The Hardy-Weinberg law is a direct extension of how genes are passed down from parents to offspring on an individual basis to the same process for a whole population. Because of this, we will again use a
Punnett square. Recall that in setting up the Punnett square, we put the genotype of the gametes from one parent on top and the other parent on one side. Then, we carry down the gene from one parent and carry across the gene from the other parent to determine the genotypes and their proportions in the next generation. When we want to extend this Punnett square analysis to a whole population, we must include the genes from all parents in this population. When we include all, rather than individual, parents, the proportions of different genes present in the population are represented.
Let's take a hypothetical example of a field of flowers. Let's say we planted a field of pink four-o'clock flowers. Recall from chapter 2 that four-o'clock flower color is a case of incomplete dominance in which heterozygotes Rr are pink, homozygotes RR are red, and homozygotes rr are white. So, if the whole field has pink flowers we know that all the plants have the genotype Rr. If these flowers were to pollinate each other, we can predict what the proportions of resulting offspring will be. Remember that Rr parents will all generate equal numbers of Rand r-carrying gametes. This can be represented in a Punnett square as 50 percent, or 0.5 R and 0.5 r, for all parents (figure 10.2). Then, we multiply the numbers for each of the genotypes to get 0.25, or 25 percent, for each of the four categories of offspring. The interpretation of this Punnett square is that in the next generation in that field, there will be approximately 25 percent RR, or red, 50 percent Rr, or pink, and 25 percent rr, or white flowers. This result would be expected if each flower had equal chances of pollinating and being pollinated, each resulting fertilized flower set its seeds, and all the seeds grew into new plants.
Suppose now we come back the following year to look at this field of flowers that, now, has red, pink, and white flowers in a 1:2:1 (25 percent, 50 percent, and 25 percent) ratio. What frequency of red, pink, and white flowers do we expect to see next year? First of all, what is the frequency, or the proportion, of R and r genes in the flowers this year? We can calculate it since we know the proportion of the three genotypes:
For 0.5 Rr since half of 0.5 is 0.25, we get 0.25 R and 0.25 r
So, in total, there are 0.5 R genes and 0.5 r genes, which is what we started with when we had all pink flowers in our field! Let's now cal-
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