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Modelling loss of allelic diversity (Monte Carlo method)

If we consider two parent organisms P1 and P2, with alleles (at a given locus L) (A1,A2) and (A3,A4) respectively.

Through the processes of meiotic division and fertilization, each parent passes one allele to each child. Mendel's first law of genetics (the law of segregation) observes that the children of these parents will consist of equal numbers of four genotypes:

(A1,A3), (A1,A4), (A2,A3), (A2,A4)

If organisms with each of these genotypes survive to breed then the four alleles (A1, A2, A3, A4) will be maintained within the population. However, if not all genotypes survive, there may be loss of allelic diversity.

Example: two children survive each round, with no selection effects, and no mutation. (This can be studied with pen, paper, and a random number generator)

Starting with the two parents:

Generation 01: (A1,A2), (A3,A4)
Possible children: (A1,A3), (A1,A4), (A2,A3), (A2,A4)
Surviving children: (A2,A4), (A2,A3)

Generation 02: (A2,A4), (A2,A3)
Possible children: (A2,A2), (A2,A3), (A4,A2), (A4,A3)
Surviving children: (A4,A2), (A2,A3)

Generation 03: (A4,A2), (A2,A3)
Possible children: (A4,A2), (A4,A3), (A2,A2), (A2,A3)
Surviving children: (A4,A3), (A2,A3)

Generation 04: (A4,A3), (A2,A3)
Possible children: (A4,A2), (A4,A3), (A3,A2), (A3,A3)
Surviving children: (A3,A2), (A3,A2)

Generation 05: (A3,A2), (A3,A2)
Possible children: (A3,A3), (A3,A2), (A2,A3), (A2,A2)
Surviving children: (A2,A3), (A3,A2)

Generation 06: (A2,A3), (A3,A2)
Possible children: (A2,A3), (A2,A2), (A3,A3), (A3,A2)
Surviving children: (A2,A3), (A2,A2)

Generation 07: (A2,A3), (A2,A2)
Possible children: (A2,A2), (A2,A2), (A3,A2), (A3,A2)
Surviving children: (A3,A2), (A3,A2)

Generation 08: (A3,A2), (A3,A2)
Possible children: (A3,A3), (A3,A2), (A2,A3), (A2,A2)
Surviving children: (A3,A2), (A3,A2)

Generation 09: (A3,A2), (A3,A2)
Possible children: (A3,A3), (A3,A2), (A2,A3), (A2,A2)
Surviving children: (A2,A3), (A2,A3)

Generation 10: (A2,A3), (A2,A3)
Possible children: (A2,A2), (A2,A3), (A3,A2), (A3,A3)
Surviving children: (A3,A3), (A2,A3)

Generation 11: (A3,A3), (A2,A3)
Possible children: (A3,A2), (A3,A3), (A3,A2), (A3,A3)
Surviving children: (A3,A3), (A3,A2)

Generation 12: (A3,A3), (A3,A2)
Possible children: (A3,A3), (A3,A3), (A3,A2), (A3,A2)
Surviving children: (A3,A2), (A3,A3)

Generation 13: (A3,A2), (A3,A3)
Possible children: (A3,A3), (A3,A3), (A2,A3), (A2,A3)
Surviving children: (A3,A3), (A3,A3)

In this run, with 2 surviving organisms every generation, diversity was reduced from 4 alleles to 1 allele in 13 generations.

Diversity may be maintained longer if there are more surviving children.



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Created 21/7/99