For the experiment giving rise to the data in Table 3.2, an algebraically natural assumption is that the allowable double matings occur as a Poisson process at a rate proportional to the product of the single-mating rates. It is also natural—physically if not mathematically - to allow separate factors for single and double wells, and a reduced rate for wells in which one male does double duty. Formulate this statement as a Poisson log-linear model or four-class multinomial model, and check whether the data are in compliance with the product assumption. For this exercise, the multinomial assumption in section 3.3.4 may be used. (The computation for this question may involve the entire table, but parameter estimates and other conclusions must be a function of the column totals only. Why so?)

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Single matings Double matings Gen ce CS SC SS cc.ss cs.sc cc.cs SC.SS 2 110 11 6 0 6 1 0 2 0 7 2 1 0 4 9 10 11 13 15 1 3 2 1 2 2 0 16 17 20 21 26 31 37 111 2 112 5 113 9 8 1 2 3 1 35 3 0 2 11332- ON-7 0 0 0 1 2 2 0 2 8 3 223 42167 7 9 5 10 8 11 17 == 19 4 4 2 0 2 1 2 3 2 0 1 3 1 2 7 7 13 10 11 543 in 5 1 7 3 3 18 8 11 17 4 9 12 4 5 7 6 2522529 3 5 4 1 7 11 3 7 2 6 44 32510 4 1 2 0 1 0 1 3 0 1 2 1 0 Null Total wells 6W W NO WONN O + + Oo 0 17 9 2 3 3 45 24 47 23 48 14 42 15 48 10 46 23 18 32 24 37 23 9 24 36 22 69