Don Edwards

The Efficiency of Simulation-Based Multiple Comparisons

A frequently encountered problem in practice is that of simultaneous interval estimation of p linear combinations of a parameter beta in the setting of (or equivalent to) a univariate linear model. This problem has been solved adequately only in a few settings when the covariance matrix of the estimator is diagonal; in other cases, conservative solutions can be obtained by the methods of Scheffé, Bonferroni, or Sidák (1967, Journal of the American Statistical Association 62, 626-633). Here we investigate the efficiency of using a simulated critical point for exact intervals, which has been suggested before but never put to serious test. We find the simulation-based method to be completely reliable and essentially exact. Sample size savings are substantial (in our settings): 3-19% over the Sidák method, 4-37% over the Bonferroni method, and 27-33% over the Scheffé method. We illustrate the efficiency and flexibility of the simulation-based method with case studies in physiology and marine ecology.

Nonpoint source runoff modeling A comparison of a forested watershed and an urban watershed on the South Carolina coast

Storm water runoff volumes, flow rates and sediment loads from a forested watershed and an urbanized watershed draining into adjacent estuaries were compared using the distributed parameter (grid cell) agricultural nonpoint source runoff (AGNPS) model. The comparisons were based on 10 simulated rainfall events. Effects of impervious surfaces on runoff and sediment transport were also investigated with the model. The 38 ha forested watershed, representing undeveloped land in coastal South Carolina, was covered with mixed second-growth hardwoods and pines with interspersed cypress wetlands. The urbanized watershed was 15 ha of single-family residential and commercial land and included a four-lane interstate highway segment. Both watersheds had sandy soils and low stream bed slopes ( < 0.5%). This paper shows that the model equations, although intended for agricultural watersheds, also applied to forested and urban land use. The hydrologic submodel was calibrated with 10 rain events ranging from 19–102 mm total rainfall. Simulation results indicated runoff volume was on average 5.5 × (±2.7) and sediment yield 5.5 × (±2.3) greater from the urban watershed than from the forested watershed. The ratio of rainfall volume to runoff volume was on average 14.5% higher in the urban watershed compared to the forested watershed. In the AGNPS model, runoff volumes were governed by the total impervious area and were independent of other impervious surface spatial characteristics (size, shape, location, contiguity). Simulation results indicated eroded sediment from both watersheds originated predominantly within the channels. Adding simulated impervious surface area increased runoff volumes linearly and peak flow rates exponentially, flow rates and sediment loads were controlled by impervious surface spatial characteristics. Maximum sediment loads from the urban watershed occurred when disconnected patches of impervious surface covered 35% of the watershed. Maximum differences between the forested and urban watersheds occurred at low rainfall depths ( < 75 mm). Future nonpoint source runoff modelling should incorporate ground water dynamics, the spatial and temporal variability of rainfall, and accumulation and wash-off of specific pollutants.

Multiple Comparisons with the Best Treatment

Abstract Let π1, π2, …, π k be k ≥ 2 sources of observations (treatments, populations) and suppose the “goodness” of treatment π i is characterized by the size of an unknown real-valued parameter θ i . Let θ[k] = max1≤i≤k θ i . If π i is preferred to π j when θ i > θ j , the parameters δ i = θ[k] — θ i , i = 1, 2, …, k reflect in an inverse sense the “goodness” of each treatment relative to the “best” treatment. A general technique for obtaining simultaneous confidence intervals on the δ i is demonstrated with several examples. This technique can be applied in any setting where comparison-with-control intervals can be computed regarding any π j as the control. These results have special importance in ranking and selection problems in that the process of generating upper bounds on the δ i generates traditional confidence statements of both the indifference zone and the subset selection schools, simultaneously, as established by Hsu (1981).

Kriging in estuaries: as the crow flies, or as the fish swims?

Abstract Geostatistical methods are becoming an essential tool for understanding the spatial distribution of biological and chemical species in estuaries. At the heart of these methods are the spatial prediction/mapping methods known as “kriging”; these can construct statistically optimal predictions for data at unobserved locations using a relatively small, spatially explicit sample. The prediction at any given location is a weighted average of the sample values, where the weights depend on the distances between the sample sites and the target location. For most geostatistical settings, distances are computed “as the crow flies”, i.e. Euclidean distance. For measurements made in estuarine streams, however, intuition suggests that distances between sites should be measured “as the fish swims”, i.e. the length of the shortest in-water path between two sites. Our study evaluated the relative accuracy of eight kriging methods for predicting contaminant and water quality variables measured in an urbanized estuary in South Carolina. The eight methods were defined by all combinations of three factors, each at two levels: (a) Distance metric (Euclidean vs. in-water); (b) semivariogram type (spherical vs. linear) and (c) model trend component (distance to the inlet mouth; without vs. with). For four of the eight variables studied, the in-water distances provided prediction accuracy improvement on the order of 10–30% of prediction error variance. In two of these cases, the improvement only occurred when in-water distances were used together with a model trend component. Choice of semivariogram did not have much effect on prediction accuracy. Although the overall improvement in prediction accuracy was unpredictable and modest, considering the additional difficulties associated with in-water distances, the results suggest that the integration of Geographic Information System (GIS)-based network analysis with kriging using in-water distances merits further research.

Ecosystem response to bivalve density reduction: management implications

Coastal ecosystems are easily overexploited and changed by physical and biological factors. In this paper, we discuss current ideas and arguments for coastal ecosystem management with an emphasis on systems that have large bivalve filter feeder components. For centuries the species or population approach has been utilized in fisheries management. With the growing knowledge base on specific environmental effects and relationships, it has become increasingly evident that a broad or holistic approach to fisheries management in these systems is usually more appropriate. An ongoing ecosystem scale experiment in which oysters are completely removed from tidal creeks is described and used as a case study. The experimental design takes estimates of the systems carrying capacity into account. Using the population or species approach to monitor the oysters, the only observable change after the experimental manipulation was a slight increase in summer somatic growth and elevated recruitment of oysters in creeks with oyster reefs removed. These data are interpreted as an indication that the creeks with oysters present are below or near carrying capacity. However, when nekton, plankton and water chemistry data are also examined a much more complicated picture emerges. During the summer growing season, nekton biomass in all creeks is often greater than oyster biomass. Also, our calculations show that oysters do not produce enough ammonium to satisfy phytoplankton productivity, but nekton, water column remineralization and sediments can account for most of the deficit. Finally, microflagellates, which are a preferred food for the oysters, dominate the phytoplankton during the summer growing season and diatoms dominate the colder months. The timing of the change in phase of phytoplankton dominance seems to mirror the seasonal arrival and departure times of nekton in the creeks. We argue that dense bivalve reefs and beds are indicative of intense positive feedback loops that make their ecosystems susceptible to dramatic changes in structure. Such changes have not been reported for natural systems, but are found in systems influenced by over-fishing, nutrient loading and pollution. Thus, the management of sustainable fisheries in coastal ecosystems requires an understanding of the ecosystem science and the realization that systems dominated by bivalves exhibit complex responses that are not easily explained by linear dynamics.

Effects of experimental fire regimes on the population dynamics of Schwalbea americana L.

We studied the effects of experimental fire regimes, (dormant season fire, growing season fire, growing season mowing and control, i.e., no experimental treatment) on populations of the USA federally endangered, Schwalbea americana L. between 1992 and 1996. Although this species occurs in fire-maintained habitat in the Southeastern USA, there is concern about the use of fire for such rare populations. The purpose of the study was to examine how seasonal timing of fire and fire suppression affect population demography, flowering phenology and spatial distribution; to identify modes of persistence associated with fire regimes; and to determine if summer mowing provides a management alternative to fire. Fire-induced flowering was demonstrated in this species. Seasonal timing of burns appears to have relatively little consequence on population structure or spatial extent, but alters flowering phenology. Burning, regardless of season, resulted in increased population density and expansion in areal extent. Two possible mechanisms of persistence between fire events were identified including regression from reproductive stage to vegetative stage in the absence of fire and dormancy of individual plants for one or more seasons. Growing season mowing does not appear to be an adequate substitute for burning.

ISSUES AND THEMES FOR NATURAL RESOURCES TRENDAND CHANGE DETECTION

The 1996 ASA/EPA/ESA/SBI workshop on Ecological Resource Monitoring: Change and Trend Detection, was a successful interaction between quantitative ecologists and environmental statisticians. In this brief comment, a few of the overriding themes are noted and discussed, in particular: (1) the many difficulties encountered in applying traditional formal statistical methods to environmental studies; (2) the differences between design-based and model-based inferences; and (3) the issue of judgment vs. probability sampling.

Autoregressive trend analysis: an example using long-term ecological data

One of the most basic questions concerning a sequence of ecosystem measurements is the presence or absence of a trend. An 11 year monthly record of meiofauna abundance and physical variables is used to illustrate a trend analysis. The analysis models the errors about a regression line as an autoregressive process, a special case of ARIMA time series models. Predicting with confidence and rational planning of future temporal spacing and replication with regard to the trend question are discussed.

Comment: The First Data Analysis Should be Journalistic

Bayesian statistical methods can be considered an attempt at mathematical formalization of the natural scientific process of interpretation of data in light of preexisting information. As such, their use, and the degree to which they are used, is largely a question of efficiency. In some instances it may be appropriate to incorporate prior information into an analysis to the extent that this information is deemed reliable by all concerned; it will not often be the case in an ecological study, however, that information satisfying these constraints is substantial. In the most important distributional setting a frequentist confi- dence interval is identical to a noninformative Bayesian credible interval, and it is asserted that in most other cases where noninformative priors are used, these two will be very similar; the primary data analysis in an ecological study should probably be of one of these two forms. It is conjectured that, in order to be mathematically tractable, decision theoretic methods (Bayesian or not) will often deal with a dangerously short action-space time frame. Finally, Empirical Bayesian methods and hierarchical models in general are powerful new methods that should be used, with caution, to the extent that their superstructural assump- tions are reliable.

Assessing the impacts of anthropogenic and physiographic influences on grass shrimp in localized salt-marsh estuaries

Abstract The complexity and severity of ecological impacts associated with coastal development demand that resource managers explore new spatial analytical techniques combined with multidisciplinary scientific expertise for proactive coastal zone management. Arising from these environmental concerns and the identified need for adequate databases and integrated models, a long-term study of the impacts of urbanization on localized estuaries of the South eastern United States was initiated in 1990. A goal of this study was to examine the role of Geographic Information Processing (GIP) to integrate data and scientific expertise for the identification, assessment, and modeling of anthropogenic and physiographic relationships within estuaries. This goal is being achieved through the implementation and utilization of a multi-agency Geographic Information System (GIS) and the development and validation of spatially explicit models. This work presents spatial modeling efforts that incorporate land use and land cover characteristics with fisheries data to assess and predict the impacts of anthropogenic and natural influences on key species that inhabit critical estuarine wetlands and streams. A spatial assessment of two small, high-salinity estuaries suggests that upland development adjacent to critical estuarine habitat limits the population size and distribution of adult and larval grass shrimp ( Palaemonetes pugio (Holthuis)). Modeled spatial distributions of adult populations suggest the existence of estuarine ‘deserts’ — wetlands and stream reaches adjacent to commercial and residential land use void of natant fauna. This papers approach is being developed for coastal resource managers to predict the impact of proposed landscape modifications prior to occurrence of changes.