Evaluation of sampling methods and assessment of the sample size to estimate the weed seedbank in soil, taking into account spatial variability

As field sampling is time consuming, it is necessary to develop efficient sampling techniques to obtain accurate estimates of the weed seedbank in soil. The relative efficiency between sampling schemes depends on the spatial variability in weed seed density across agricultural fields. Spatial variability of the weed seed density was characterized by theoretical correlograms. A systematic sampling (square grill) scheme was considered and it was found that, taking into account spatial variability, this sampling scheme was more efficient than simple random sampling. As a result, the sample size can be reduced in comparison with that given in previous studies, where spatial correlation was ignored. The reduction depends on the correlation structure defined as a function of the ratio, tau, between the nugget effect and the sill of the variogram. The maximum reduction of the sample size, without loss of either precision or confidence level corresponds to the case where there is no nugget effect, tau = 0. The opposite extreme case, where the reduction is nil, corresponds to the case of a pure nugget effect tau = 1. The abaci based on given expressions are provided to determine the sample size in species whose spatial pattern can be fitted either to a Poisson or to a negative binomial distribution.