The estimation of the size of a finite population is a problem encountered
in a variety of applications.
One standard statistical approach relies on the well-known mark-recapture
sampling, which may require high costs and cause disturbance to the population
of interest.
These considerations have motivated the search for alternative sampling
strategies that allow to estimate the size of a population from a single capture occasion. Hettiarachchige [Hettiarachchige C.K.H., PhD Thesis, University of Melbourne, http://hdl.handle.net/11343/118636, (2016)] proposes a method that is viable when the population is made of only two generations: a group of generators and one of generated units.
We investigate Bayesian methods alternative to the frequentist estimators used by the original author. Preliminary results give evidence of competing performance of the Bayesian approach, which in some cases sensibly outperforms the frequentist alternatives.
The novelty in the research project is laid in the exploitation of genetic data in order to formulate modelling proposals that allow to estimate the size of a population using a single sample, replacing the widely used mark-recapture sampling techniques.
Indeed, genetic data have become increasingly important in ecology and conservation biology in the last decades and their use in estimating the population size have been already considered in Schwartz, M.K. and Tallmon, D.A. and Luikart, G. (Review of DNA-based census and effective population size estimators, Animal Conservation forum 1 (4), 293 - 299 (1998), Cambridge University Press). The underlying idea is that the degree of biological relationship between a sample of individuals from the population provides information about the population they come from and DNA profiles can be used to detect the degree of relatedness between individuals.
In practice an individual is marked by its presence in the sample, and recaptured if the sample contains one or more of its close relatives, allowing to generalize from recapture of self to recapture of closely-related kin.
The strength of this kind of techniques, especially for endangered species where
collecting data may be demanding and expensive, is that no further captures of the same individual are required. Furthermore, the disturbance to individuals or their natural habitats is not desirable, hence these interactions should be minimal. Finally, there are contexts in which the alive-releasing of the individual in the population is not feasibile and single sample estimates would constitute the unique solution (fishery).
The problem with this approach is that it is sensibly more complex than the ordinary capture-recapture method and may be strictly problem/population dependant. The formulation of a general model, appliable to a wide class of populations, is a difficult challenge and the currently available models depend on hypotheses on the population that are hardly matched in real life.
I would like to take up this challenge, immerging the procedure in a fully Bayesian framework in place of the commonly used frequentist one (Hettiarachchige, C.K.H.: Inference from single occasion capture experiments using genetic markers, PhD Thesis (2016)). The hope is that its great flexibility and the almost unlimited number of modeling proposals it opens the door to, will lead to a more general and robust framework.