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On your house plants, you had a large population of herbivorous spider mites exhibiting color polymorphism. Homozygous recessive individuals are black, indicated as rr. The other allele exhibits complete dominance over the r allele.

Assume the population was initially at Hardy–Weinberg equilibrium with equal frequencies of the two alleles. However, a predatory mite entered the colony, causing a population bottleneck. Only 10 spider mites survived: 2 were red heterozygotes and 8 were black.

In an attempt to control the spider mites, you sprayed a pesticide that eliminated the predatory mites but not the spider mites. In the absence of predation, the spider mites randomly mated, and there was no evolution, returning the population to Hardy–Weinberg equilibrium within a generation.

Estimate the proportion of spider mites in your current population that are red.

Answer :

Answer:

In Hardy-Weinberg equilibrium, the model is given as:

p^2 + 2pq + q^2 = 1,

Where,

p^2 is frequency of homogeneous with dominant genotype

2pq is frequency of heterogeneous

q^2 is frequency of homogeneous that are recessive.

The recessive is black(rr)

The dominant is red.

Survived spider mites after the predatory mite enters the colony is 2 red and 8 black.

After the sprayed pesticide killed off the predatory mite, but not the spider mites, and the population was back at Hardy–Weinberg equilibrium, The estimate proportion of the homogeneous with dominant gene(That is, Red) is:

p^2 = 2^2 = 4

Explanation:

The Hardy-Weinberg model states that a population will remain at genetic equilibrium as long as five conditions are met:

(1) No change in the DNA sequence.

(2) No migration

(3) A very large population size

(4) Random mating

(5) No natural selection.

Final answer:

The proportion of red spider mites in the current population is estimated to be 20%.

Explanation:

Under Hardy-Weinberg equilibrium, the frequencies of alleles in a population remain constant from generation to generation if certain conditions are met. In this scenario, the population of spider mites experienced a bottleneck due to the presence of a predatory mite, resulting in a decrease in population size. Only 10 spider mites survived, with 2 being heterozygous for the dominant allele and 8 being homozygous recessive.

After removing the predatory mite, the spider mites randomly mated and returned to Hardy-Weinberg equilibrium. Based on the Hardy-Weinberg equation (p² + 2pq + q² = 1), we can calculate the proportion of red spider mites by determining the frequency of heterozygous individuals carrying the dominant allele (2pq).

Since there are 10 spider mites in the population and 2 of them are heterozygous, the proportion of red spider mites would be 2 divided by 10, which is 0.2 or 20%.

Learn more about Hardy-Weinberg equilibrium here:

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