The astonishing diversity of cichlid fishes of Lake Victoria is maintained by the preferences of females for males of their own species. To understand how the species arose in the first place, it is important to know the genetic basis of this preference in females. Researchers crossed two species of cichlids, Pundamilia pundamilia and P. nyererei, and raised their offspring (“F₁ hybrids”) to adulthood. They measured degree of preference by the female F₁ fish for P. pundamilia males over P. nyererei males (Haeslery and Seehausen 2005). They then crossed the F₁ hybrids with each other to produce a second generation of hybrids (the “F₂ ”), which they also raised to adulthood and measured the same index of female preference. If a small number of genes are important in determining the preference, then the variance of the preference index will differ between these two generations (it will be highest in the F₂ hybrids). The researchers measured preference in 20 F₁ individuals and 33 F₂ individuals. The results are given below. Assume preference has a normal distribution in both populations.

a. Choose a type of graph and compare the frequency distributions of female preference index in the F₁ and F₂ hybrids. What difference is suggested?

b. Calculate the variances of female preference index in the two hybrid crosses. Do the numbers agree with your visual estimate in (a)?

c. Test whether the variance of female preference index differs between the two crosses.

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F2F2 hybrids: 0.380,0.380, 0.271,0.271, 0.211,0.211, 0.188,0.188, 0.157,0.157, 0.140, 0.140, 0.131,0.131, 0.126,0.126, 0.126,0.126, 0.065,0.065, 0.048,0.048, 0.048,0.048 0.024,0.024, 0.017,0.017, 0.017,0.017, 0.000,0.000, 0.000,0.000, -0.009,-0.009, -0.009,-0.009, -0.014,-0.014, -0.032,-0.032, -0.032,-0.032,-0.044,-0.044, -0.063,-0.063,-0.068,-0.068,-0.082,-0.082,-0.082,-0.082, -0.082,-0.082, -0.143,-0.143, -0.198,-0.198,-0.300,-0.300,-0.314,-0.314,-0.348-0.348 F1F1 hybrids: 0.114,0.114, 0.101,0.101, 0.080,0.080, 0.082,0.082, 0.080,0.080, 0.067, 0.067, 0.054,0.054, 0.015,0.015, 0.015,0.015, 0.007,0.007, 0.007,0.007, -0.019, -0.019,-0.019,-0.019, -0.019,-0.019, -0.024,-0.024, -0.034,-0.034,-0.049, -0.049,-0.058,-0.058,-0.099,-0.099,-0.105-0.105