Page 35 - Genetics_From_Genes_to_Genomes_6th_FULL_Part1

2.2 Genetic Analysis According to Mendel 27

testcross yields all yellow round offspring (testcross A), you 1/4 : 2/4 : 1/4. Thus, you can find the probability of AA bb
can sell your test plant, because you know it is homozygous Cc Dd by multiplying the probability of each independent
for both pea color and pea shape. If your testcross yields event: AA (1/4 of the progeny produced by Aa × Aa); bb
1/2 yellow round and 1/2 yellow wrinkled (testcross B), or (1/4); Cc (2/4); Dd (2/4):
1/2 yellow round and 1/2 green round (testcross C), you know 1/4 × 1/4 × 2/4 × 2/4 = 4/256 = 1/64.
that the candidate plant in question is genetically homozygous
for one trait and heterozygous for the other and must there- The Punnett square approach would provide the same
fore be discarded. Finally, if the testcross yields 1/4 yellow answer, but it would require much more time.
round, 1/4 yellow wrinkled, 1/4 green round, and 1/4 green If instead of a specific genotype, you want to predict
wrinkled (testcross D), you know that the plant is a hete- the probability of a certain phenotype, you can again use
rozygote for both the pea color and the pea shape genes. the product rule as long as you know the phenotypic ratios
produced by each pair of alleles in the cross. For example,
if in the multihybrid cross of Aa Bb Cc Dd × Aa Bb Cc Dd,
Geneticists Use Mendel’s Laws you want to know how many offspring will show the dom-
to Calculate Probabilities and inant A trait (genotype AA or Aa = 1/4 + 2/4, or 3/4), the
Make Predictions recessive b trait (genotype bb = 1/4), the dominant C trait
(genotype CC or Cc = 3/4), and the dominant D trait (gen-
Mendel performed several sets of dihybrid crosses and also otype DD or Dd = 3/4), you simply multiply:
carried out multihybrid crosses: matings between the F 1 3/4 × 1/4 × 3/4 × 3/4 = 27/256.
progeny of pure-breeding parents that differed in three or
more unrelated traits. In all of these experiments, he ob- In this way, the rules of probability make it possible to pre-
served numbers and ratios very close to what he expected dict the outcome of very complex crosses.
on the basis of his two general biological principles: The You can see from these examples that particular prob-
alleles of a gene segregate during the formation of egg or lems in genetics are amenable to particular modes of analysis.
sperm, and the alleles of different genes assort indepen- As a rule of thumb, Punnett squares are excellent for visualiz-
dently of each other. Mendel’s laws of inheritance, in con- ing simple crosses involving a few genes, but they become
junction with the mathematical rules of probability, provide unwieldy in the dissection of more complicated matings.
geneticists with powerful tools for predicting and interpret- Direct calculations of probabilities, such as those in the two
ing the results of genetic crosses. But as with all tools, they preceding problems, are useful when you want to know the
have their limitations. We examine here both the power and chances of one or a few outcomes of complex crosses. If,
the limitations of Mendelian analysis. however, you want to know all the outcomes of a multihybrid
First, the power: Using simple Mendelian analysis, it is cross, a branched-line diagram is the best way to go as it will
possible to make accurate predictions about the offspring keep track of all the possibilities in an organized fashion.
of extremely complex crosses. Suppose you want to predict Now, the limitations of Mendelian analysis: Like Mendel,
the occurrence of one specific genotype in a cross involv- if you were to breed pea plants or corn or any other organ-
ing several independently assorting genes. For example, if ism, you would most likely observe some deviation from the
hybrids that are heterozygous for four traits are allowed to ratios you expected in each generation. What can account for
self-fertilize—Aa Bb Cc Dd × Aa Bb Cc Dd—what propor- such variation? One element is chance, as witnessed in the
tion of their progeny will have the genotype AA bb Cc Dd? common coin toss experiment. With each throw, the proba-
You could set up a Punnett square to answer the question. bility of the coin coming up heads is equal to the likelihood
Because for each trait there are two different alleles, the it will come up tails. But if you toss a coin 10 times, you may
number of different eggs or sperm is found by raising 2 to get 30% (3) heads and 70% (7) tails, or vice versa. If you toss
n
the power of the number of differing traits (2 , where n is it 100 times, you are more likely to get a result closer to the
the number of traits). By this calculation, each hybrid par- expected 50% heads and 50% tails. The larger the number of
4
ent in this cross with 4 traits would make 2 = 16 different trials, the lower the probability that chance significantly
kinds of gametes. The Punnett square depicting such a skews the data. The statistical benefit is one reason Mendel
cross would thus contain 256 boxes (16 × 16). worked with large numbers of pea plants.
Setting up such a square may be fine if you live in a Mendel’s laws, in fact, have great predictive power for
monastery with a bit of time on your hands, but not if populations of organisms, but they do not tell us what will
you’re taking a 1-hour exam. It would be much simpler to happen in any one individual. With a garden full of self-
analyze the problem by breaking down the multihybrid fertilizing monohybrid pea plants, for example, you can
cross into four independently assorting monohybrid expect that 3/4 of the F 2 progeny will show the dominant
crosses. Remember that the genotypic ratios of each mono- phenotype and 1/4 the recessive, but you cannot predict the
hybrid cross are 1 homozygote for the dominant allele, to phenotype of any particular F 2 plant. In Chapter 5, we dis-
2 heterozygotes, to 1 homozygote for the recessive allele = cuss mathematical methods for assessing whether the