Understanding the drivers underlying fluctuations in the size of animal populations is central to ecology, conservation biology, and wildlife management. Reliable estimates of survival probabilities are key to population viability assessments, and patterns of variation in survival can help inferring the causal factors behind detected changes in population size. We investigated whether variation in age‐ and sex‐specific survival probabilities could help explain the increasing trend in population size detected in a small, discrete population of bottlenose dolphins Tursiops truncatus off the east coast of Scotland. To estimate annual survival probabilities, we applied capture–recapture models to photoidentification data collected from 1989 to 2015. We used robust design models accounting for temporary emigration to estimate juvenile and adult survival, multistate models to estimate sex‐specific survival, and age models to estimate calf survival. We found strong support for an increase in juvenile/adult annual survival from 93.1% to 96.0% over the study period, most likely caused by a change in juvenile survival. Examination of sex‐specific variation showed weaker support for this trend being a result of increasing female survival, which was overall higher than for males and animals of unknown sex. Calf survival was lower in the first than second year; a bias in estimating third‐year survival will likely exist in similar studies. There was some support first‐born calf survival being lower than for calves born subsequently. Coastal marine mammal populations are subject to the impacts of environmental change, increasing anthropogenic disturbance and the effects of management measures. Survival estimates are essential to improve our understanding of population dynamics and help predict how future pressures may impact populations, but obtaining robust information on the life history of long‐lived species is challenging. Our study illustrates how knowledge of survival can be increased by applying a robust analytical framework to photoidentification data.