How to design a sampling scheme for rare events In sampling design for ecology we often come across sampling rare events. For instance estimating the total number of animals in a region. To achieve minimum logistic cost, we apply systematic sampling with large sized grids, where each gird represents a certain sized area. The total is then estimated by the mean density (number/area per grid) multiplied by the total area of the region. This often results in overestimation the total when the sampling grid hit a cluster of animals (high peak). On the other hand, the location of such clusters is difficult to determine prior to sampling design and it may vary.
Does anyone have any suggestions or good idea about how to handle this kind of sampling design? 
The ultimate goal is to increase precision of the estimate. However, in practice some theoretically sound solutions might be logistically too expensive, and we are also interested in more practical solutions, such as just to optimize the sampling grid. So both theoretical and practical solutions are welcome.
 A: Not my area of expertise, so I expect a better answer to be along.
Designing the grid
Let us say you sample 1% of the area of each grid. 
The number of animals you find in that 1% is probably Poisson distributed since it is a count and your estimate for the final number of animals in the specific area of the grid would one hundred times the observed number, correct?
The variance of the Poisson distribution is the same as the mean. This means that your main error comes from those areas where there are relatively many animals.
This suggests that if you have an a priori estimate of the density you should make the grid finer in places where you expect many animals. Having the same product of density and size in each area of the grid should yield good results. 
Don't go this post-hoc by subdiving the grid because you observed many animals there, this will lead to a bias because it corrects over-estimates but not under-estimates. 
Change the estimation method
There is also a model-based option, similar to what is usually done in field trials. Fit a mixed Poisson regression model to the data using a spatial covariance structure. This will effectively smooth the number of animals you observed in each area of the grid, so that individual over- and underestimatations are corrected.
This paper by Mohebbi, Wolfe and Forbes uses a similar method for disease mapping: 
Mohebbi, M., Wolfe, R., & Jolley, D. (2011). A poisson regression approach for modelling spatial autocorrelation between geographically referenced observations. BMC medical research methodology, 11(1), 133.
A: If the animals tend to cluster in any way, then the standard method for estimating abundance is adaptive sampling. The basic idea: once a target animal is found,  a search of the neighboring areas is launched. See this accessible exposition: http://wiki.awf.forst.uni-goettingen.de/wiki/index.php. A recent text is George A. F. Seber, M. Mohammad Salehi (2013), Adaptive Sampling Designs: Inference for Sparse and Clustered Populations (Springer Briefs in Statistics)
