Modelling state uncertainty with photo series data for the estimation of breeding success in a cliff-nesting seabird

Abstract

Breeding success in cliff-nesting seabirds has until now been estimated through repeated nest checks by field workers during the breeding season. The use of automatic cameras offers a method for collecting mark–recapture data that can be modelled in order to estimate productivity without making recurring inspections. This saves expense and work hours in the field and allows for more colonies to be monitored. Capture histories for Brünnich’s Guillemot Uria lomvia breeding sites in a colony on Svalbard were generated using a series of photos taken by a time-lapse camera during the breeding season. To account for state uncertainty for the offspring when only the adult could be observed on the breeding site, we applied a multievent model. We estimated egg survival, hatching success and chick survival rates by modelling state transitions. Subsequently, the estimates were used to calculate breeding success. In order to assess the performance of the model, we compared the estimates with field observations of productivity. The observed breeding success in the study plot lay within the confidence intervals of the breeding success estimated by our model. We show that automatic cameras can be used to collect data which, by the application of new modelling techniques, will provide reliable estimates of demographic parameters that are vital for research and management of cliff-nesting birds. The method presented is a very good supplement to physical examination or “manual” around-the-clock monitoring of breeding birds.

Appendix

The probability to hatch before occasion 2 and survive as a chick until the last occasion K is denoted h(2) and is given by

$$ h(2) = \varphi^{{{\text{egg}},{\text{egg}}}} \times \varphi^{{{\text{egg}},{\text{chick}}}} (1) \times \varphi^{{{\text{chick}},{\text{chick}}\;K{ - }2}} , $$

where $\varphi^{{{\text{egg}},{\text{egg}}}}$ is the probability for an egg to survive between two occasions, $\varphi^{{{\text{egg}},{\text{chick}}}}$ is the probability for an egg to hatch between occasions 1 and 2, and $\varphi^{{{\text{chick}},{\text{chick}}}}$ is the probability for a chick to survive between two occasions.

The probability to hatch between occasions 2 and 3 and then survive as a chick until the last occasion K is given by

$$ h(3) = \varphi^{{{\text{egg}},{\text{egg}}2}} \times (1 - \varphi^{{{\text{egg}},{\text{chick}}}} (1)) \times \varphi^{{{\text{egg}},{\text{chick}}}} (2) \times \varphi^{{{\text{chick}},{\text{chick}}\;K{ - }3}} , $$

where $\varphi^{{{\text{egg}},{\text{chick}}}}$ is the probability for an egg to hatch between any two occasions after occasion 2.

The probability to hatch at occasion 4 ≤ t ≤ K−1 and to survive as a chick until the last occasion is given by

$$ h(t) = \varphi^{{{\text{egg}},{\text{egg}}\;t - 1}} \times (1 - \varphi^{{{\text{egg}},{\text{chick}}}} (1)) \times (1 - \varphi^{{{\text{egg}},{\text{chick}}}} (2))^{t - 3} \times \varphi^{{{\text{egg}},{\text{chick}}}} (2) \times \varphi^{{{\text{chick}},{\text{chick}}\;K - t}} . $$

We can estimate the breeding success denoted BS from the sum of probability to hatch:

$$ {\text{BS}} = \sum\limits_{i = 2}^{K - 1} {p(i)}.$$

This formula can easily be adapted to the case where the probability $\varphi^{{{\text{chick}},{\text{chick}}}}$ and the length of the time interval are not constant.