Iacomo Jonasson posted an update 1 week, 3 days ago
This paper argues that the general recommendation given by Kendall & White (2009) regarding sampling with replacement in occupancy studies based on spatial replication should be taken with care as sampling with replacement can introduce estimation bias for scenarios that can be considered ecologically realistic. The results presented by KW09 hold for a system well described by a constant proportion of occupied subunits within occupied sites. However, other descriptions may sometimes be more appropriate, and sampling recommendations derived Selleckchem LY294002 from the constant proportion scenario may not hold. For instance, as shown in this paper, if the system is better described by a probability of subunit occupancy independent of the occupancy status of other subunits within the same site, then a recommendation of sampling without replacement would be more appropriate, as a negative bias may be induced in the estimator of occupancy if sampling is carried out with replacement. It is advisable to take this into consideration when designing the sampling protocol rather than assuming that selecting samples with replacement is always the best strategy to follow. Sometimes sampling with replacement may be logistically costly or impractical; therefore, it is important to assess whether it is beneficial for the properties of the occupancy estimator. The choice of whether to sample with or without replacement is relevant when the sample size (i.e. the number of replicates per site, K) is large compared to the number of spatial subunits per sampling site (N). When the sampling site contains many subunits, both approaches yield essentially the same result as, under sampling with replacement, the probability of sampling an already sampled subunit is small. It is often considered that the binomial distribution (which models the process of sampling with replacement) approximates well the hypergeometric distribution (which models the process of sampling without replacement) when the sample size is less than a tenth of the total population size (Wild & Seber 2000, p. 210), that is, in our case if K?<?0��1N. This rule of thumb gives a useful indication on when it is relevant to consider whether to use replacement or not. However, the best way to evaluate the actual impact on the occupancy estimator is to simulate the proposed design. Another issue that influences the relevance of this choice is the mobility of the species (or rate of decay of tracks in the case of track surveys) compared to the timing of the replicate surveys. In the two scenarios analysed, here it was assumed that the occupancy status of each spatial subunit did not change between replicate surveys. As pointed out by KW09, when this is not the case and the occupancy status of spatial subunits is independent of their status in previous replicate surveys (e.g. for highly mobile species), both sampling strategies yield the same results.