Return to the data set concerning the relationship between the distance from bushland and the level of predation on seeds, introduced in Exercise 3 in Chapter 7. In the earlier analysis of these data, it was assumed that the percentage of predation could be regarded as a normally distributed variable.

(a) Using the information on the number of seeds of each species per cage, convert each value of the percentage of predation (‘%pred’) to the actual number of seeds removed by predation.

(b) Refit your mixed model to the data, using the number of seeds removed by predation as the response variable, and specifying an appropriate error distribution for this response variable, and an appropriate link function to relate the response variable to the linear model.

(c) Obtain diagnostic plots of the residuals. Do these plots indicate that the assumptions underlying the analysis are more nearly fulfilled as a result of the changes to the response variable, the error distribution and the link function?

(d) Make a graphical display, showing the fitted relationship between the proportion of seeds removed by predation and the distance from the bushland, taking into account any other model terms (i.e. residue, cage type, species and/or interaction terms) that your analysis indicates are important. Your plot should also show the scatter of the observed values around this relationship.