Hartl, Jones - Genetics. Principlers and analysis - 1998 (522927), страница 22
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He realized that there should be 27 differentgenotypes present in the F2 progeny, so he self-fertilized each of the 639 plants to determine its genotype for eachof the three traits. Mendel alludes to the amount of work this experiment entailed by noting that ''of all theexperiments, it required the most time and effort."The result of the experiment is shown in Figure 2.13. From top to bottom, theFigure 2.12With independent assortment, the expected ratio of phenotypes in atrihybrid cross is obtained by multiplying the three independent 3 : 1ratios of the dominant and recessive phenotypes.
A dash used in agenotype symbol indicates that either the dominant or the recessive allele ispresent; for example, W— refers collectively to the genotypes WW and Ww.(The expected numbers total 640 rather than 639 because of round-off error.)Page 47Figure 2.13Results of Mendel's analysis of the genotypes formed in the F2 generation of a trihybrid cross with the allelic pairsW, w and G, g and P, p.
In each pair of numbers, the red entry is the expected number and the black entry is theobserved. Note that each gene, by itself, yields a 1 : 2 : 1 ratio of genotypes and that each pair of genes yields a1 : 2 : 1 : 2 : 4 : 2 : 1 : 2 : 1 ratio of genotypes.three Punnett squares show the segregation of W and w from G and g in the genotypes PP, Pp, and pp. In each cell,the number in red is the expected number of plants of each genotype, assuming independent assortment, and thenumber in black is the observed number of each genotype of plant.
The excellent agreementPage 48confirmed Mendel in what he regarded as the main conclusion of his experiments:"Pea hybrids form germinal and pollen cells that in their composition correspond in equal numbers to all theconstant forms resulting from the combination of traits united through fertilization."In this admittedly somewhat turgid sentence, Mendel incorporated both segregation and independent assortment. Inmodern terms, what he means is that the gametes produced by any hybrid plant consist of equal numbers of allpossible combinations of the alleles present in the original true-breeding parents whose cross produced the hybrids.For example, the cross WW gg × ww GG produces F1 progeny of genotype Ww Gg, which yields the gametes WG,Wg, wG, and wg in equal numbers. Segregation is illustrated by the 1 : 1 ratio of W : w and G : g gametes, andindependent assortment is illustrated by the equal numbers of WG, Wg, wG, and wg gametes.2.3—Mendelian Inheritance and ProbabilityA working knowledge of the rules of probability for predicting the outcome of chance events is basic tounderstanding the transmission of hereditary characteristics.
In the first place, the proportions of the different typesof offspring obtained from a cross are the cumulative result of numerous independent events of fertilization.Further-more, in each fertilization, the particular combination of dominant and recessive alleles that come togetheris random and subject to chance variation.In the analysis of genetic crosses, the probability of an event may be considered as equivalent to the proportion oftimes that the event is expected to be realized in numerous repeated trials. Likewise, the proportion of times that anevent is expected to be realized in numerous repeated trials is equivalent to the probability that it is realized in asingle trial.
For example, in the F2 generation of the hybrid between pea varieties with round seeds and those withwrinkled seeds, Mendel observed 5474 round seeds and 1850 wrinkled seeds (Table 2.1). In this case, theproportion of wrinkled seeds was 1850/(1850 + 5474) = 1/3.96, or very nearly 1/4. We may therefore regard 1/4 asthe approximate proportion of wrinkled seeds to be expected among a large number of progeny from this cross.Equivalently, we can regard 1/4 as the probability that any particular seed chosen at random will be wrinkled.Evaluating the probability of a genetic event usually requires an understanding of the mechanism of inheritanceand knowledge of the particular cross.
For example, in evaluating the probability of obtaining a round seed from aparticular cross, you need to know that there are two alleles, W and w, with W dominant over w; you also need toknow the particular cross, because the probability of round seeds is determined by whether the cross isWW × ww, in which all seeds are expected to be round,Ww × Ww, in which 3/4 are expected to be round, orWw × ww, in which 1/2 are expected to be round.In many genetic crosses, the possible outcomes of fertilization are equally likely. Suppose that there are n possibleoutcomes, each as likely as any other, and that in m of these, a particular outcome of interest is realized; then theprobability of the outcome of interest is m/n.
In the language of probability, an outcome of interest is typicallycalled an event. As an example, consider the progeny produced by self-pollination of an Aa plant; four equallylikely progeny genotypes (outcomes) are possible: namely AA, Aa, aA, and aa. Two of the four possible outcomesare heterozygous, so the probability of a heterozygote is 2/4, or 1/2.Mutually Exclusive Events: The Addition RuleSometimes an outcome of interest can be expressed in terms of two or more possibilities. For example, a seed withthe pheno-Page 49type of "round" may have either of two genotypes, WW and Ww.
A seed that is round cannot have both genotypesat the same time. With events such as the formation of the WW or Ww genotypes, only one event can be realized inany one organism, and the realization of one event in an organism precludes the realization of others in the sameorganism. In this example, realization of the genotype WW in a plant precludes realization of the genotype Ww inthe same plant, and the other way around.
Events that exclude each other in this manner are said to be mutuallyexclusive. When events are mutually exclusive, their probabilities are combined according to the addition rule.Addition Rule: The probability of the realization of one or the other of two mutually exclusive events, A orB, is the sum of their separate probabilities.In symbols, where Prob is used to mean probability, the addition rule is writtenThe addition rule can be applied to determine the proportion of round seeds expected from the cross Ww × Ww.The round-seed phenotype results from the expression of either of two genotypes, WW and Ww, which are mutuallyexclusive. In any particular progeny organism, the probability of genotype WW is 1/4 and that of Ww is 1/2.
Hencethe overall probability of either WW or Ww isBecause 3/4 is the probability of an individual seed being round, it is also the expected proportion of round seedsamong a large number of progeny.Independent Events: The Multiplication RuleEvents that are not mutually exclusive may be independent, which means that the realization of one event has noinfluence on the possible realization of any others.
For example, in Mendel's crosses for seed shape and color, thetwo traits are independent, and the ratio of phenotypes in the F2 generation is expected to be 9/16 round yellow,3/16 round green, 3/16 wrinkled yellow, and 1/16 wrinkled green. These proportions can be obtained byconsidering the traits separately, because they are independent. Considering only seed shape, we can expect the F2generation to consist of 3/4 round and 1/4 wrinkled seeds.
Considering only seed color, we can expect the F2generation to consist of 3/4 yellow and 1/4 green. Because the traits are inherited independently, among the 3/4 ofthe seeds that are round, there should be 3/4 that are yellow, so the overall proportion of round yellow seeds isexpected to be 3/4 × 3/4 = 9/16. Likewise, among the 3/4 of the seeds that are round, there should be 1/4 green,yielding 3/4 × 1/4 = 3/16 as the expected proportion of round green seeds.
The proportions of the other phenotypicclasses can be deduced in a similar way. The principle is that when events are independent, the probability that theyare realized together is obtained by multiplication.Successive offspring from a cross are also independent events, which means that the genotypes of early progenyhave no influence on the relative proportions of genotypes in later progeny. The independence of successiveoffspring contradicts the widespread belief that in each human family, the ratio of girls to boys must "even out" atapproximately 1 : 1, and so, if a family already has, say, four girls, they are somehow more likely to have a boy thenext time around. But this belief is not supported by theory, and it is also contradicted by actual data on the sexratios in human sibships.
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