Two neighborhood-free plot designs for adaptive sampling of forests

Adaptive cluster sampling (ACS) has the potential of being superior for sampling rare and geographically clustered populations. However, setting up an efficient ACS design is challenging. In this study, two adaptive plot designs are proposed as alternatives: one for fixed-area plot sampling and the other for relascope sampling (also known as variable radius plot sampling). Neither includes a neighborhood search which makes them much easier to execute. They do, however, include a conditional plot expansion: at a sample point where a predefined condition is satisfied, sampling is extended to a predefined larger cluster-plot or a larger relascope plot. Design-unbiased estimators of population total and its variance are derived for each proposed design, and they are applied to ten artificial and one real tree position maps to estimate density (number of trees per ha) and basal area (the cross-sectional area of a tree stem at breast height) per hectare. The performances—in terms of relative standard error (SE%)—of the proposed designs and their non-adaptive alternatives are compared. The adaptive plot designs were superior for the clustered populations in all cases of equal sample sizes and in some cases of equal area of sample plots. However, the improvement depends on: (1) the plot size factor; (2) the critical value (the minimum number of trees triggering an expansion); (3) the subplot distance for the adapted cluster-plots, and (4) the spatial arrangement of the sampled population. For some spatial arrangements, the improvement is relatively small. The adaptive designs may be particularly attractive for sampling in rare and compactly clustered populations with critical value of 1, subplot distance equal to the diameter of initial circular plots, or plot size factor of 2.5 for an initial basal area factor of 2.     

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.     

Detecting Rare Species with Random or Subjective Sampling: a Case Study of Red-Listed Saproxylic Beetles in Boreal Sweden

Abstract:  Efficient sampling design in field studies is important for economical and statistical reasons. We compared two ways to distribute sampling effort over an area, either randomly or subjectively. We searched for red-listed saproxylic (wood-living) beetles in 30 spruce stands in boreal Sweden by sifting wood from dead trees. We randomly selected positions within each stand with a geographic positioning system and sampled the nearest dead tree (random sample). In the same stand we also sampled dead trees that, based on literature, were likely to host such species (subjective sampling). The subjective sampling (two to five samples per stand, depending on stand size) was compared with the higher, random sampling effort (fixed level of 12 samples/stand). Subjective sampling was significantly more efficient. Red-listed species were found in 36% of the subjective samples and in 16% of the random samples. Nevertheless, the larger random effort resulted in a comparable number of red-listed species per stand and in 13 detected species in total (vs. 12 species with subjective sampling). Random sampling was less efficient, but provided an unbiased alternative more suitable for statistical purposes, as needed in, for example, monitoring programs. Moreover, new species-specific knowledge can be gained through random searches.     

A diameter increment model for Crimean pine (Pinus nigra Arnold) and Calabrian pine (Pinus brutia Ten.) stands in Isparta region, Turkey

The purpose of this research was to test the precision of a diameter increment model for the estimation of future periodic diameter increment. Individual trees of Crimean pine (Pinus nigra Arnold) and Calabrian pine (Pinus brutia Ten.) located in both natural and plantation stands were selected. For that reason, normal closed canopy, pure, even-aged and undisturbed stands were examined. In 2002, plots were sampled in three natural and three plantation stands in Isparta region of Turkey. The number of sampling points in sample plots ranged from 19 to 55. In each sampling point, a subject tree and six competitors were selected. In each sampling point, subject tree and competitor trees were stem mapped (x and y coordinate system), and diameter (dbh), total height, age, and 10-yrs radial increment recorded. The predictors of a distance dependent diameter increment model were chosen that included tree level (diameter (d), competition index (CI), and age (t)) and stand level (basal area (G), and site index (SI)) characteristics as well as their transformations. The best fit index of the regression model was pursued in trials with variable combinations. The models explained 65%, 60%, 68% and 50% of the variation in individual tree diameter increment of Crimean pine and Calabrian pine for both natural and plantations stands, respectively. These models can be estimated diameter increment of individual trees at highly significant level (p<0.001).     

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.     

An Inverse Gaussian distribution of tree frequencies based on tree size

Forest stand management often depends on data from a single fixed area inventory plot located at random in a forest stand. The plot provides detailed information about tree size distribution but not about per unit area tree frequency distribution unless one assumes a Poisson (POI) distribution. The POI assumption ignores any relationship between a tree's size and its demand for growing space. This study argues for the Inverse Gaussian (IG) distribution as a more realistic model. Maximum likelihood estimates of the IG parameters are obtained from a transformation of tree size data (diameter) to proxies of tree counts. Data from two stands indicated that an IG model was better at predicting the tree frequency distribution than a POI model.     

Tree growth inference and prediction from diameter censuses and ring widths.

Estimation of tree growth is based on sparse observations of tree diameter, ring widths, or increments read from a dendrometer. From annual measurements on a few trees (e.g., increment cores) or sporadic measurements from many trees (e.g., diameter censuses on mapped plots), relationships with resources, tree size, and climate are extrapolated to whole stands. There has been no way to formally integrate different types of data and problems of estimation that result from (1) multiple sources of observation error, which frequently result in impossible estimates of negative growth, (2) the fact that data are typically sparse (a few trees or a few years), whereas inference is needed broadly (many trees over many years), (3) the fact that some unknown fraction of the variance is shared across the population, and (4) the fact that growth rates of trees within competing stands are not independent. We develop a hierarchical Bayes state space model for tree growth that addresses all of these challenges, allowing for formal inference that is consistent with the available data and the assumption that growth is nonnegative. Prediction follows directly, incorporating the full uncertainty from inference with scenarios for "filling the gaps" for past growth rates and for future conditions affecting growth. An example involving multiple species and multiple stands with tree-ring data and up to 14 years of tree census data illustrates how different levels of information at the tree and stand level contribute to inference and prediction.     

Wood Density as a Conservation Tool: Quantification of Disturbance and Identification of Conservation‐Priority Areas in Tropical Forests

Abstract: Inventories of tree species are often conducted to guide conservation efforts in tropical forests. Such surveys are time consuming, demanding of expertise, and expensive to perform and interpret. Approaches to make survey efforts simpler or more effective would be valuable. In particular, it would be good to be able to easily identify areas of old‐growth forest. The average density of the wood of a tree species is closely linked to its successional status. We used tree inventory data from eastern Borneo to determine whether wood density can be used to quantify forest disturbance and conservation importance. The average density of wood in a plot was significantly and negatively related to disturbance levels, with plots with higher wood densities occurring almost exclusively in old‐growth forests. Average wood density was unimodally related to the diversity of tree species, indicating that the average wood density in a plot might be a better indicator of old‐growth forest than species diversity. In addition, Borneo endemics had significantly heavier wood than species that are common throughout the Malesian region, and they were more common in plots with higher average wood density. We concluded that wood density at the plot level could be a powerful tool for identifying areas of conservation priority in the tropical rain forests of Southeast Asia.     

Chilean Blue Whales as a Case Study to Illustrate Methods to Estimate Abundance and Evaluate Conservation Status of Rare Species

Abstract: Often abundance of rare species cannot be estimated with conventional design‐based methods, so we illustrate with a population of blue whales (Balaenoptera musculus) a spatial model‐based method to estimate abundance. We analyzed data from line‐transect surveys of blue whales off the coast of Chile, where the population was hunted to low levels. Field protocols allowed deviation from planned track lines to collect identification photographs and tissue samples for genetic analyses, which resulted in an ad hoc sampling design with increased effort in areas of higher densities. Thus, we used spatial modeling methods to estimate abundance. Spatial models are increasingly being used to analyze data from surveys of marine, aquatic, and terrestrial species, but estimation of uncertainty from such models is often problematic. We developed a new, broadly applicable variance estimator that showed there were likely 303 whales (95% CI 176–625) in the study area. The survey did not span the whales' entire range, so this is a minimum estimate. We estimated current minimum abundance relative to pre‐exploitation abundance (i.e., status) with a population dynamics model that incorporated our minimum abundance estimate, likely population growth rates from a meta‐analysis of rates of increase in large baleen whales, and two alternative assumptions about historic catches. From this model, we estimated that the population was at a minimum of 9.5% (95% CI 4.9–18.0%) of pre‐exploitation levels in 1998 under one catch assumption and 7.2% (CI 3.7–13.7%) of pre‐exploitation levels under the other. Thus, although Chilean blue whales are probably still at a small fraction of pre‐exploitation abundance, even these minimum abundance estimates demonstrate that their status is better than that of Antarctic blue whales, which are still <1% of pre‐exploitation population size. We anticipate our methods will be broadly applicable in aquatic and terrestrial surveys for rarely encountered species, especially when the surveys are intended to maximize encounter rates and estimate abundance.     

Mitochondrial control region sequence analyses indicate dispersal from the US East Coast as the source of the invasive Indo-Pacific lionfish Pterois volitans in the Bahamas

Lionfish are popular aquarium fish from the Indo-Pacific that have invaded the western Atlantic. Two species, Pterois volitans and P. miles, were well established along the United States east coast before the first lionfish were reported from the Bahamas in 2004, where they quickly dispersed throughout the archipelago by 2007. The source of the Bahamian lionfish invasion has been in question because of the hypothesized low connectivity between Florida and Bahamas reef species as well as the temporal lag in their arrival in the Bahamas. Mitochondrial control region haplotypes (680 bp) were determined and analyzed for lionfish specimens from the Bahamas, North Carolina, and two sites within their native range (Indonesia and the Philippines). Exact tests, pairwise F _st and AMOVA analyses all showed no significant differentiation between the Bahamas and North Carolina specimens. The similarity between the Bahamas and North Carolina lionfish was also reflected in a minimum spanning network and neighbor-joining distance tree generated from the data. Sequence analyses also revealed the presence of only Pterois volitans, as no P. miles were detected in the Bahamian sample. These results indicate that the source of the Bahamian lionfish is egg and larval dispersal from the United States east coast population, and support previous models of reef fish dispersal that suggest a low level of connectivity between the Bahamas and east coast of Florida.     

Mortality of large trees and lianas following experimental drought in an Amazon forest

Severe drought episodes such as those associated with El Ni?o Southern Oscillation (ENSO) events influence large areas of tropical forest and may become more frequent in the future. One of the most important forest responses to severe drought is tree mortality, which alters forest structure, composition, carbon content, and flammability, and which varies widely. This study tests the hypothesis that tree mortality increases abruptly during drought episodes when plant-available soil water (PAW) declines below a critical minimum threshold. It also examines the effect of tree size, plant life form (palm, liana, tree) and potential canopy position (understory, midcanopy, overstory) on drought-induced plant mortality. A severe, four-year drought episode was simulated by excluding 60% of incoming throughfall during each wet season using plastic panels installed in the understory of a 1-ha forest treatment plot, while a 1-ha control plot received normal rainfall. After 3.2 years, the treatment resulted in a 38% increase in mortality rates across all stems >2 cm dbh. Mortality rates increased 4.5-fold among large trees (>30 cm dbh) and twofold among medium trees (10-30 cm dbh) in response to the treatment, whereas the smallest stems were less responsive. Recruitment rates did not compensate for the elevated mortality of larger-diameter stems in the treatment plot. Overall, lianas proved more susceptible to drought-induced mortality than trees or palms, and potential overstory tree species were more vulnerable than midcanopy and understory species. Large stems contributed to 90% of the pretreatment live aboveground biomass in both plots. Large-tree mortality resulting from the treatment generated 3.4 times more dead biomass than the control plot. The dramatic mortality response suggests significant, adverse impacts on the global carbon cycle if climatic changes follow current trends.     

Tree species diversity and its relationship to stand parameters and geomorphology features in the eastern Black Sea region forests of Turkey

We studied the effects of stand parameters (crown closure, basal area, stand volume, age, mean stand diameter number of trees, and heterogeneity index) and geomorphology features (elevation, aspect and slope) on tree species diversity in an example of untreated natural mixed forest stands in the eastern Black Sea region of Turkey. Tree species diversity and basal area heterogeneity in forest ecosystems are quantified using the Shannon-Weaver and Simpson indices. The relationship between tree species diversity basal area heterogeneity stand parameters and geomorphology features are examined using regression analysis. Our work revealed that the relationship between tree species diversity and stand parameters is loose with a correlation coefficient between 0.02 and 0.70. The correlation of basal area heterogeneity with stand parameters fluctuated between 0.004 and 0.77 (R2). According to our results, stands with higher tree species diversity are characterised by higher mean stand diameter number of diameter classes, basal area and lower homogeneity index value. Considering the effect of geomorphology features on tree species or basal area heterogeneity we found that all investigated relationships are loose with R < or = 0.24. A significant correlation was detected only between tree species diversity and aspect. Future work is required to verify the detected trends in behaviour of tree species diversity if it is to estimate from the usual forest stand parameters and topography characteristics.     

Effects of Forest Management on Amphibians and Reptiles in Missouri Ozark Forests

Abstract:  As part of the Missouri Ozark Forest Ecosystem Project (MOFEP), we experimentally evaluated the impacts of forest management on the relative abundance of amphibians and reptiles in Missouri's Ozark forests (U.S.A.). Using large study sites (average size of 400 ha) as the experimental unit, we tested the effects of uneven-aged and even-aged forest management treatments compared with no-harvest management (i.e., control) on the relative abundance of 13 focal amphibian and reptile species. Within even-aged management sites, we also focused on the local-scale effects of clearcutting on these species by comparing relative abundance among plots located within clearcut stands, 50 m away from clearcut stands, and 200 m away from clearcut stands. Pretreatment sampling of species abundance occurred from 1992 through 1995, and post-treatment sampling occurred from 1997 through 2000. At the landscape scale, treatment significantly affected the abundance of Bufo americanus . This species declined less on even-aged management sites than on control sites, but the general decline on all sites suggests that other factors may have contributed to this result. Within even-aged management sites, most amphibian species declined and some reptile species increased relative to pretreatment abundances within clearcut stands. We found significant effects of distance from clearcut for two amphibian species, Ambystoma maculatum and Rana clamitans, and two reptile species, Scincella lateralis and Sceloporus undulatus . In general, we conclude that clearcuts within even-aged management sites locally affected amphibian and reptile species but, at a larger spatial scale, we did not detect significant effects of even-aged and uneven-aged forest management. These findings represent relatively short-term data but suggest that forest management and maintenance of biodiversity may be compatible when relatively small amounts of the landscape are disturbed.     

Spatially explicit modeling of overstory manipulations in young forests: Effects on stand structure and light

Young forests can be manipulated in diverse ways to enhance their ecological values. We used stem maps from two dense, second-growth stands in western Washington and a spatially explicit light model (tRAYci) to simulate effects of five silvicultural manipulations on diameter distribution, species composition, spatial patterning, and light availability. Each treatment removed 30% of the basal area, but differed in how trees were selected for removal. Three primary treatments were thin from below (removing the smallest trees), random thin (removing trees randomly), and gap creation (removing all trees in circles ∼1 tree height in diameter). Two additional treatments combined elements of these approaches: random ecological thin (a mixture of thin from below and random thin) and structured ecological thin (a mixture of thin from below and gap creation).     

Using simulation to explore the functional relationships of terrestrial carnivore population indices

Population indices based on visits to detection stations commonly are used to monitor wildlife populations. Inferences about populations are based on 1 of 2 measures: (1) change in the proportion of stations visited at least once or (2) change in the cumulative number of visits by unique individuals. The functional relationships between index responses and population density is poorly understood and can lead to misinterpretation of index data when an incorrect functional relationship (e.g. linear) is assumed. We created a flexible simulation environment to study the response of detection-based population indices under a wide variety of conditions meant to reflect species life history and study design. Proportional indices exhibited non-linear saturating responses to changes in population density while cumulative indices responded linearly. Shapes of responses were functions of home range sizes, individual detection probabilities, and spatial arrangement of animals and sampling stations. Non-linear relationships of proportional indices lead to under-estimation of mean population density when data are aggregated from multiple detection stations deployed in a heterogeneous landscape. Cumulative indices have significant statistical advantages over proportional indices including smaller sample sizes required to detect density change, linearity, consistent index responses across a wide range of densities, and ability to aggregate data to meet minimum sample size requirements. Our simulation provides a flexible tool for the interpretation of station-based population indices.     

Quantifying Habitat Requirements of Tree-Living Species in Fragmented Boreal Forests with Bayesian Methods

Abstract:  Quantitative conservation objectives require detailed consideration of the habitat requirements of target species. Tree-living bryophytes, lichens, and fungi are a critical and declining biodiversity component of boreal forests. To understand their requirements, Bayesian methods were used to analyze the relationships between the occurrence of individual species and habitat factors at the tree and the stand scale in a naturally fragmented boreal forest landscape. The importance of unexplained between-stand variation in occurrence of species was estimated, and the ability of derived models to predict species' occurrence was tested. The occurrence of species was affected by quality of individual trees. Furthermore, the relationships between occurrence of species at the tree level and size and shape of stands indicated edge effects, implying that some species were restricted to interior habitats of large, regular stands. Yet for the habitat factors studied, requirements of many species appeared similar. Species occurrence also varied between stands; most of the seemingly suitable trees in some stands were unoccupied. The models captured most variation in species occurrence at tree level. They also successfully accounted for between-stand variation in species occurrence, thus providing realistic simulations of stand-level occupancy of species. Important unexplained between-stand variation in species occurrence warns against a simplified view that only local habitat factors influence species' occurrence. Apparently, similar stands will host populations of different sizes due to historical, spatial, and stochastic factors. Thus, habitat suitability cannot be assessed simply by population sizes, and stands lacking a species may still provide suitable habitat and merit protection.     

A novel statistical method for classifying habitat generalists and specialists

We develop a novel statistical approach for classifying generalists and specialists in two distinct habitats. Using a multinomial model based on estimated species relative abundance in two habitats, our method minimizes bias due to differences in sampling intensities between two habitat types as well as bias due to insufficient sampling within each habitat. The method permits a robust statistical classification of habitat specialists and generalists, without excluding rare species a priori. Based on a user-defined specialization threshold, the model classifies species into one of four groups: (1) generalist; (2) habitat A specialist; (3) habitat B specialist; and (4) too rare to classify with confidence. We illustrate our multinomial classification method using two contrasting data sets: (1) bird abundance in woodland and heath habitats in southeastern Australia and (2) tree abundance in second-growth (SG) and old-growth (OG) rain forests in the Caribbean lowlands of northeastern Costa Rica. We evaluate the multinomial model in detail for the tree data set. Our results for birds were highly concordant with a previous nonstatistical classification, but our method classified a higher fraction (57.7%) of bird species with statistical confidence. Based on a conservative specialization threshold and adjustment for multiple comparisons, 64.4% of tree species in the full sample were too rare to classify with confidence. Among the species classified, OG specialists constituted the largest class (40.6%), followed by generalist tree species (36.7%) and SG specialists (22.7%). The multinomial model was more sensitive than indicator value analysis or abundance-based phi coefficient indices in detecting habitat specialists and also detects generalists statistically. Classification of specialists and generalists based on rarefied subsamples was highly consistent with classification based on the full sample, even for sampling percentages as low as 20%. Major advantages of the new method are (1) its ability to distinguish habitat generalists (species with no significant habitat affinity) from species that are simply too rare to classify and (2) applicability to a single representative sample or a single pooled set of representative samples from each of two habitat types. The method as currently developed can be applied to no more than two habitats at a time.     

Determining association networks in social animals: choosing spatial–temporal criteria and sampling rates

Social Network Analysis has become an important methodological tool for advancing our understanding of human and animal group behaviour. However, researchers tend to rely on arbitrary distance and time measures when defining ‘contacts’ or ‘associations’ between individuals based on preliminary observation. Otherwise, criteria are chosen on the basis of the communication range of sensor devices (e.g. bluetooth communication ranges) or the sampling frequencies of collection devices (e.g. Global Positioning System devices). Thus, researchers lack an established protocol for determining both relevant association distances and minimum sampling rates required to accurately represent the network structure under investigation. In this paper, we demonstrate how researchers can use experimental and statistical methods to establish spatial and temporal association patterns and thus correctly characterise social networks in both time and space. To do this, we first perform a mixing experiment with Merino sheep (Ovis aries) and use a community detection algorithm that allows us to identify the spatial and temporal distance at which we can best identify clusters of previously familiar sheep. This turns out to be within 2–3 m of each other for at least 3 min. We then calculate the network graph entropy rate—a measure of ease of spreading of information (e.g. a disease) in a network—to determine the minimum sampling rate required to capture the variability observed in our sheep networks during distinct activity phases. Our results indicate the need for sampling intervals of less than a minute apart. The tools that we employ are versatile and could be applied to a wide range of species and social network datasets, thus allowing an increase in both the accuracy and efficiency of data collection when exploring spatial association patterns in gregarious species.     

Estimating Population Size of Elusive Animals with DNA from Hunter-Collected Feces: Four Methods for Brown Bears

Abstract:  Noninvasive genetic methods can be used to estimate animal abundances and offer several advantages over conventional methods. Few attempts have been made, however, to evaluate the accuracy and precision of the estimates. We compared four methods of estimating population size based on fecal sampling. Two methods used rarefaction indices and two were based on capture-mark-recapture (CMR) estimators, one combining genetic and field data. Volunteer hunters and others collected 1904 fecal samples over 2 consecutive years in a large area containing a well-studied population of brown bears ( Ursus arctos ). On our 49,000-km² study area in south-central Sweden, population size estimates ranged from 378 to 572 bears in 2001 and 273 to 433 bears in 2002, depending on the method of estimation used. The estimates from the best model in the program MARK appeared to be the most accurate, based on the minimum population size estimate from radio-marked bears in a subsection of our sampling area. In addition, MARK models included heterogeneity and temporal variation in detection probabilities, which appeared to be present in our samples. All methods, though, incorrectly suggested a biased sex ratio, probably because of sex differences in detection probabilities and low overall detection probabilities. The population size of elusive animals can be estimated reliably over large areas with noninvasive genetic methods, but we stress the importance of an adequate and well-distributed sampling effort. In cases of biased sampling, calibration with independent estimates may be necessary. We recommend that this noninvasive genetic approach, using the MARK models, be used in the future in areas where sufficient numbers of volunteers can be mobilized.