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# Mathematical problems in genetics and natural selection

In a population of 1,500 wild rabbits found along the coast of Oregon, dark brown fur (B) is dominant to tan fur (b). Genetic analysis of the population revealed the following genotypic frequencies: 750 BB, 450 Bb, 300 bb

1) Suppose that the tan rabbits fitness is 9% less that dark brown rabbits. What is the selection coefficient for the tan allele?

2) How many of each genotype would you expect after one generation (given the starting point above)?

3) In the same population of rabbits, body mass is normally distributed with an average of 8 kg. Large rabbits stay warmer because they can better retain heat. After an especially cold winter, the average body mass of the breeding adult population was 8.7 kg. Heritability was established by researchers to be 0.65. What was the selection response? What was the expected average body mass of the next rabbit generation (the offspring of the parents which survived the winter)?

#### Solution Preview

Hello!

I hope this explanation helps you to better understand the material. Quantitative genetics can be very daunting, but once you practice a bit, you'll become much better at recognizing the variables in the data and using the equations.

I'm a little confused as to the reference of genetype frequencies in the first paragraph, since the numbers that are given are NOT the frequencies but the number of individuals in the ...

#### Solution Summary

In this solution, I walk the student through the following quantitative genetics problem:

In a population of 1,500 wild rabbits found along the coast of Oregon, dark brown fur (B) is dominant to tan fur (b). Genetic analysis of the population revealed the following genotypic frequencies: 750 BB, 450 Bb, 300 bb

1) Suppose that the tan rabbits fitness is 9% less that dark brown rabbits. What is the selection coefficient for the tan allele?

2) How many of each genotype would you expect after one generation (given the starting point above)?

3) In the same population of rabbits, body mass is normally distributed with an average of 8 kg. Large rabbits stay warmer because they can better retain heat. After an especially cold winter, the average body mass of the breeding adult population was 8.7 kg. Heritability was established by researchers to be 0.65. What was the selection response? What was the expected average body mass of the next rabbit generation (the offspring of the parents which survived the winter)?

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