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Natural Selection Probability Models

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Natural Selection Probability Models

A population of beetles lives on dark volcanic soil. In this simplified model, color is inherited: D produces dark shells and is dominant to d, which produces light shells only in dd beetles. Predators are more likely to spot light beetles. Use the scene and study data below to model how survival and chance can affect a population. Show calculations where needed.

Study data

Researchers observed 100 beetles of each color. These percentages describe survival during one season; they are not guarantees for individual beetles.

Shell color

Beetles observed

Survival rate

Dark

100

80%

Light

100

30%

Build and test the models

For allele-probability questions, use the stated simplified assumptions: alleles combine randomly, and each offspring's outcome is independent unless a question says otherwise. A probability describes a chance, not a certain result.

1.From the study data, what is the probability that a randomly chosen dark beetle survives one season? Write it as a decimal and a percentage.

2.If 100 dark beetles and 100 light beetles have the survival rates in the study data, how many survivors of each color would the model predict? State the total predicted survivors, too.

3.A surviving beetle is selected at random from the model's predicted 110 survivors. What is the probability it is dark? Give a fraction and an approximate percentage.

4.In a different population, the allele frequency of d is q = 0.30, so the frequency of D is p = 0.70. Under random allele pairing, use q² to find the expected fraction of light-shelled dd offspring.

5.With p = 0.70 and q = 0.30, what fraction of offspring are expected to be Dd? Use 2pq and show the calculation.

6.A beetle has genotype Dd. Which shell color does the model predict it will have, and why?

7.Suppose a population begins with 50 dark and 50 light beetles. Apply the study survival rates to predict survivors of each color. Which color makes up the larger share of survivors?

8.In a small sample of 4 dark beetles, assume each has an independent 0.80 chance of survival. What is the probability that all 4 survive? Choose the correct answer.

0.0016
0.4096
0.8000
0.9600

9.A student says, “Because dark beetles survive more often in this study, every dark beetle will survive and every light beetle will die.” Is this statement true or false? Explain using the survival probabilities.

10.Use the study data to explain how natural selection could change the population over several generations. Include what happens to the relative number of dark beetles and one reason the change is not perfectly predictable.