A Robustness Study of N-Mixture Models in Estimating Animal Population Sizes

INTRODUCTION The size of an animal population, also known as “abundance”, is a crucial parameter that carries significance within the field of statistics, as well as many other academic disciplines, like biology and zoology. This figure is also relevant to people outside academia, from government officials considering lists of endangered species to potential contributors to special interest groups, such as the World Wildlife Fund. It is apparent that there is a diverse body that is impacted by the estimate of abundance. In the past, the most popular method that has been used to estimate abundance is the capture-recapture method. The essence of this procedure is to capture two separate samples of animals, marking and releasing individuals in the initial sample and observing the proportion of marked animals in the second, independently obtained sample. While this process is rather straightforward and has been widely accepted by researchers, it can be fairly demanding. It requires a high level of physical effort on the part of the capturers and it also may not be practical for certain animal species that are difficult to capture. An alternative to the capture-recapture method is the simple count method. The simple count method estimates abundance from a collection of simple counts of observations of the animal of interest. While this process is much more convenient in the sense that a researcher can observe animals rather than physically capture them, especially for extensive examinations, it is susceptible to errors when estimating parameters. A solution to the shortcomings of these methods is to use the N-Mixture model, as proposed by J. Andrew Royle. This model utilizes the observation counts obtained from the simple count method, regarding those counts as ones derived from a binomial distribution, using a parameter for abundance at site i,