Model and Assumptions The Royle-Nichols model allows estimation of abundance from multiple observations of present-absent animals without specifically marking the animal. This model represents the spatial distribution of the species observed. Several assumptions are made but two of them are fundamental for this model. First one is that the spatial distribution of the animals across survey sites follows Poisson distribution, and second is the probability of detecting an animal at a site is a function of how many animals are actually at that site. The Poisson distribution represents the mechanism of spatial distribution which is simply how many animals occur at each site within the study area. This model assumes that each site is home to a certain number of species and this number does not change overtime, which means no deaths, births, immigration or emigration of the observed species. The Poisson distribution has as the mean parameter λ (“lambda”) which is the mean abundance across the observed sites.
The probability density formula of for Poisson distribution is F(x)= (e^- λ)* (λ^x)/ x! Where x is the number of animals at a given site and F(x) is the generic term of any probability distribution. Given this information we can find the probability that a specific number of animals occupy a given site. The graph for this formula takes different shapes. For example, if we calculate this function for λ=3 and x=5 animals, the result is a probability of 0.10. The graph