The Monohybrid Cross
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You should be comfortable with the definitions of gene, allele, homozygous, and heterozygous, and understand that gametes are haploid cells formed by meiosis.
Why this matters
The monohybrid cross is the foundational experiment that revealed the particulate nature of inheritance.
Before Gregor Mendel, the prevailing view was that traits blended in offspring, much like mixing blue and yellow paint to make green. Mendel’s meticulous work with pea plants demonstrated that traits are inherited as discrete units that do not blend but segregate and recombine. By tracking a single trait across generations, he established the predictable ratios that form the basis of classical genetics. This lecture focuses on the mechanics of the monohybrid cross, specifically how the segregation of alleles during gamete formation leads to the characteristic phenotypic ratios observed in the second filial generation.
The Logic of the Monohybrid Cross
To understand the monohybrid cross, imagine a simple system where only one trait is under consideration, such as flower colour in pea plants. Let us assume that purple flower colour is dominant over white. We begin with two pure-breeding lines: one that always produces purple flowers and another that always produces white flowers. When these two parents are crossed, the first filial generation, or F1 generation, consists entirely of purple-flowered plants. This might seem to suggest that the white trait has disappeared, but Mendel’s genius lay in his next step. He allowed the F1 plants to self-pollinate, producing the second filial generation, or F2 generation. In this F2 generation, the white flowers reappeared, but not in a random proportion. Instead, for every three purple flowers, there was one white flower. This 3:1 ratio is the hallmark of the monohybrid cross. The underlying reason is that each F1 plant carries one allele for purple and one for white. During the formation of gametes, these alleles separate, so each gamete receives only one allele. When two F1 plants mate, the random combination of these gametes results in a predictable distribution of genotypes and phenotypes. This process is not about blending; it is about the mechanical sorting of discrete genetic units. The dominance of the purple allele masks the presence of the white allele in the heterozygous state, but the white allele remains intact and can be expressed when two copies come together. This clear, reproducible pattern provided the first solid evidence that inheritance follows specific, mathematical rules rather than being a matter of chance or blending.
Genotypic and Phenotypic Ratios
The distinction between genotype and phenotype is crucial in interpreting the results of a monohybrid cross. The genotype refers to the specific allelic composition of an individual, while the phenotype is the observable trait. In a cross between two heterozygous individuals, denoted as \( \text{Aa} \times \text{Aa} \), the possible gametes from each parent are \( \text{A} \) and \( \text{a} \), each with a probability of \( 0.5 \). Using a Punnett square, we can visualise the four possible combinations of these gametes. One combination is \( \text{AA} \), two are \( \text{Aa} \), and one is \( \text{aa} \). This yields a genotypic ratio of \( 1:2:1 \). However, if allele \( \text{A} \) is completely dominant over allele \( \text{a} \), both \( \text{AA} \) and \( \text{Aa} \) individuals will display the dominant phenotype. Therefore, the phenotypic ratio is \( 3:1 \), with three individuals showing the dominant trait and one showing the recessive trait. It is important to note that the genotypic ratio provides more detailed information than the phenotypic ratio, as it distinguishes between homozygous dominant and heterozygous individuals. This distinction becomes critical in breeding programs and genetic counselling, where knowing the carrier status of an individual is essential for predicting the outcomes of future crosses. The 3:1 phenotypic ratio is a statistical expectation based on large sample sizes; in small samples, deviations from this ratio are common due to random sampling error.
Probability and the Product Rule
The outcomes of a monohybrid cross can be calculated using the rules of probability. The product rule states that the probability of two independent events occurring together is the product of their individual probabilities. In the case of the monohybrid cross, the formation of a zygote involves two independent events: the contribution of an allele from the maternal gamete and the contribution of an allele from the paternal gamete. For a heterozygous parent \( \text{Aa} \), the probability of producing an \( \text{A} \) gamete is \( 0.5 \), and the probability of producing an \( \text{a} \) gamete is also \( 0.5 \). To calculate the probability of an \( \text{AA} \) offspring, we multiply the probability of the maternal \( \text{A} \) gamete by the probability of the paternal \( \text{A} \) gamete: \( 0.5 \times 0.5 = 0.25 \). Similarly, the probability of an \( \text{aa} \) offspring is \( 0.5 \times 0.5 = 0.25 \). For the heterozygous \( \text{Aa} \) offspring, there are two possible pathways: maternal \( \text{A} \) and paternal \( \text{a} \), or maternal \( \text{a} \) and paternal \( \text{A} \). The sum rule states that the probability of either of two mutually exclusive events occurring is the sum of their individual probabilities. Thus, the probability of an \( \text{Aa} \) offspring is \( (0.5 \times 0.5) + (0.5 \times 0.5) = 0.25 + 0.25 = 0.50 \). These probabilities correspond directly to the genotypic ratio of \( 1:2:1 \). Understanding these probabilistic foundations allows for the extension of these principles to more complex crosses involving multiple genes, where the independence of segregation for different loci allows for the multiplication of probabilities across traits.
Test Crosses and Genotype Determination
While the phenotypic ratio of a monohybrid cross can confirm the presence of dominance, it does not always reveal the underlying genotype of an individual displaying the dominant phenotype. An individual with the dominant phenotype could be either homozygous dominant \( \text{AA} \) or heterozygous \( \text{Aa} \). To distinguish between these two possibilities, a test cross is performed. A test cross involves mating the individual of unknown genotype with a homozygous recessive individual \( \text{aa} \). If the unknown individual is homozygous dominant \( \text{AA} \), all offspring will receive an \( \text{A} \) allele from the unknown parent and an \( \text{a} \) allele from the recessive parent, resulting in all heterozygous \( \text{Aa} \) offspring with the dominant phenotype. If the unknown individual is heterozygous \( \text{Aa} \), half of the offspring will receive an \( \text{A} \) allele and half will receive an \( \text{a} \) allele. When combined with the \( \text{a} \) allele from the recessive parent, this results in a 1:1 ratio of dominant to recessive phenotypes in the offspring. The appearance of even a single recessive offspring in a test cross is definitive proof that the unknown parent was heterozygous, as a homozygous dominant parent cannot produce a recessive offspring. This technique is fundamental in genetics for determining the genotype of individuals and is widely used in animal breeding and plant improvement programs to identify carriers of recessive traits.
The concept
Mendel's law of segregation
Paired alleles separate into different gametes.
A common misconception is that the 3:1 phenotypic ratio implies that the recessive allele is 'weaker' or less common in the population. In reality, the ratio is a result of the segregation of alleles in heterozygotes and the dominance relationship between alleles. The frequency of alleles in a population is determined by evolutionary forces such as selection, drift, and migration, not by the dominance relationship itself. A recessive allele can be very common in a population even if the recessive phenotype is rare, as seen in many human genetic disorders. C
Worked example
Problem. In a species of flower, red petals are dominant (\( R \)) over white petals (\( r \)). A red-flowered plant is crossed with a white-flowered plant, and 50% of the offspring have white petals. Determine the genotype of the red-flowered parent and calculate the probability that two offspring from this cross are both red-flowered.
- Identify the genotype of the white-flowered parent. Since white is recessive, the genotype must be \( rr \).
- Analyze the offspring ratio. A 50% white offspring ratio indicates a 1:1 phenotypic ratio, which is characteristic of a test cross between a heterozygote and a homozygote recessive.
- Deduce the genotype of the red-flowered parent. To produce \( rr \) offspring, the red parent must contribute an \( r \) allele. Since it is red, it must also have an \( R \) allele. Thus, the genotype is \( Rr \).
- Determine the probability of a single red offspring. The cross is \( Rr \times rr \). The possible offspring are \( Rr \) (red) and \( rr \) (white), each with a probability of \( 0.5 \). Therefore, \( P(\text{red}) = 0.5 \).
- Calculate the probability of two independent red offspring. Using the product rule, \( P(\text{red and red}) = P(\text{red}) \times P(\text{red}) = 0.5 \times 0.5 = 0.25 \).
Units check. Probability is a dimensionless quantity, so no units are required, but the result is expressed as a decimal or percentage.
Three quick tests
- What is the genotypic ratio of the F2 generation in a standard monohybrid cross between two heterozygotes?
Answer
The genotypic ratio is 1:2:1, representing one homozygous dominant, two heterozygous, and one homozygous recessive individual. - If a plant with the dominant phenotype is crossed with a recessive plant and all offspring show the dominant phenotype, what is the most likely genotype of the dominant parent?
Answer
The dominant parent is most likely homozygous dominant, as a heterozygous parent would produce a 1:1 ratio of dominant to recessive offspring. - Why is the product rule applicable to the calculation of offspring genotypes in a monohybrid cross?
Answer
The product rule applies because the contribution of alleles from the maternal and paternal gametes are independent events, and the genotype of the offspring is determined by the combination of these two independent contributions.
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Lecture notes drafted with a local model and checked line by line by the editor; every number in the worked example was recomputed.
Concepts cited: T-012 · Threads: information, evolution