburov, Mansoor QA Mathematics According to the Holy Quran, the evolution of life is the result of divine will and divine guidance. One of the key elements of natural selection is that offspring sometimes vary from their parents. For instance, a yellow buttery may have a black offspring. This kind of variation and mutation, though rare, tends to occur in all species. Over a long period of time, the cumulative effect of such mutations leads to an entirely new specie. Evolution describes the change in genetic material of a population of organisms through successive generations. In this paper we consider the evolution operator, namely quadratic stochastic operators, that naturally occurs to describe the transmission of a trait from parents to their offspring. This operator describes evolutionary dynamics of the considered population. The long run behavior of evolution operator plays an important role in many applied problems. We consider Mendelian inheritance for a single gene with three alleles and assuming that prior to the formation of the new generation each gene has the possibility to mutate, that is, to change into a gene of the other kind, and show that the rare mutation can transform regular dynamical system into chaotic one. As corollary we have that evolutionary operator with rare mutation of alleles contradict to Darwin’s evolution theory on genetic level. Revelation and Science, IIUM 2014-06 Article PeerReviewed application/pdf en http://irep.iium.edu.my/37168/1/Paper_Rev.4%281%292014.pdf Ganikhodjaev, Nasir and Saburov, Mansoor (2014) On rare mutation, chaos and Darwin’s theory. Revelation and Science, 4 (1). pp. 37-44. ISSN 2229-9947 http://journals.iium.edu.my/revival/index.php/revival/rt/printerFriendly/111/0
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Ganikhodjaev, Nasir Saburov, Mansoor On rare mutation, chaos and Darwin’s theory
description	According to the Holy Quran, the evolution of life is the result of divine will and divine guidance. One of the key elements of natural selection is that offspring sometimes vary from their parents. For instance, a yellow buttery may have a black offspring. This kind of variation and mutation, though rare, tends to occur in all species. Over a long period of time, the cumulative effect of such mutations leads to an entirely new specie. Evolution describes the change in genetic material of a population of organisms through successive generations. In this paper we consider the evolution operator, namely quadratic stochastic operators, that naturally occurs to describe the transmission of a trait from parents to their offspring. This operator describes evolutionary dynamics of the considered population. The long run behavior of evolution operator plays an important role in many applied problems. We consider Mendelian inheritance for a single gene with three alleles and assuming that prior to the formation of the new generation each gene has the possibility to mutate, that is, to change into a gene of the other kind, and show that the rare mutation can transform regular dynamical system into chaotic one. As corollary we have that evolutionary operator with rare mutation of alleles contradict to Darwin’s evolution theory on genetic level.
format	Article
author	Ganikhodjaev, Nasir Saburov, Mansoor
author_facet	Ganikhodjaev, Nasir Saburov, Mansoor
author_sort	Ganikhodjaev, Nasir
title	On rare mutation, chaos and Darwin’s theory
title_short	On rare mutation, chaos and Darwin’s theory
title_full	On rare mutation, chaos and Darwin’s theory
title_fullStr	On rare mutation, chaos and Darwin’s theory
title_full_unstemmed	On rare mutation, chaos and Darwin’s theory
title_sort	on rare mutation, chaos and darwin’s theory
publisher	Revelation and Science, IIUM
publishDate	2014
url	http://irep.iium.edu.my/37168/ http://irep.iium.edu.my/37168/ http://irep.iium.edu.my/37168/1/Paper_Rev.4%281%292014.pdf
first_indexed	2023-09-18T20:53:19Z
last_indexed	2023-09-18T20:53:19Z
_version_	1777410139637153792

On rare mutation, chaos and Darwin’s theory

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