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Did Mendel Cheat
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That is, Mendel had less than one chance in one hundred of randomly picking seven traits on the seven different chromosomes. However, L. Douglas and E. Novitski in 1977 analyzed Mendel s data in a different way. To understand their analysis, you have to know that two genes suf ciently far apart on the same chromosome will appear to assort independently (to be discussed in chapter 6). Thus, Mendel s choice of characters showing independent assortment has to be viewed in light of the lengths of the chromosomes. That is, Mendel could have chosen two genes on the same chromosome that would still show independent assortment. In fact, he did. For example, stem length and pod texture (wrinkled or
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smooth) are on the fourth chromosome pair in peas. In their analysis, Douglas and Novitski report that the probability of randomly choosing seven characteristics that appear to assort independently is actually between one in four and one in three. So it seems that Mendel did not have to manipulate his choice of characters in order to hide the failure of independent assortment. He had a one in three chance of naively choosing the seven characters that he did, thereby uncovering no deviation from independent assortment. The second claim that Mendel fabricated data comes from a careful analysis of Mendel s paper by R. A. Fisher, a brilliant English statistician and population geneticist. In a paper in 1936, Fisher pointed out two problems in Mendel s work. First, all of Mendel s published data taken together t their expected ratios better than chance alone would predict. Second, some of Mendel s data t incorrect expected ratios. This second error on Mendel s part came about as follows.
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A simple test of Mendel s rule of independent assortment is the testcrossing of the dihybrid plant. We would predict, for example, that if we crossed an RrYy F1 individual with an rryy individual, the results would include four phenotypes in a 1:1:1:1 ratio, as shown in gure 2.18. Mendel s data veri ed this prediction (box 2.2). We will proceed to look at a trihybrid cross in order to develop general rules for multihybrids. A trihybrid Punnett square appears in gure 2.19. From this we can see that when a homozygous dominant and a homozygous recessive individual are crossed in the P1 generation, plants in the F1 generation are capable of producing eight gamete types. When these F1 individuals are selfed, they in turn produce F2 offspring of twentyseven different genotypes in a ratio of sixty-fourths. By extrapolating from the monohybrid through the trihybrid, or simply by the rules of probability, we can construct table 2.3, which contains the rules for F1 gamete
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production and F2 zygote formation in a multihybrid cross. For example, from this table we can gure out the F2 offspring when a dodecahybrid (twelve segregating genes: AA BB CC . . . LL aa bb cc . . . ll) is selfed.The F1 organisms in that cross will produce gametes with 212, or 4,096, different genotypes. The proportion of homozygous recessive offspring in the F2 generation is 1/(2n)2 where n 12, or 1 in 16,777,216. With complete dominance, there will be 4,096 different phenotypes in the F2 generation. If dominance is incomplete, there can be 312, or 531,441, different phenotypes in the F2 generation.
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GENOTYPIC INTERACTIONS
Often, several genes contribute to the same phenotype. An example occurs in the combs of fowl ( g. 2.20). If we cross a rose-combed hen with a pea-combed rooster (or vice versa), all the F1 offspring are walnut-combed. If we
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