Mendelian ratios are modified in crosses involving autotetraploids. 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, predict the F₁ and F₂ results of such a cross. Assume that synapsis between chromosome pairs is random during meiosis.

Verified step by step guidance

1. Step 1: Understand the genetic setup. We have an autotetraploid organism with four copies of each gene. The green seed trait is dominant (W), and white seed is recessive (w). The homozygous green parent genotype is WWWW, and the homozygous white parent genotype is wwww.
2. Step 2: Determine the genotype of the F₁ generation. Since the green parent (WWWW) is crossed with the white parent (wwww), all F₁ offspring will inherit two W alleles from the green parent and two w alleles from the white parent, resulting in the genotype WWww.
3. Step 3: Understand allele segregation in autotetraploids. During meiosis, chromosome pairing (synapsis) is random, so gametes can have different combinations of W and w alleles. The possible gametes from a WWww individual can be calculated using the binomial distribution for allele segregation.
4. Step 4: Calculate the gamete genotype frequencies from the F₁ (WWww). The possible gametes are WW, Ww, and ww, with probabilities given by the formula for combinations of alleles in autotetraploid meiosis: \(P(k) = \frac{\binom{2}{k} \binom{2}{2-k}}{\binom{4}{2}}\), where \(k\) is the number of W alleles in the gamete.
5. Step 5: Predict the F₂ generation genotypes and phenotypes by crossing the gametes from the F₁ generation. Use the gamete frequencies to set up a Punnett square or probability matrix, then determine the genotype frequencies of the F₂. Since only one dominant allele is needed for green seeds, calculate the proportion of green (at least one W) and white (all w) phenotypes.

Key Concepts

Autotetraploidy and Chromosome Pairing

Autotetraploids have four copies of each chromosome, originating from genome duplication within a species. During meiosis, chromosomes can pair randomly as bivalents or multivalents, affecting segregation patterns. This random synapsis alters expected Mendelian ratios compared to diploids, influencing genotype and phenotype frequencies in offspring.

Dominance and Allelic Interaction in Polyploids

In polyploids, a single dominant allele can mask the effect of multiple recessive alleles, producing the dominant phenotype. For a trait controlled by one dominant allele (e.g., green seeds), any genotype with at least one 'W' allele will show green seeds, while only the homozygous recessive (wwww) shows white seeds. This affects phenotypic ratios in progeny.

Segregation and Phenotypic Ratios in Polyploid Crosses

Segregation in autotetraploids follows more complex patterns due to multiple chromosome copies and random pairing. The F₁ generation from a homozygous dominant (WWWW) crossed with homozygous recessive (wwww) will be all heterozygous (Wwww) and green. The F₂ generation shows modified ratios, with a higher proportion of dominant phenotypes than diploid Mendelian ratios due to multiple allele combinations.