Question

Mendelian ratios are modified in crosses involving autotet. raploids. Assume that one plant expresses the dominant trait green seeds and is homozygous (WWWW). This plant is crossed to one with white seeds that is also homozygous (wwww). If only one dominant allele is sufficient to produce green seeds, pre- dict the \(F_{1}\) and \(F_{2}\) results of such a cross. Assume that synapsis between chromosome pairs is random during meiosis.

Short answer

Question: Predict the F1 and F2 generation results of a cross between two homozygous autotetraploid plants, one with dominant green seeds and the other with recessive white seeds, given that only one dominant allele is needed for the expression of the green seed trait. Answer: The F1 generation will have all green-seeded offspring. The F2 generation will have a predicted phenotypic ratio of approximately 80 green seeds to 1 white seed.

Step-by-step solution

Cross the Parental Generation (P) plants

In this step, we will cross the two homozygous plants to produce the \(F_{1}\) generation. The plant with green seeds is homozygous dominant (WWWW) and the plant with white seeds is homozygous recessive (wwww). Since we are given that synapsis between chromosome pairs is random, when these two plants are crossed, all of the gametes produced by the green seeded plant will carry a W allele, while all the gametes produced by the white seeded plant will carry a w allele. Therefore, when fertilization takes place, the genotype of the resulting \(F_{1}\) offspring will be WWWW x wwww -> WwWwWwWw.

Determine Phenotype of \(F_{1}\) Generation

Now that we have the genotype of the \(F_{1}\) generation (WwWwWwWw), we need to determine their phenotype. Since we are given that only one dominant allele (W) is sufficient to produce green seeds, the presence of any W allele in the genotype will result in green seeds. Thus, all the \(F_{1}\) offspring will have green seeds because they all have at least one W allele present in their genotype.

Cross the \(F_{1}\) Generation to Produce \(F_{2}\) Generation

To produce the \(F_{2}\) generation, we need to cross the \(F_{1}\) generation plants with themselves (WwWwWwWw x WwWwWwWw). In order to predict the phenotypic ratio of the \(F_{2}\) generation, we will use the Binomial theorem. Here's an explanation of how to apply the Binomial theorem in this case: - Since the four homologous chromosomes undergo random synapsis during meiosis, each chromosome in the autotetraploid can pair with any one of the other three homologous chromosomes equally. - Given that W is the dominant allele and w is the recessive allele, we can write the probability of forming a green seed as \(P(W) = (W + w)^4\) which is equivalent to \((a + b)^n\) in the Binomial theorem. - Using the Binomial theorem, we can expand \((W + w)^4\) as follows: \((1 + W)^4 = 1 + {4\choose1}W + {4\choose2}W^2 + {4\choose3}W^3 + W^4\) where \({n\choose k}\) is the binomial coefficient and \(W\) represents the probability of having a dominant allele. - Since the genotype of the \(F_{1}\) generation is (WwWwWwWw), the probability of having a dominant allele in the gamete is 0.5, and therefore we can replace \(W\) with 0.5 in the equation above to obtain the probability of each genotype in the \(F_{2}\) generation.

Calculate the \(F_{2}\) Generation Phenotypes

Once we have expanded and simplified the expression from step 3, we will get the probability distribution of genotypes in the \(F_{2}\) generation: \((1+0.5)^4 = 1 + 4(0.5) + 6(0.5)^2 + 4(0.5)^3 + (0.5)^4 = 1 + 2 + 1.5 + 0.5 + 0.0625\) Now we can determine the \(F_{2}\) generation phenotype ratios based on this distribution: - Green seeds (having at least one W allele): \(1 + 2 + 1.5 + 0.5 = 5\) - White seeds (having all w alleles): \(0.0625 = \frac{1}{16}\) Thus, the predicted phenotypic ratio of the \(F_{2}\) generation is 5 green seeds: \(\frac{1}{16}\) white seeds (approximately 80:1 when rounding the numbers).

Key concepts

Autotetraploids

Autotetraploids are organisms that have four sets of chromosomes, meaning they are tetraploid. In simpler terms, while typical diploid organisms have two copies of each chromosome, autotetraploids have four. This genetic configuration can result from chromosome duplication, and it is particularly common in plants.
Understanding the role of autotetraploids in genetics is crucial because their unique chromosome structure affects how traits are inherited and expressed. In the context of Mendelian genetics, this larger number of chromosome sets can lead to atypical inheritance patterns because more alleles can mix during reproduction.
During meiosis in autotetraploids, each chromosome has multiple pairing options (random synapsis), which affects the formation of gametes. Consequently, the cross-breeding of autotetraploid organisms, like the plants in the exercise, requires adjusted calculations to predict the outcome of offspring traits. Instead of the usual Mendelian 3:1 phenotypic ratio seen in diploids, autotetraploids can produce more complex patterning, as more combinations of alleles are possible.

Dominant and Recessive Alleles

In genetics, alleles are variations of a gene that determine specific traits. Alleles can be dominant or recessive in their expression. Dominant alleles are those that overshadow the effect of another allele. For example, if an organism carries one dominant allele and one recessive allele for a particular trait, the dominant allele will usually determine the phenotype – the trait that is expressed.
In the exercise scenario, we have plants with a dominant allele represented by 'W' which gives green seeds, and a recessive allele 'w' which results in white seeds. The concept of dominant and recessive alleles is straightforward when looking at diploid organisms (having two alleles per gene). Still, when applied to autotetraploids, it's a bit more complex. In an autotetraploid, having any one dominant allele in the set of four is sufficient to express the dominant trait. So even one 'W' among four alleles can result in the dominant phenotype of green seeds.
This concept is crucial for predicting phenotypic outcomes in offspring, especially when crossing plants with different homozygous traits (e.g., WWWW x wwww) as shown in the exercise.

Phenotypic Ratios

Phenotypic ratios describe the proportion of different traits appearing in offspring from a genetic cross. Mendelian genetics typically involves a simple calculation to predict these ratios based on known genotypes.
In the exercise provided, we deal with an autotetraploid plant cross, and calculating phenotypic ratios becomes more complex but crucial. The presence of four alleles per gene means more combinations are possible, leading to a different distribution of traits than in a typical diploid cross. In the exercise, the resultant offspring phenotypes from a cross of green seed and white seed plants leads to mixed gametes, necessitating the use of the Binomial theorem to ascertain the phenotypic ratio.
To determine the ratio of green to white seed phenotypes in the F2 generation, we used expanded binomial coefficients to figure out probabilities of different allele combinations from the gametes. With the dominant trait (W) being prevalent whenever present, most of the resulting offspring exhibit the dominant phenotype leading to a significant skew in the phenotypic ratios. As calculated, this logic predicts an approximately 80:1 ratio of green to white seeds, highlighting the impact of dominant alleles in autotetraploid inheritance patterns.