Estimating reaction norms for age and size at maturation when age at first reproduction is unknown

We describe a novel method to estimate the probabilities of maturing at age as a function of size; these probabilities can often be interpreted as probabilistic reaction norms for age and size at maturation. Such estimations are useful for describing the maturation process independently of the processes of growth and mortality, and they can also help to disentangle phenotypic plasticity from evolutionary changes in maturation. The estimation method can be used when mature and immature individuals are representatively sampled over two consecutive seasons, even when maturing individuals are not distinguished. Confidence intervals are derived for the reaction norm parameters using a bootstrap approach. Using simulated data, the method is shown to be asymptotically unbiased and robust to moderate violations of the main simplifying assumptions. However, it is relatively sensitive to small sample sizes: the method is not robust when fewer than about 100 individuals (mature and immature) are sampled from a cohort at a certain age. The method is illustrated by an application to Georges Bank cod stock (Gadus morhua) but can be used for any type of organism