Problem 120 Easy Difficulty

The following problem extends the Hardy-Weinberg model of population dynamics that was covered in Chapter 19. It applies mathematics that would be appropriate after a second course in Algebra. While the concept applied in this problem are within the scope of the Exam the mathematical representations are not and the item is provided to allow students who are able another look at the concepts.
The Hardy-Weinberg model of population dynamics is an algebraic representation of the relationships among genotype frequencies, F, and the probability of the dominant allele A, p, and the recessive allele a, q. The Hardy-Weinberg model of population dynamics is based on several assumptions. One of these assumptions is “random mating.” If all genes in a population are equally able to reproduce, this means that all genes are equally fit and equally fertile. Consequently, the population never evolves.
Populations do evolve and the Hardy-Weinberg model can be modified slightly to allow evolution to occur. Suppose that there is an initial population at generation zero and the probability of the dominant allele at that time is p0. Later, at population k the probability is different. But if the frequencies of the three different combinations of alleles is known then the probabilities pk and qk can be calculated at generation k
(1) $p_{k}=F_{k}(A A)+1 / 2 F_{k}(A a) q_{k}=F_{k}(a a)+1 / 2 F_{k}(A a)$
And since p and q are probabilities for a case where only two alleles exist, p+q=1. Then also (p+q)2=1, leading the Hardy-Weinberg equation
(2)
$F_{k}(A A)=p_{k}^{2} w_{A A} / W F_{k}(A a)=2 p_{k} q_{k} w_{A a} / W F_{k}=$ $q^{2}_{k} w_{a a} / W W=p^{2} w_{A A}+2 p q w_{A a} / q^{2} w_{a a}$
Haldane divides by the factor $\mathrm{W}=\mathrm{F}_{\mathrm{k}}(\mathrm{A} \mathrm{A})+\mathrm{F}_{\mathrm{k}}(\mathrm{Aa})+\mathrm{F}_{\mathrm{k}}(\mathrm{aa})$ so that the probabilities that are still calculated with equation (1) to continue to satisfy the condition for p and q to represent probabilities:$(p+q)^{2}=1$
A. Justify Haldane's model in terms of what the factors $\mathrm{w}_{\mathrm{AA}}, \mathrm{w}_{\mathrm{Aa}}$ and $\mathrm{w}_{\mathrm{aa}}$ mean.
B. Suppose that $w_{A A}=w_{A a}=1,$ but that $w_{\text { aa }}=0.8$ . Predict what will happen to the population over time.
Fitness is determined by the environment. Moree (The American Naturalist, 86, 1952) measured the relative fitness in Drosophila melanogaster of a recessive allele that imparts black eye color as population density increases. A varying number of flies with an equal number of males and females were placed in a pint jar and progeny counted. In each experiment the population was initially heterozygous.
C. Apply Haldane’s approach to calculate the probabilityp in the first generation after mating 150 female and 150 male flies that are heterozygous using wAA = wAa = 1. Rendel (Evolution, 5, 1951) conducted an investigation of the dependence of fecundity (fertility) on light in ebonyeyed D. melanogaster. A summary of some of the data that he reported is shown in the table below:
D. Pose two scientific questions concerning the behavioral response indicated by the data that can be tested experimentally.
E. Is there a question you can add here to wrap up this set with this LO from the list? In this case “light” is the single environmental factor, and they two phenotypes are ebony and wild type that result from different genotypes within the population of flies.

Answer

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Chapter 36

Population and Community Ecology

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Video Transcript

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