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Fraction of butterflies have a homozygous dominant phenotype is 13/100 or 13%.

Explain is Hardy-Weinberg principle.

The Hardy-Weinberg principle states that allele and genotype frequencies in populations remain constant even in the absence of evolutionary mechanisms. Ultimately, the Hardy-Weinberg principle models populations without evolution under the following conditions: No mutation. No Immigration.

p² + 2pq + q² = 0

Where, p² = frequency of dominant (BB) allele

q² = frequency of recessive (bb) allele

2pq = frequency of heterozygous dominant (bb) allele

For the given question:

Since white is recessive (bb), and 40% of the butterflies are white, then bb = q² = 0.4.

To determine q,

which is the frequency of the recessive allele = q²

q =√0.4

q = 0.632

Since, p + q = 1,

1 - 0.63 = 0.37

p = 0.37

So, the frequency of dominant allele = p²

p² = 0.1369

The dominant brown butterflies are 13%

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