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 鈥渞andom mating.鈥� 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鈥檚 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 鈥渓ight鈥� is the single environmental factor, and they
two phenotypes are ebony and wild type that result from different genotypes
within the population of flies.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine 
