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Comment
. 2016 Jan;202(1):9-13.
doi: 10.1534/genetics.115.181057.

Admixture Models and the Breeding Systems of H. S. Jennings: A GENETICS Connection

Noah A Rosenberg  1
Affiliations
Comment

Admixture Models and the Breeding Systems of H. S. Jennings: A GENETICS Connection

Noah A Rosenberg. Genetics. 2016 Jan.
No abstract available

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Figures

Figure 1
Figure 1
The table of number sequences from Jennings (1916). Row F contains the Fibonacci numbers, and row G, the Jacobsthal numbers.
Figure 2
Figure 2
Admixture proportions and allele frequencies for females and males in an X-chromosomal model. The values plotted can be interpreted equivalently as (1) the X-chromosomal proportions of admixture from source population 1 in a random female and a random male in the nth generation, in an admixture model in which the mothers of the offspring individuals present in generation 1 all enter from source population 1 and the fathers all enter from source population 2 (Goldberg and Rosenberg 2015); (2) in generation n, the frequencies in females and males of an X-chromosomal allele A after a cross of an AA female and an aY male, followed by n − 1 generations of random mating (Jennings 1916); and (3) in generation n, the frequencies in females and males of an X-chromosomal allele A after the nth generation of random mating, starting in generation 0 from a population of AA females and aY males (Jennings 1916). The value for females is given by Equation 3 and the value for males by Equation 4. Noting that the closed-form expression for the Jacobsthal numbers is Jn = [2n − (−1)n]/3, it follows that at generation n, both quantities plotted are constrained by a lower bound (2n − 1)/(3 × 2n−1) and an upper bound (2n + 1)/(3 × 2n−1).
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References

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