### Summary

- Top of page
- Summary
- Introduction
- Cetacean abundance surveys in the California Current
- Materials and methods
- Results
- Discussion
- Acknowledgements
- References
- Supporting Information

**1.** Estimating temporal trends in animal abundance is central to ecology and conservation, but obtaining useful trend estimates is challenging when animal detection rates vary across surveys (e.g. because of differences in observers or conditions). Methods exist for obtaining abundance estimates using capture–recapture and distance sampling protocols, but only recently have some of these been extended to allow direct estimation of abundance trends when detection rates vary. Extensions to distance sampling for >2 surveys have not yet been demonstrated.

**2.** We demonstrate a Bayesian approach for estimating abundance and population trends, using a time series of line-transect data for endangered fin whales *Balaenoptera physalus* off the west coast of the United States. We use a hierarchical model to partition state and observation processes. Population density is modelled as a function of covariates and random process terms, while observed counts are modelled as an overdispersed Poisson process with rates estimated as a function of population density and detection probability, which is modelled using distance sampling theory. We used Deviance Information Criteria to make multi-model inference about abundance and trend estimates.

**3.** Bayesian posterior distributions for trend parameters provide strong evidence of increasing fin whale abundance in the California Current study area from 1991 to 2008, while individual abundance estimates during survey years were considerably more precise than previously reported estimates using the same data. Assuming no change in underlying population dynamics, we predict continued increases in fin whale numbers over the next decade. Our abundance projections account for both sampling error in parameter estimates and process variance in annual abundance about the mean trend.

**4.***Synthesis and applications.* Bayesian hierarchical modelling offers numerous benefits for analysing animal abundance trends. In our case, these included its implicit handling of sampling covariance, flexibility to accommodate random effects and covariates, ability to compare trend models of different functional forms and ability to partition sampling and process error to make predictions. Ultimately, by placing distance sampling within a more general hierarchical framework, we obtained more precise abundance estimates and an inference about fin whale trends that would have otherwise been difficult.