A mathematical model to describe the demographic dynamics of long-lived raptor species.

• Problems on population dynamics of interest in biology and ecology are investigated. • A mathematical model to describe the evolution of long-lived raptor species is introduced. • Estimates for the reproductive parameters involved in the model are provided. • An algorithm based on approximate Bayesian computation methods is proposed. • The dynamics of the black vulture colony located at National Park of Monfragüe (Spain) is described. Population viability analysis of threatened large and long-lived raptor species has strong limitations due to the restricted demographic information available for these species. In this work, we mathematically model the demographic dynamics of these raptor species through time-indexed branching processes. By assuming the more general non-parametric statistical setting, we determine accurate estimates for the most relevant reproductive parameters involved in the model. To this end, we propose an algorithm based on approximate Bayesian computations methods. As illustration, by using real data of counts of the number of pairs in the population, we apply the proposed statistical and computational methods to describe the demographic dynamics of the Eurasian black vulture colony located at National Park of Monfragüe (Spain), which appears to be both the largest and densest breeding colony worldwide. In the scenario of these data-poor species, the class of time-indexed branching processes introduced appears to be appropriate and a more cost-effective method to evaluate dynamics and viability of the populations, applicable to the conservation of these taxa. [ABSTRACT FROM AUTHOR]