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## Mendel and the Gene Idea

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**Modern genetics began in an abbey garden, where a monk named**Gregor Mendel documented the particulate mechanism of inheritance**Pea plants have several advantages for genetics**• pea plants are available in many varieties with distinct heritable features (characters) with different variants (traits)**another advantage of peas is that Mendel had strict control**over which plants mated with which Each pea plant has male (stamens) and female (carpal) sexual organs**in nature, pea plants typically self-fertilize, fertilizing**ova with their own sperm • however, Mendel could also move pollen from one plant to another to cross-pollinate plants**In a typical breeding experiment, Mendel would**cross-pollinate (hybridize) two contrasting, true-breeding pea varieties**The true-breeding parents are the P generation and their**hybrid offspring are the F1 generation**Mendel would then allow the F1 hybrids to self-pollinate to**produce an F2 generation**it was mainly Mendel’s quantitative analysis of F2 plants**that revealed the two fundamental principles of heredity: the law of segregation and the law of independent assortment**In the law of segregation, the two alleles for a character**are packaged into separate gametes For each character, an organism inherits two alleles, one from each parent**If two alleles differ, then one, the dominant allele, is**fully expressed in the organism’s appearance The other, the recessive allele, has no noticeable effect on the organism’s appearance**A Punnett square predicts the results of a genetic cross**between individuals of known genotype**An organism with two identical alleles for a character is**homozygous for that character (pure) TT or tt**Organisms with two different alleles for a character is**heterozygous for that character (hybrid) Tt**A description of an organism’s traits is its phenotype**(see) A description of its genetic makeup is its genotype (letters) • two organisms can have the same phenotype but have different genotypes if one is homozygous dominant and the other is heterozygous**It is not possible to predict the genotype of an organism**with a dominant phenotype • the organism must have one dominant allele, but it could be homozygous dominant or heterozygous**A testcross, breeding a homozygous recessive with dominant**phenotype, but unknown genotype, can determine the identity of the unknown allele**In the law of independent assortment, each pair of alleles**segregates into gametes independently**Mendelian inheritance reflects rules of probability**• Mendel’s laws of segregation and independent assortment reflect the same laws of probability that apply to tossing coins or rolling dice**the probability scale ranged from zero (an event with no**chance of occurring) to one (an event that is certain to occur) the probability of tossing heads with a normal coin is ½**the probability of rolling a 3 with a six-sided die is 1/6,**and the probability of rolling any other number is 1 - 1/6 = 5/6 • when tossing a coin, the outcome of one toss has no impact on the outcome of the next toss**each toss is an independent event, just like the**distribution of alleles into gametes**We can use the rule of multiplication to determine the**chance that two or more independent events will occur together in some specific combination • compute the probability of each independent event**then, multiply the individual probabilities to obtain the**overall probability of these events occurring together • the probability that two coins tossed at the same time will land heads up is 1/2 x 1/2 = 1/4**The rule of multiplication also applies to dihybrid crosses**• for a heterozygous parent (BbRr) the probability of producing a BR gamete is 1/2 x 1/2 = 1/4**We can use this to predict the probability of a particular**F2 genotype without constructing a 16-part Punnett square • the probability that an F2 plant will have a BBRR genotype from a heterozygous parent is 1/16 (1/4 chance for a BR ovum and 1/4 chance for a BR sperm)**The rule of addition also applies to genetic problems**• under the rule of addition, the probability of an event that can occur two or more different ways is the sum of the separate probabilities of those ways**For example, there are two ways that F1 gametes can combine**to form a heterozygote • the dominant allele could come from the sperm and the recessive from the ovum (probability = 1/4)**or, the dominant allele could come from the ovum and the**recessive from the sperm (probability = 1/4) • the probability of a heterozygote is 1/4 + 1/4 = 1/2**We can combine the rules of multiplication and addition to**solve complex problems in Mendelian genetics**Let’s determine the probability of finding two recessive**phenotypes for at least two of three traits resulting from a trihybrid cross between pea plants that are AaBbRr and Aabbrr**there are five possible genotypes that fulfill this**condition: aabbRr, aaBbrr, Aabbrr, AAbbrr, and aabbrr**we would use the rule of multiplication to calculate the**probability for each of these genotypes and then use the rule of addition to pool the probabilities for fulfilling the condition of at least two recessive traits**The probability of producing a aabbRr offspring:**The probability of producing aa = 1/2 x 1/2 = 1/4 The probability of producing bb = 1/2 x 1 = 1/2 The probability of producing Rr = 1/2 x 1 = 1/2**Therefore, the probability of all three being present**(aabbRr) in one offspring is 1/4 x 1/2 x 1/2 = 1/16 For aaBbrr: 1/4 x 1/2 x 1/2 = 1/16 For Aabbrr: 1/2 x 1/2 x 1/2 = 2/16 For AAbbrr: 1/4 x 1/2 x 1/2 = 1/16 For aabbrr: 1/4 x 1/2 x 1/2 = 1/16**Therefore, the chance of at least two recessive traits is**6/16 • while we cannot predict with certainty the genotype or phenotype of any particular seed from the F2 generation of a dihybrid cross, we can predict the probabilities that it will fit a specific genotype of phenotype**Extending Mendelian Genetics**Some alleles show incomplete dominance where heterozygotes show a distinct intermediate phenotype, not seen in homozygotes**this is not blended inheritance because the traits are**separable (particulate) as seen in further crosses • offspring of a cross between heterozygotes will show three phenotypes: both parentals and the heterozygote**A clear example of incomplete dominance is seen in flower**color of snapdragons A cross between a white-flowered plant and a red-flowered plant will produce all pink F1 offspring**self-pollination of the F1 offspring produces 25% white, 25%**red, and 50% pink offspring**Incomplete and complete dominance are part of a spectrum of**relationships among alleles • at the other extreme from complete dominance is codominance in which two alleles affect the phenotype in separate, distinguishable ways**Because an allele is dominant does not necessarily mean that**it is more common in a population than the recessive allele**For example, polydactyly, in which individuals are born with**extra fingers or toes, is due to an allele dominant to the recessive allele for five digits per appendage**however, the recessive allele is far more prevalent than the**dominant allele in the population • 399 individuals out of 400 have five digits per appendage