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Math 8 · Science
Genetics and evolution · Genetics and inheritance

Dominance and recessiveness

Gregor Mendel crossed thousands of pea plants over several years, patiently counting how many plants of each type he obtained in every generation. From those numbers came three laws that, a century and a half later, still explain why two brown-eyed parents can have a blue-eyed child.

Gene, allele, genotype and phenotype

In a litter of rabbits born to black parents, some young may have white fur, while in other crosses all the offspring are identical to their parents. Where is that information physically stored, and how can a trait be passed on when the parents do not show it?

Pair of homologous chromosomes, one maternal and one paternal, with the same banding pattern; at the same gene locus, the maternal one carries allele A and the paternal one carries allele a, so the genotype is Aa. gene locus allele A allele a maternal chromosome paternal chromosome pair of homologous chromosomes · genotype Aa
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Define the terms gene, allele, genotype, and phenotype, and provide a simple example relating them (for instance, flower color).

Define the terms gene, allele, genotype, and phenotype, and provide a simple example relating them (for instance, flower color).

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Explain what it means for an allele to be dominant and for an allele to be recessive. Can a recessive trait be expressed in a heterozygous individual? Explain your…

Explain what it means for an allele to be dominant and for an allele to be recessive. Can a recessive trait be expressed in a heterozygous individual? Explain your reasoning.

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Dominance, homozygosity and heterozygosity

Three plants with their pairs of homologous chromosomes: AA and Aa have a flower with the dominant phenotype (purple) and aa has a flower with the recessive phenotype (pale); AA and Aa share the phenotype but not the genotype. AA homozygous A A dominant Aa heterozygous A a dominant aa homozygous a a recessive AA and Aa: same phenotype, different genotype
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The diagram shows a Punnett square for a cross between two heterozygous individuals (Aa × Aa). Complete the missing cell and, assuming allele A (dark color) is dominant…

The diagram shows a Punnett square for a cross between two heterozygous individuals (Aa × Aa). Complete the missing cell and, assuming allele A (dark color) is dominant over a (light color), state the genotypic and phenotypic ratios of the offspring.

A a A a AA Aa Aa ?
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Explain the difference between homozygous and heterozygous, and state which of the two can produce two different types of gametes for that trait and which produces only…

Explain the difference between homozygous and heterozygous, and state which of the two can produce two different types of gametes for that trait and which produces only one.

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A mouse shows the recessive phenotype for coat color. What is its genotype with complete certainty? And if it showed the dominant phenotype? Explain why in one case we…

A mouse shows the recessive phenotype for coat color. What is its genotype with complete certainty? And if it showed the dominant phenotype? Explain why in one case we know it for sure and in the other we do not.

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Mendel's laws: uniformity and segregation

Mendel crossed pure-breeding yellow peas with pure-breeding green peas and obtained an F1 with $100\%$ yellow seeds; when he crossed those plants with each other, he counted 6,022 yellow and 2,001 green (a $75\%$ to $25\%$ split). How did the green color reappear intact after having disappeared completely in the previous generation?

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Mendel crossed a pure-breeding yellow-seeded pea plant (AA) with a green-seeded one (aa). State the genotype and the phenotype of the whole first generation (F1) and…

Mendel crossed a pure-breeding yellow-seeded pea plant (AA) with a green-seeded one (aa). State the genotype and the phenotype of the whole first generation (F1) and state in your own words Mendel's first law, or law of uniformity.

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A homozygous dominant plant (AA) is crossed with a heterozygous one (Aa). Draw the corresponding Punnett square and state the genotypic and phenotypic ratios of the…

A homozygous dominant plant (AA) is crossed with a heterozygous one (Aa). Draw the corresponding Punnett square and state the genotypic and phenotypic ratios of the offspring.

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The F1 plants from the cross between pure yellow and green peas are all yellow and heterozygous. If the F1 plants are allowed to self-pollinate, calculate the genotypic…

The F1 plants from the cross between pure yellow and green peas are all yellow and heterozygous. If the F1 plants are allowed to self-pollinate, calculate the genotypic and phenotypic ratios of the F2 and state Mendel's second law, or law of segregation.

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Probability in genetics and the testcross

A couple who are carriers of a recessive disease have a first child with the disease and fear trying for a second pregnancy, thinking the risk will be higher now that there has already been one case. Does what happened in one pregnancy affect the next, or does each child start from scratch?

4 × 4 grid with the 16 equally likely combinations of the genotypes of two children of an Aa × Aa couple; only one, aa in both, corresponds to 1/4 × 1/4 = 1/16. 2nd child 1st child AA Aa aA aa AA Aa aA aa aa, aa P(aa) = 1/4 P(aa) = 1/4 P(both aa) = 1/4 × 1/4 = 1/16 16 equally likely combinations
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In dogs, black coat (N) is dominant over brown coat (n). A heterozygous male is crossed with a brown-coated female. Calculate the probability that a puppy will have a…

In dogs, black coat (N) is dominant over brown coat (n). A heterozygous male is crossed with a brown-coated female. Calculate the probability that a puppy will have a brown coat.

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A couple, both with the dominant phenotype for a trait, have a child with the recessive phenotype. Deduce the genotypes of the parents and explain how it is possible for…

A couple, both with the dominant phenotype for a trait, have a child with the recessive phenotype. Deduce the genotypes of the parents and explain how it is possible for the child to display a trait that neither parent shows.

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Cystic fibrosis is a severe autosomal recessive hereditary disease ($a$). A healthy couple visits a genetic counseling clinic after discovering that both are…

Cystic fibrosis is a severe autosomal recessive hereditary disease ($a$). A healthy couple visits a genetic counseling clinic after discovering that both are heterozygous carriers ($Aa$). They wish to have two children.

  1. a) Reasonably calculate the probability that at least one of the two children is born affected by the disease, and compare it with the probability that both are born healthy.
  2. b) After their first child is born completely healthy, they say with relief: "Since the first one was spared, the risk for the second one is lower." Refute their belief by explaining what the actual genetic risk is for the second child, and calculate the probability that this first healthy child is a carrier of the causative allele.
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Dihybrid inheritance and Mendel's third law

Diagram of an AaLl × AaLl dihybrid cross: the 3:1 ratios of each gene (color and texture) combine at random and give the 9:3:3:1 phenotype ratio in the offspring. AaLl × AaLl (two independent genes) color gene 3 yellow : 1 green texture gene 3 smooth : 1 wrinkled combine at random 9 yellow-smooth : 3 yellow-wrinkled : 3 green-smooth : 1 green-wrinkled ratio 9 : 3 : 3 : 1

Back to the beginning: two brown-eyed parents can have a blue-eyed child if both are heterozygous ($Aa$): each contributes the recessive allele $a$ in their gamete and there is a $25\%$ probability ($1/4$) that the child is homozygous recessive ($aa$).

Summary

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