Sampling of sparse species with probability proportional to prediction.

In this article, a 3P sampling (Probability Proportional to Prediction) approach is presented for surveying sparse species connected to certain types of substrates. The method uses the surveyor's judgement of the probability of finding the species on a substrate as the base for selection of substrates for species inventories. The method is presented together with estimators, variances and variance estimators. The method is first presented for sampling based on all substrates in a study area and then as a subsampling technique in a two-stage design in which plots or strips are selected in a first stage. The presented approach was evaluated as a subsampling technique in a strip survey of calicioid lichen species associated with coarse broadleaf trees. In comparison with a simple random subsampling without replacement, 3P subsampling was in one study area found to be an improvement with 30-55% in terms of standard errors. The improvement was more modest in the other study area, only between 10-16%. The strip survey with 3P subsampling was more cost-efficient than a strip survey without subsampling except in one case. Based on the results in the test, 3P sampling seems to have a potential for sampling sparse species.