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Molecular genetics · Mendelian genetics

Mendelian crosses

In 2nd Bachillerato, genetics problems are no longer limited to the cross of a single gene: the university entrance exam requires you to handle the notation fluently, deduce genotypes from observed ratios and solve complete dihybrid crosses. This section formalises that skill.

Before you start, make sure you know: Meiosis (4th ESO)
Before you start, make sure you know: Dominance and recessiveness (4th ESO)

Gene, allele and genetic notation

When two yellow pea plants of a certain origin are crossed, $300$ yellow seeds and $100$ green seeds are obtained: how can a colour absent from the parents reappear if inheritance does not blend hereditary factors?

Pair of homologous chromosomes, one maternal and one paternal, with the same locus at the same height: the maternal one carries allele A and the paternal one allele a, so the genotype is Aa, heterozygous. pair of homologous chromosomes locus allele A allele a maternal chromosome paternal chromosome genotype: Aa (heterozygous)
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In pea plants, the allele for smooth seeds (R) is dominant over that for wrinkled seeds (r). Two heterozygous plants are crossed. State the genotypes of the parents, the…

In pea plants, the allele for smooth seeds (R) is dominant over that for wrinkled seeds (r). Two heterozygous plants are crossed. State the genotypes of the parents, the gametes each one produces and the expected genotypic and phenotypic ratios in the offspring.

Solve
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In dogs, short hair (L) is dominant over long hair (l). State all the possible genotypes of a short-haired dog and the genotype of a long-haired dog, and explain why…

In dogs, short hair (L) is dominant over long hair (l). State all the possible genotypes of a short-haired dog and the genotype of a long-haired dog, and explain why there is no doubt about the genotype when the phenotype is recessive.

Solve

First and second laws: the monohybrid cross

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In tomato plants, red fruit (R) is dominant over yellow (r). A homozygous red-fruited plant is crossed with a yellow-fruited plant. State the genotype and the phenotype…

In tomato plants, red fruit (R) is dominant over yellow (r). A homozygous red-fruited plant is crossed with a yellow-fruited plant. State the genotype and the phenotype of the whole F1 and reason whether any yellow-fruited plant can appear in it.

Solve
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In rabbits, a black coat (N) is dominant over a brown one (n). A heterozygous male is crossed with a brown-coated female. State the ratios expected in the offspring and…

In rabbits, a black coat (N) is dominant over a brown one (n). A heterozygous male is crossed with a brown-coated female. State the ratios expected in the offspring and calculate how many rabbits of each phenotype are to be expected in a litter of 40 young.

Solve
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Two pure-breeding lines of an ornamental plant, one with red flowers and one with white flowers, are crossed, and the whole F1 has red flowers. State the genotypes of…

Two pure-breeding lines of an ornamental plant, one with red flowers and one with white flowers, are crossed, and the whole F1 has red flowers. State the genotypes of the parental generation and of the F1, and the phenotypic ratios expected in the F2 obtained by self-fertilisation of the F1.

Solve

The test cross and probability in genetics

Product rule: the probability that each child is aa is 1/4, and the probability that both children are aa at the same time is 1/4 × 1/4 = 1/16. 1st child: P(aa) = 1/4 2nd child: P(aa) = 1/4 1/4 × 1/4 P(both aa) = 1/4 × 1/4 = 1/16
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What is a test cross and what is it used for? Design the cross that would make it possible to find out whether a black-coated mouse (a dominant trait) is homozygous or…

What is a test cross and what is it used for? Design the cross that would make it possible to find out whether a black-coated mouse (a dominant trait) is homozygous or heterozygous, stating what results you would expect in each case.

Solve
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When two purple-flowered plants are crossed with each other, the offspring consists of 37 purple-flowered plants and 13 white-flowered ones. a) Deduce the genotypes of…

When two purple-flowered plants are crossed with each other, the offspring consists of 37 purple-flowered plants and 13 white-flowered ones. a) Deduce the genotypes of the parental plants and justify your answer from the observed ratios. b) Explain which cross you would carry out to find out whether a purple plant from the offspring is homozygous or heterozygous, stating what results would be expected in each case.

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Polydactyly (having extra fingers) is due in humans to an autosomal dominant allele (P), while the normal number of fingers depends on the recessive allele (p). A…

Polydactyly (having extra fingers) is due in humans to an autosomal dominant allele (P), while the normal number of fingers depends on the recessive allele (p). A heterozygous polydactylous man has children with a woman with the normal number of fingers. a) State the genotypes of both. b) Calculate the probability that their first child will be polydactylous. c) Calculate the probability that their first two children will have the normal number of fingers.

Solve

Third law: the complete dihybrid cross

Mendel crossed dihybrid plants with yellow round seeds and obtained in the offspring $315$ yellow round, $101$ yellow wrinkled, $108$ green round and $32$ green wrinkled: why do combinations absent from the grandparents appear, and what mathematical rule fixes that $9:3:3:1$ ratio?

Four-by-four Punnett square for the dihybrid cross AaBb × AaBb: sixteen genotypes coloured according to their phenotype, in a 9:3:3:1 ratio. AaBb × AaBb: 16 equally likely combinations AB Ab aB ab AB Ab aB ab AABB AABb AaBB AaBb AABb AAbb AaBb Aabb AaBB AaBb aaBB aaBb AaBb Aabb aaBb aabb 9/16 A_B_: two dominant characteristics 3/16 Abb: A dominant, b recessive 3/16 aaB_: a recessive, B dominant 1/16 aabb: two recessive characteristics _ = either allele (A or a; B or b) Phenotypic ratio 9 : 3 : 3 : 1
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In a cross between two double heterozygotes for two traits with complete dominance (AaBb × AaBb), state what phenotypic ratios are to be expected in the offspring and…

In a cross between two double heterozygotes for two traits with complete dominance (AaBb × AaBb), state what phenotypic ratios are to be expected in the offspring and which two conditions must be met in order to obtain exactly those ratios.

Solve
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A pea plant with yellow, smooth seeds, of genotype AaBb, is crossed with a plant with green, wrinkled seeds (aabb). Knowing that both genes assort independently, state…

A pea plant with yellow, smooth seeds, of genotype AaBb, is crossed with a plant with green, wrinkled seeds (aabb). Knowing that both genes assort independently, state the gametes formed by each plant and the genotypic and phenotypic ratios of the offspring.

Solve
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In pea plants, a tall stem (T) is dominant over a dwarf stem (t) and the axial position of the flowers (A) is dominant over the terminal position (a). A double…

In pea plants, a tall stem (T) is dominant over a dwarf stem (t) and the axial position of the flowers (A) is dominant over the terminal position (a). A double heterozygous plant is crossed with a dwarf plant with terminal flowers. a) State the genotypes of both parents and the gametes each one produces. b) Determine the phenotypic ratios expected in the offspring. c) State which of Mendel's laws allows this result to be predicted and what it consists of.

Solve

From observed ratios to genotype

A guinea pig breeder gets from one pair $28$ black, curly-coated offspring, $31$ black with straight hair, $9$ white curly and $11$ white with straight hair: how do you deduce the exact genotype of the parents by breaking those figures down one characteristic at a time?

Three Punnett squares coloured by phenotype: Aa × aa gives 1:1, Aa × Aa gives 3:1 and AaBb × AaBb gives 9:3:3:1, each with its parental genotype. observed ratio → parental genotype Aa aa Aaaa Aaaa 1:1 Aa × aa Aa Aa AAAa Aaaa 3:1 Aa × Aa ABAbaBab AB Ab aB ab 9:3:3:1 AaBb × AaBb = Aa × Aa and Bb × Bb each characteristic is compared with its own Mendelian ratio
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Two pea plants with yellow, smooth seeds are crossed and the offspring obtained has three quarters yellow seeds and one quarter green seeds, all of them smooth. Deduce,…

Two pea plants with yellow, smooth seeds are crossed and the offspring obtained has three quarters yellow seeds and one quarter green seeds, all of them smooth. Deduce, with reasoning, the genotypes of the two parents for each of the two traits.

Solve
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In dogs, black hair (B) is dominant over brown (b) and short hair (L) is dominant over long hair (l). Two black, short-haired dogs, both of genotype BbLl, are crossed…

In dogs, black hair (B) is dominant over brown (b) and short hair (L) is dominant over long hair (l). Two black, short-haired dogs, both of genotype BbLl, are crossed with each other. a) State how many types of gametes each parent produces and what they are. b) Calculate the expected proportion of black, long-haired puppies. c) Calculate the expected proportion of double heterozygous puppies.

Solve
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A double heterozygous plant (AaBb) for two independent genes with complete dominance is self-fertilised. a) Calculate what proportion of the offspring will show the…

A double heterozygous plant (AaBb) for two independent genes with complete dominance is self-fertilised. a) Calculate what proportion of the offspring will show the recessive phenotype for both traits. b) Calculate what proportion will show the dominant phenotype for only one trait. c) Explain what Mendel's third law (the law of independent assortment) consists of and how it relates to the previous question.

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Summary

See all the exercises in this section