Hartl, Jones - Genetics. Principlers and analysis - 1998 (522927), страница 41
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A serious and almost inexplicable discrepancy has, however, appeared, in that in two series of resultsthe numbers observed agree excellently with the two to one ratio, which Mendel himself expected, but differsignificantly from what should have been expected had his theory been corrected to allow for the small size of histest progenies. . . .
Although no explanation can be expected to be satisfactory, it remains a possibility amongothers that Mendel was deceived by some assistant who knew too well what was expected.Source: Annals of Science 1: 115–137Figure 3.20, and observe that each curve is labeled with its degrees of freedom. To determine the P value for thedata in Table 3.2, in which the X2 value is 3 (3.00), first find the location of X2 = 3 along the x-axis in Figure 3.20.Trace vertically from 3 until you intersect the curve with 1 degree of freedom. Then trace horizontally to the leftuntil you intersect the y-axis, and read the P value; in this case, P = 0.08.
This means that chance alone wouldproduce a X2 value as great as or greater than 3 in about 8 percent of experiments of the type in Table 3.2; and,because the P value is within the blue region, the goodness of fit to the hypothesis of a 3 : 1 ratio of wildtype:mutant is judged to be satisfactory.As a second illustration of the X2 test, we will determine the goodness of fit of Mendel's round versus wrinkled datato the expected 3 : 1 ratio. Among the 7324 seeds that he observed, 5474 were round and 1850 were wrinkled. Theexpected numbers are (3/4) × 7324 = 5493 round andPage 114(1/4) × 7324 = 1831 wrinkled.
The X2 value is calculated asThe fact that the X2 is less than 1 already implies that the fit is very good. To find out how good, note that thenumber of degrees of freedom equals 2 — 1 = 1 because there are two classes of data (round and wrinkled). FromFigure 3.20, the P value for X2 = 0.26 with 1 degree of freedom is approximately 0.65.
This means that in about 65percent of all experiments of this type, a fit as bad or worse would be expected simply because of chance; onlyabout 35 percent of all experiments would yield a better fit.3.6—Are Mendel's Data Too Good to Be True?Many of Mendel's experimental results are very close to the expected values. For the ratios listed in Table 2.1 inChapter 2, the X2 values are 0.26 (round versus wrinkled seeds), 0.01 (yellow versus green seeds), 0.39 (purpleversus white flowers), 0.06 (inflated versus constricted pods), 0.45 (green versus yellow pods), 0.35 (axial versusterminal flowers), and 0.61 (long versus short stems). (As an exercise in X2, you should confirm these calculationsfor yourself.) All of the X2 tests have P values of 0.45 or greater (Figure 3.20), which means that the reportedresults are in excellent agreement with the theoretical expectations.The statistician Ronald Fisher pointed out in 1936 that Mendel's results are suspiciously close to the theoreticalexpectations.
In a large number of experiments, some experiments can be expected to yield fits that appear doubtfulsimply because of chance variation from one experiment to the next. In Mendel's data, the doubtful values that areto be expected appear to be missing. Figure 3.21 shows the observed deviations in Mendel's experiments comparedwith the deviations expected by chance. (The measure of deviation is the square root of the X2 value, assignedeither a plus or a minus sign according to whether the dominant or the recessive phenotypic class was in excess ofthe expected number.) For each magnitude of deviation, the height of the yellow bar gives the number ofexperiments that Mendel observed with such a magnitude of deviation, and the orange bar gives the number ofexperiments expected to deviate by this amount as a result of chance alone. There are clearly too few experimentswith deviations smaller than -1 or larger than +1.
This type of discrepancy could be explained if Mendel discardedor repeated a few experiments with large deviations that made him suspect that the results were not to be trusted.Did Mendel cheat? Did he deliberately falsify his data to make them appear better? Mendel's paper reportsextremely deviant ratios from individual plants, as well as experiments repeated a second time when the firstresults were doubtful. These are not the kinds of things that a dishonest person would admit. Only a small bias isnecessary to explain the excessive goodness of fit in Figure 3.21.
In a count of seeds or individual plants, onlyabout 2 phenotypes per 1000 would need to be assigned to the wrong category to account for the bias in the 91percent of the data generated by the testing of monohybrid ratios. The excessive fit could also be explained if threeor four entire experiments were discarded or repeated because deviant results were attributed to pollencontamination or other accident. After careful reexamination of Mendel's data in 1966, the evolutionary geneticistSewall Wright concluded,Mendel was the first to count segregants at all.
It is rather too much to expect that he would be aware of the precautions nowknown to be necessary for completely objective data. . . . Checking of counts that one does not like, but not of others, can lead tosystematic bias toward agreement. I doubt whether there are many geneticists even now whose data, if extensive, would stand upwholly satisfactorily under the X2 text. . . . Taking everything into account, I am confident that there was no deliberate effort atfalsification.Page 115Figure 3.21Distribution of deviations observed in 69 of Mendel's experiments(yellow bars) compared with expected values (orange bars).
There is nosuggestion that the data in the middle have been adjusted to improvethe fit. However, several experiments with large deviations mayhave been discarded or repeated, because there are not so manyexperiments with large deviations as might be expected.Mendel's data are some of the most extensive and complete "raw data" ever published in genetics. Additionalexaminations of the data will surely be carried out as new statistical approaches are developed. However, theprincipal point to be emphasized is that up to the present time, no reputable statistician has alleged that Mendelknowingly and deliberately adjusted his data in favor of the theoretical expectation.Chapter SummaryThe chromosomes in somatic cells of higher plants and animals are present in pairs.
The members of each pair arehomologous chromosomes, and each member is a homolog. Pairs of homologs are usually identical in appearance,whereas nonhomologous chromosomes often show differences in size and structural detail that make them visiblydistinct from each other. A cell whose nucleus contains two sets of homologous chromosomes is diploid. One setof chromosomes comes from the maternal parent and the other from the paternal parent. Gametes are haploid. Agamete contains only one set of chromosomes, consisting of one member of each pair of homologs.Mitosis is the process of nuclear division that maintains the chromosome number when a somatic cell divides.Before mitosis, each chromosome replicates, forming a two-part structure consisting of two sister chromatidsjoined at the centromere (kinetochore).
At the onset of mitosis, the chromosomes become visible and, atmetaphase, become aligned on the metaphase plate perpendicular to the spindle. At anaphase, the centromere ofeach chromosome divides, and the sister chromatids are pulled by spindle fibers to opposite poles of the cell. Theseparated sets of chromosomes present in telophase nuclei are genetically identical.Meiosis is the type of nuclear division that takes place in germ cells, and it reduces the diploid number ofchromosomes to the haploid number.
The genetic material is replicated before the onset of meiosis, so eachchromosome consists of two sister chromatids. The first meiotic division is the reduction division, which reducesthe chromosome number by half. The homologous chromosomes first pair (synapsis) and then, at anaphase I,separate.
The resulting products contain chromosomes that consist of two chromatids attached to a commoncentromere. However, as a result of crossing-over, which takes place in prophase I, the chromatids may not begenetically identical along their entire length. In the second meiotic division, the centromeresPage 116divide and the homologous chromatids separate. The end result of meiosis is the formation of four geneticallydifferent haploid nuclei.A distinctive feature of meiosis is the synapsis, or side-by-side pairing, of homologous chromosomes in thezygotene substage of prophase I. During the pachytene substage, the paired chromosomes become connected bychiasmata (the physical manifestations of crossing-over) and do not separate until anaphase I.
This separation iscalled disjunction (unjoining), and failure of chromosomes to separate is called nondisjunction. Nondisjunctionresults in a gamete that contains either two copies or no copies of a particular chromosome. Meiosis is the physicalbasis of the segregation and independent assortment of genes. In Drosophila, an unexpected pattern of inheritanceof the X-linked white gene was shown to be accompanied by nondisjunction of the X chromosome; theseobservations gave experimental proof of the chromosome theory of heredity.Unlike other chromosome pairs, the X and Y sex chromosomes are visibly different and contain different genes. Inmammals and in many insects and other animals, as well as in some flowering plants, the female contains two Xchromosomes (XX) and hence is homogametic, and the male contains one X chromosome and one Y chromosome(XY) and hence is heterogametic.
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