Question

In foxes, two alleles of a single gene, \(P\) and \(p\), may result in lethality \((P P),\) platinum coat \((P p),\) or silver coat \((p p) .\) What ratio is obtained when platinum foxes are interbred? Is the \(P\) allele behaving domi- nantly or recessively in causing (a) lethality; (b) platinum coat color?

Short answer

Answer: When platinum foxes are interbred, the resulting ratio is 1 Lethal:2 Platinum:1 Silver. The P allele behaves dominantly in causing lethality but recessively in causing platinum coat color.

Step-by-step solution

Set up the cross

We will initially set up the cross between the two platinum foxes (Pp), denoting the parents as P1 and P2. Parent 1 (P1): Pp Parent 2 (P2): Pp

Determine possible gametes

Now we will find possible gametes that these parents can produce. Both parents can produce two gametes, either containing the allele \(P\) or the allele \(p\). P1 gametes: P or p P2 gametes: P or p

Performing Punnett square

In order to cross the alleles, we will put the gametes from P1 and P2 into a Punnett square. This will help us determine the possible genotype combinations and their frequencies in the offspring. ``` P p +---+---+ P | PP | Pp| +---+---+ p | Pp | pp| +---+---+ ```

Calculate the ratios

From the Punnett square, we can calculate the ratios of the genotypes and phenotypes in the offspring. There are three different combinations: \(PP\) - Lethal, \(Pp\) - Platinum coat, and \(pp\) - Silver coat. 1. Lethality (\(PP\)): 1 out of 4 offspring (25%) 2. Platinum coat (\(Pp\)): 2 out of 4 offspring (50%) 3. Silver coat (\(pp\)): 1 out of 4 offspring (25%) Thus, the ratio obtained when platinum foxes are interbred is 1 Lethal:2 Platinum:1 Silver.

Determine the dominance of the P allele

Now we will analyze the behavior of the \(P\) allele for (a) lethality and (b) platinum coat color. (a) Lethality: The \(P\) allele behaves dominantly in causing lethality, as the \(PP\) genotype, which has both \(P\) alleles, leads to lethality in foxes. (b) Platinum coat color: In this case, the \(P\) allele behaves recessively, as a single \(P\) allele does not lead to platinum coat color - foxes must inherit one \(p\) allele and one \(P\) allele (\(Pp\)) to have platinum coat color, which means that the silver coat color trait (\(p\) allele) is dominant over platinum coat color when both alleles are present together.

Key concepts

Genotype Combinations

Understanding genotype combinations is crucial when predicting offspring characteristics using a Punnett square cross. In genetics, the term 'genotype' refers to the combination of alleles an organism has for a specific gene. Each parent contributes one allele for a gene, which can result in different combinations in their offspring.

For example, in the exercise involving platinum and silver coat color in foxes, the two alleles are represented as 'P' and 'p'. When two platinum foxes with the genotype 'Pp' are interbred, their offspring can have three possible genotype combinations: 'PP' (homozygous dominant), 'Pp' (heterozygous), and 'pp' (homozygous recessive). A Punnett square, which is a visual representation of a genetic cross, allows us to easily determine these combinations and their likelihood.

Each box within the Punnett square represents a potential combination from the parents' gametes, which shows not only the genotype but also allows us to infer the phenotype—the observable characteristics—of the offspring, based on what we know about allele dominance.

Allele Dominance

Allele dominance is a fundamental concept in genetics that describes how different forms (alleles) of the same gene interact to produce a certain characteristic in an organism. When dealing with inheritance, it's crucial to understand which allele is dominant as it will determine the phenotypic outcome.

An allele can be dominant, recessive, or co-dominant. A dominant allele will express its trait even if there is only one copy present, denoted as heterozygous (Pp). On the other hand, a recessive allele only expresses its trait when two copies are present, which means the organism is homozygous recessive (pp).

In the context of the fox coat color example from the exercise, we see that the allele 'P' is dominant in the context of lethality, meaning that any fox with one or two 'P' alleles will not survive. However, it behaves recessively in terms of platinum coat color since two different alleles, 'Pp', must be present for the phenotype to appear. This nuanced understanding of allele dominance helps further clarify the phenotypic outcomes of genetic crosses.

Phenotypic Ratios

The phenotypic ratio is a key factor that geneticists use to predict the outcomes of genetic crosses. It represents the ratio of different phenotypes (physical expressions of a trait) that can result from a given genetic cross.

To determine phenotypic ratios, we first need to work out the possible genotype combinations as shown in the Punnett square. From there, we infer the corresponding phenotypes based on our understanding of allele dominance.

In our fox example, there are two visible phenotypes, platinum and silver coat colors, and one lethal (non-visible) outcome. From the Punnett square analysis, we predict that out of every four offspring, on average, there will be one lethal, two platinum, and one silver. This simplifies to a phenotypic ratio of 1:2:1 for this particular cross. The ability to calculate phenotypic ratios is invaluable in genetics, allowing breeders, researchers, and students to forecast the distribution of traits in offspring populations.