Applied Biomathematics' Research Strengths

We develop practical, quantitative methods for addressing environmental and ecological problems encountered in viability analysis and impact assessment. The approaches are often based on risk analysis and ecological or demographic models of biological populations or spatial variation. Methods developed by Applied Biomathematics are used by several federal and state agencies, many industrial and private laboratories, and hundreds of academic institutions. Our research addresses the following areas.

• Assessing species extinction risks
• GIS-based habitat suitability models
• Species recovery and viability analysis
• Wildlife management

• Ecological Toxicology
• Environmental risk assessment
• Environmental Remediation
• Uncertainty propagation
• Quality assurance for risk analysis
• Reliability analysis
• Disease cluster detection
• Spatial analysis
• Detecting global change consequences

Ecology, Conservation and Wildlife Management

Assessing species extinction risks.

Analyzing interacting factors that place a species at risk of extinction often involves mathematical models that predict future changes in its abundance and distribution from available information about its ecology. We've applied our ecological models to ecological risk analyses for a variety of organisms, including fish species (e.g., Redhorse and Shortnose Sturgeon), threatened and endangered birds (e.g., Marbled Murrelet and California least tern), and rare plants.

GIS-based habitat suitability models.

Several kinds of research questions in ecology require analysis of the patterns and processes that are played out over geographical space. For instance, to predict population-level responses of wildlife to resource destruction, we need to interpret and analyze habitat maps. Our risk analysis models incorporate demographic information as well as habitat data organized by a geographic information system (GIS). AB has constructed spatially explicit models of avian populations reacting to changes in habitat suitability. These have included metapopulation models of the northern spotted owl and the California gnatcatcher. We have recently expanded these models to include integration of landscape and metapopulation models and multispecies ecological valuation methods.

Species recovery and viability analysis.

Our risk assessment methods can forecast the chances of population growth. Such analyses are important in predicting the viability of endangered or threatened species and in assessing the likelihood of success for proposed recovery plans. We've also applied these methods to biological resource management problems, such as deer control strategies and recovery of commercial fish stocks after population crashes resulting from heavy metal pollution and other kinds of impacts.

Wildlife management.

Risk analysis methods that combine demographic and habitat information can be used to assist wildlife management. We developed models to assist in habitat management for a Red-cockaded Woodpecker population, and have developed statistical methods to analyze deer management strategies. Currently, we are developing methods to evaluate the impact of forest management plans on wildlife.

Environmental And Human Health Risks

Ecological toxicology.

        Standard bioassays for assessing the impact of toxicants on natural systems use 'indicator' species such as polychaetes or daphnia, and individual-level assessment endpoints such as growth, survivorship and fecundity. As a result, it has been difficult to interpret the results from such bioassays in terms of population-level consequences. One cannot predict from these bioassays, for instance, how likely it is that an exposed population will decline in abundance. We have developed methods for assessing effects at the level of the entire population, using the type of data collected at the individual level in typical ecotoxicological tests. The extrapolation is a step toward the ultimate goal of understanding the ecosystem-level consequences wrought by contaminants, a goal which remains an open research question.

Environmental risk assessment.

Environmental risk assessment is at a crossroads. The traditional methodology based on worst case analyses has been stridently criticized as hyperconservative and unrepresentative. However, the methods proposed to replace it can be overly optimistic unless a great deal of empirical information is available to the analyst. AB's research on approaches with fewer data requirements has led to promising new methods for risk assessment. We have developed software that implements fuzzy arithmetic and other novel uncertainty propagation methods that complement traditional worst case and Monte Carlo analyses. We have applied these new methods to a variety of environmental problems including assessing pesticide misapplication and minimizing unplanned risk in environmental remediation strategies.

Environmental remediation.

How clean is clean enough? What remediation target assures us that the probabilities of environmental exposures being larger than a given magnitude are sufficiently low?

Uncertainty propagation.

Although we may measure an empirical quantity, we cannot always specify a precise numerical value for it. This may be because the value is changing unpredictably with time or across space. Or it may be because the quantity is very hard to measure precisely. For instance, the measurement error associated with the tally of fish in a lake is often almost as big as the estimated value itself. There are many methods for propagating the uncertainty of such numbers through mathematical calculations, including Monte Carlo methods, interval analysis, and fuzzy arithmetic. Applied Biomathematics' research in uncertainty propagation has focused on which approach is appropriate for problems in ecological risk analysis. The factors that determine the optimal approach involve the nature of the uncertainty, how much empirical information is available, and what assumptions the analyst is willing to make. We have also developed several new methods that are useful in particular situations where information is incomplete, including probability bounds analysis, dependency bounds analysis, and deconvolution methods for inverting expressions involving uncertain numbers.

Quality assurance for risk analysis.

        Although a probabilistic risk assessment is widely regarded as the most comprehensive kind of uncertainty analysis, there are usually several assumptions that have not been justified by empirical information but are made for the sake of mathematical convenience. For example, an analyst typically specifies precise statistical distributions to be used as inputs even though evidence for them may be fairly sparse. In some cases, there is controversy about the form of the model itself, including the nature of the dependencies among the variables and even the mathematical functions that tie them together. Applied Biomathematics has developed simple methods and software that allow one to directly compute bounds on the probabilities of adverse events and therefore provide estimates of the reliability of a probabilistic risk assessment. We have also developed software that automatically checks calculation streams for dimensional concordance and balance of units.

Reliability analysis.

Forecasting the reliability of complex engineered systems (such as the systems in a nuclear power plant) generally requires systematic and comprehensive analysis. As existing facilities get older, the problems of testing and repair scheduling remain crucial. In particular, the task of analyzing the reliability of complex engineered systems with aging components becomes even more sensitive. The computer software used by the nuclear industry and its regulators to address time-dependent risk effects associated with technical specifications did not provide a bounding evaluation of risk in case of unknown characteristics. We have developed new models and techniques to improve our capability to realistically describe time-dependent and test-frequency-dependent risk factors.

Disease cluster detection.

        In most cases, when public health officials first hear about alleged disease clusters, there are only a handful of disease cases. In such situations, traditional methods for determining whether clustering is statistically significant cannot be used because sample sizes are so small. We have developed approaches to cluster detection based on combinatorial expressions for exact calculation of probability. These methods are suitable for the very small sample sizes that often characterize alleged clusters of diseases such as cancer. Our investigations of the statistical power of these tests under various sample sizes and clustering conditions allow us to predict which test(s) would be most useful in different circumstances.

Spatial analysis.

Several kinds of research questions in both human health and ecology require analyzing the patterns and processes that are played out over geographical space. For instance, prediction of the population-level responses of wildlife to resource destruction requires interpretation and analysis of habitat maps. We have constructed spatially explicit models of avian populations reacting to changes in habitat suitability. In the context of human health, the spatial and temporal patterns in which disease incidences are expressed may reveal crucial information about the underlying causes for the disease. AB has explored new methods in biogeographic statistics. In combination with traditional ecological and epidemiological methods, they should enable us to answer several basic questions about whether electromagnetic field exposures from power lines have health consequences for human populations.

Detecting global change consequences.

Since plants at the edges of their geographical ranges are physiologically stressed, they may form very sensitive detectors of incipient environmental change such as degradation by pollution or climatic shifts. However, these vegetation frontiers have special properties owing to ecological interactions that complicate the process of observing and measuring environmental flux. We are developing methods to recognize such structures from satellite imagery of vegetation and classify them according to their sensitivity to environmental change.

For more information

Applied Biomathematics
100 North Country Road
Setauket, New York 11733
Tel: 631-751-4350
Fax: 631-751-3435
info@ramas.com