Estimability, estimation, and matrix models for seabird populations

Matrix population models can be used to evaluate impacts on a suite of population attributes, e.g. life expectancy or time intervals between important life stages, in addition to population growth rate. Using matrix models to understand these population level effects relies in part on our ability to estimate transition rates for multi-state models. Mark-recapture methods provide a natural and robust format for multi-state parameter estimation but still face challenges such as evaluating parameter redundancy. We discuss use of constraints, a new method for determining parameter redundancy, estimation, and analysis of population attributes for multi-state models. We use breeding processes for the Wandering Albatross (Diomedea exulans) as an example. This four stage model includes: 1) successful breeders; 2) unsuccessful breeders; 3) non-breeders whose previous breeding attempt succeeded; and 4) non-breeders whose previous breeding attempt failed. Two unobservable stages (3 and 4) exacerbate parameter redundancy problems in this model. We found most redundancy problems can be eliminated with simple parameter constraints, except when all survivals are time-dependent and estimated separately. Time-dependence is important in all parameters; survival, probability of breeding, and breeding success. Breeding probabilities show the greatest differences among states and over time. These are the first survival estimates for a biennial seabird that account for non-breeders being unobservable. Matrix model analysis showed similarities and also striking differences among stages.  Life expectancy was similar among stages, whereas individuals who skip breeding the year following a failed breeding attempt (stage 4) take much longer to return to breeding than birds in any other stage (4 years versus < 2 years).  Correspondingly, the number of successful breeding attempts over their lifetime was also lower for stage 4 than any other stage.