Lorenzo Fattorini

Area-based lidar-assisted estimation of forest standing volume

Airborne laser scanning (lidar) technology is increasingly being applied in forest ecosystem surveys. This research note proposes a design-based approach for the lidar-assisted estimation of forest standing volume when ground surveys are performed by means of fixed-area plots. The lidar measurement of the height of the upper canopy (digital crown model) is performed for the whole study area, and the resulting pixel heights are adopted as auxiliary information to couple with the standing volume acquired on the ground by means of sample plots. The ratio estimator for the total volume of the forest is derived in a complete design-based framework together with an unbiased estimator of its sampling variance and the corresponding confidence interval. The proposed procedure has been tested in Bosco della Fontana, a lowland forest in Northern Italy, obtaining a 95% confidence interval for the total volume, which is approximately 2/3 smaller than that obtained by solely using information arising from field plots.

The use of replicated plot, line and point sampling for estimating species abundance and ecological diversity

The paper deals with the problem of estimating diversity indexes for an ecological community. First the species abundances are unbiasedly and consistently estimated using designs based on n random and independent selections of plots, points or lines over the study area. The problem of sampling elusive populations is also considered. Finally, the diversity index estimates are obtained as functions of the abundance estimates. The resulting estimators turn out to be asymptotically (n large) unbiased, even if a considerable bias may occur for a small n. Accordingly, the method of jackknifing is made use of in order to reduce bias.

Monitoring and assessing old-growth forest stands by plot sampling

Abstract Forest inventories are evolving towards multipurpose resource surveys, broadening their scope by including additional topics such as biodiversity issues. Surprisingly, few quantitative surveys have been devoted to old‐growth forests, even if they constitute the most acknowledged forest biodiversity icons. In this framework, the use of probabilistic sampling may provide an effective as well as rigorous support for monitoring and assessing old‐growth forests. To this purpose, the present paper proposes a two‐phase sampling scheme. In the first phase, a coarse survey of few floristic and stand structural attributes is carried out by means of small plots systematically placed on the study area. Subsequently, in the second phase, a fine assessment of a large number of ecological attributes is performed on a subset of enlarged plots selected among the first‐phase ones by means of simple random sampling without replacement. The proposed sampling scheme is implemented for monitoring and assessing the old forests of Cilento National Park (southern Italy). Results and comments are provided as an exemplicative case study.

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.

Design-based diagnostics for k-NN estimators of forest resourcesThis article is one of a selection of papers from Extending Forest Inventory and Monitoring over Space and Time.

The k-nearest neighbours (k-NN) method constitutes a possible approach to improve the precision of the Horvitz–Thompson estimator of a single interest variable using auxiliary information at the estimation stage. Improvements are likely to occur when the neighbouring structure in the space of auxiliary variables is similar to the neighbouring structure in the space of the survey variables. Populations suitable for k-NN can be identified via the scores of the first principal component computed on the variance–covariance matrix of auxiliary variables. If the first principal component explains a large portion of the whole variability, distances among scores provide good approximations of distances in the space of auxiliary variables in such a way that the effectiveness of k-NN can be assessed by plotting the first principal component scores versus the sampled values of each of the interest variables. Monotone relationships with high values of Spearman’s correlation coefficients should denote effectiveness. O...

Extending large-scale forest inventories to assess urban forests

Urban areas are continuously expanding today, extending their influence on an increasingly large proportion of woods and trees located in or nearby urban and urbanizing areas, the so-called urban forests. Although these forests have the potential for significantly improving the quality the urban environment and the well-being of the urban population, data to quantify the extent and characteristics of urban forests are still lacking or fragmentary on a large scale. In this regard, an expansion of the domain of multipurpose forest inventories like National Forest Inventories (NFIs) towards urban forests would be required. To this end, it would be convenient to exploit the same sampling scheme applied in NFIs to assess the basic features of urban forests. This paper considers approximately unbiased estimators of abundance and coverage of urban forests, together with estimators of the corresponding variances, which can be achieved from the first phase of most large-scale forest inventories. A simulation study is carried out in order to check the performance of the considered estimators under various situations involving the spatial distribution of the urban forests over the study area. An application is worked out on the data from the Italian NFI.

Estimation of small woodlot and tree row attributes in large-scale forest inventories

Forest surveys performed over a large scale (e.g. national inventories) involve several phases of sampling. The first phase is usually performed by means of a systematic search of the study region, in which the region is partitioned into regular polygons of the same size and points are randomly or systematically selected, one per polygon. In most cases, first-phase points are selected and recognized in orthophotos or very high resolution satellite images available for the whole study area. Disregarding the subsequent phases, the first phase of sampling can be effectively adopted to select small woodlots and tree rows, in the sense that a unit is selected when at least one first-phase point falls within it. On the basis of such a scheme of sampling, approximately unbiased estimators of abundance, coverage and other physical attributes readily measurable from orthophotos (e.g. tree-row length) are proposed, together with estimators of the corresponding variances. A simulation study is performed in order to check the performance of the estimators under several distributions of units over the study area (random, clustered, spatially trended).

Roe and fallow deer: are they compatible neighbours?

The analysis of the relationships between population density and habitat features is important to evaluate the ecological needs of a species, its potential impact on ecosystems and its interspecific interactions. We analysed the spatial variation of roe deer Capreolus capreolus and fallow deer Dama dama densities in a Mediterranean area in summer 2007 and winter 2007/2008. Previous research has shown that fallow deer can actively displace and exclude roe deer from natural feeding sites. Here we show that both species have the greatest densities in ecotone habitats between wood and open fields (abandoned olive groves and pastures), but with contrasting geographic patterns. The fallow deer showed the greatest densities in the central northern part of the study area near to local historical release sites. The densities of roe deer were great where fallow deer were rare and low where fallow deer were abundant. Spatial overlap was great at the habitat scale, indicating a high potential for competition, but was low at the plot scale, suggesting that partitioning of space occurred at a fine scale. Supporting great numbers of deer, the ecotone areas are crucial for the management of ecosystems. We suggest that roe deer avoid areas with great densities of fallow deer and that interspecific interference from the latter affects the density and distribution of the former both at a fine and at a large scale.

Random versus stratified location of transects or points in distance sampling: theoretical results and practical considerations

A composite approach mixing design-based and model-based inference is considered for analyzing line-transect or point-transect data. In this setting, the properties of the animal abundance estimator stem from the sampling scheme adopted to locate transects or points on the study region, as well as from the modeled detection probabilities. Moreover, the abundance estimation can be viewed as a “generalized” version of Monte Carlo integration. This approach permits to prove the superiority of the stratified placement of transects or points (based on a regular tessellation of the study region) over the uniform random placement. Even if the result was already established for the fixed-area sampling, i.e., when a perfect detection takes place, it was lacking in distance sampling. Comparisons with other widely-applied schemes pursuing an even placement of transects or points are also considered.

Statistical inference on accumulation curves for inventorying forest diversity: A design-based critical look

Abstract Statistical inference on accumulation curves is considered from a design-based perspective. Preliminaries on probabilistic sampling of plants and species are given, emphasizing the fundamental role of independent replications of the sampling scheme. The role of rarefaction curves as a tool for making inference on the effectiveness of the sampling procedures to compile accurate species lists is outlined. Design-based and model-based inference are discussed and compared. Some future developments for design-based inference are considered.