An organism has alleles R₁ and R₂ on one pair of homologous chromosomes, and it has alleles T₁ and T₂ on another pair. Diagram these pairs of homologs at the end of metaphase I, the end of telophase I, and the end of telophase II, and show how meiosis in this organism produces gametes in expected Mendelian proportions. Assume no crossover between homologous chromosomes.

Verified step by step guidance

1. Step 1: Understand the genetic setup. The organism has two pairs of homologous chromosomes: one pair with alleles R₁ and R₂, and another pair with alleles T₁ and T₂. Each homologous chromosome carries one allele of each gene.
2. Step 2: Diagram the chromosomes at the end of metaphase I. At this stage, homologous chromosomes are paired and aligned at the metaphase plate. You should show two pairs of homologs: one pair with R₁ and R₂ aligned together, and the other pair with T₁ and T₂ aligned together. Each chromosome consists of two sister chromatids.
3. Step 3: Diagram the chromosomes at the end of telophase I. After the first meiotic division, homologous chromosomes separate into two different cells. Each cell will have one chromosome from each pair (either R₁ or R₂, and either T₁ or T₂), but still with sister chromatids attached.
4. Step 4: Diagram the chromosomes at the end of telophase II. The second meiotic division separates sister chromatids. Each of the four resulting cells (gametes) will have one chromatid from each chromosome pair, carrying either R₁ or R₂ and either T₁ or T₂.
5. Step 5: Explain Mendelian proportions. Since there is no crossover, the alleles segregate independently according to Mendel's laws. The gametes will have combinations R₁T₁, R₁T₂, R₂T₁, and R₂T₂ in equal proportions (1:1:1:1), reflecting independent assortment of the two gene pairs.

Key Concepts

Homologous Chromosomes and Alleles

Homologous chromosomes are pairs of chromosomes, one from each parent, that carry the same genes but may have different alleles. In this question, alleles R₁ and R₂ are on one homologous pair, and T₁ and T₂ on another. Understanding their pairing and segregation during meiosis is essential to track how genetic variation is passed to gametes.

Stages of Meiosis I and II

Meiosis consists of two divisions: Meiosis I separates homologous chromosomes, and Meiosis II separates sister chromatids. Key stages include metaphase I (homologs aligned), telophase I (homologs separated), and telophase II (sister chromatids separated). Recognizing chromosome arrangement at these stages helps visualize allele distribution in gametes.

Mendelian Inheritance and Gamete Formation

Mendelian inheritance predicts that alleles segregate independently and assort into gametes in specific ratios. Without crossover, alleles on different chromosome pairs segregate independently, producing gametes with combinations of R₁ or R₂ and T₁ or T₂ in expected Mendelian proportions (1:1:1:1). This principle explains genetic variation in offspring.