## Shifting Alleles and Evolution

As an example, let's use a population of brown rabbits which live in a forested area. Allele *A*, which produces brown fur, is beneficial as these rabbits easily blend into their forest environment. Within this population is an allele *B* which produces white fur. White fur is less advantageous because it does not camouflage the rabbits as well as brown fur, and these rabbits are less likely to survive to adulthood and reproduce. As a result, the rabbit population consists largely of brown rabbits with a few carrying the white fur allele but not expressing it.

Now let's say the climate changes, and the forest turns into a snow covered environment due to an ice age. Now, rabbits that have white fur blend in perfectly to the snow and rabbits with brown fur are more likely to stand out to predators. Allele *B* has become more beneficial and allele *A*, which produces the brown colored fur, is less so. Due to changes in the environment, the frequency for allele *B* will likely rise as the frequency for allele *A* drops. These changes in allele frequency are the direct result of changing environments and adaptations by the population to that new environment.

## Calculating Allele Frequencies

There are thousands of alleles for thousands of genes within populations. A larger population generally will maintain allele frequencies, advantageous or not, for longer periods of time due to their size. Imagine that a large population is represented by a four-lane highway and a small population is represented by a narrow dirt road. If half of the alleles in the small population 'fall off' the narrow road, there is an easier chance that one specific allele will be completely lost and go extinct. On our four-lane highway, one or two individuals might fall off the road, but the chance that one allele will disappear or change dramatically in frequency this way is lessened. However, while two differing alleles are occupying the same road, one will almost always out-compete the other for expression in the population over a long period of time.

But how do we calculate which allele will begin to decrease based on the current environmental state? We can use the **Hardy-Weinberg model**, which states alleles *p* and *q*, expressed in a population as the genotypes *pp*, *pq*, and *qq*, together represent 100% of the population. Remember, we double alleles because each individual receives a copy of each chromosome from both of their parents and therefore carries two alleles for each trait.

## Hardy-Weinberg Frequencies

We can express the alleles in the population using the following formula:

**p² + 2pq + q² = 1**

This formula above is based on a Punnett square which shows the expected genotypes given two individuals with both a *p* and *q* allele.

Using these frequencies, we can estimate at which generation an allele will become fixed (stay in the population) or when it will be lost (go extinct).

As one allele becomes less prevalent in a population, it begins to decline, and we can track that rate using the Hardy Weinberg equation. We know that p² + 2pq + q² = 1, so if we know the frequency of *p* or *q*, we can calculate the other. Let's say that the frequency of allele *p* in a population is 3.1 percent.

Since we know *p*=0.031 we can find *q* by saying *q*=1-0.031 which is 0.969.

*p*=0.031

*q*=0.969

Now let's plug the numbers into the equation p² + 2pq + q² = 1

0.031² + 2(0.031)(0.969) + 0.969²

0.0009 + .0601 + 0.9389 = 1 (Depending on the number of decimal points used results may appear to be 0.999 which can be rounded to 1)

So from this equation we know the frequencies of alleles in the population.

0.09% of the population will carry two copies of the *p* allele (genotype *pp*).

6% of the population will carry both the *p* and *q* allele (genotype *pq*).

93.89% of the population will carry two copies of the *q* allele (genotype *qq*).

From this we can gather that individuals with the *q* allele are more likely to survive to adulthood and pass their genes on to offspring, and that this variation of the trait is more advantageous. We can also say, assuming no significant environmental shift takes place to make it more advantageous, that the *p* allele will probably continue to decrease as it is present in such a low percentage of the population.

## Lesson Summary

Alleles are variations in genes that code for specific traits. Different combinations of alleles for a single trait will create different phenotypes, or physical traits like fur color or eye color in our examples. Depending on the environment of a given population, allele frequencies will usually favor one allele over the other. As environments and populations evolve, allele frequencies change to favor the new environment. Allele frequencies can be calculated to find the percentage of individuals with a specific allele using the Hardy-Weinberg equation (p² + 2pq + q² = 1), which represents the distribution of alleles by genotype (*pp*, *pq*, and *qq*).