A Bivariate Discrete Model of Changing Colour in Blackbirds

Summary

As first-winter male Blackbirds (Turdus merula) mature, the eye ring and bill colours change from black to yellow. Interest is in the change over time of both colours and their interrelationship. Mantel’s score statistic is used to test for association between eye ring and bill colour, measured on a discrete scale. A constant global cross-ratio model is developed which incorporates changes in each feature and the association between orbital ring and upper mandible colours. Marginal changes are fitted as logistic models of cumulative probabilities, linear over time. Association is measured by dichotomizing both responses, taking the cross-ratio of the resulting 2x2 table of probabilities, and constraining this expression to be equal for all times and possible dichotomies. Evidence from the data under study suggests that the colour of orbital rings changed faster than that of upper mandibles.