P. Braunsteins, S. Hautphenne, C. Minuesa Abril
Population-size-dependent branching processes are models which describe the evolution of populations where individuals give birth independently of each other according to a probability distribution which depends on the current population size. A special case is the branching process with a carrying capacity, which is an appropriate model for populations with logistic growth, whose size tends to fluctuate around a threshold value corresponding to the maximum number of individuals that the ecosystem can support in view of its resources.
In this work, we propose an estimator for the mean of the offspring distribution at each population size based on the observation of the number of individuals up to a certain generation, and we derive its asymptotic properties. Since those processes become extinct almost surely, this requires us to study the corresponding estimators for the Q-process, which corresponds to the original process conditional on not becoming extinct in a distant future.
Keywords: branching process, population-size-dependence, inference, carrying capacity
Scheduled
RM-1 Ramiro Melendreras Award
September 3, 2019 4:50 PM
I3L1. Georgina Blanes building