Using Inverse Probability Bootstrap Sampling to Eliminate Sample Induced Bias in Model Based Analysis of Unequal Probability Samples.

In ecology, as in other research fields, efficient sampling for population estimation often drives sample designs toward unequal probability sampling, such as in stratified sampling. Design based statistical analysis tools are appropriate for seamless integration of sample design into the statistical analysis. However, it is also common and necessary, after a sampling design has been implemented, to use datasets to address questions that, in many cases, were not considered during the sampling design phase. Questions may arise requiring the use of model based statistical tools such as multiple regression, quantile regression, or regression tree analysis. However, such model based tools may require, for ensuring unbiased estimation, data from simple random samples, which can be problematic when analyzing data from unequal probability designs. Despite numerous method specific tools available to properly account for sampling design, too often in the analysis of ecological data, sample design is ignored and consequences are not properly considered. We demonstrate here that violation of this assumption can lead to biased parameter estimates in ecological research. In addition, to the set of tools available for researchers to properly account for sampling design in model based analysis, we introduce inverse probability bootstrapping (IPB). Inverse probability bootstrapping is an easily implemented method for obtaining equal probability re-samples from a probability sample, from which unbiased model based estimates can be made. We demonstrate the potential for bias in model-based analyses that ignore sample inclusion probabilities, and the effectiveness of IPB sampling in eliminating this bias, using both simulated and actual ecological data. For illustration, we considered three model based analysis tools--linear regression, quantile regression, and boosted regression tree analysis. In all models, using both simulated and actual ecological data, we found inferences to be biased, sometimes severely, when sample inclusion probabilities were ignored, while IPB sampling effectively produced unbiased parameter estimates.

Assessing macroinvertebrate biodiversity in freshwater ecosystems: advances and challenges in DNA-based approaches.

Assessing the biodiversity of macroinvertebrate fauna in freshwater ecosystems is an essential component of both basic ecological inquiry and applied ecological assessments. Aspects of taxonomic diversity and composition in freshwater communities are widely used to quantify water quality and measure the efficacy of remediation and restoration efforts. The accuracy and precision of biodiversity assessments based on standard morphological identifications are often limited by taxonomic resolution and sample size. Morphologically based identifications are laborious and costly, significantly constraining the sample sizes that can be processed. We suggest that the development of an assay platform based on DNA signatures will increase the precision and ease of quantifying biodiversity in freshwater ecosystems. Advances in this area will be particularly relevant for benthic and planktonic invertebrates, which are often monitored by regulatory agencies. Adopting a genetic assessment platform will alleviate some of the current limitations to biodiversity assessment strategies. We discuss the benefits and challenges associated with DNA-based assessments and the methods that are currently available. As recent advances in microarray and next-generation sequencing technologies will facilitate a transition to DNA-based assessment approaches, future research efforts should focus on methods for data collection, assay platform development, establishing linkages between DNA signatures and well-resolved taxonomies, and bioinformatics.

The relative influence of geographic location and reach-scale habitat on benthic invertebrate assemblages in six ecoregions.

The objective of this study was to determine the relative influence of reach-specific habitat variables and geographic location on benthic invertebrate assemblages within six ecoregions across the Western USA. This study included 417 sites from six ecoregions. A total of 301 taxa were collected with the highest richness associated with ecoregions dominated by streams with coarse substrate (19-29 taxa per site). Lowest richness (seven to eight taxa per site) was associated with ecoregions dominated by fine-grain substrate. Principle component analysis (PCA) on reach-scale habitat separated the six ecoregions into those in high-gradient mountainous areas (Coast Range, Cascades, and Southern Rockies) and those in lower-gradient ecoregions (Central Great Plains and Central California Valley). Nonmetric multidimensional scaling (NMS) models performed best in ecoregions dominated by coarse-grain substrate and high taxa richness, along with coarse-grain substrates sites combined from multiple ecoregions regardless of location. In contrast, ecoregions or site combinations dominated by fine-grain substrate had poor model performance (high stress). Four NMS models showed that geographic location (i.e. latitude and longitude) was important for: (1) all ecoregions combined, (2) all sites dominated by coarse-grain sub strate combined, (3) Cascades Ecoregion, and (4) Columbia Ecoregion. Local factors (i.e. substrate or water temperature) seem to be overriding factors controlling invertebrate composition across the West, regardless of geographic location.

Effects of sample standardization on mean species detectabilities and estimates of relative differences in species richness among assemblages.

Ecological surveys provide the basic information needed to estimate differences in species richness among assemblages. Comparable estimates of the differences in richness between assemblages require equal mean species detectabilities across assemblages. However, mean species detectabilities are often unknown, typically low, and potentially different from one assemblage to another. As a result, inferences regarding differences in species richness among assemblages can be biased. We evaluated how well three methods used to produce comparable estimates of species richness achieved equal mean species detectabilities across diverse assemblages: rarefaction, statistical estimators, and standardization of sampling effort on mean taxonomic similarity among replicate samples (MRS). We used simulated assemblages to mimic a wide range of species-occurrence distributions and species richness to compare the performance of these three methods. Inferences regarding differences in species richness based on rarefaction were highly biased when richness estimates were compared among assemblages with distinctly different species-occurrence distributions. Statistical estimators only marginally reduced this bias. Standardization on MRS yielded the most comparable estimates of differences in species richness. These findings have important implications for our understanding of species-richness patterns, inferences drawn from biological monitoring data, and planning for biodiversity conservation.

Setting expectations for the ecological condition of streams: the concept of reference condition.

An important component of the biological assessment of stream condition is an evaluation of the direct or indirect effects of human activities or disturbances. The concept of a "reference condition" is increasingly used to describe the standard or benchmark against which current condition is compared. Many individual nations, and the European Union as a whole, have codified the concept of reference condition in legislation aimed at protecting and improving the ecological condition of streams. However, the phrase "reference condition" has many meanings in a variety of contexts. One of the primary purposes of this paper is to bring some consistency to the use of the term. We argue the need for a "reference condition" term that is reserved for referring to the "naturalness" of the biota (structure and function) and that naturalness implies the absence of significant human disturbance or alteration. To avoid the confusion that arises when alternative definitions of reference condition are used, we propose that the original concept of reference condition be preserved in this modified form of the term: "reference condition for biological integrity," or RC(BI). We further urge that these specific terms be used to refer to the concepts and methods used in individual bioassessments to characterize the expected condition to which current conditions are compared: "minimally disturbed condition" (MDC); "historical condition" (HC); "least disturbed condition" (LDC); and "best attainable condition" (BAC). We argue that each of these concepts can be narrowly defined, and each implies specific methods for estimating expectations. We also describe current methods by which these expectations are estimated including: the reference-site approach (condition at minimally or least-disturbed sites); best professional judgment; interpretation of historical condition; extrapolation of empirical models; and evaluation of ambient distributions. Because different assumptions about what constitutes reference condition will have important effects on the final classification of streams into condition classes, we urge that bioassessments be consistent in describing the definitions and methods used to set expectations.

The structure of variation and its influence on the estimation of status: indicators of condition of lakes in the Northeast, U.S.A.

One goal of regional-scale sample surveys is to estimate the status of a resource of interest from a statistically drawn representative sample of that resource. An expression of status is the frequency distribution of indicator scores capturing variability of attributes of interest. However, extraneous variability interferes with the status description by introducing bias into the frequency distributions. To examine this issue, we used data from a regional survey of lakes in the Northeast U.S. collected by the U.S. Environmental Protection Agency's Environmental Monitoring and Assessment Program (EMAP). We employ a components of variance model to identify sources of extraneous variance pertinent to status descriptions of physical, chemical, and biological attributes of the population of lakes in the NE. We summarize the relative magnitude of four components of variance (lake-to-lake, year, interaction, and residual) for each indicator and illustrate how extraneous variance biases the status descriptions. We describe a procedure that removes this bias from the status descriptions to produce unbiased estimates and introduce a novel method for estimating the 'cost' of removing the bias (expressed as either increased sampling uncertainty or additional samples needed to achieve the target precision in the absence of bias). We compare the relative magnitude of the four variance components across the array of indicators, finding in general that conservative chemical indicators are least affected by extraneous variance, followed by some nonconservative indicators, with nutrient indicators most affected by extraneous variance. Intermediate were trophic condition indicators (including sediment diatoms), fish species richness and individuals indicators, and zooplankton taxa richness and individuals indicators. We found no clear patterns in the relative magnitude of variance components as a function of several methods of aggregating fish and zooplankton indicators (e.g., level of taxonomy, or species richness vs. numbers of individuals).