Camera trap monitoring of unmarked animals: a map of the relationships between population size estimators

The use of camera traps to monitor unmarked animal populations has expanded during the last decade, leading to the development of several density estimation methods. This plethora of methods may be confusing for the newcomer to the field. Some methods, such as the random encounter model, require the knowledge of the mean travel speed of the animals, while others, such as camera trap distance sampling, do not rely on such assumptions. Different methods, like instantaneous sampling, camera trap distance sampling, and the association model, rely on similar types of data, but do not seem identical. In this article, I explore the relationships between different density estimators, including the random encounter model, the random encounter and staying time model, the time-to-event model, camera-trap distance sampling, the association model, and the space-to-event model. I show how these different estimators are related under two simplifying assumptions (perfect detectability, and animal movements following the ideal gas model). I develop a map of mathematical relationships between these estimators, which can help newcomers to understand how these methods are interconnected.