I have a number of animal observations, and want to deduce the number of territories (i.e. the number of individual animals) from this.
More formally, the problem can be stated as follows: Each observation is a triple consisting of two coordinates and a date. Observations on the same date are assumed to be different animals, whereas observations in close proximity but on different dates might come from the same animal.
I'm looking for the minimal number of territories which can explain all of these observations. Each territory is assumed to be a circle, whose radius is known in advance and the same for all territories. An observation can be assigned to a territory if it falls within that circle, but two observations made on the same date must not be assigned to the same territory. In this model, territories may overlap. An observation may lie within one circle and still be assigned to a different one inside which it lies as well.
Is there an established procedure or algorithm to answer this kind of question? If so, is it an exact optimal solution or an approximation? Do you know of any R package to perform this kind of computation?
At the end of the day, it would also be nice to know which observations have been assigned to the same territory. I believe that with the above definition, this assignment is not uniquely defined in most cases. I'd be also interested in established procedures to make a decision among these alternatives.
If you know of techniques to address this general kind of question, i.e. identifying territories, but the assumptions are different from those stated above, I'd still value a comment providing a useful name or reference.