A distance dependent contagion function for vector-based data

Landscape pattern is of primary interest to landscape ecologists and landscape metrics are used to quantify landscape pattern. Metrics are commonly defined and calculated on raster-based land cover maps. One metric is the contagion, existing in several versions, e.g., unconditional and conditional, used as a measure of fragmentation. However, mapped data is sometimes in vector-based format or there may be no mapped data but only a point sample. In this study a definition of contagion for such cases is investigated. The metric is an extension of the usual contagion, based on pairs of points at varying distances and gives a function of the distance. In this study the extended contagion is calculated for vector-based delineated real landscapes and for simulated ones. Both unconditional and conditional contagions are studied using two classification systems. The unconditional contagion function was decreasing and convex, with upper and lower limits highly correlated to the Shannon diversity index, thus carrying only area proportion information. The spatial information lies in the speed by which the function converges to the lower limit; using a proxy function this can be expressed by a single parameter b, with high values for fragmented landscapes. No proxy function was found for the conditional contagion, for which only qualitative information was found. The extended contagion is applicable both in patch mosaic models of landscapes and in gradient-based models, where landscape characteristics change continuously without distinct borders between patches. The extended contagion can be useful in sample based surveys where there no map of the entire landscape is available.     

Sample based estimation of landscape metrics; accuracy of line intersect sampling for estimating edge density and Shannon’s diversity index

A recent trend is to estimate landscape metrics using sample data and cost-efficiency is one important reason for this development. In this study, line intersect sampling (LIS) was used as an alternative to wall-to-wall mapping for estimating Shannon’s diversity index and edge length and density. Monte Carlo simulation was applied to study the statistical performance of the estimators. All combinations of two sampling designs (random and systematic distribution of transects), four sample sizes, five transect configurations (straight line, L, Y, triangle, and quadrat), two transect orientations (fixed and random), and three configuration lengths were tested, each with a large number of simulations. Reference was 50 photos of size 1 km², already manually delineated in vector format by photo interpreters using GIS environment. The performance was compared by root mean square error (RMSE) and bias. The best combination for all three metrics was found to be the systematic design and as response design the straight line configuration with random orientation of transects, with little difference between the fixed and random orientation of transects. The rate of decrease of RMSE for increasing sample size and line length was studied with a mixed linear model. It was found that the RMSE decreased to a larger degree with the systematic design than the random one, especially with increasing sample size. Due to the nonlinearity in the definition of Shannon diversity estimator its estimator has a small and negative bias, decreasing with sample size and line length. Finally, a time study was conducted, measuring the time for registration of line intersections and their lengths on non-delineated aerial photos. The time study showed that long sampling lines were more cost-efficient than short ones for photo-interpretation.     

Estimation bias under model selection for distance sampling detection functions

Many simulation studies have examined the properties of distance sampling estimators of wildlife population size. When assumptions hold, if distances are generated from a detection model and fitted using the same model, they are known to perform well. However, in practice, the true model is unknown. Therefore, standard practice includes model selection, typically using model comparison tools like Akaike Information Criterion. Here we examine the performance of standard distance sampling estimators under model selection. We compare line and point transect estimators with distances simulated from two detection functions, hazard-rate and exponential power series (EPS), over a range of sample sizes. To mimic the real-world context where the true model may not be part of the candidate set, EPS models were not included as candidates, except for the half-normal parameterization. We found median bias depended on sample size (being asymptotically unbiased) and on the form of the true detection function: negative bias (up to 15% for line transects and 30% for point transects) when the shoulder of maximum detectability was narrow, and positive bias (up to 10% for line transects and 15% for point transects) when it was wide. Generating unbiased simulations requires careful choice of detection function or very large datasets. Practitioners should collect data that result in detection functions with a shoulder similar to a half-normal and use the monotonicity constraint. Narrow-shouldered detection functions can be avoided through good field procedures and those with wide shoulder are unlikely to occur, due to heterogeneity in detectability.     

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.     

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).     

Methods for estimating peak physiological performance and correlating performance measures

Estimates of animal performance often use the maximum of a small number of laboratory trials, a method which has several statistical disadvantages. Sample maxima always underestimate the true maximum performance, and the degree of the bias depends on sample size. Here, we suggest an alternative approach that involves estimating a specific performance quantile (e.g., the 0.90 quantile). We use the information on within-individual variation in performance to obtain a sampling distribution for the residual performance measures; we use this distribution to estimate a desired performance quantile for each individual. We illustrate our approach using simulations and with data on sprint speed in lizards. The quantile method has several advantages over the sample maximum: it reduces or eliminates bias, it uses all of the data from each individual, and its accuracy is independent of sample size. Additionally, we address the estimation of correlations between two different performance measures, such as sample maxima, quantiles, or means. In particular, because of sampling variability, we propose that the correlation of sample means does a better job estimating the correlation of population maxima than the estimator which is the correlation of sample maxima.     

Null model analysis of species nestedness patterns

Nestedness is a common biogeographic pattern in which small communities form proper subsets of large communities. However, the detection of nestedness in binary presence-absence matrices will be affected by both the metric used to quantify nestedness and the reference null distribution. In this study, we assessed the statistical performance of eight nestedness metrics and six null model algorithms. The metrics and algorithms were tested against a benchmark set of 200 random matrices and 200 nested matrices that were created by passive sampling. Many algorithms that have been used in nestedness studies are vulnerable to type I errors (falsely rejecting a true null hypothesis). The best-performing algorithm maintains fixed row and fixed column totals, but it is conservative and may not always detect nestedness when it is present. Among the eight indices, the popular matrix temperature metric did not have good statistical properties. Instead, the Brualdi and Sanderson discrepancy index and Cutler's index of unexpected presences performed best. When used with the fixed-fixed algorithm, these indices provide a conservative test for nestedness. Although previous studies have revealed a high frequency of nestedness, a reanalysis of 288 empirical matrices suggests that the true frequency of nested matrices is between 10% and 40%.     

Impacts of Chronic Anthropogenic Noise from Energy‐Sector Activity on Abundance of Songbirds in the Boreal Forest

Abstract: The effects of human activities in forests are often examined in the context of habitat conversion. Changes in habitat structure and composition are also associated with increases in the activity of people with vehicles and equipment, which results in increases in anthropogenic noise. Anthropogenic noise may reduce habitat quality for many species, particularly those that rely on acoustic signals for communication. We compared the density and occupancy rate of forest passerines close to versus far from noise‐generating compressor stations and noiseless well pads in the boreal forest of Alberta, Canada. Using distance‐based sampling, we found that areas near noiseless energy facilities had a total passerine density 1.5 times higher than areas near noise‐producing energy sites. The White‐throated Sparrow (Zonotrichia albicollis), Yellow‐rumped Warbler (Dendroica coronata), and Red‐eyed Vireo (Vireo olivaceus) were less dense in noisy areas. We used repeat sampling to estimate occupancy rate for 23 additional species. Seven had lower conditional or unconditional occupancy rates near noise‐generating facilities. One‐third of the species examined showed patterns that supported the hypothesis that abundance is influenced by anthropogenic noise. An additional 4 species responded negatively to edge effects. To mitigate existing noise impacts on birds would require approximately $175 million. The merits of such an effort relative to other reclamation actions are discussed. Nevertheless, given the $100 billion energy‐sector investment planned for the boreal forest in the next 10 years, including noise suppression technology at the outset of construction, makes noise mitigation a cost‐effective best‐management practice that might help conserve high‐quality habitat for boreal birds.     

Cross-validation of species distribution models: removing spatial sorting bias and calibration with a null model

Species distribution models are usually evaluated with cross-validation. In this procedure evaluation statistics are computed from model predictions for sites of presence and absence that were not used to train (fit) the model. Using data for 226 species, from six regions, and two species distribution modeling algorithms (Bioclim and MaxEnt), I show that this procedure is highly sensitive to "spatial sorting bias": the difference between the geographic distance from testing-presence to training-presence sites and the geographic distance from testing-absence (or testing-background) to training-presence sites. I propose the use of pairwise distance sampling to remove this bias, and the use of a null model that only considers the geographic distance to training sites to calibrate cross-validation results for remaining bias. Model evaluation results (AUC) were strongly inflated: the null model performed better than MaxEnt for 45% and better than Bioclim for 67% of the species. Spatial sorting bias and area under the receiver-operator curve (AUC) values increased when using partitioned presence data and random-absence data instead of independently obtained presence-absence testing data from systematic surveys. Pairwise distance sampling removed spatial sorting bias, yielding null models with an AUC close to 0.5, such that AUC was the same as null model calibrated AUC (cAUC). This adjustment strongly decreased AUC values and changed the ranking among species. Cross-validation results for different species are only comparable after removal of spatial sorting bias and/or calibration with an appropriate null model.     

Hierarchical Bayes estimation of hunting success rates

Although most post-season harvest surveys are conducted at the state level, the effective management of wildlife populations often requires estimates of hunting success rate, hunting pressure and harvest at the sub-area (such as management unit, regional, or county) level.Sample sizes for some sub-areas are often very small or even zero. Because of small sample sizes, estimates for small sub-areas often yield unacceptably large standard errors. In this article, a hierarchical Bayes model is used to estimate hunting success rates at the sub-area level from post-season harvest surveys. The computation is done by Gibbs sampling and adaptive rejection sampling techniques. The method is illustrated using data from the Missouri Turkey Hunting Survey 1994 Spring Season. The Bayesian estimates are close to the frequency estimates for the sub-areas with large sample sizes and more stable than the frequency estimates for those with small sample sizes. The Bayesian estimates will be more useful to wildlife biologists in estab-lishing hunting regulation on small sub-areas at no additional survey cost.     

Reassessment of the Use of Fire as a Management Tool in Deciduous Forests of Eastern North America

Prescribed burning is increasingly being used in the deciduous forests of eastern North America. Recent work suggests that historical fire frequency has been overestimated east of the prairie–woodland transition zone, and its introduction could potentially reduce forest herb and shrub diversity. Fire‐history recreations derived from sedimentary charcoal, tree fire scars, and estimates of Native American burning suggest point‐return times ranging from 5–10 years to centuries and millennia. Actual return times were probably longer because such records suffer from selective sampling, small sample sizes, and a probable publication bias toward frequent fire. Archeological evidence shows the environmental effect of fire could be severe in the immediate neighborhood of a Native American village. Population density appears to have been low through most of the Holocene, however, and villages were strongly clustered at a regional scale. Thus, it appears that the majority of forests of the eastern United States were little affected by burning before European settlement. Use of prescribed burning assumes that most forest species are tolerant of fire and that burning will have only a minimal effect on diversity. However, common adaptations such as serotiny, epicormic sprouting, resprouting from rhizomes, and smoke‐cued germination are unknown across most of the deciduous region. Experimental studies of burning show vegetation responses similar to other forms of disturbance that remove stems and litter and do not necessarily imply adaptation to fire. The general lack of adaptation could potentially cause a reduction in diversity if burning were introduced. These observations suggest a need for a fine‐grained examination of fire history with systematic sampling in which all subregions, landscape positions, and community types are represented. Responses to burning need to be examined in noncommercial and nonwoody species in rigorous manipulative experiments. Until such information is available, it seems prudent to limit the use of prescribed burning east of the prairie–woodland transition zone. Reevaluación del Uso de Fuego como Herramienta de Manejo en Bosques Deciduos de América del Norte     

Empirical study of GARCH models with leverage effect in an environmental application

Atmospheric carbon dioxide concentration (ACDC) level is an important factor for predicting temperature and climate changes. We analyze the conditional variance of a function of ACDC level known as ACDC level growth rate (ACDCGR) using the generalised autoregressive conditional heteroskedasticity (GARCH) and GARCH models with leverage effect. The data are a subset of the well known Mauna Loa atmosphere carbon dioxide record. We test for the presence of stylized facts in the ACDCGR time series. The performance of GARCH models are compared to EGARCH, TGARCH and PGARCH models. Model fit measures AIC, BIC and likelihood is calculated for each fitted model. The results do confirm the presence of some of important stylized facts in the ACDCGR time series, but the presence of leverage effect is not significant . The out of sample one step ahead forecasting performances of the models based on RMSE and MAE metrics are evaluated. EGARCH model with student $t$ disturbances showed the best fit and a valid forecasting performance. A bootstrap algorithm is employed to calculate confidence intervals for future values of ACDCGR time series and its volatility. The constructed bootstrap confidence intervals showed a reasonable performance.     

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.     

Understanding uncertainty in the effect of low-head dams on fishes of Great Lakes tributaries.

Small dams represent one of the most widespread human influences on riverscapes. Greater understanding of how these structures affect aquatic organisms is needed to ensure that decisions regarding their construction and removal strike an appropriate balance between components of human and ecosystem services. Within the basin of the Laurentian Great Lakes, the effects that in-stream barriers (dams) used to control the non-native, parasitic sea lamprey (Petromyzon marinus) on the diversity of non-target fishes is a significant concern for fishery managers. A previous study indicated that upstream changes in the species richness of non-target fishes observed in 24 streams with a sea lamprey barrier relative to paired reference streams (a measure of effect size) was variable across the basin. We examined the degree to which the variance in effect size could be attributed to imprecision in the field sampling protocol used to estimate effect sizes, differences in catchment-scale landscape attributes between barrier and reference streams within pairs, and differences in landscape attributes at different spatial scales among barrier streams. Simulation modeling and analyses of repeated field measurements made for a subset of streams demonstrated that a large variance in effect size is expected for the field sampling design and that estimates of effect size measured for individual barrier streams are imprecise. Regression models and multimodel inference methods based on Akaike's Information Criterion provided less support for hypotheses linking effect size to landscape attributes. Mean effect size, adjusted for the influences of landscape characteristics within and across stream pairs, provides the most reliable and least biased estimate of the effect of sea lamprey barriers on the richness of nontarget fish species. With the information currently available, landscape characteristics of catchments cannot be used to help decision makers anticipate effects sizes for candidate streams being considered for future barrier construction. Our findings will help fishery managers in the Laurentian Great Lakes make more informed decisions regarding the use and placement of sea lamprey barriers and achieve their objective of delivering an integrated pest management plan for sea lamprey control that is environmentally and economically sound and socially acceptable.     

Using multilevel spatial models to understand salamander site occupancy patterns after wildfire

Studies of the distribution of elusive forest wildlife have suffered from the confounding of true presence with the uncertainty of detection. Occupancy modeling, which incorporates probabilities of species detection conditional on presence, is an emerging approach for reducing observation bias. However, the current likelihood modeling framework is restrictive for handling unexplained sources of variation in the response that may occur when there are dependence structures such as smaller sampling units that are nested within larger sampling units. We used multilevel Bayesian occupancy modeling to handle dependence structures and to partition sources of variation in occupancy of sites by terrestrial salamanders (family Plethodontidae) within and surrounding an earlier wildfire in western Oregon, USA. Comparison of model fit favored a spatial N-mixture model that accounted for variation in salamander abundance over models that were based on binary detection/non-detection data. Though catch per unit effort was higher in burned areas than unburned, there was strong support that this pattern was due to a higher probability of capture for individuals in burned plots. Within the burn, the odds of capturing an individual given it was present were 2.06 times the odds outside the burn, reflecting reduced complexity of ground cover in the burn. Ther was weak support that true occupancy was lower within the burned area. While the odds of occupancy in the burn were 0.49 times the odds outside the burn among the five species, the magnitude of variation attributed to the burn was small in comparison to variation attributed to other landscape variables and to unexplained, spatially autocorrelated random variation. While ordinary occupancy models may separate the biological pattern of interest from variation in detection probability when all sources of variation are known, the addition of random effects structures for unexplained sources of variation in occupancy and detection probability may often more appropriately represent levels of uncertainty.     

Addressing onsite sampling in recreation site choice models

Independent experts and politicians have criticized statistical analyses of recreation behavior, which rely upon onsite samples due to their potential for biased inference. The use of onsite sampling usually reflects data or budgetary constraints, but can lead to two primary forms of bias in site choice models. First, the strategy entails sampling site choices rather than sampling individuals—a form of bias called endogenous stratification. Under these conditions, sample choices may not reflect the site choices of the true population. Second, exogenous attributes of the individuals sampled onsite may differ from the attributes of individuals in the population—the most common form in recreation demand is avidity bias. We propose addressing these biases by combining two the existing methods: Weighted Exogenous Stratification Maximum Likelihood estimation and propensity score estimation. We use the National Marine Fisheries Service's Marine Recreational Fishing Statistics Survey to illustrate methods of bias reduction, employing both simulated and empirical applications. We find that propensity score based weights can significantly reduce bias in estimation. Our results indicate that failure to account for these biases can overstate anglers' willingness to pay for improvements in fishing catch, but weighted models exhibit higher variance of parameter estimates and willingness to pay.     

Metrics for quantifying how much different threats contribute to red lists of species and ecosystems

Red lists are a crucial tool for the management of threatened species and ecosystems. Among the information red lists provide, the threats affecting the listed species or ecosystem, such as pollution or hunting, are of special relevance. This information can be used to quantify the relative contribution of different threat factors to biodiversity loss by disaggregating the cumulative extinction risk across species into components that can be attributed to certain threats. We devised and compared 3 metrics that accomplish this and may be used as indicators. The first metric calculates the portion of the temporal change in red list index (RLI) values that is caused by each threat. The second metric attributes the deviation of an RLI value from its reference value to different threats. The third metric uses extinction probabilities that are inferred from red list categories to estimate the contribution of a threat to the expected loss of species or ecosystems within 50 years. We used data from Norwegian Red Lists to test and evaluate these metrics. The first metric captured only a minor portion of the biodiversity loss caused by threats because it ignores species whose red list category does not change. Management authorities will often be interested in the contribution of a given threat to the total deviation from the optimal state. This was measured by the remaining metrics. The second metric was best suited for comparisons across countries or taxonomic groups. The third metric conveyed the same information but uses numbers of species or ecosystem as its unit, which is likely more intuitive to lay people and may be preferred when communicating with stakeholders or the general public.     

Spatial heterogeneity influences native and nonnative plant species richness

Spatial heterogeneity may have differential effects on the distribution of native and nonnative plant species richness. We examined the effects of spatial heterogeneity on native and nonnative plant species richness distributions in the central part of Rocky Mountain National Park, Colorado, USA. Spatial heterogeneity around vegetation plots was characterized using landscape metrics, environmental/topographic variables (slope, aspect, elevation, and distance from stream or river), and soil variables (nitrogen, clay, and sand). The landscape metrics represented five components of landscape heterogeneity and were measured at four spatial extents (within varying radii of 120, 240, 480, and 960 m) using the FRAGSTATS landscape pattern analysis program. Akaike's Information Criterion adjusted for small sample size (AICc) was used to select the best models from a set of multiple linear regression models developed for native and nonnative plant species richness at four spatial extents and three levels of ecological hierarchy (i.e., landscape, land cover, and community). Both native and nonnative plant species richness were positively correlated with edge density, Simpson's diversity index and interspersion/juxtaposition index, and were negatively correlated with mean patch size. The amount of variation explained at four spatial extents and three hierarchical levels ranged from 30% to 70%. At the landscape level, the best models explained 43% of the variation in native plant species richness and 70% of the variation in nonnative plant species richness (240-m extent). In general, the amount of variation explained was always higher for nonnative plant species richness, and the inclusion of landscape metrics always significantly improved the models. The best models explained 66% of the variation in nonnative plant species richness for both the conifer land cover type and lodgepole pine community. The relative influence of the components of spatial heterogeneity differed for native and nonnative plant species richness and varied with the spatial extent of analysis and levels of ecological hierarchy. The study offers an approach to quantify spatial heterogeneity to improve models of plant biodiversity. The results demonstrate that ecologists must recognize the importance of spatial heterogeneity in managing native and nonnative plant species.