Formalisations of Evolutionary Biology 509dynamics explains this result. Since the factorsAandado not blend and they
segregate in the gametes and combine again in the zygote, the results are fully
explained. Crossing theAAplants withaaplants will yield onlyAaplants:
Sperm
A A
Ova a Aa Aa
a Aa AaBreeding onlyAaplants will yield the .25:.5:.25 ratios:Sperm
A a
Ova A AA Aa
a Aa aaTwo of four cells yieldAathat is .5 of the possible combinations. Each ofAA
andaa occupy only one cell in four, that is, .25 of the possible combinations.
In contemporary population genetics, Mendel’s factors are called alleles. The
location on the chromosome where a pair of alleles is located is called a locus.
Sometime the term gene is used as a synonym for allele but this usage is far too
loose. Subsequently, I will explore the confusion, complexity and controversy over
the definition of “gene.” Mendel’s dynamics assumed diallelic loci: two alleles per
locus. His dynamics are easily extended to cases where each locus has many alleles
any two of which could occupy the locus.
The basic features of Mendel’s dynamics were modified and extended early in the
20 thcentury. G. Udny Yule [1902] was among the first to explore the implications
of Mendel’s system for populations. In a verbal exchange between Yule and R.C.
Punnett in 1908, Yule asserted that a novel dominant allele arising among a 100%
recessive alleles would inexorably increase in frequency until it reach 50%. Punnett
believing Yule to be wrong but unable to provide a proof, took the problem to G.
H. Hardy. Hardy, a mathematician, quickly produced a proof by using variables
where Yule had used specific allelic frequencies. In effect, he developed a simple
mathematical model. He published his results in 1908. What emerged from the
proof was a principle that became central to population genetics, namely, after
the first generation, allelic frequencies would remain the same for all subsequent
generations; an equilibrium would be reached after just one generation. Also
in 1908, Wilhelm Weinberg published similar results and articulated the same
principle (the original paper is in German, and English translation is in Boyer
[1963]). Hence, the principle is known as the Hardy-Weinberg principle or the
Hardy-Weinberg equilibrium.^37 In parallel with these mathematical advances was
(^37) William Castle [1903] also generated the equilibrium principle using numerical analysis but