Question

In a series of crosses between two true-breeding strains of peaches, the \(F_{1}\) generation was uniform, producing 30 -g peaches. The \(F_{2}\) fruit mass ranges from 38 to 22 g at intervals of 2 g. (a) Using these data, determine the number of polygenic loci involved in the inheritance of peach mass. (b) Using gene symbols of your choice, give the genotypes of the parents and the \(F_{1}\)

Short answer

There are 4 polygenic loci involved in the inheritance of peach mass. b) What are the genotypes of the parents and the \(F_{1}\) generation using gene symbols of our choice? Using the gene symbols A, B, C, and D: Parent 1 genotype: AABBCCDD (increases mass) Parent 2 genotype: aabbccdd (decreases mass) \(F_{1}\) genotype: AaBbCcDd

Step-by-step solution

Identify the number of phenotypic categories in the \(F_{2}\) generation

We are given that the peaches in the \(F_{2}\) generation have a mass ranging from 22g to 38g, with increments of 2g. Let's calculate the number of phenotypic categories by counting the mass values: 22g, 24g, 26g, 28g, 30g, 32g, 34g, 36g, 38g. There are 9 phenotypic categories in the \(F_{2}\) generation.

Determine the number of polygenic loci using the formula

Now that we have the number of phenotypic categories as 9, we can use the formula \(n = 1 + 2L\) to find the number of polygenic loci (L): \(9 = 1 + 2L\) Subtract 1 from both sides: \(8 = 2L\) Divide both sides by 2: \(4 = L\) There are 4 polygenic loci involved in the inheritance of peach mass.

Choose gene symbols and provide genotypes for parents

Now that we know there are 4 polygenic loci, let's choose gene symbols; we will use A, B, C, and D. Here, uppercase letters (A, B, C, D) will represent genes that increase peach mass, and lowercase letters (a, b, c, d) will represent genes that decrease peach mass. Both parental strains are true-breeding, so their genotypes will be homozygous. Since the \(F_{1}\) generation has a uniform mass, we can assume one parent has a genotype that increases mass, and the other parent has a genotype that decreases mass. Therefore: Parent 1 genotype: AABBCCDD (increases mass) Parent 2 genotype: aabbccdd (decreases mass)

Determine the genotype of the \(F_{1}\) generation

When crossing the two homozygous true-breeding parental strains, all offspring in the \(F_{1}\) generation will inherit one allele from each parent for each locus. So, the genotype of the \(F_{1}\) generation will be: \(F_{1}\) genotype: AaBbCcDd #Summary# In this exercise, we determined that there are 4 polygenic loci involved in the inheritance of peach mass. The genotypes of the parental strains are AABBCCDD and aabbccdd, while the genotype of the \(F_{1}\) generation is AaBbCcDd.

Key concepts

F2 Generation Phenotypes

Understanding the phenotypes of the F2 generation in polygenic inheritance is integral for genetics studies. By breeding two pure strains of peaches, which resulted in F1 offspring with uniform fruit masses, a diverse range of peach masses were observed when the F1 generation was self-pollinated to produce the F2 offspring.

This diversity is a direct consequence of the different combinations of alleles inherited from the F1 generation. The phenotypic variation in the F2 generation of peaches ranged from 22g to 38g at 2g intervals, totaling nine distinct phenotypic categories. This variation indicates that multiple genes are influencing the trait, which is the essence of polygenic inheritance – a single trait controlled by more than one gene.

Through the observed phenotypic categories, we can infer the complexity of inheritance patterns and predict the genetic constitution that leads to such varied physical characteristics in offspring. Students can further visualize this concept by imagining a bag of marbles with different colors representing different genes. When you pull out combinations, the total color mix represents the collective effect of these genes on the phenotype – akin to the various peach masses observed.

True-breeding Strains

The term true-breeding strains is used to describe organisms that, when mated with others of the same genotype, produce offspring that carry the same phenotype. In the exercise, the two true-breeding strains of peach trees consistently produce fruit of a particular mass; one strain yields heavier peaches and the other lighter ones.

When discussing true-breeding organisms, we're essentially talking about individuals that are homozygous at specific gene loci that determine a particular trait. As a result, they can pass on these genetic traits with high predictability. In this case, one parent peach strain could be represented as AABBCCDD (where each capital letter represents a dominant allele for greater mass) and the other as aabbccdd (where each lowercase letter represents a recessive allele for lesser mass). These genotypes reflect pure lines where the alleles for a specific trait are identical.

In practical classroom terms, we might compare true-breeding strains to a recipe that always comes out the same each time it's used. Consistency is key, and true-breeding organisms provide that genetic consistency that is invaluable for controlled breeding experiments in genetics.

Genotypic Categories

In genetics, genotypic categories refer to the different genetic make-ups or combinations that can arise from breeding. With reference to the problem of peach mass, the various combinations of the alleles A, a, B, b, C, c, D, and d from both homozygous parents create the F1 generation with heterozygous genotypes. Each F2 offspring then has a unique combination of these alleles, leading to a variety of genotypic categories.

The offspring's phenotype for a specific trait is the outcome of the interaction of alleles from the polygenic loci. The F2 generation arises from selfing or intercrossing of F1 individuals, their genotypic make-up being a mix of the four polygenic loci genes from both parents, can be visualized as a Punnett Square with multiple alleles.

In classroom activities, these categories can be grouped, counted, and used to deduce ratios that provide insight into the genetic architecture of the trait in question. Understanding how these categories are formed and how they relate to phenotypes can give students a clearer view of the stochastic nature of inheritance, despite the apparent deterministic genetics.