In an experiment using quantitative genetic approaches to investigate the evolution of butterfly eye-spots as a model system for understanding development. There are 3 groups of butterfly populations: small (mean diameter = 2.6 mm), intermediate (3.4 mm), and large eyespots (3.9 mm). Each group comprises 1/3 of the population. The heritability of eyespot diameter in this population is 0.17. 1)What is the expected size (give a number value in mm) of the eyespots in the next generation if:
a) Only the group with the small eyespots is allowed to reproduce
b) Only the intermediate eyespots
c) Small and large eyespot are mixed together and allowed to reproduce
2) For each group, why might eyespots in the next generation not equal to what you might expect?
To calculate the expected size of the eyespots in the next generation, we will use the concept of heritability and the mean diameter values provided for each group.
1) Expected size of eyespots in the next generation:
a) Only the group with small eyespots reproduces:
Since heritability measures the proportion of phenotypic variation that is due to genetic variation, we can expect the smaller eyespots to have a higher probability of being passed on to the next generation. Therefore, the expected size of the eyespots in the next generation would be similar to the mean diameter of the small eyespots, which is 2.6 mm.
b) Only the intermediate group reproduces:
Similarly, if only the intermediate-sized eyespots reproduce, we can expect the next generation to have eyespots similar in size to the mean diameter of the intermediate eyespots, which is 3.4 mm.
c) Small and large eyespots mixed together:
In this case, since small and large eyespots are mixed together and allowed to reproduce, the expected size of the eyespots in the next generation would be an average of the mean diameters of the small and large eyespots: (2.6 mm + 3.9 mm) / 2 = 3.25 mm.
2) Reasons why eyespots in the next generation might not equal the expected values:
a) Genetic recombination and variation:
During reproduction, genetic recombination can occur and result in offspring with different combinations of genes. This genetic variation may influence the size of the eyespots in the next generation and cause deviations from the expected values.
b) Environmental factors:
The environment can also influence the development and expression of traits. Factors such as nutrition, temperature, or other external conditions may impact the size of the eyespots, leading to variations in the next generation that differ from the expected values.
c) Mutation:
Mutations are random changes in the DNA sequence that can lead to new genetic variations. If mutations affect genes related to eyespot size, they can introduce new variations in the next generation that may not match the expected values.
d) Selection pressure:
If there are selective pressures acting on butterfly populations, such as predators preferring larger or smaller eyespots, it could impact the evolution of eyespot size. This selection pressure may cause the next generation's eyespots to deviate from the expected values as individuals with advantageous traits are more likely to survive and reproduce.
To answer the question, we need to use the concept of heritability and population genetics. Let's break down each part of the question:
1) a) If only the group with small eyespots is allowed to reproduce:
Since heritability is a measure of the proportion of phenotypic variation that is due to genetic factors, we can expect that the next generation will have smaller eyespots on average. This is because the group with small eyespots has a smaller mean diameter, suggesting that there is a higher frequency of genes for smaller eyespots in that group.
To calculate the expected size, we need to use the breeder's equation:
Response = Heritability × Selection Differential
In this case, the selection differential is the difference between the mean of the selected group and the mean of the overall population. Let's denote it as ΔS.
Given that the heritability (h^2) is 0.17, and we are only allowing the group with small eyespots to reproduce, the selection differential (ΔS) would be equal to the mean diameter of the small eyespot group (2.6 mm) minus the mean diameter of the overall population (((2.6 * 1/3) + (3.4 * 1/3) + (3.9 * 1/3)) = 3.3 mm).
So, the expected size of the eyespots in the next generation would be:
Response = 0.17 × (2.6 - 3.3) = 0.17 × (-0.7) = -0.119 mm
Therefore, we can expect the eyespots in the next generation to be smaller by approximately 0.119 mm.
b) If only the group with intermediate eyespots is allowed to reproduce:
Following the same logic, the selection differential (ΔS) would be the mean diameter of the intermediate eyespot group (3.4 mm) minus the mean diameter of the overall population (3.3 mm).
So, the expected size of the eyespots in the next generation would be:
Response = 0.17 × (3.4 - 3.3) = 0.17 × 0.1 = 0.017 mm
Therefore, we can expect the eyespots in the next generation to increase in size by approximately 0.017 mm.
c) If the small and large eyespots are mixed together and allowed to reproduce:
The selection differential (ΔS) would be the mean diameter of the mixed group (((2.6 * 1/3) + (3.9 * 1/3)) = 3.25 mm) minus the mean diameter of the overall population (3.3 mm).
So, the expected size of the eyespots in the next generation would be:
Response = 0.17 × (3.25 - 3.3) = 0.17 × (-0.05) = -0.0085 mm
Therefore, we can expect the eyespots in the next generation to be slightly smaller by approximately 0.0085 mm.
2) Eyespots in the next generation might not equal what we expect due to various factors, such as environmental influences, genetic mutations, genetic recombination during reproduction, and genetic drift. These factors can introduce changes in the genetic composition of the population, leading to variations in the eyespot size that deviate from the expected values. Additionally, natural selection may act differently on the different groups, favoring certain sizes of eyespots over others, thereby affecting the observed outcomes.