Table 2 Description of variables used in the analyses

alpha

Annual reporting rate of ring wear

\(\frac{{I_{t} }}{{N_{t} + K_{t - 1} }}\)

I_t is the number of birds reported with a worn ring for the first time during year t, N_t is the number of birds ringed during year t and K_t−1 is the cumulative number of ringed birds up to year t − 1. We also included a scenario where K is adjusted with annual survival of 90%

beta

Proportion of birds with worn rings that were later resighted by other observers

\(\frac{{I_{o} }}{I}\)

I is the number of birds with a ring reported as worn, and I_o is a subset of birds which were later resighted by other observers (o) than the observer that first reported the worn ring

epsilon

Proportion of birds (that were resighted after a ring was reported worn the first time) that were reported again as having a worn ring

\(\frac{{I_{r} }}{{I_{o} }}\)

I_o is the number of birds with worn rings which were later resighted by observers other than the observer that first reported the worn ring, and I_r is a subset of I_o in which at least one repeat observer noted the worn ring

gamma

Proportion of future resightings (after the initial reporting of a worn ring) in which the ring was also reported worn

\(\frac{{O_{R} }}{O}\)

O is the number of repeat observations after the first reporting of a worn ring, and O_R is a subset of the repeat observations in which a ring was also reported as worn

theta

Probability of a bird having a worn ring

Binom(W ~ _A*C)

W is a binomial probability that a bird has a worn ring given that the ring had age A and colour C