A mouse from a true-breeding population with nomal gait was...

A mouse from a true-breeding population with nomal gait was crossed to a mouse displaying an odd gait called "dancing." The $\mathrm{F}_1$ animals all showed normal gait. a. If dancing is caused by homozygosity for the recessive allele of a single gene, what proportion of the $\mathrm{F}_2$ mice should be dancers? b. If mice must be homozygous for recessive alleles of both of two different genes to have the dancing phenotype, what proportion of the $\mathrm{F}_2$ should be dancers if the two genes are unlinked? c. When the $\mathrm{F}_2$ mice were obtained, 42 normal and 8 dancers were seen. Use the chi-square test to determine if these results better fit the one-gene model from part $a$ or the two-gene model from part $b$.

A mouse from a true-breeding population with nomal gait was crossed to a mouse displaying an odd gait called "dancing." The $\mathrm{F}_1$ animals all showed normal gait.
a. If dancing is caused by homozygosity for the recessive allele of a single gene, what proportion of the $\mathrm{F}_2$ mice should be dancers?
b. If mice must be homozygous for recessive alleles of both of two different genes to have the dancing phenotype, what proportion of the $\mathrm{F}_2$ should be dancers if the two genes are unlinked?
c. When the $\mathrm{F}_2$ mice were obtained, 42 normal and 8 dancers were seen. Use the chi-square test to determine if these results better fit the one-gene model from part $a$ or the two-gene model from part $b$.

Key Concepts

Independent Assortment

This principle of genetics states that alleles of different genes segregate independently of one another during gamete formation. When considering a two-gene model where the dancing phenotype requires homozygosity for recessive alleles at both loci, the independent assortment of these genes results in a compounded reduction in the expected frequency of the phenotype in the F2 generation.

Recessive Inheritance

Recessive inheritance refers to traits that are expressed phenotypically only when an individual has two copies of the recessive allele. In the context of the problem, normal gait being dominant and 'dancing' being recessive means that individuals must be homozygous recessive to display the dancing phenotype, directly influencing the expected proportions in offspring.

Chi-Square Test for Goodness of Fit

The chi-square test is a statistical method used to compare observed data with expected outcomes based on a genetic model. In genetic crosses, it helps determine whether the discrepancies between observed and predicted ratios of phenotypes (such as normal versus dancing gait) are due to chance or suggest that a different genetic model (for example, one-gene versus two-gene inheritance) might better explain the data.

Mendelian Inheritance

This concept explains how traits are transmitted from parents to offspring through discrete units called alleles. In cases where one trait is governed by one gene, the simple dominant and recessive relationships (as well as more complex scenarios involving multiple genes) determine the expected ratios of phenotypes in subsequent generations such as the F1 and F2 progeny.

Punnett Square Analysis

Punnett squares are a visual tool used to predict the genotype and phenotype distribution in the offspring from a particular genetic cross. By arranging the alleles from each parent, one can calculate the proportions of different genotypes under various inheritance models (e.g., one-gene versus two-gene control) which helps in predicting the appearance of recessive traits in the F2 generation.

Transcript

00:01 All right, guys, we're going to take a look at a pretty typical genetics problem in which we have a mouse from a true breeding population with a normal gate that has crossed to a mouse displaying an odd gate that they call dancing.

00:14 So you can see here, i've kind of assigned an allele type to each phenotype.

00:19 So remember when we're talking about the letters or the genetics, we call that the genotype.

00:23 When we're talking about the physical trait displayed, we call that the phenotype.

00:27 So you can think physical characteristic or trait.

00:29 Okay.

00:31 And so they talk about basically making a cross.

00:34 And so the cross that they're talking about, they would have had a big g, big g, and they would have crossed with a little g, little g.

00:42 That's where that true breeding, that term comes in.

00:46 And so we know that when this cross happens, all individuals are going to be big g, little g, just based on the way the alleles line up.

00:55 So even though all of these mice will appear to have, have the normal g -the themselves.

01:01 They'll all be carrying this little g -allel, meaning that in the next generation, we can see mice that exhibit that dancing.

01:11 So let's just remind ourselves that these are individuals from the f -1 generation.

01:18 Okay.

01:18 So now we're going to take those individuals and we're going to cross them with each other.

01:23 So this is going to be our f -1 cross.

01:26 And so we basically just need to do a simple four square box here.

01:30 And we know that both individuals are big g, little g, and so we line our punnet square up like this.

01:39 So we know that looking at these mice, that having the possession of just one dominant allele will give the mouse the trait of normal gait.

01:51 On the other hand, in order for our mouse to have the dancing trait, they need to be homozygous and they need to have two little g's.

02:00 Okay, so when we look at our phenotypic traits, we wind up with one, two, three out of our four.

02:09 So three quarters or 75 % are what we call normal.

02:19 Okay? and then here we can see we only have one fourth or 25 % that are dance.

02:29 So to answer the first part of the question, we would expect that 25 % of our mouse population would exhibit the dancing allele for their gates, dancing alleles for their gates, giving them that dancing phenotype, and then 75 % would have the alleles that would give them a normal gate phenotype.

02:54 And then, so the next part of the question asks us to use a kai squared method, we're going to use a kai squared method in order to compare an actual observed value with our statistically expected value.

03:13 So let's do that now.

03:17 So what they give us is they say that we have 42 mice that are normal and eight mice that are dancing.

03:31 And so we're going to use that information.

03:36 We have kind of a series of steps that we have to put forth in order to take this information and decide whether it's statistically significant that it's actually happening.

03:48 And it's not just based on chance alone.

03:51 So we're going to have to make a table in order to do this.

03:55 And so, and then we're going to have to use that information that we obtain from our table and we're going to have to compare it to a p chart and decide.

04:05 What the information we have means.

04:10 Okay, so the actual equation for kai squared looks something like this.

04:15 It's kai squared.

04:16 It's not an x.

04:18 And then it is equal to the sum.

04:24 The computer doesn't want to draw here.

04:26 The sum of our observed value minus our expected value, and we square that, and we divide it by our expect.

04:37 Value.

04:38 And you can see here that i've kind of drawn a chart for us.

04:42 This will help us just kind of work through our problem and keep all of our numbers very straightforward so that we don't get confused.

04:49 Okay.

04:50 So if we remember back to our original problem, they told us that we had 50 mice total and 42 of them, that's our observed value, were normal.

05:02 And then eight were dancing.

05:05 Okay.

05:06 So in order to kind of compare that to what we would expect, remember we thought we would see a 75 % to 25 % ratio normal to dancing in the population based on our alleles.

05:20 And so what we would expect to see here would be 37 .5, because that's 75 % of the 50 mice population that we have here...

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