5.31∗ Biologists are interested in the distribution of the cytoplasmic heritable determinant of the yeast, Saccharomyces cerevisiae, which exhibits prion-like properties. In an experiment, samples of yeast cells each have effectively, at time zero, an unknown number, m, of inanimate markers, which distribute themselves randomly over the two daughter cells, when cells divide at some unknown rate λ. What is recorded, in a number of replicated samples, is the percentage of cells containing markers. In each of four experiments, the replicate percentages are given below. Experiments A and B are essentially equivalent, but experiments C and D involve unknown time-shifts, which differ between the two experiments.

(i) Suggest a probability model for these data, and consider how you would fit the model using least-squares.

(ii) Consider how you might also make use of the following data on the growth of a yeast colony:

time (hrs) 1 2.17 3 4 5 OD 0.2 0.286 0.392 0.54 0.746