Caterina Pisani

A three-phase sampling strategy for large-scale multiresource forest inventories

This article considers a two-phase estimation for the areal extent of K land categories partitioning a study region and a three-phase estimation for the biomass of W forest categories out of the K. In the first phase, a sample of N points is selected according to the unaligned systematic sampling. In the second phase, the selected points are partitioned into L strata on the basis of aerial photos. Then, a total sample of n < N points is selected by stratified sampling and the selected points are visited on the ground and correctly classified into one of K categories. The information achieved in the second phase is sufficient for obtaining an unbiased estimator of the areal extent vector together with a conservative estimator of its variance-covariance matrix. As to the estimation of the biomass of the W forest categories, in the third phase the second-phase sample is further partitioned into substrata on the basis of ground information. Finally, a total sample of m < n points is selected by stratified sampling. Then a plot of adequate radius centered at each point is considered and the biomass is recorded within. An unbiased estimator of the biomass vector is derived together with a conservative estimator of its variance-covariance matrix. The proposed strategy also makes it possible to obtain the calibrated estimator of the areal extent vector as well as estimators for the sums or ratios of the areal extents and biomasses. The application of the strategy in the Italian National Forest Inventory is considered.

Two-stage estimation of ungulate abundance in Mediterranean areas using pellet group count

A design-based strategy for estimating wildlife ungulate abundance in a Mediterranean protected area (Maremma Regional Park) is considered. The estimation is based on pellet group count (clearance count technique) in a set of plots, whose size and number is established on the basis of practical considerations and available resources. The sampling scheme involves a preliminary stratification and subsequent two-stage sampling. In the first stage, large strata (defined through habitat features) are partitioned into spatial units and a sample of units is selected by means of a sampling scheme ensuring inclusion probabilities proportional to unit size, but avoiding the selection of contiguous units. Then, the abundances of the selected units are estimated in a second stage, in which plots are located using a random scheme ensuring an even coverage of the units. In small strata, only the second stage is performed. Unbiased estimators of abundance and conservative estimators of their variances are derived for each strata and for the whole study area. The proposed strategy has been applied since the Summer of 2006 and the estimation results reveal substantial improvement with respect to the previous results obtained by means of an alternative strategy.

A permutation-based combination of sign tests for assessing habitat selection

The analysis of habitat selection in radio-tagged animals is approached by comparing the portions of use against the portions of availability observed for each habitat type. Since data are linearly dependent with singular variance-covariance matrices, standard multivariate statistical tests cannot be applied. To bypass the problem, compositional data analysis is customarily performed via log-ratio transform of sample observations. The procedure is criticized in this paper, emphasizing the several drawbacks which may arise from the use of compositional analysis. An alternative nonparametric solution is proposed in the framework of multiple testing. The habitat use is assessed separately for each habitat type by means of the sign test performed on the original observations. The resulting p values are combined in an overall test statistic whose significance is determined permuting sample observations. The theoretical findings of the paper are checked by simulation studies. Applications to case studies previously considered in literature are discussed.

Variance decomposition in two-stage plot sampling: theoretical and empirical results

The statistical properties of two-stage plot sampling estimators of abundance are considered. In the first stage, some spatial units are selected over the whole study area according to a suitable sampling design, while in the second stage, the selected units are surveyed with floating plot sampling to estimate the abundance within. Some insights into the accuracy of the resulting estimators are obtained by splitting the sample variance into the first and second-stage components, while performance is empirically checked by means of a simulation study. Simulation results show that, in most situations, a relevant amount of the overall variance is due to the second stage sampling.

Design-based asymptotics for two-phase sampling strategies in environmental surveys

&NA; We analyse design‐based properties of two‐phase strategies for estimating totals and nonlinear functions of totals for environmental populations when the sampling schemes are uniquely determined by points placed in the study region. In the first phase, points are located using tessellation stratified sampling, whereas in the second phase a finite population sampling scheme is adopted. We give sufficient conditions on second‐phase designs that ensure consistency, and we investigate the variance convergence rate for some familiar schemes.

Inference on diversity from forest inventories: a review

A number of international agreements and commitments emphasize the importance of appropriate monitoring protocols and assessments as prerequisites for sound conservation and management of the world’s forest ecosystems. Mandated periodic surveys, like forest inventories, provide a unique opportunity to identify and properly satisfy natural resource management information needs. Distinctively, there is an increasing need for detecting diversity by means of unambiguous diversity measures. Because all diversity measures are functions of tree species abundances, estimation of tree diversity indices and profiles is inevitably performed by estimating tree species abundances and then estimating indices and profiles as functions of the abundance estimates. This strategy can be readily implemented in the framework of current forest inventory approaches, where tree species abundances are routinely estimated by means of plots placed onto the surveyed area in accordance with probabilistic schemes. The purpose of this paper is to assess the effectiveness of this strategy by reviewing theoretical results from published case studies. Under uniform random sampling (URS), that is when plots are uniformly and independently located on the study region, consistency and asymptotic normality of diversity index estimators follow from standard limit theorems as the sampling effort increases. In addition, variance estimation and bias reduction are achieved using the jackknife method. Despite its theoretical simplicity, URS may lead to uneven coverage of the study region. In order to avoid unbalanced sampling, the use of tessellation stratified sampling (TSS) is suggested. TSS involves covering the study region by a polygonal grid and randomly selecting a plot in each polygon. Under TSS, the diversity index estimators are consistent, asymptotically normal and more precise than those achieved using URS. Variance estimation is possible and there is no need to reduce bias.

Tree Community Ordering by Diversity Profiles: an Application to Chestnut Coppices

The ecological and economical relevance of sweet chestnut (Castanea sativa Mill.) has long been related to its widespread geographical distribution and multipurpose product potential. In Italy, chestnut management represents a paradigmatic example of the potential conflict between landowner targets and tree species diversity conservation. Distinctively, the relationships between silvicultural treatment and tree species diversity of chestnut coppices are here investigated by means of diversity profiles to assess tree diversity of six stands in Central Italy. The stands were purposively selected in such a way to be characterized by the same site conditions but with different silvicultural features (age, number of thinning). Plot sampling was performed across the stands and their tree diversity was compared and ordered by means of intrinsic diversity profiles estimated from the sample data. The achieved results suggest alternative suitable options for managing chestnut coppice stands in order to enhance tree biodiversity while maintaining timber production.

Two-stage adaptive cluster sampling

Adaptive cluster sampling is usually applied when estimating the abundance of elusive, clustered biological populations. It is commonly supposed that all individuals in the selected area units are detected by the observer, but in many acutal situations this assumption may be highly unrealistic and some individuals may be missed. This paper deals with the problem of handling imperfect detectability in adaptive cluster sampling by using a pure design-based approach. A two-stage adaptive procedure is proposed where the abundance in the selected units is estimated by replicated counts.

Design-based maps for continuous spatial populations

&NA; We analyse the estimation of values of a survey variable throughout a continuum of points in a study area when a sample of points is selected by a probabilistic sampling scheme. At each point, the value is estimated using an inverse distance weighting interpolator, and maps of the survey variable can be obtained. We investigate the design‐based asymptotic properties of the interpolator when the study area remains fixed and the number of sampled points approaches infinity, and we derive conditions ensuring design‐based asymptotic unbiasedness and consistency. The conditions essentially require the existence of a pointwise or uniformly continuous function describing the behaviour of the survey variable and the use of spatially balanced designs to select points. Finally, we propose a computationally simple mean squared error estimator.

Design-based inference on Bernstein type estimators for continuous populations

The estimation of the values of a variable at any point of a study area is performed using Bernstein polynomials when the sampling scheme is implemented by selecting a point in each polygon of a regular grid overimposed onto the area. The evaluation of the precision of the resulting estimates is investigated under a completely design-based framework. Moreover, as the main contribution to the mean squared error of the Bernstein-type estimator is due to the bias, also a pseudo-jackknife estimator is proposed. The performance of both estimators is investigated theoretically and by means of a simulation study. An application to a soil survey performed in Berkshire Downs in Oxfordshire (UK) is considered.