A new design for sampling with adaptive sample plots

Adaptive cluster sampling (ACS) is a sampling technique for sampling rare and geographically clustered populations. Aiming to enhance the practicability of ACS while maintaining some of its major characteristics, an adaptive sample plot design is introduced in this study which facilitates field work compared to “standard” ACS. The plot design is based on a conditional plot expansion: a larger plot (by a pre-defined plot size factor) is installed at a sample point instead of the smaller initial plot if a pre-defined condition is fulfilled. This study provides insight to the statistical performance of the proposed adaptive plot design. A design-unbiased estimator is presented and used on six artificial and one real tree position maps to estimate density (number of objects per ha). The performance in terms of coefficient of variation is compared to the non-adaptive alternative without a conditional expansion of plot size. The adaptive plot design was superior in all cases but the improvement depends on (1) the structure of the sampled population, (2) the plot size factor and (3) the critical value (the minimum number of objects triggering an expansion). For some spatial arrangements the improvement is relatively small. The adaptive design may be particularly attractive for sampling in rare and compactly clustered populations with an appropriately chosen plot size factor.     

Adaptive cluster sampling with clusters selected without replacement and stopping rule

Adaptive cluster sampling (ACS) has received much attention in recent years since it yields more precise estimates than conventional sampling designs when applied to rare and clustered populations. These results, however, are impacted by the availability of some prior knowledge about the spatial distribution and the absolute abundance of the population under study. This prior information helps the researcher to select a suitable critical value that triggers the adaptive search, the neighborhood definition and the initial sample size. A bad setting of the ACS design would worsen the performance of the adaptive estimators. In particular, one of the greatest weaknesses in ACS is the inability to control the final sampling effort if, for example, the critical value is set too low. To overcome this drawback one can introduce ACS with clusters selected without replacement where one can fix in advance the number of distinct clusters to be selected or ACS with a stopping rule which stops the adaptive sampling when a predetermined sample size limit is reached or when a given stopping rule is verified. However, the stopping rule breaks down the theoretical basis for the unbiasedness of the ACS estimators introducing an unknown amount of bias in the estimates. The current study improves the performance of ACS when applied to patchy and clustered but not rare populations and/or less clustered populations. This is done by combining the stopping rule with ACS without replacement of clusters so as to further limit the sampling effort in form of traveling expenses by avoiding repeat observations and by reducing the final sample size. The performance of the proposed design is investigated using simulated and real data.     

Evaluation of sampling methods for the estimation of structural indices in forest stands

The paper is about the accurate (i.e. unbiased and precise) and efficient estimation of structural indices in forest stands. We present SIAFOR, a computer programme for the calculation of four nearest-neighbour indices, which describe the spatial arrangement of tree positions, the distribution pattern of species, and the size differentiation between trees. The study uses SIAFOR as a sampling simulator in eight completely stem-mapped forest stands of varying area and structural complexity. We statistically evaluate two sample types (distance and plot sampling), comparing sampling error, bias and minimum sample size for index estimation. We introduce the concepts of measurement expansion factor (MEF) and design expansion factor (DEF) for the technical evaluation of sample type efficiency (optimal sample type). Results indicate that sampling error can reach high levels and that minimum sample sizes for index estimation often amply exceed the limit of 20% of tree density or 20 trees per species per hectare, that we set as the highest feasible sample size in normal situations. We found clear feasibility limits (in terms of minimal tree densities and reachable accuracy levels) for the estimation of all investigated indices. Generally, equal or higher sample sizes are needed for plot sampling than for distance sampling to reach equal accuracy levels. Nevertheless, plot sampling resulted more efficient for the estimation of tree size differentiation at low to medium accuracy levels. For all other investigated indices distance sampling resulted more efficient than plot sampling. Minimum sample size increases with accuracy and is negatively correlated with tree density. At a given accuracy level minimum sample size is highest for the estimation of relative mingling and lowest for tree size differentiation; furthermore it is generally lower in large stands than in small ones. Because of the consistency of our conclusions in all of the investigated stands, we think they apply in most stands of similar area (between 1 and 10 ha) and species diversity (not more than four species).     

Adaptive two-stage one-per-stratum sampling

We briefly describe adaptive cluster sampling designs in which the initial sample is taken according to a Markov chain one-per-stratum design (Breidt, 1995) and one or more secondary samples are taken within strata if units in the initial sample satisfy a given condition C. An empirical study of the behavior of the estimation procedure is conducted for three small artificial populations for which adaptive sampling is appropriate. The specific sampling strategy used in the empirical study was a single random-start systematic sample with predefined systematic samples within strata when the initially sampled unit in that stratum satisfies C. The bias of the Horvitz-Thompson estimator for this design is usually very small when adaptive sampling is conducted in a population for which it is suited. In addition, we compare the behavior of several alternative estimators of the standard error of the Horvitz-Thompson estimator of the population total. The best estimator of the standard error is population-dependent but it is not unreasonable to use the Horvitz-Thompson estimator of the variance. Unfortunately, the distribution of the estimator is highly skewed hence the usual approach of constructing confidence intervals assuming normality cannot be used here.     

Triangulation based inclusion probabilities: a design-unbiased sampling approach

A probabilistic sampling approach for design-unbiased estimation of area-related quantitative characteristics of spatially dispersed population units is proposed. The developed field protocol includes a fixed number of 3 units per sampling location and is based on partial triangulations over their natural neighbors to derive the individual inclusion probabilities. The performance of the proposed design is tested in comparison to fixed area sample plots in a simulation with two forest stands. Evaluation is based on a general approach for areal sampling in which all characteristics of the resulting population of possible samples is derived analytically by means of a complete tessellation of the areal sampling frame. The example simulation shows promising results. Expected errors under this design are comparable to sample plots including a much greater number of trees per plot.     

Estimation of rare and clustered population mean using stratified adaptive cluster sampling

For many clustered populations, the prior information on an initial stratification exists but the exact pattern of the population concentration may not be predicted. Under this situation, the stratified adaptive cluster sampling (SACS) may provide more efficient estimates than the other conventional sampling designs for the estimation of rare and clustered population parameters. For practical interest, we propose a generalized ratio estimator with the single auxiliary variable under the SACS design. The expressions of approximate bias and mean squared error (MSE) for the proposed estimator are derived. Numerical studies are carried out to compare the performances of the proposed generalized estimator over the usual mean and combined ratio estimators under the conventional stratified random sampling (StRS) using a real population of redwood trees in California and generating an artificial population by the Poisson cluster process. Simulation results show that the proposed class of estimators may provide more efficient results than the other estimators considered in this article for the estimation of highly clumped population.

     

Network inclusion probabilities and Horvitz-Thompson estimation for adaptive simple Latin square sampling

Consider a survey of a plant or animal species in which abundance or presence/absence will be recorded. Further assume that the presence of the plant or animal is rare and tends to cluster. A sampling design will be implemented to determine which units to sample within the study region. Adaptive cluster sampling designs Thompson (1990) are sampling designs that are implemented by first selecting a sample of units according to some conventional probability sampling design. Then, whenever a specified criterion is satisfied upon measuring the variable of interest, additional units are adaptively sampled in neighborhoods of those units satisfying the criterion. The success of these adaptive designs depends on the probabilities of finding the rare clustered events, called networks. This research uses combinatorial generating functions to calculate network inclusion probabilities associated with a simple Latin square sample. It will be shown that, in general, adaptive simple Latin square sampling when compared to adaptive simple random sampling will (i) yield higher network inclusion probabilities and (ii) provide Horvitz-Thompson estimators with smaller variability.     

Using forest inventory data to assess fisher resting habitat suitability in California.

The fisher (Martes pennanti) is a forest-dwelling carnivore whose current distribution and association with late-seral forest conditions make it vulnerable to stand-altering human activities or natural disturbances. Fishers select a variety of structures for daily resting bouts. These habitat elements, together with foraging and reproductive (denning) habitat, constitute the habitat requirements of fishers. We develop a model capable of predicting the suitability of fisher resting habitat using standard forest vegetation inventory data. The inventory data were derived from Forest Inventory and Analysis (FIA), a nationwide probability-based sample used to estimate forest characteristics. We developed the model by comparing vegetation and topographic data at 75 randomly selected fisher resting structures in the southern Sierra Nevada with 232 forest inventory plots. We collected vegetation data at fisher resting locations using the FIA vegetation sampling protocol and centering the 1-ha FIA plot on the resting structure. To distinguish used and available inventory plots, we used nonparametric logistic regression to evaluate a set of a priori biological models. The top model represented a dominant portion of the Akaike weights (0.87), explained 31.5% of the deviance, and included the following variables: average canopy closure, basal area of trees <51 cm diameter breast height (dbh), average hardwood dbh, maximum tree dbh, percentage slope, and the dbh of the largest conifer snag. Our use of routinely collected forest inventory data allows the assessment and monitoring of change in fisher resting habitat suitability over large regions with no additional sampling effort. Although models were constrained to include only variables available from the list of those measured using the FIA protocol, we did not find this to be a shortcoming. The model makes it possible to compare average resting habitat suitability values before and after forest management treatments, among administrative units, across regions and over time. Considering hundreds of plot estimates as a sample of habitat conditions over large spatial scales can bring a broad perspective, at high resolution, and efficiency to the assessment and monitoring of wildlife habitat.     

Modeling individual tree mortality for crimean pine plantations

Individual tree mortality model was developed for crimean pine (Pinus nigra subsp. pallasiana) plantations in Turkey. Data came from 5 year remeasurements of the permanent sample plots. The data comprises of 115 sample plots with 5029 individual trees. Parameters of the logistic equation were estimated using weighted nonlinear regression analysis. Approximately 80% of the observations were used for model development and 20% for validation. The explicatory variables in the model were ratio of diameter of the subject tree and basal area mean diameter of the sample plot as measure of competition index for individual trees, basal area and site index. All parameter estimates were found highly significant (p < 0.001) in predicting mortality model. Chi-square statistics indicate that the most important variable is d / d(q), the second most important is site index, and the third most important predictor is stand basal area. Examination of graphs of observed vs. predicted mortality rates reveals that the mortality model is well behaved and match the observed mortality rates quite well. Although the phenomenon of mortality is a stochastic, rare and irregular event, the model fit was fairly good. The logistic mortality model passed a validation test on independent data not used in parameter estimation. The key ingredient for obtaining a good mortality model is a data set that is both large and representative of the population under study and the data satisfy both requirements. The mortality model presented in this paper is considered to have an appropriate level of reliability.     

Evaluation of some competition indices for the construction of Lebanon cedar (Cedrus libani A. Rich.) stand models

The purpose of this research is to test the precision of some published competition indices of Lebanon cedar (Cedrus libani A. Rich.) for the estimation of future periodic diameter increment of individual trees. Twenty- nine published competition indices were tested, using fifteen separate sets of data and their pooled values, collected from various stand age and site quality classes Lebanon cedar at Antalya. Temporary sample plots were taken in Elmali-Qamkuyusu (9 sample plots) and Finike-Pinarcik (6 sample plots) in 2001. Every plot was stem mapped (x and y coordinate system), diameter (dbh), total height, crown length, crown diameter and 10-year radial increment were recorded for trees greater than 4 cm in dbh. Then, in order to evaluate these competition indices for the prediction of the periodic diameter increment of the individual trees. Three linear models have been constructed for each competition index. It was found that the competition indices (Daniels et al., 1986; Biging and Dobbertin, 1995; Pukkala and Kolstr?m, 1987; Hegyi, 1974) with larger influence-zone areas produce better results.     

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.     

Natural tree collectives of pure oriental spruce [Picea orientalis (L.) Link] on mountain forests in Turkey

Distribution area of oriental spruce [Picea orientalis (L.) Link.] in the world is only in the north-east of Turkey and Caucasian. Because of being the semi monopoly tree with respect to its distribution and representing the upper forest line, it is necessary to analyse, evaluate and model the stand structures of oriental spruce forests in Turkey. In this research, some sampling plots were selected in timberline and treeline in the subalpine forest zone in Turkey. In these sampling plots some information about occurrence and development of the tree collectives was obtained. A total of 12 sampling plots (6 in timberline and 6 of them in treeline) were studied and horizontal and vertical stand profiles were obtained, while number of trees ranges between 2-86 in the tree collectives in treeline and in timberline 3-12. According to this, area per tree in treeline and in timberline is determined as 1.02 m2 and 3.75 m2 on an average respectively. Mean age of trees to reach breast height is 43 years in treeline sampling plots and 22 years in timberline sampling plots. According to the ratio of h (mean height) / d1.30 (diameter at breast height), stand stability values were calculated and it was determined if the stands were stable on the basis of the sampling plots. Stability values of the sampling plots changed between 33 and 75.     

A review of adaptive cluster sampling: 1990–2003

Adaptive cluster sampling (ACS) is an adaptive sampling scheme which operates under the rule that when the observed value of an initially selected sampling unit satisfies some condition of interest, C, other additional units in some pre-defined accompanying neighborhood are also added to the sample. In turn, if any of these additional units satisfy C, then their corresponding unit neighborhoods are added to the sample as well, and so on. This process stops when no additional units satisfying C are encountered. This paper will provide a review of the major developments and issues in ACS since its introduction by Thompson (1990) [Journal of the American Statistical Association, 85, 1050–1059].     

Application of adaptive cluster sampling to low-density populations of freshwater mussels

Freshwater mussels appear to be promising candidates for adaptive cluster sampling because they are benthic macroinvertebrates that cluster spatially and are frequently found at low densities. We applied adaptive cluster sampling to estimate density of freshwater mussels at 24 sites along the Cacapon River, WV, where a preliminary timed search indicated that mussels were present at low density. Adaptive cluster sampling increased yield of individual mussels and detection of uncommon species; however, it did not improve precision of density estimates. Because finding uncommon species, collecting individuals of those species, and estimating their densities are important conservation activities, additional research is warranted on application of adaptive cluster sampling to freshwater mussels. However, at this time we do not recommend routine application of adaptive cluster sampling to freshwater mussel populations. The ultimate, and currently unanswered, question is how to tell when adaptive cluster sampling should be used, i.e., when is a population sufficiently rare and clustered for adaptive cluster sampling to be efficient and practical? A cost-effective procedure needs to be developed to identify biological populations for which adaptive cluster sampling is appropriate.     

Hotspots of Epiphytic Lichen Diversity in Two Young Managed Forests

Understanding within-stand variation in diversity of epiphytes will provide an improved basis for producing timber while conserving biological diversity. Two 80-ha, 50–year–old managed stands of conifers were surveyed to locate 0.4 ha putative "diversity" plots, the areas appearing most diverse in lichen epiphytes. These plots were generally located in areas made heterogeneous by canopy gaps, wolf trees (trees with large-diameter lower branches), and old-growth remnant trees. "Matrix" plots, in contrast, were chosen at random from the remaining, more homogenous forest. Diversity plots hosted from 25% to 40% more epiphytic lichen species than matrix plots in both stands. The strongest within-stand gradients in species composition were correlated with percentage of plot occupied by gaps and wolf trees. Percentage of the plot in gaps was correlated with species richness (r = 0.79). In the more structurally diverse stand, diversity and abundance of nitrogen-fixing "cyanolichens" were correlated with percentage of the plot occupied by gaps (0.5 < r < 0.9), and alectorioid lichens were correlated with percentage of the plot occupied by old-growth remnant trees (0.5 < r < 0.6). In the stand with more homogenous structure, percentage of the plot under gaps was correlated with regionally common species that were otherwise absent or sparse in the matrix. Protecting gaps, hardwoods, wolf trees, and old-growth remnant trees during thinning or other partial cutting is likely to promote the majority of epiphytic macrolichens in young conifer forests. Because these features are easily recognized on aerial photos and on the ground by land managers, it is practical to manage for forest structures that would promote lichen diversity.     

抚育间伐对栓皮栎种群空间分布格局的影响

抚育间伐是一种重要的改善林木生长条件的经营措施,对林分结构和动态具有重要影响。为研究抚育间伐对林木种群空间结构与格局影响的内在机制,以间伐和未间伐的栓皮栎人工林为研究对象,通过设置2个100 m×100 m样地并进行每木定位和调查,在采用径级结构代替年龄结构方法将栓皮栎种群划分为幼树(2 cm≤DBH<5 cm)、小树(5 cm≤DBH<13 cm)和大树(DBH≥13 cm)3个生长阶段的基础上,分别采用Ripley’s K函数衍生的g(r)函数和双变量g12(r)函数,对栓皮栎种群空间分布点格局及不同生长阶段栓皮栎种群之间的关联性进行了研究。结果表明,间伐和未间伐样地栓皮栎种群空间分布点格局分别在0-16 m和0-33 m距离尺度内呈聚集分布,而分别在大于16 m和33 m距离尺度内呈随机分布;间伐和未间伐样地栓皮栎幼树、小树和大树的株数比分别为8?741?699和261?1134?683,且间伐样地栓皮栎幼树、小树和大树种群分别在0-14、1-16、0-6 m距离尺度内呈现均匀或聚集分布,而在其他距离尺度上表现为随机分布;栓皮栎幼树、小树和大树之间仅在间伐样地0-6 m距离尺度内呈现一定的相关性,而在未间伐样地更大的距离尺度内有显著的关联性,如栓皮栎幼树和大树之间在6-38 m距离尺度上呈显著正相关。因此,抚育间伐一定程度上使得栓皮栎种群在更大距离尺度上呈现出随机分布状态,并弱化了不同生长阶段的林木栓皮栎种群的关联性,这调整了栓皮栎种群空间竞争关系,有利于大径级林木个体的培育。该研究可以为开展抚育间伐对林木种群的影响的研究提供理论依据,也可以为制定科学合理的抚育技术措施提供参考。     

Empirical likelihood confidence intervals for adaptive cluster sampling

Adaptive cluster sampling (ACS) is an efficient sampling design for estimating parameters of rare and clustered populations. It is widely used in ecological research. The modified Hansen-Hurwitz (HH) and Horvitz-Thompson (HT) estimators based on small samples under ACS have often highly skewed distributions. In such situations, confidence intervals based on traditional normal approximation can lead to unsatisfactory results, with poor coverage properties. Christman and Pontius (Biometrics 56:503–510, 2000) showed that bootstrap percentile methods are appropriate for constructing confidence intervals from the HH estimator. But Perez and Pontius (J Stat Comput Simul 76:755–764, 2006) showed that bootstrap confidence intervals from the HT estimator are even worse than the normal approximation confidence intervals. In this article, we consider two pseudo empirical likelihood functions under the ACS design. One leads to the HH estimator and the other leads to a HT type estimator known as the Hájek estimator. Based on these two empirical likelihood functions, we derive confidence intervals for the population mean. Using a simulation study, we show that the confidence intervals obtained from the first EL function perform as good as the bootstrap confidence intervals from the HH estimator but the confidence intervals obtained from the second EL function perform much better than the bootstrap confidence intervals from the HT estimator, in terms of coverage rate.     

Rain forest fragmentation and the proliferation of successional trees

The effects of habitat fragmentation on diverse tropical tree communities are poorly understood. Over a 20-year period we monitored the density of 52 tree species in nine predominantly successional genera (Annona, Bellucia, Cecropia, Croton, Goupia, Jacaranda, Miconia, Pourouma, Vismia) in fragmented and continuous Amazonian forests. We also evaluated the relative importance of soil, topographic, forest dynamic, and landscape variables in explaining the abundance and species composition of successional trees. Data were collected within 66 permanent 1-ha plots within a large (approximately 1000 km2) experimental landscape, with forest fragments ranging from 1 to 100 ha in area. Prior to forest fragmentation, successional trees were uncommon, typically comprising 2-3% of all trees (> or =10 cm diameter at breast height [1.3 m above the ground surface]) in each plot. Following fragmentation, the density and basal area of successional trees increased rapidly. By 13-17 years after fragmentation, successional trees had tripled in abundance in fragment and edge plots and constituted more than a quarter of all trees in some plots. Fragment age had strong, positive effects on the density and basal area of successional trees, with no indication of a plateau in these variables, suggesting that successional species could become even more abundant in fragments over time. Nonetheless, the 52 species differed greatly in their responses to fragmentation and forest edges. Some disturbance-favoring pioneers (e.g., Cecropia sciadophylla, Vismia guianensis, V. amazonica, V. bemerguii, Miconia cf. crassinervia) increased by >1000% in density on edge plots, whereas over a third (19 of 52) of all species remained constant or declined in numbers. Species responses to fragmentation were effectively predicted by their median growth rate in nearby intact forest, suggesting that faster-growing species have a strong advantage in forest fragments. An ordination analysis revealed three main gradients in successional-species composition across our study area. Species gradients were most strongly influenced by the standlevel rate of tree mortality on each plot and by the number of nearby forest edges. Species-composition also varied significantly among different cattle ranches, which differed in their surrounding matrices and disturbance histories. These same variables were also the best predictors of total successional-tree abundance and species richness. Successional-tree assemblages in fragment interior plots (>150 m from edge), which are subjected to fragment area effects but not edge effects, did not differ significantly from those in intact forest, indicating that area effects per se had little influence on successional trees. Soils and topography also had little discernable effect on these species. Collectively, our results indicate that successional-tree species proliferate rapidly in fragmented Amazonian forests, largely as a result of chronically elevated tree mortality near forest edges and possibly an increased seed rain from successional plants growing in nearby degraded habitats. The proliferation of fast-growing successional trees and correlated decline of old-growth trees will have important effects on species composition, forest dynamics, carbon storage, and nutrient cycling in fragmented forests.     

The application of adaptive cluster sampling for rare subtidal macroalgae

Adaptive cluster sampling (ACS) is a targeting sampling method that provides unbiased abundance estimators for populations of rare species that may be inadequately sampled with simple random sampling (SRS). ACS has been used successfully to estimate abundances of rockfish and sardine larvae from shipboard surveys. In this study, we describe the application of ACS for subtidal macroalgae. Using SCUBA, we measured abundances of Codium mamillosum, C. pomoides, and Halimeda cuneata at three islands and two levels of wave exposure. The three species were relatively patchy and could be sampled with ACS at one site per dive. Their distributions differed among islands and with exposure to wave energy, with H. cuneata found at only one island. ACS is a useful tool for understanding the spatial distribution and abundance of populations of rare benthic species, but, as was the case in this study, may not be as efficient as sampling with SRS with comparable replication.     

Complex national sampling design for long-term monitoring of protected dry grasslands in Switzerland

We describe a probabilistic sampling design of circular permanent plots for the long-term monitoring of protected dry grasslands in Switzerland. The population under study is defined by the perimeter of a national inventory. The monitoring focus is on the species composition of the protected grassland vegetation and derived conservation values. Efficient trend estimations are required for the whole country and for some predefined target groups (six biogeographical regions and eleven vegetation types). The target groups are equally important regardless of their size. Consequently, intensified sampling of the less frequent groups is essential for sample efficiency. The prior information needed to draw a targeted sample is obtained from the sampling frame and external databases. The logistics and generalized delineation of the target population may pose further problems. Thus, investments in fieldwork and travel time should be well balanced by selecting a cluster sample. Second, any access problems in the field and non-target units in the sample should be compensated for by selecting reserve plots as they otherwise may considerably reduce the effective sample size. Finally, the design has to be flexible as the sampling frame may change over time and sampling intensity might have to be adjusted to redefined budgets or requirements. Likewise, the variables and biological items of interest may change. To fulfil all these constraints and to optimally use the available prior information, we propose a multi-stage self-weighted unequal probability sampling design. The design uses modern techniques such as: balanced sampling, spreading, stratified balancing, calibration, unequal probability sampling and power allocation. This sampling design meets the numerous requirements of this study and provides a very efficient estimator.