Experimental design for spatial sampling applied to the study of tropical forest regeneration

For practical reasons, estimating seed production in tropical forest is only possible by sampling. Classical sampling designs (random or systematic) give poor estimations of seed abundance. The spatial disposition of the trees, combined with nonuniform seed dispersal, leads to a highly heterogeneous spatial distribution of the seeds. We propose a random stratified sampling design based on a model that takes account of seed dispersal processes and the location of the trees. We assume a gamma distribution for dispersal distances. The overall seed dispersal area is divided into adjacent quadrats. In each quadrat, the number of seeds follows a Poisson distribution with the mean derived from the model. We estimate model parameters from the results of a previous study and give the variance of the Horvitz-Thompson estimator of population total for stratified and random sampling designs. A simulation study is used to find the optimal number of strata, and the performance of the sampling design is evaluated. For each model, we compared the variance of the estimator of population total obtained with the stratified sampling design with that obtained with the random sampling design with the same sample size. The stratified sampling design is, on average, 25 times as precise as the random sampling design.