AP Biology 5.3-5.4: Mendelian and Non-Mendelian Genetics

What is a trait, and how does it differ from a characteristic?

A characteristic is a heritable feature, such as flower color; a trait is a particular form of that feature, such as violet or white flowers.

Continuous versus discontinuous variation

Continuous variation produces a range of phenotypes, often because many genes contribute to a characteristic such as height. Discontinuous variation produces distinct categories, such as violet versus white flowers, which made Mendel’s patterns easier to detect.

Why was the garden pea an effective model organism for Mendel’s inheritance experiments?

Pea plants naturally self-fertilize and can be maintained as true-breeding lines, mature within one season, and produce many offspring. These features allowed Mendel to control crosses, examine several generations quickly, and distinguish reliable patterns from chance.

True-breeding organism

An organism that consistently produces offspring with the same phenotype when self-fertilized or crossed with another organism of the same line. In a single-gene system, true-breeding individuals are typically homozygous.

Hybridization

A cross between two genetically different individuals, often true-breeding parents with contrasting traits, to study inheritance.

How did Mendel prevent self-fertilization during a controlled pea-plant cross?

He removed the anthers from the flower receiving pollen before they matured, preventing it from producing its own pollen. He then transferred pollen from a selected plant to the recipient’s stigma.

What do the symbols $P$, $F_1$, and $F_2$ represent in a genetic cross?

$P$ denotes the parental generation, $F_1$ the first filial or offspring generation, and $F_2$ the offspring produced when $F_1$ individuals reproduce, often by self-fertilization.

Reciprocal cross

A pair of crosses in which the parental roles are reversed: the trait contributed by the male in one cross is contributed by the female in the other. Mendel found similar results for reciprocal crosses of his pea traits.

What did Mendel’s reciprocal-cross results suggest about the inheritance of the pea traits?

The outcome generally did not depend on whether a particular allele came from the pollen-producing or ovule-producing parent. This supports inheritance patterns in which the two parental contributions have equivalent roles.

How did Mendel’s results challenge the blending theory of inheritance?

The blending theory predicted intermediate offspring and loss of parental traits. Mendel instead observed that one trait could be absent in $F_1$ offspring and reappear unchanged in $F_2$, showing that hereditary factors remain discrete.

What did Mendel mean by saying that traits are transmitted as discrete units?

Each parent contributes one hereditary factor, now understood as an allele, to an offspring. The parental factors remain distinct rather than blending into an intermediate factor.

What pattern did Mendel observe when true-breeding violet-flowered peas were crossed with true-breeding white-flowered peas?

All $F_1$ offspring had violet flowers. When the $F_1$ plants self-fertilized, the $F_2$ generation contained approximately three violet-flowered plants for every one white-flowered plant.

What did Mendel infer from the reappearance of a recessive trait in the $F_2$ generation?

The recessive factor had not been destroyed or blended in the $F_1$ generation. Instead, it was present but masked by the dominant factor and could be inherited by later offspring.

Dominant trait

A trait expressed in a heterozygote under a simple dominant-recessive inheritance pattern. Its phenotype can result from either a homozygous dominant or heterozygous genotype.

Recessive trait

A trait masked in a heterozygote under a simple dominant-recessive pattern and expressed only when the individual is homozygous recessive.

Allele

One of two or more alternative forms of a gene located at the same locus on homologous chromosomes. Alleles arise through mutation and can produce different versions of a characteristic.

How do homologous chromosomes relate to alleles in a diploid organism?

A diploid organism has homologous chromosome pairs, with one chromosome inherited from each parent. The same gene locus occurs on both homologs, and the alleles at that locus may be identical or different.

Why are gametes haploid while zygotes are diploid?

Meiosis produces haploid gametes containing one chromosome from each homologous pair. Fertilization combines two gametes, restoring the diploid chromosome number in the zygote.

Genotype versus phenotype

The genotype is an organism’s allele combination, including alleles that are not visibly expressed. The phenotype is the organism’s observable characteristics resulting from its genotype and its interaction with the environment.

Homozygous and heterozygous

An individual is homozygous at a locus when it has two identical alleles, such as $YY$ or $yy$. It is heterozygous when it has two different alleles, such as $Yy$.

How should uppercase and lowercase symbols be used in a simple Mendelian notation system?

An uppercase letter represents the dominant allele and the corresponding lowercase letter represents the recessive allele, such as $V$ for violet and $v$ for white flower color. Genotypes are written with two allele symbols in diploid organisms.

In a simple dominant-recessive system, which genotypes produce the dominant and recessive phenotypes?

Both $AA$ and $Aa$ produce the dominant phenotype, while only $aa$ produces the recessive phenotype.

Probability

A numerical measure of how likely an event is. A probability of $1$ means the event is certain, while a probability of $0$ means it is impossible.

How is empirical probability calculated?

Empirical probability is calculated from observations: $P(\text{event}) = \frac{\text{number of \times the event occurs}}{\text{total number of opportunities}}$.

How does theoretical probability differ from empirical probability?

Theoretical probability is predicted from a model of equally likely outcomes, whereas empirical probability is calculated from actual observed results. Empirical frequencies tend to approach theoretical probabilities as sample size increases.

Why are large offspring samples important when evaluating Mendelian ratios?

Small samples can deviate substantially from expected ratios because of random chance. Large samples reduce the relative effect of chance and generally produce observed frequencies closer to theoretical probabilities.

Product rule of probability

For independent events $A$ and $B$, the probability that both occur is $P(A \text{ and } B)=P(A)\times P(B)$. The word “and” commonly signals use of this rule.

Sum rule of probability

For mutually exclusive outcomes $A$ and $B$, the probability that either occurs is $P(A \text{ or } B)=P(A)+P(B)$. The word “or” commonly signals use of this rule.

When can the product rule be used in a genetic probability calculation?

It can be used when the events are independent and must occur together. For example, if two traits each have a $3/4$ probability of showing their dominant phenotype, the probability of both is $(3/4)(3/4)=9/16$.

When must multiple pathways be combined using the sum rule?

Use the sum rule when the same outcome can occur through mutually exclusive pathways. For example, exactly one dominant phenotype in a two-trait cross can occur as dominant-recessive or recessive-dominant, so their pathway probabilities are added.

What is the probability of obtaining two dominant phenotypes in an independently assorting dihybrid $F_2$ cross?

Each trait has a $3/4$ probability of showing its dominant phenotype, so $P=(3/4)(3/4)=9/16$.

What is the probability of obtaining exactly one dominant phenotype in a dihybrid cross when each trait independently shows a dominant phenotype with probability $3/4$?

$P=(3/4)(1/4)+(1/4)(3/4)=3/16+3/16=6/16=3/8$.

Monohybrid cross

A genetic cross that examines inheritance of one characteristic, typically between individuals differing at one gene locus. Its offspring are called monohybrids.

Punnett square

A grid that lists possible gametes from each parent and combines them to display possible offspring genotypes. It predicts expected genotype frequencies and, when dominance relationships are known, phenotype frequencies.

What genotype and phenotype result from crossing true-breeding dominant and recessive parents, $YY\times yy$?

Every offspring receives $Y$ from one parent and $y$ from the other, so all offspring are $Yy$ and show the dominant phenotype, yellow seeds.

What genotypic and phenotypic ratios are expected from a monohybrid cross of two heterozygotes, $Yy\times Yy$?

The genotype ratio is $YY:Yy:yy=1:2:1$. With complete dominance, the phenotype ratio is $3$ dominant to $1$ recessive.

Why are there two heterozygous outcomes in the Punnett square for $Yy\times Yy$?

A heterozygote can result from a $Y$ egg and a $y$ sperm or from a $y$ egg and a $Y$ sperm. These distinct fertilization pathways have the same genotype and phenotype, so both must be counted.

How can the $3:1$ phenotypic ratio be derived from the $1:2:1$ genotypic ratio?

The $YY$ and $Yy$ genotypes both show the dominant phenotype and together account for $1/4+2/4=3/4$ of offspring. The $yy$ genotype accounts for $1/4$, producing a $3:1$ phenotype ratio.

What did Mendel’s $F_3$ self-crosses reveal about the genotypes of dominant-phenotype $F_2$ plants?

All recessive-phenotype $F_2$ plants bred true as homozygous recessive. Among dominant-phenotype $F_2$ plants, one-third were homozygous dominant and two-thirds were heterozygous and produced an approximately $3:1$ ratio.

Test cross

A cross between an individual showing a dominant phenotype but having an unknown genotype and a homozygous recessive individual. The offspring reveal whether the unknown parent is homozygous dominant or heterozygous.

How does a test cross distinguish $AA$ from $Aa$ when both parents show the dominant phenotype?

Cross the unknown individual with $aa$. An $AA\times aa$ cross produces all dominant-phenotype $Aa$ offspring, whereas an $Aa\times aa$ cross produces approximately half $Aa$ dominant offspring and half $aa$ recessive offspring.

Law of segregation

The two alleles for a gene separate during gamete formation, so each haploid gamete receives only one allele. The alleles reunite randomly at fertilization.

Law of independent assortment

During gamete formation, allele pairs for different genes assort independently of one another when the genes are unlinked or sufficiently far apart on the same chromosome. This allows probability calculations for separate traits to be multiplied.

Incomplete dominance

A non-Mendelian pattern in which neither allele is completely dominant, so a heterozygote has an intermediate phenotype. A cross of two heterozygotes commonly produces a $1:2:1$ phenotypic ratio.

Codominance

A non-Mendelian pattern in which both alleles are fully expressed in a heterozygote. The heterozygote displays both parental phenotypes rather than an intermediate phenotype.

Multiple alleles

A gene has multiple allelic forms in the population, although each diploid individual still carries only two alleles. The ABO blood-group system is an example, with $I^A$, $I^B$, and $i$ alleles.

Epistasis

A gene interaction in which an allele at one locus masks or modifies the phenotypic effect of a gene at another locus. Because one gene affects the expression of another, epistatic crosses can produce ratios that differ from the standard $9:3:3:1$ dihybrid ratio.

Polygenic inheritance

Inheritance in which multiple genes contribute to one characteristic, often through additive effects. It produces continuous variation, such as the range of human heights or skin tones.

Sex-linked traits

Traits controlled by genes located on sex chromosomes, especially the X chromosome. X-linked recessive traits are more common in males because males have only one X chromosome and therefore express a recessive allele carried on it.