According to Hardy-Weinberg equilibrium,
p2 + 2pq + q2 = 1
here p is frequency of allele "B" & q is frequency of allele "b".
Allele frequency = No. of copies of an allele in a population / Total no. of all alleles for that gene in a population
Genotype frequency = No. of individuals with a particular genotype in a population / Total no. of individuals in a population
ANS 1. A population will be in Hardy-Weinberg equilibrium if it fits the equation p2 + 2pq + q2 = 1
Here p2 = genotype frequency of BB
q2 = genotype frequency of bb
2pq = genotype frequency of Bb
CALCULATIONS :
Allele frequency of "p" = 90 + 2(55) / 2(55) + 2(90) + 2(10) = 0.65
Allele frequency of "q" = 90+ 2(10) / 2(55) + 2(90) + 2(10) = 0.35
EXPECTED GENOTYPE FREUENCIES -
"BB" = p2 = (0.65)2 = 0.4225 ; expected number of BB rats = 0.4225*155 = 65.48 or 65 approx.
actual number of BB rats = 55
"Bb" = 2pq = 2*0.65*0.35 = 0.455 ; expected number of Bb rats = 0.455*155 = 70.525 or 71 approx.
actual number of Bb rats = 90
"bb" = q2 = (0.35)2 = 0.1225 ; expected number of bb rats = 0.1225*155 = 18.98 or 19 approx.
actual number of bb rats = 10
ACTUAL GENOTYPE FREQUENCIES -
p2 = Individuals with BB genotype / Total population i.e. 55/155 = 0.354 or 35.4%
q2 = Individuals with bb genotype / Total population i.e. 10/155 = 0.064 or 6.4%
2pq = Individuals with Bb genotype / Total population i.e. 90/155 = 0.580 or 58%
p2 + 2pq + q2 = 0.354 + 0.580 + 0.064 = 0.998 (approx. 1)
Yes, the population is in Hardy-Weinberg equilibrium. This means under a given set of assumptions, the allele and genotype frequencies will not change over the course of many generations. The dominant traits do not necessarily increase from one generation to another.
ANS 2. From the above results, population of gray (Bb) rats is better adapted and population of white (bb) rats is maladaptive. This could be possibly due to the natural selection of gray and brown rats because of gray-brown lichen which protected them from being hunted. White rats could be easily spotted against gray-brown lichen and hence, their population declined than expected.
ANS 3. Evolution is a slow and gradual process. One year is very short time span. So, the answer will be NO. Change in first and second generation individuals are due to natural selection. This is beacuse in second year, lichens were wiped off. So now, white rats were selected naturally against brown and gray rats.
The more fit genotypes in 2nd generation are Bb and bb and maladaptive genotype is BB.
In generation 2,
allele frequency of p = 2(15) + 60/ 2(15) + 2(60) + 2(45) = 0.375
allele frequency of q = 2(45) + 60/ 2(15) + 2(60) + 2(45) = 0.625
Expected genotype frequency of BB = p2 = 0.140
Actual Genotype frequency of BB = 15/120 = 0.125
Expected genotype frequency of bb = q2 = 0.390
Actual genotype frequency of bb = 45/120 = 0.375
Expected genotype frequency of Bb = 2pq = 2*0.375*0.625 = 0.468
Actual genotype frequency of Bb = 60/120 = 0.5
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