California gnatcatcher and cactus wren: spatially explicit population models for two target species of the Natural Community Conservation Planning effort in Southern California
Software: RAMAS/GIS, Metapop
Citation: Akçakaya, H.R. and J.L. Atwood. 1997. A habitat-based metapopulation model of the California Gnatcatcher. Conservation Biology 11:422-434
Project description
This project aims at developing habitat-based metapopulation models for the California gnatcatcher Polioptila californica and the cactus wren Campylorhynchus brunneicapillus in central and coastal regions of Orange County, California. The California gnatcatcher (a federally-listed threatened species) and cactus wren are two of the three "target species" in the State of California's Natural Community Conservation Planning (NCCP) program. The target species are considered as surrogates for the conservation of coastal sage scrub, a plant community that has decreased substantially from its historic coverage as a result of urban and agricultural development, and has become fragmented.
In this project RAMAS/GIS was applied to the habitat and demographic data on the two target species. The application started with a statistical analyses of observation locations, and GIS maps for elevation, slope, and vegetation (exported from ARC/Info) to characterize the habitat of the two birds. The habitat maps were validated by predicting the habitat suitability values for one half of observation locations, with the model estimated from the other half, and by predicting the habitat suitability values for location of singles, with the model estimated from location of pairs.
The habitat maps were then analyzed to determine the spatial structure of the metapopulation model. These data were combined with demographic parameters estimated from field work conducted by Atwood et al. (1995) to produce spatially-explicit, stage-structured, stochastic metapopulation models for the two species. Simulations and sensitivity analyses with these models pointed out to the relative importance of density dependence and temporal variation in vital rates (including the frequency and the magnitude of catastrophic declines in vital rates as was observed in the winter of 1994-95).
Viability of Bell's Sage Sparrow Under Altered Fire Regimes: Integrating Landscape, Habitat, and Metapopulation Modeling Approaches
Software: RAMAS/GIS, Metapop
Citation: Akçakaya, HR, Franklin J, Syphard AD, Stephenson JR. 2005. Viability of Bell's Sage Sparrow (Amphispiza belli ssp. belli): altered fire regimes. Ecological Applications 15:521-531.
Project description
We modeled the viability of a Bell's Sage Sparrow (Amphispiza belli ssp. belli) metapopulation under different fire regimes in the foothills and mountains of San Diego County, California, USA. Our approach integrates a landscape model, which predicts the vegetation composition and age under three fire regimes, a habitat model, which interprets the resulting landscape in terms of its suitability for the Sage Sparrow, and a metapopulation model, which predicts the viability of the species based on a dynamic spatial structure as determined by the landscape and the habitat models. Bell's Sage Sparrow depends on early successional shrubland (chaparral) habitat, especially when the availability of preferred open coastal subshrub vegetation is limited.
The three fire rotation intervals (FRI) used in the landscape model were 'current' (30 year FRI) representing the effect of increased human ignitions, 'natural' (90 year FRI) representing the historic shrubland fire regime at higher elevations without the effect of human ignitions, and 'long' (150 year FRI) representing a hypothetic endpoint of very low fire frequency. The results indicated that the viability of the Sage Sparrow was highest under the 'current' fire regime scenario, slightly lower under the 'natural', and lowest under the 'long' fire regime scenario.
Viability of the Northern Spotted Owl Metapopulation in the Northwestern U.S.
Software: RAMAS/GIS, Metapop
Citation : Akçakaya, H.R. and M.G. Raphael. 1998. Assessing human impact despite uncertainty: viability of the northern spotted owl metapopulation in the northwestern USA. Biodiversity and Conservation 7:875-894.
Project description
This project focused on factors affecting the viability of the Northern Spotted Owl Strix occidentalis caurina throughout its range in the United States. The study used RAMAS GIS to incorporate two sources of variability in determining the threat the species faces. One of the goals of the project was to demonstrate the effect of uncertainty (resulting from lack of information or measurement error) on the assessment of human impact.
Methods: Variability vs. Uncertainty
The study used RAMAS GIS to develop a spatially-explicit, stage-structured, stochastic metapopulation model of the Northern Spotted Owl throughout its range in the United States. The model was used to evaluate the viability of the metapopulation using measures such as risk of decline and time to extinction. The model incorporated natural variation (resulting from temporal fluctuations in environmental factors) in the form of randomly distributed vital rates (survivals and fecundities). In addition, demographic stochasticity was modeled to describe chance variations in reproduction, survival and dispersal. These types of natural variation (environmental and demographic) were used to express the model results in probabilistic terms such as the viability of the species (for example in terms of the chance of survival or risk of extinction).
Uncertainties that result from a lack of knowledge were incorporated in the form of parameter ranges, and were used to estimate upper and lower bounds on the estimated viability of the species. The effects of this type of uncertainty on the assessment of human impact was analyzed by comparing the species' viability under current conditions, and under an assumed loss of spotted owl habitat in the next 100 years.
Results: Viability
Based on the habitat maps provided by the Forest Service, RAMAS GIS found 18 habitat patches. The size distribution of the patches was very skewed, with the 4 largest patches making up about 96% of the total area of all patches, and the seven largest making up about 98%. Because of the large differences in sizes of neighboring populations, the viability results (risk of decline) were not very sensitive to the rate of inter-patch dispersal of juvenile spotted owls.
Results: Effect of uncertainty
The model predicted a large difference between lower and upper bounds on the viability of the northern spotted owl, based on the best-case and worst-case scenarios which were parameter combinations that resulted in best and worst chance for survival. According to sensitivity analyses, the viability of the metapopulation was most sensitive to the set of vital rates used (the dependence of fecundities and survival rates on habitat), and also sensitive to the degree of spatial correlation among vital rates of the populations, and to the carrying capacities of the populations. In addition, metapopulation occupancy was sensitive to dispersal and Allee effects. Thus, the ranges of parameters were quite large, and resulted in wide range of risks of extinction. Despite this uncertainty, the results were sensitive to parameters related to habitat loss: under all assumptions and combinations of parameters, the model predicted that habitat loss results in substantially higher risks of metapopulation decline. This result demonstrated that even with relatively large uncertainties, risk-based model results can be used to reliably assess human impact.
A habitat-based metapopulation model of the California Gnatcatcher
Software: RAMAS/GIS, Metapop
Citation: Akçakaya and Atwood (1997; Conservation Biology 11:422-434).`
Project description
California Gnatcatcher (Polioptila c. californica) is a federally threatened subspecies inhabiting the coastal sage scrub community in southern California. The coastal sage scrub is a distinctive plant community that has declined due to extensive agricultural and urban development in this area. Our project involved an analysis of the dynamics of the California Gnatcatcher in central and coastal Orange County, California. Using GIS data, we developed and validated a habitat model for the species in this analysis. We then used this habitat model as a basis of a metapopulation model, which included demographic data such as fecundity, survival, as well as variability in these demographic rates.
Habitat Modeling Based on GIS Data:
We used GIS data (raster maps exported from ARC/INFO) on the vegetation and topography of an approximately 850 km² region of Orange County, California. Using this data and the locations of gnatcatcher pair observations, we estimated a habitat model with logistic regression. Significant variables included the percentage of coastal sage scrub, elevation, distance from grasslands, distance from "trees" (forest, woodland, chaparral), and various interactions among these variables. We validated the model by estimating the habitat function using only data on gnatcatcher locations in the northern half of the study area, and predicting the habitat suitability of the locations where gnatcatcher pairs were observed in the southern half. We entered the habitat model in RAMAS GIS to create a habitat suitability map (see Figure).
ENVIRONMENT
Metapopulation Modeling
We used RAMAS GIS to identify patches in the habitat suitability map. A habitat patch is a cluster of suitable cells that can support a local gnatcatcher population. The collection of these local populations make up the gnatcatcher metapopulation in the study area. Thus we used the habitat model to calculate the spatial structure of the metapopulation, including size and location of habitat patches and the distances among them. RAMAS GIS also calculated the average and total habitat suitability in each patch. We combined the spatial structure of the model with demographic parameters (such as survival, fecundity, dispersal, and catastrophe) that we estimated with data from field studies This resulted in a stage-structured, stochastic, spatially-explicit metapopulation model. Using this model, we simulated the dynamics of the metapopulation under various assumptions.
Results and Future Directions
The model predicted a high risk of decline in the next 50 years with most combinations of parameters. However, there was a considerable range of outcomes due to uncertainties in parameters. Results were most sensitive to density-dependent effects, the probability of weather-related catastrophes, adult survival, and adult fecundity. Based on data used in the model, the greatest difference in results was given when the simulation's time horizon was only a few decades, suggesting that modeling based on longer or shorter time horizons may underestimate the effects of alternative management actions. For more information see Akçakaya and Atwood (1997; Conservation Biology 11:422-434).
We are planning to refine the model in the future, and use it to assess or rank management and conservation alternatives. One type of management that can be evaluated with this kind of a model is habitat conservation and restoration. Suppose, for example, that three of the habitat patches identified in this study are potential candidates for habitat conservation and restoration. If these patches vary in size, then there would a total of 7 alternatives (ranging from restoring only the smallest patch to restoring all three). These, plus the "no action" alternative, can be evaluated by running a series of simulations that incorporate the expected improvements in the carrying capacity and other parameters of the patches where habitat would be restored.
Cost Benefit Graph
The 8 options can then be ranked in order of increasing effectiveness (in, for example, reducing the risk of extinction). For this example, we might expect that the larger the area where habitat is improved, the lower the extinction risk of the gnatcatchers. The obvious choice is to improve the habitat in all three patches. In reality the choices are much less obvious, because improving all three patches may cost more than what is available for California gnatcatcher habitat management, which means we need to consider the costs as well. We could rank the 8 options with respect to both their benefit (reduction in risk of extinction) and with respect to their cost (see Figure above). Such a graph allows the evaluation of each conservation action in terms of costs and benefits, without falling into the trap of assigning a monetary value to the existence of a species.
Metapopulation Dynamics of the California Least Tern
Software: RAMAS/GIS, Metapop
Citation: Akçakaya, H.R., J.L. Atwood, D. Breininger, C.T. Collins, and B. Duncan. 2003. Metapopulation dynamics of the California least tern. Journal of Wildlife Management 67:829-842.
Project description
The California Least Tern (Sterna antillarum browni) is federally listed as an endangered species. Its nesting habitat has been degraded, and many colony sites are vulnerable to predation and human disturbance. In this study, we developed a metapopulation model for the California least tern that can be used to predict persistence of populations along the Pacific coast and the effects of various management actions. We demonstrate the use of the model by estimating the effect of reducing predation impact in various populations.
Apart from restricting human access to nesting sites, most management efforts have concentrated on predation, an important source of reduced fecundity. In the model, each cluster of nearby colonies is defined as a population. Within each population, the model includes age-structure, year-to-year changes in survival and fecundity, regional “catastrophes” (strong El Niño/Southern Oscillation events), and local catastrophes (reproductive failure due to predation). The model predicted a continuing population increase and a low risk of a substantial decline in the next 50 years. However, this result was sensitive to assumptions about vital rates. Under a pessimistic scenario, the model predicted a high risk of decline, although a low risk of extinction. We simulated the effect of predator management by reducing the probability of reproductive failure due to predation. The improvement in viability was not the same for management in all populations (it ranged from 1% to 4% for single populations, and up to 8% when all populations were included). Results indicated that the number and location of populations selected for focused management influenced the effectiveness of management efforts.
Marbled Murrelet in Oregon and California
Software: RAMAS/GIS, Metapop
Location of study: Oregon and California
Project description
Marbled Murrelet is listed as threatened under the Endangered Species Act in California, Oregon, and Washington. It is also listed as endangered under the California Endangered Species Act. Habitat destruction through forest harvest is generally regarded as the main cause of population decline, although mortality in gill-nets, in oil spills, or as a result of predation are also thought to play significant roles.
Applied Biomathematics has undertaken an analysis of the dynamics of the Marbled Murrelet metapopulation. In this project, we used RAMAS GIS, developed by Applied Biomathematics. Our analysis involved estimating the risk of decline of the Marbled Murrelet populations in southern Oregon and northern California, under various assumptions and management considerations.
Helmeted Honeyeater in Victoria, Australia
Software: RAMAS/GIS, Metapop
Citation: Akçakaya et al. (1995; Biological Conservation 73:169-176).
Project description
The Helmeted Honeyeater, Lichenostomus melanops cassidix, is an endangered bird species endemic to Victoria, Australia. In our analysis, we used spatial data (raster maps exported from ARC/INFO) on the habitat requirements of the helmeted honeyeater, and results of habitat modeling by Pearce et al. (1994) to create a habitat suitability map. We used RAMAS GIS to define the patch structure in this habitat map. We then combine this patch structure with demographic data to build a stage-structured, stochastic metapopulation model.
Integrating Landscape and Metapopulation Modeling Approaches: Viability of the Sharp-Tailed Grouse in a Dynamic Landscape
Software: RAMAS/GIS, Landscape
Published: Akçakaya HR, Radeloff VC, Mladenoff DJ, He HS. 2004. Integrating landscape and metapopulation modeling approaches: viability of the sharp-tailed grouse in a dynamic landscape. Conservation Biology 18(2):526-537.
Presented: The 2002 Annual Meeting of the Society for Conservation Biology
Authors: H. Resit Akçakaya, Volker C. Radeloff, David J. Mladenoff, Hong S. He
Location of study: northwestern Wisconsin
Integrating Landscape and Metapopulation Modeling Approaches: Viability of the Sharp-tailed Grouse in a Dynamic Landscape
Project description
We analyze the effect of forest management options on the viability of the Sharp-tailed Grouse, Tympanuchus phasianellus, in the Pine Barrens region of northwestern Wisconsin using a model that integrates landscape and metapopulation modelling approaches. Our model simulates metapopulations in dynamic and fragmented habitats; it allows population viability analyses based on temporal changes in the habitat patch structure, brought about by processes such as succession, disturbances, and silviculture. Both the landscape and metapopulation components are spatially dynamic models.
The landscape component (LANDIS) predicts landscape dynamics in the form of a time series of maps that describe the tree species composition and age distribution at each decade. These maps are then combined into a time series of patch structures, which form the dynamic spatial structure of the metapopulation component (RAMAS). The results indicate that the viability of the Sharp-tailed Grouse in the Pine Barrens depends both on landscape dynamics and on demographic variables such as fecundity and mortality. Ignoring the landscape dynamics gave overly optimistic results, and results based only on landscape dynamics (ignoring demography) led to a different ranking of the management options than the ranking based on the more realistic model that incorporated both landscape and demographic dynamics.
Spotted Owl metapopulation in southern California
Software: RAMAS/GIS, Metapop
Published: Journal of Animal Ecology 63:775-785 (1994)
Authors: William S. Lahaye, R. J. Gutierrez, H Resit Akcakaya
Location of study: southern california
Project description
The California spotted owl Strix occidentalis occidentalis (Xantus) is found in the Sierra Nevada and in a series of isolated populations in the mountains of southern California.
We developed a model to assess the risk of decline of the southern California spotted owl metapopulation. We modelled the spatial structure of this metapopulation by incorporating distance-dependent dispersal and correlation among the population growth rates.
Demographic characteristics of the largest insular population were estimated from colour-ringing the majority of the territorial population. This owl population declined dramatically during the study period, 1987-1993.
If the observed decline continues and similar declines are occurring in the other populations, our viability analysis predicts that this metapopulation has a high risk of going extinct in the next 30 to 40 years.
If the observed decline is due to naturally occurring environmental fluctuations (drought), and thus temporary, the model results indicate substantial decline, but a low probability of total metapopulation extinction.
Our results indicated that the risk of decline is quite sensitive to the correlations among population growth rates. Increased correlation increased the risk of decline.
FISH & INVERTEBRATE
Redhorse Sucker
Software: RAMAS/GIS, Metapop
Funding: Electric Power Research Institute and American Electric Power Service Corporation
Authors: Karen V. Root, Resit Akçakaya
Location of study: southeastern Ohio
RAMAS® Ecological Risk Model for Assessing Temperature Effects on Redhorse Sucker Species in the Muskingum River
Project description
Using data provided by the American Electric Power Service Corporation (AEP) on the golden redhorse (GRH), the silver redhorse (SRH) and the shorthead redhorse (SHRH) populations in the Muskingum River in Ohio, we addressed the question of what impact elevated water temperatures produced by the Muskingum River Power Plant (MRPP) and Conesville Power Plant (CPP) might have on these fish.
We used census data from consecutive years to estimate an age-structured model, and data from whole-river surveys to estimate abundance of populations in each section of the river between dams. We modeled the effect of elevated temperatures on survival and fecundity, based on data from a short-term thermal exposure experiment. We input these data into a RAMAS Metapop model, and ran simulations under various scenarios of temperature regimes. model
Because of the incompleteness of demographic data, we were forced to make several assumptions about the dynamics of the redhorse species in the Muskingum River. Because of these assumptions, the results of this analysis should be interpreted with caution. In general, exposure to elevated temperatures increased the predicted risk of decline of all three species. The increase in risk is substantially lower if, during the warmest periods, fish dispersed to tributaries, where temperatures are assumed to be about 4-5°C cooler.
The sensitivity analyses identified the most important parameters, and thus pointed out the most useful types of data that can be collected to improve the model. These included a long-term mark-recapture study designed to estimate survival rates at an annual time scale at different temperature regimes, densities and habitats; a parallel study focusing on recruitment; and an extensive habitat sampling in all tributary streams suspected to be used as refugia.
Shortnose Sturgeon (Connecticut River, MA and CT)
Software: RAMAS/GIS, Metapop
Funding:Electric Power Research Institute and Northeast Utilities
Authors: Karen V. Root, Resit Akçakaya
Location of study: Connecticut River, MA and CT
Ecological Risk Analysis for the Shortnose Sturgeon Populations in the Connecticut River
Project description
This project focused on two populations in the Connecticut River separated by the Holyoke Dam, with particular emphasis on the effects of migration on long-term survival. We developed a stage-based stochastic metapopulation model using RAMAS Metapop. Based on the existing data, the model results suggested that the observed stability of the two populations is possible either with reproduction in both upper and lower populations and small to moderate rates of dispersal between them, or with no fecundity in the lower population, very high fecundity in the upper population and high rate of net downstream dispersal. We also assessed the extinction risk of the two populations under various sets of assumptions, and explore the combinations of upper population fecundity and downstream migration that might compensate for lack of reproduction in the lower population.
The results of the model demonstrate the type of questions that may be addressed with a modeling approach. However, the specific model predictions are not reliable due to a lack of data. To model the shortnose sturgeon populations of the Connecticut River, we made a number of assumptions, which could have an impact on the predictions. Our results suggest that large change in the fecundity and/or migration rates included in the model will have large effects on the long-term survival and final abundance of these shortnose sturgeon populations. This research, therefore, highlights three key areas for future research: (1) a better estimate of the annual fecundity its temporal variation in both the upper and lower populations, (2) a more accurate measurement of the rate of downstream movement, (3) estimates of annual survival rates, and their temporal variation, for ages less than 5 years.
Daphnia magna and Neanthes arenaceodentata (for marine sediment toxicity tests)
Software: RAMAS/GIS, Metapop
Funding: Army Corps of Engineers Waterways Experiment Station
Published: Bridges TS, Wright RB, Gray BR, Gibson AB, Dillon TM. 1996. Chronic toxicity of Great Lakes sediments to Daphnia magna: elutriate effects on survival, reproduction and population growth. Ecotoxicology 5:83-102.
Ferson S, Ginzburg LR, Goldstein RA. 1996. Inferring ecological risk from toxicity bioassays. Water, Air and Soil Pollution. 90:71-82.
Authors: Scott Ferson, H. Resit Akçakaya, Pedro Silva
Assessing Risks to Population Dynamics of Aquatic Animals From Dredged Materials
Project description
Daphnia magna and the polychaete (Neanthes arenaceodentata) are widely used to monitor the toxicity of dredge spoils. Traditionally measured variates such as acute mortality, depression of fecundity, and rate of developmental abnormalities are difficult to interpret and present a confusing array of 'endpoints' to decision makers. Applied Biomathematics developed population-level models for the two species to develop a sensible scheme to express impacts in terms of the entire population's dynamics. Because the populations are grown under controlled laboratory conditions, environmental variability is minimal. However, measurement error is still often quite large, and the uncertainty it induces must be propagated by the model to determine the reliability of the final assessment.
Blueback Herring Alosa aestivalis (R.B. Russell Dam, GA and SC)
Threadfin Shad Dorosoma petenense (R.B. Russell Dam, GA and SC)
Software: RAMAS/GIS, Metapop
Funding: Army Corp of Engineers and Electric Power Research Institute
Authors: Karen V. Root, Scott Ferson
Location of study: border between South Carolina and Georgia
Assessment of Population-Level Threat from Entrainment at Russell Dam on Thurmond Reservoir Fishes
Project description
This project evaluates entrainment impacts on five fish species in the J. Strom Thurmond Reservoir (JSTR) on the border between South Carolina and Georgia. Two species, threadfin shad and blueback herring, are both short-lived and their growth is strongly regulated by density. Each has a robust reproductive potential and appear to rebound quickly from impacts. The third and fourth fishes, striped bass and hybrid bass, are long-lived species. They do not reproduce in the reservoir and instead are annually stocked. Little is known about the black crappie, the fifth species, in this reservoir.
To predict the long-term population-level consequences of the mortality induced by the pump storage operation at the Richard B. Russell Dam, we developed a stochastic demographic model that captures the essential population dynamics of the species. Using data supplied by U.S. Army Corps of Engineers Waterways Experiment Station, the Georgia Cooperative Fisheries and Wildlife Research Unit, and Aquacoustics, Inc., we parameterized baseline models for the five fish species. These models were then modified to reflect the impacts of entrainment and impingement predicted from pumpback operations. Specifically, the modified models incorporated two different entrainment scenarios: Scenario A models are based on entrainment data collected from August 31, 1993 to October 31, 1996. They depict the long-term effects of the mean water year entrainment using the mean entrainment rate as well as higher rates specified by both the Army Corps and state fisheries groups. For each fish species, a single Scenario B model is presented, representing the effects of mean water year entrainment based on a 12-month expansion of Phase III entrainment data. With these baseline and entrainment models, we used Monte Carlo simulation to make separate probabilistic forecasts for the risks of population decline, assuming that these conditions persist 50 years into the future.
Simulation outputs suggest that entrainment affects the five species to varying degrees. The maximum increase in risk for threadfin shad is 5% above background. Entrainment increases the risk of decline for blueback herring a maximum of 33%. For the hybrid bass and striped bass, there are increases in stocking rates of 20% and 28%, respectively. Essentially, entrapment mitigates any frequency in decline. Therefore, the model provides guidelines on the level of risk for various degrees of entrainment and potential management actions to mitigate the possible negative effects.
Arianta Arbustorum Snail
Software: RAMAS/GIS, Metapop
Published: Oecologia 105: 475-483 (1996)
Authors: Bruno Baur, H. Resit Akçakaya
Location of study: northeastern Switzerland
Effects of population subdivision and catastrophes on the persistence of a land snail metapopulation
Project description
We modeled the dynamics of a metapopulation of the land snail Arianta arbustorum in northeastern Switzerland to investigate the effect of population subdivision on the persistence of a land snail metapopulation and to analyze the interaction between spatial factors, population subdivision, and catastrophes. We developed a spatially structured, stochastic, age-structured metapopulation model with field data from previous studies on the metapopulation in Switzerland as well as experimental and meteorological data. The model incorporated distance-dependent dispersal through stream banks, correlated environmental fluctuations, and catastrophes resulting from heavy rains. The results point to various complex interactions among factors involved in metapopulation dynamics, and suggest that in some cases population subdivision may act as a way to decrease threats from environmental fluctuations and catastrophes.
Habitat suitability map for the California Gnatcatcher, Orange County, CA. Darker red indicates more suitable habitat, white indicates insuitable habitat. The black lines show the borders of habitat patches identified by RAMAS®/GIS.
CONSERVATION
Software for Evaluating the Impact of Forest Management Plans on Wildlife: Linking Landscape and Metapopulation Models
Software: RAMAS/GIS, Landscape
Funding: Funded by Department of Agriculture
Authors: P.I: H. Resit Akçakaya
Project description
In this project, we integrated the landscape model LANDIS with the metapopulation model RAMAS, and created a software tool for evaluating the viability of an endangered species under alternative forest management and conservation options. LANDIS predicts changes in the forest stand structure, including species composition, dominant tree species, and age distribution. RAMAS simulates the dynamics of species that inhabit distinct habitat patches. Both models are flexible, i.e., they can be (and have been) easily customized by the users to apply to different landscapes and species. The software we developed combines the features of both, and is applicable to multiple systems. This effort has resulted in a prototype program that was sent to several investigators for testing, was used in the case studies, and was demonstrated at several professional meetings.
The software we developed in this project represents the first attempt at establishing a spatially explicit link between the landscape and the metapopulation approaches, allowing an analysis of population viability based on landscape dynamics brought about by natural and human mediated processes such as succession, disturbances, and silviculture. In addition, the integration of two generic, spatially explicit models will allow application of this approach to other cases of species living in fragmented and dynamic habitats. The most important challenge to the practical use of this approach in conservation and management of species in dynamic landscapes would come from obtaining sufficiently precise estimates of model parameters. Future developments focusing on statistical methods of data analysis and parameter estimation would greatly enhance the usefulness of this approach.
The software tool we are developing in this project will be used by forest managers to assess the affect of changes in the landscape on the threatened and endangered species. Such landscape changes include natural disturbances such as fire and windthrow, as well as human-mediated changes such as timber harvest. The software integrates two modeling approaches to achieve its goal of allowing planners and managers to explore the viability of an endangered species under alternative forest management and conservation options. The first model is a landscape model, which predicts changes in the forest structure (age and species composition) in 10-year time steps. The second is a metapopulation model that estimates the extinction risk of the species, by simulating their dynamics in the changing habitat predicted by the landscape model. The integration of these two well-developed and widely used approaches to modeling will enable more realistic evaluation of schedule and type of timber harvest from the point of view of threatened and endangered species in the landscape.
Assessing Status and Trends of Threatened Species from Uncertain Monitoring Data
Software: RAMAS/GIS,
Funding:National Science Foundation.
Presented: Expanded summary of the presentation at the 2004 Annual Meeting of the Society for Conservation Biology (Saturday, July 31, 4:00 pm)
Authors: H. Resit Akçakaya, David Myers
Location of study: Applied Biomathematics, Setauket, NY
Project description
Range (spatial distribution) and population trends (temporal dynamics) are two important attributes of a species, and are used in most assessments of species status, including the U.S. Endangered Species Act, the IUCN criteria, and NatureServe's Heritage Status criteria. Measures of spatial distribution include extent of occurrence (EOO; or range size), and area of occupancy (AOO, or occupied habitat). Measures of temporal trend include past, current, and expected future population declines, usually calculated over 1 to 3 generations.
These measures of spatial distribution and temporal trend are often known with large uncertainties. The causes of these uncertainties include observations with different levels of reliability (e.g., because they are old or unconfirmed),
observation locations that are uncertain
discontinuities in the distribution, and to what extend they should be excluded from the calculation of EOO
inconsistencies in the resolution and position of the measurement grid (for AOO);
censuses with different sample sizes and/or reliabilities
uncertainty in generation length.
We are developing methods to address these uncertainties, and to estimate these three measures as uncertain quantities. These methods include using alpha-hulls (a generalization of convex hulls or minimum convex polygons) to calculate EOO, finding minimum and maximum possible polygons and grid counts based on location uncertainty and grid registration uncertainty, using scale-area curves for estimating AOO for a standard reference grid size, and performing fuzzy regression (including least squares and parameter-bounding methods) for estimating the range of population trends.
Modeling the Effect of Human Population on Land Use and Species Viability
Software: RAMAS/GIS
Funding:This project is funded by the National Science Foundation.
Presented: The 2004 Annual Meeting of the Society for Conservation Biology (Sunday, August 1, 8:30 am)
Authors: H. Resit Akçakaya, W. Troy Tucker
Location of study: Applied Biomathematics, Setauket, NY
Project description
This project aims to develop methods and software to evaluate or explore the impact of human population and land-use changes on species viability. Changes in human population and land use affect the viability of native species through habitat loss to agriculture, urban sprawl, and industrial development; habitat fragmentation; decreased habitat quality; and increased direct harvest of species. Applied Biomathematics has developed internationally known RAMAS software for modeling the effect of changes in the quality and amount of habitat on the viability of species. The methods being developed in this project will allow the incorporation of the human element into this methodology. It will lead to software that will be used to forecast the changes in the human population, and the effect of these changes on the land-use and resource-use patterns. These results will be used to predict the changes in the habitat of native species, and to assess species viability and persistence. Projecting landscape change is prerequisite to conservation planning.
Both natural and anthropogenic processes drive landscape change. Relevant human ecological impacts include habitat loss due to direct human use for agriculture and housing, landscape fragmentation due to roads and development, and habitat quality decline due to altered drainage, soil loss, nutrient leaching, pollution, selective harvest, wildfire suppression, the introduction of exotic species, and grazing. Simulating human-induced landscape change remains difficult and problematic and no one best solution has emerged. We have developed an eclectic modeling framework that integrates spatially explicit landscape and metapopulation models with models of human social, economic, and demographic change. This framework is applicable to cases where sophisticated and data intensive models of human population and landscape interaction exist, as well as to cases where data is sparse and anthropogenic impacts are not well understood. In the latter case, while precision may be difficult to achieve, accurate predictions of landscape change relevant to population viability over useful time horizons are possible.
A Multispecies Approach to Ecological Assessment and Conservation
Software: RAMAS/GIS
Funding: National Science Foundation SBIR grant.
Published: 2003. A multi-species approach to ecological valuation and conservation. Conservation Biology 17:196-206
Presented: A poster by Karen V. Root at the ESA/BES meeting on April 12, 2000, Orlando, FL
Authors: Root, K.V., H.R. Akçakaya and L.R. Ginzburg.
Project description
The conservation of ecosystems focuses on evaluating individual sites or landscapes based on their component species. To produce a map of conservation values, we developed a method to weight habitat-suitability maps for individual species by species-specific extinction risks. The value of a particular site reflects the importance and magnitude of the threats facing the component species of the ecological community. We applied this approach to a set of species from the California Gap Analysis Project. The resulting map of multispecies conservation values identified the areas with the best habitat for the species most vulnerable to extinction. These methods are flexible and can accommodate the quantity and quality of data available for each individual species in both the development of the habitat-suitability maps and the estimation of the extinction risks. Additionally, the multispecies conservation value can accommodate specific conservation goals, such as preservation of local endemics, making it useful for prioritizing conservation and management actions. This approach provides an estimate of the ecological worth of a site based on habitat characteristics and quantitative models in terms of all the ecological components of a site, rather than a single threatened or endangered species.
Ecological Boundary Delineation
Software: RAMAS/GIS
Funding: Electric Power Research Institute
Authors: Scott Ferson
Project Description
This project will collect the diversity of methods that are currently being used to draw ecological boundaries in a single friendly software package. These methods are used to find the borders around wetlands, fragile habitats, to locate vegetation structures sensitive to environmental change, and to plan human activities with the least environmental impact. The methods must contend with complex multivariate data which is often noisy, but which may not have been sampled thoroughly on a grid, but only at a few single points, or possibly across transects. By offering these disparate analytical methods in one environment, researchers will be better able to compare their properties and better choose among the alternative methods.
Despite the importance of ecological boundaries in a variety of scientific questions and a multiplicity of management strategies, very little research has been focused on delineating ecological boundaries. Virtually all maps of biological resources produced before 1970 were drawn by eye, without the benefit of any formal algorithm for determining the positions of boundaries. Cornell systematist William L. Brown (of character displacement fame) humorously offered Brown's Rule which states that the boundary between two species will be drawn where the fewest samples have been taken. Over the last two decades, algorithmic approaches have been employed, but they have used poorly documented, often ad hoc methods whose properties were not well or widely understood.
Lately, the mapping of ecological boundaries has become a common activity among environmental engineers and managers, ecologists, land use planners, and biological reserve designers. Many applications arise in diverse areas such as critical habitat mapping, home range demarcation, land use partitioning, wetland delineation, vegetation mapping, ecotone identification, and patch boundary localization. But each of these applications harks to the same problem of where to draw the line to separate regions. Each of these applications has one or more methods which were usually designed from scratch for its particular purpose. Surprisingly little systematic attention has been paid to how these boundary delineation methods behave, or to the similarities or discrepancies among them, or to whether one might be much better than another.
Drawing boundaries on maps is largely controlled by pragmatic considerations. Legal and political realities force managers to draw lines somewhere (even when the empirical information is sketchy) and these lines sometimes then take on a life of their own which is often unjustified by the underlying ecological reality. Once the position of the boundary has been decided, it is sometimes difficult to return to an ecologically meaningful description even if the situation changes or the original determination was flawed. Since the justification for the boundary was ad hoc in the first place, it is often even more difficult for a researcher to be effective in arguing that the line should be moved or reconsidered. Thus, it can be doubly difficult to overcome the troublesome (but natural) legalistic inertia that seems to accompany drawing a line.
While the simple boundary delineation methods currently available in software packages such as GIS and image analysis systems may be adequate for incidental use in research and planning, in cases where the drawing of boundaries is central or even crucial to the question or goal, much more sophisticated methods must be employed. We propose to develop a microcomputer software shell (tentatively named EcoBound) containing a comprehensive variety of these methods for delineating ecological boundaries that can be applied to sparse points, transects, or grids of possibly multivariate environmental data. The shell will be modular in design so as to accommodate inclusion of future methods. By collecting the diverse methods into one shell with a convenient interface for communication with GIS, image analysis and general statistical packages, this research will facilitate consistent and rational usage of the various methods available. By using objective methods with known statistical properties, researchers will be better equipped to defend the conclusions they finally draw. Likewise, when the determination method is well understood and conveniently accessible in software, others can check the conclusions with new data, alternate methods, or different assumptions, and thereby improve the quality of the review process.
Discovering Ecotones
Software: RAMAS/GIS
Funding: Electric Power Research Institute and Empire State Electric Energy Research Corporation
Published: Ferson, S., C. Kurtz, and D. Slice. 1995. Sensitive Landscape Features for Detecting Biotic Effects of Global Change. Electric Power Research Institute EPRI TR-105216, Palo Alto, CA.
Authors: Scott Ferson
Location of study: southern California
Project Description
Remote sensing observations of vegetation have been suggested as a means to detect the effects of global change, and some research efforts in this direction have yielded good results in forecasting variations on a seasonal level. Despite this experience however, there is little confidence that this approach can be used to detect incipient global change effects on vegetation. Thus broad-scale remote sensing approaches are not likely to be a source of timely observations during the coming years when crucial policy decisions need to be made.
The suggestion that monitoring efforts concentrate on vegetation boundaries (called ecotones) where plants are presumed to be near the edge of their physiological tolerance has serious complications. In particular, ecotones that are especially sharp and obvious to observers are the least sensitive to the kinds of environmental alterations induced by global changes. However, there is a class of transition zones that, although more subtle in appearance, are strongly sensitive to environmental changes and thus would be ideal for use as monitors of incipient global changes. We propose to develop the necessary methodology to detect the various classes of vegetation ecotones and distinguish sensitive ones for monitoring the environment. Timberlines (and other ecotones) are poor indicators for global change effects.
Thermal Effects on Trophic Community Function
Software: RAMAS/GIS
Funding: Electric Power Research Institute and Carolina Power and Light
Authors: Scott Ferson
Location of study: southeastern United States
Project Description
Extensive biological monitoring data have been collected for ten years about the aquatic community in a black-water reservoir in the southeastern United States. The reservoir community is typical of many similar water bodies in the region. The most abundant fish species is bluegill Lepomis macrochirus. The dominant predator in the reservoir is largemouth bass Micropterus salmoides. Is the decade-long record of ecological data sufficient to permit the determination of the potential long-term population-level consequences of relaxing environmental regulations on thermal discharges from a power plant?
Despite the quality of the biological sampling data, there will always be some uncertainty in predicting the true risk of future population declines, due to inherent variability of climate, reservoir inflow, nutrient cycling, etc. associated with population response. Nevertheless, it may be possible to predict the relative effect of a marginal change in environmental conditions compared to the background risk for the populations of interest.
The analysis included the patterns of temperature fluctuations and fish, zooplankton and phytoplankton abundances over the last ten years. The reason for including the lower food chain levels is that thermal impacts may have indirect effects through trophic interactions that are more pronounced than the direct effects of temperature on the fish species.
Even using worst case assumptions about how increases in discharge temperature would translate into increases in water temperature, simulation results suggest that relaxing thermal discharge limits by a few degrees is likely to have little or no effect on the risk that largemouth bass will experience population declines of any magnitude. The effect on bluegill, on the other hand, appears to depend on when during the year the temperature increases occur. If the increases affect maximum summer temperatures, there may be a beneficial effect so that the risk of bluegill population declines are actually reduced. However, if the increases affect maximum springtime temperatures during the spawning period, there may be an increase in the risk of population decline, although this increased risk for bluegill has virtually no impact on its predator, largemouth bass. The available data and the simulations based on them offer no suggestion of any adverse indirect ecological effects on either species by temperature impacts on their food supply lower on the food chain.
Linking Landscape Data with Population Viability Analysis
Software: RAMAS/GIS
Funding: Electric Power Research Institute
Authors: H. Resit Akçakaya
Project description
The goal of this project was to develop a user-friendly software based on the methodology for habitat-based metapopulation viability analysis, developed under funding from the National Science Foundation. The result of the project was the software RAMAS GIS.
Methodology for Habitat-based Metapopulation Viability Analysis
Software: RAMAS/GIS, Metapop
Funding: National Science Foundation (SBIR)
Published: Akçakaya, H.R., M.A. McCarthy and J. Pearce. 1995. Linking landscape data with population viability analysis: management options for the helmeted honeyeater. Biological Conservation 73:169-176.
Authors: H. Resit Akçakaya
Location of study: Victoria, Australia
Project description
The goal of this project was to develop a methodology for habitat-based metapopulation viability analysis. The methods developed in this projects were later implemented as the RAMAS GIS software. The methods were applied to analyze the metapopulation dynamics of, and management alternatives for, an endangered bird species in Victoria, Australia.
ENGINEERING
Accounting for epistemic and aleatory uncertainty in early system design NASA SBIR Phase 2 Final Report
Software: RAMAS/GIS
Funding: Electric Power Research Institute and Carolina Power and Light
Authors: Scott Ferson
Location of study: Applied Biomathematics 100 North Country Road Setauket, NY
Project description
This project extends Probability Bounds Analysis to model epistemic and aleatory uncertainty during early design of engineered systems in an Integrated Concurrent Engineering environment. This method uses efficient analytic and semi-analytic calculations, is more rigorous than probabilistic Monte Carlo simulation, and provides comprehensive and (often) best possible bounds on mission-level risk as a function of uncertainty in each parameter. Phase 1 demonstrated the capability to robustly model uncertainty during early design. Phase 2 will build on the Phase 1 work by 1) Implementing the PBA technology in Excel-mediated computing tools, 2) Fashioning an interface for these tools that enables fast and robust elicitation of expert knowledge, 3) Initiating the development of a library of such elicitations, 4) Demonstrating the application of the tools, interface and library in an interactive, distributedcomputing environment, 5) Developing case studies, and 6) Creating tutorial documentation. Important applications of these new tools include the ability to rapidly and rigorously explore uncertainty regarding alternate designs, determine risk-based margins that are robust to surprise, and incorporate qualitatively described risks in quantitative analyses. This suite of capabilities is not currently available to systems engineers and cannot be provided by more traditional probabilistic risk assessment methods. The primary application envisioned for the extended PBA technology at NASA is the analysis of uncertainty and risk in subsystem, system, and mission design in an Integrated Concurrent Engineering environment like the IDC at LaRC. The methods, algorithms, libraries, and software developed will be of use in a wide variety of commercial activities that involve physicsor non-physics-based systems design, reliability assessment, or risk analysis. Applications where NASA may use the technology while serving as a vendor include: (1) Uncertainty and risk analysis during commercial spacecraft subsystem component, subsystem, system, and/or mission early design, (2) Integrated analysis of qualitative and quantitative uncertainty during commercial operations and organization design, restructuring and/or risk and reliability analysis, (3) Commercial organizational and/or mission risk reduction modeling, and (4) Incorporation of quantitative uncertainty and risk analysis in quantitative system-wide, mission-wide, and/or organization-wide probabilistic risk-based margin determination metrics and management procedures.
2. Identification and Significance of the Innovation The proposed work extends Probability Bounds Analysis (PBA) to model epistemic and aleatory uncertainty during early design of engineered systems in an Integrated Concurrent Engineering (ICE) environment. This method uses efficient analytic and semi-analytic calculations, is more rigorous than Monte Carlo simulation, and provides comprehensive and (often) best possible bounds on mission-level risk as a function of uncertainty in each parameter. Phase 1 demonstrated the capability to robustly model variability (aleatory uncertainty) and incertitude (epistemic uncertainty) during early design. The new methods are intended to (1) allow rapid, rigorous, and more complete exploration of alternate designs in the mission- and engineeringconstrained trade space; (2) provide a rigorous rationale for risk-based margin determination that is robust to surprise; (3) facilitate the incorporation of qualitatively described risks in quantitative risk analysis; (4) support the integration of physics and non-physics based risks in mission-wide risk analysis; and (5) permit sensitivity analysis at the mission, system, subsystem, and component levels that identifies the importance of specific uncertainties to uncertainty at higher levels and allows the rapid exploration of alternate strategies and designs. This suite of PBA capabilities is not currently available to systems engineers and cannot be provided by more traditional probabilistic risk assessment methods.
HUMAN HEALTH
Quality Assurance Methods for Monte Carlo Risk Analysis
Software: RAMAS/GIS
Funding:National Institutes of Health (NIH)
Published:
Ferson, S. 1996. What Monte Carlo methods cannot do. Human and Environmental Risk Assessment.
Ferson, S. 1996. Reliable calculation in probabilistic logic: accounting for small sample size and model uncertainty. Proceedings of Intelligent Systems: A Semiotic Perspective. National Institute for Standards and Technology, Gaithersburg, Maryland.
Authors: Scott Ferson
Project description
Although probabilistic risk assessments based on Monte Carlo simulation methods are now routinely used to forecast public health consequences of various management and regulatory decisions regarding potential environmental toxicants, the reliability of the probabilistic assessments is rarely estimated. Mostly this is because the sensitivity studies this would require are extremely cumbersome. We propose to test the feasibility of a direct approach to estimating reliability that is based on probability bounds (i.e. interval bounds on cumulative distribution functions that model the risk of adverse consequences). These bounds can be constructed to contain model uncertainty comprehensively and representation error rigorously.
The probability bounds approach can be used to redress some of the most serious criticisms commonly leveled against Monte Carlo assessments, including (1) input distributions are unknown, (2) correlations and dependencies among variables are ignored, and (3) mathematical structure of the model is questionable. To establish feasibility, we will conduct case studies that illustrate its use, establish its data requirements, conservatism and workability, derive optimal formulas for use with some common mathematical operations, and explore how empirical information can be used in practice to tighten the bounds. The probability bounds approach is expected to be vastly easier to use than current second-order Monte Carlo methods.
Detecting Disease Clusters in Structured Environments
Software: RAMAS/GIS
Funding: National Institutes of Health (NIH) and by New York State Science and Technology Foundation
Published: Ferson, S. 1996. Reliable calculation in probabilistic logic: accounting for small sample size and model uncertainty. Proceedings of Intelligent Systems: A Semiotic Perspective. National Institute for Standards and Technology, Gaithersburg, Maryland.
Authors: Scott Ferson
Project Description
One the difficulties faced by health professionals in detecting of disease clusters is that the data sets are often small and inferences must be based on a relative handful of observations. It is crucial for the health professional to know what statistical tests are best in these small-environment problems, and to have these methods available in a user-friendly computer package. A variety of new, rapid, and exact combinatorial expressions for cluster analysis of patterns of disease have been proposed. Investigations into the statistical power of both these and other previously published methods for cluster detection in structured small environments will be used to recommend different tests for different kinds of problems and different amounts of data.
An interactive program called EPIC (Exact Probabilities for Incidence Clustering) that includes an intuitive interface and a thorough set of tutorials and guidelines will help the professional choose the best statistical test for a particular problem. EPIC will allow the health professional to investigate allegations of disease clustering within small, structured environments, such as families, sibships, wards, classrooms, cell blocks, job types, age classes or locations within a building. When sample sizes are small (as is almost always the case in real circumstances of public health concern), exact statistical methods are necessary since the approximate methods usually used only yield accurate estimates with data sets are large.
Exact methods guarantee that Type I error can be controlled to any desired level. Although a few exact methods based on matrix occupancy models have previously been described for data sets with perfectly regular structure, no exact methods were applicable when, for instance, families were of different sizes. EPIC will provide, for the first time, general exact statistical methods for use with small data sets in structured environments. It will allow public health professionals in the research and regulatory communities access to these new methods in a flexible and powerful microcomputer implementation.
Spatial clustering of childhood cancers in the Denver Metroplex
Software: RAMAS/GIS
Funding: Radian Corporation, with funding from Electric Power Research Institute (EPRI)
Authors: Scott Ferson
Location of study: Denver
Project description
Although we could detect no spatial clustering of childhood cancers at the finest resolution of individual cases and controls, analysis with aggregated data using census information detected statistically significant spatial clustering. The intensity (and significance) of the spatial clustering was even stronger at the level of entire cities in the Denver metroplex. The principal finding is that, when the locations of childhood cancers are aggregated into area/frequency data, statistical tests reveal significant spatial clustering.
This conclusion is robust in the sense that it is independent of many details of the analysis and the data and seems to persist over spatial resolutions ranging from the scale of a city to that of a census tract. This confirms the finding that there is strong spatial inhomogeneity in childhood cancer incidence across the region. The inhomogeneity cannot be removed simply by accounting for changes in the population density of children. This observation of clustering of childhood cancers has several important ramifications for the study of this cancer's phenomenology. The findings call into question many of the other statistical procedures already conducted on this data set that have assumed spatial homogeneity of disease etiology or incidence. Although often unstated, such an assumption is very common and probably affects many if not the majority of the most prominent conclusions that have been made about the Denver cancer data.
Stochastic cell proliferation models of carcinogenesis: Microcomputer software for research and risk analysis
Software: RAMAS/GIS
Funding:National Institutes of Health (NIH) and the Chemical Industry Institute of Toxicology (CIIT)
Authors: Scott Ferson
Project description
Quantitative models of carcinogenesis that are based on stochastic proliferation of cell types have been suggested by several researchers. For the most part, these models exist only as equations in articles, or, in a few cases, as specialized and non-portable software implementations. The consequence of this is that the models are not accessible to a broad audience of biologists who are impeded by the rigorous mathematics of the theoretical treatment or the awkwardness or unavailability of software.
We propose to develop easy-to-use microcomputer software in which the variety of important models of carcinogensis are implemented in a generalized package. From this platform researchers will be able to increase their intuition by exploring the consequences of the various assumptions made by the disparate models, as well as construct new models from the building blocks of basic assumptions about model structure, cell kinetics and mutation rates. Empirical toxicologists who possess data on dosage-dependent cancer incidence will also be able to use the software to estimate the risk or probability of tumorigenesis under any of the competing models. This software will permit users to develop their intuition about the competing models of carcinogensis, and make projections about the immediate hazards of carcinogenesis from a particular substance in a particular system.
Detecting sites at risk of becoming foci for Lyme disease
Software: RAMAS/GIS
Funding: National Institutes of Health (NIH)
Authors: Jeffrey Millstein
Project description
This research project aims to develop a computer model for the detection of areas at high risk for becoming foci for Lyme disease.Solving this type of problem is typically attacked by applying the techniques of statistical analysis to empirical data.
My approach is to implement fuzzy logic inference procedures as computer software so that these techniques can be applied to a public health problem for which the relationships between vectors and their habitats are not yet clearly known. The computer model uses fuzzy logic to make inferences from a rule base. Rules are constructed using relationships between variables which are described by adjectives. Adjectives can be modified by adverbs, and complex rules can be formed through conjunction. Adjectives are described graphically. The proposed computer model will require a minimal set of information about a habitat's characteristics, such as the types of extent of covering vegetation, the local climate, and the pool of hosts and reservoirs of Ixodes dammini, the tick vector of Borrelia burgdorferi, the biological agent of Lyme borreliosis. From these data the fuzzy logic inference algorithm will assess the likelihood that the specified area can support the development of Lyme disease foci.
Specific Aims
The objective of the Phase I research was to "(1) develop a computer-based platform for users to construct set-based qualitative models, and (2) customize this program to analyze data for the detection of areas at high risk for becoming foci for Lyme disease." The premise for constructing this program was to develop a novel kind of approach for rating parcels of land for the risk of becoming foci for Lyme disease. Solving this type of problem is typically attacked by applying the techniques of statistical analysis to empirical data. My approach was to implement recently developed qualitative procedures as computer software so that these techniques could be applied to a problem for which the relationships between vectors and their habitats are not yet clearly known. As stated by the CDC(1989), "Data concerning risk factors for acquiring Lyme disease are limited." Thus, the overall goal was to develop a tool for analyzing the data which are available in order to develop a more precise picture of the factors which permit foci of Lyme disease to develop.
The mathematical techniques that I proposed to utilize are commonly referred to as fuzzy logic inference. At the time, the use of fuzzy logic to solve biological problems was extremely limited and no computing platform existed. Almost exclusively, fuzzy logic techniques have been limited to use in engineering control systems. I saw an opportunity to apply these techniques to a wide class of problems of public health importance such as how to efficiently assess the risk that a particular habitat can support arthropod vectors of human diseases, such as the Ixodes dammini - Borrelia burgdorferi system.
The three-month Phase I research period allowed me to develop and test a compact fuzzy logic inference engine. This module uses fuzzy associative memory architecture and works by having users specify variables, adjectives, and a rule base. Adjectives are described graphically. The rule base has its own syntax and supports the modification of adjectives using adverbs or complementation. In addition, two types of fuzzy inference are supported; these are correlation-minimum and correlation-product inference. The system can generate syntactically correct C code for the variable definitions, the rule base and for the adjective set. This code will be used in the final stand-alone system. The inference module has been connected with crude data input and output routines for testing the general idea of rating habitat to determine the likelihood that Lyme disease foci could develop. Although a significant amount of progress was made, more work is necessary before the system is ready for commercial production.
Software Environment for Fuzzy Arithmetic
Software: RAMAS/GIS
Funding: Deutscher Akademischer Austasch Dienst
Published:Ferson, S. 1990. Ecological and environmental risk analysis: using computers to estimate impacts and uncertainties. CPSR Newsletter 8:25-28.
Ferson, S. and R. Kuhn. 1992. Propagating uncertainty in ecological risk analysis using interval and fuzzy arithmetic. Computer Techniques in Environmental Studies IV, P. Zannetti (ed.), pp. 387-401, Elsevier Applied Science, London.
Ferson, S. 1993. Using fuzzy arithmetic in Monte Carlo simulation of fishery populations. Proceedings of the International Symposium on Management Strategies for Exploited Fish Populations. Alaska Sea Grant College Program Report No. 93-02, University of Alaska, Fairbanks.
Ferson, S. and R. Kuhn. 1994. Interactive microcomputer software for fuzzy arithmetic. Proceedings of the High Consequence Operations Safety Symposium. J.A. Cooper (ed.), Sandia National Laboratories, SAND94-2364, pp. 493-506. Albuquerque, New Mexico.
Authors: Ruediger Kuhn, Scott Ferson
Project description
There are uncertainty propagation problems which are poorly suited for traditional methods such as Monte Carlo simulation because of extremely sparse data sets, ignorance about correlations among variables, or graded definitions of important quantities (how many children have high body burdens of an environmental contaminant depends on what you consider "high"). Fuzzy arithmetic was a developed for such situations as a way to make rigorous calculations without requiring subjective decisions. The Risk Calc software was developed as a part of this project.
Cluster Analysis in Space and Time
Software: RAMAS/GIS
Funding: National Institutes of Health (NIH) and the Electric Power Research Institute (EPRI)
Published: Jacquez, G.M. and L.I. Kheifets.1993. Synthetic cancer variables and the construction and testing of synthetic risk maps. Statistics in Medicine 12: 1931-1942.
Applied Biomathematics. 1993.
Oden, N. 1995. Adjusting Moran's I for population density. Statistics in Medicine 15: 783-806.
Oden, N. and G. Jacquez. 1996. Realistic power simulations compare point- and area-based disease cluster tests. Statistics in Medicine 15: 783-806.
Authors: N. Oden, G. Jacquez, L.I. Kheifets
Location of study: southern California
Project description
Diseases such as cancer are often clumped together in terms of their incidence in time or their distribution across space in ways that suggest a common environmental cause or a particular etiology or contagion process. However, humans are likely to perceive clusters even in purely randomly distributed data. The statistical problem is to determine whether there exists an excess of disease incidence--a cluster--above what might be expected by chance alone.
Some diseases may be clustered in time, so that most cases occur at a particular time of year. Other diseases, like those caused by a point release of toxic chemicals, may be clustered in space, so that most cases occur in the same place. There may also be space-time interaction, like an epidemic wave, so that pairs of cases are close both in time and space.
Statistical analysis can detect whether cases are clustered in space, in time, or whether there is space-time interaction. Useful statistical analyses include location/date methods such as Mantel's test, Knox test, Cuzick and Edwards case-control spatial clustering test, nearest neighbor statistics, and others. Complementary analyses include area/time-interval methods such as Dat's 0-1 matrix test, the Scan Test, Moran's I and Moran's I adjusted for population size, the empty cells test for rare events, Grimson's proximity test for binary events, Larsen's unimodal clustering test and the Ederer-Myers-Mantel test. Software is needed that brings all of these tests to the health professional in a convenient environment that also supports displaying of disease incidence information in multiple dimensions.
HUMAN HEALTH
Quality Assurance Methods for Monte Carlo Risk Analysis
Software: RAMAS/GIS
Funding:National Institutes of Health (NIH)
Published:
Ferson, S. 1996. What Monte Carlo methods cannot do. Human and Environmental Risk Assessment.
Ferson, S. 1996. Reliable calculation in probabilistic logic: accounting for small sample size and model uncertainty. Proceedings of Intelligent Systems: A Semiotic Perspective. National Institute for Standards and Technology, Gaithersburg, Maryland.
Authors: Scott Ferson
Project description
Although probabilistic risk assessments based on Monte Carlo simulation methods are now routinely used to forecast public health consequences of various management and regulatory decisions regarding potential environmental toxicants, the reliability of the probabilistic assessments is rarely estimated. Mostly this is because the sensitivity studies this would require are extremely cumbersome. We propose to test the feasibility of a direct approach to estimating reliability that is based on probability bounds (i.e. interval bounds on cumulative distribution functions that model the risk of adverse consequences). These bounds can be constructed to contain model uncertainty comprehensively and representation error rigorously.
The probability bounds approach can be used to redress some of the most serious criticisms commonly leveled against Monte Carlo assessments, including (1) input distributions are unknown, (2) correlations and dependencies among variables are ignored, and (3) mathematical structure of the model is questionable. To establish feasibility, we will conduct case studies that illustrate its use, establish its data requirements, conservatism and workability, derive optimal formulas for use with some common mathematical operations, and explore how empirical information can be used in practice to tighten the bounds. The probability bounds approach is expected to be vastly easier to use than current second-order Monte Carlo methods.
Detecting Disease Clusters in Structured Environments
Software: RAMAS/GIS
Funding: National Institutes of Health (NIH) and by New York State Science and Technology Foundation
Published: Ferson, S. 1996. Reliable calculation in probabilistic logic: accounting for small sample size and model uncertainty. Proceedings of Intelligent Systems: A Semiotic Perspective. National Institute for Standards and Technology, Gaithersburg, Maryland.
Authors: Scott Ferson
Project Description
One the difficulties faced by health professionals in detecting of disease clusters is that the data sets are often small and inferences must be based on a relative handful of observations. It is crucial for the health professional to know what statistical tests are best in these small-environment problems, and to have these methods available in a user-friendly computer package. A variety of new, rapid, and exact combinatorial expressions for cluster analysis of patterns of disease have been proposed. Investigations into the statistical power of both these and other previously published methods for cluster detection in structured small environments will be used to recommend different tests for different kinds of problems and different amounts of data.
An interactive program called EPIC (Exact Probabilities for Incidence Clustering) that includes an intuitive interface and a thorough set of tutorials and guidelines will help the professional choose the best statistical test for a particular problem. EPIC will allow the health professional to investigate allegations of disease clustering within small, structured environments, such as families, sibships, wards, classrooms, cell blocks, job types, age classes or locations within a building. When sample sizes are small (as is almost always the case in real circumstances of public health concern), exact statistical methods are necessary since the approximate methods usually used only yield accurate estimates with data sets are large.
Exact methods guarantee that Type I error can be controlled to any desired level. Although a few exact methods based on matrix occupancy models have previously been described for data sets with perfectly regular structure, no exact methods were applicable when, for instance, families were of different sizes. EPIC will provide, for the first time, general exact statistical methods for use with small data sets in structured environments. It will allow public health professionals in the research and regulatory communities access to these new methods in a flexible and powerful microcomputer implementation.
Spatial clustering of childhood cancers in the Denver Metroplex
Software: RAMAS/GIS
Funding: Radian Corporation, with funding from Electric Power Research Institute (EPRI)
Authors: Scott Ferson
Location of study: Denver
Project description
Although we could detect no spatial clustering of childhood cancers at the finest resolution of individual cases and controls, analysis with aggregated data using census information detected statistically significant spatial clustering. The intensity (and significance) of the spatial clustering was even stronger at the level of entire cities in the Denver metroplex. The principal finding is that, when the locations of childhood cancers are aggregated into area/frequency data, statistical tests reveal significant spatial clustering.
This conclusion is robust in the sense that it is independent of many details of the analysis and the data and seems to persist over spatial resolutions ranging from the scale of a city to that of a census tract. This confirms the finding that there is strong spatial inhomogeneity in childhood cancer incidence across the region. The inhomogeneity cannot be removed simply by accounting for changes in the population density of children. This observation of clustering of childhood cancers has several important ramifications for the study of this cancer's phenomenology. The findings call into question many of the other statistical procedures already conducted on this data set that have assumed spatial homogeneity of disease etiology or incidence. Although often unstated, such an assumption is very common and probably affects many if not the majority of the most prominent conclusions that have been made about the Denver cancer data.
Stochastic cell proliferation models of carcinogenesis: Microcomputer software for research and risk analysis
Software: RAMAS/GIS
Funding:National Institutes of Health (NIH) and the Chemical Industry Institute of Toxicology (CIIT)
Authors: Scott Ferson
Project description
Quantitative models of carcinogenesis that are based on stochastic proliferation of cell types have been suggested by several researchers. For the most part, these models exist only as equations in articles, or, in a few cases, as specialized and non-portable software implementations. The consequence of this is that the models are not accessible to a broad audience of biologists who are impeded by the rigorous mathematics of the theoretical treatment or the awkwardness or unavailability of software.
We propose to develop easy-to-use microcomputer software in which the variety of important models of carcinogensis are implemented in a generalized package. From this platform researchers will be able to increase their intuition by exploring the consequences of the various assumptions made by the disparate models, as well as construct new models from the building blocks of basic assumptions about model structure, cell kinetics and mutation rates. Empirical toxicologists who possess data on dosage-dependent cancer incidence will also be able to use the software to estimate the risk or probability of tumorigenesis under any of the competing models. This software will permit users to develop their intuition about the competing models of carcinogensis, and make projections about the immediate hazards of carcinogenesis from a particular substance in a particular system.
Detecting sites at risk of becoming foci for Lyme disease
Software: RAMAS/GIS
Funding: National Institutes of Health (NIH)
Authors: Jeffrey Millstein
Project description
This research project aims to develop a computer model for the detection of areas at high risk for becoming foci for Lyme disease.Solving this type of problem is typically attacked by applying the techniques of statistical analysis to empirical data.
My approach is to implement fuzzy logic inference procedures as computer software so that these techniques can be applied to a public health problem for which the relationships between vectors and their habitats are not yet clearly known. The computer model uses fuzzy logic to make inferences from a rule base. Rules are constructed using relationships between variables which are described by adjectives. Adjectives can be modified by adverbs, and complex rules can be formed through conjunction. Adjectives are described graphically. The proposed computer model will require a minimal set of information about a habitat's characteristics, such as the types of extent of covering vegetation, the local climate, and the pool of hosts and reservoirs of Ixodes dammini, the tick vector of Borrelia burgdorferi, the biological agent of Lyme borreliosis. From these data the fuzzy logic inference algorithm will assess the likelihood that the specified area can support the development of Lyme disease foci.
Specific Aims
The objective of the Phase I research was to "(1) develop a computer-based platform for users to construct set-based qualitative models, and (2) customize this program to analyze data for the detection of areas at high risk for becoming foci for Lyme disease." The premise for constructing this program was to develop a novel kind of approach for rating parcels of land for the risk of becoming foci for Lyme disease. Solving this type of problem is typically attacked by applying the techniques of statistical analysis to empirical data. My approach was to implement recently developed qualitative procedures as computer software so that these techniques could be applied to a problem for which the relationships between vectors and their habitats are not yet clearly known. As stated by the CDC(1989), "Data concerning risk factors for acquiring Lyme disease are limited." Thus, the overall goal was to develop a tool for analyzing the data which are available in order to develop a more precise picture of the factors which permit foci of Lyme disease to develop.
The mathematical techniques that I proposed to utilize are commonly referred to as fuzzy logic inference. At the time, the use of fuzzy logic to solve biological problems was extremely limited and no computing platform existed. Almost exclusively, fuzzy logic techniques have been limited to use in engineering control systems. I saw an opportunity to apply these techniques to a wide class of problems of public health importance such as how to efficiently assess the risk that a particular habitat can support arthropod vectors of human diseases, such as the Ixodes dammini - Borrelia burgdorferi system.
The three-month Phase I research period allowed me to develop and test a compact fuzzy logic inference engine. This module uses fuzzy associative memory architecture and works by having users specify variables, adjectives, and a rule base. Adjectives are described graphically. The rule base has its own syntax and supports the modification of adjectives using adverbs or complementation. In addition, two types of fuzzy inference are supported; these are correlation-minimum and correlation-product inference. The system can generate syntactically correct C code for the variable definitions, the rule base and for the adjective set. This code will be used in the final stand-alone system. The inference module has been connected with crude data input and output routines for testing the general idea of rating habitat to determine the likelihood that Lyme disease foci could develop. Although a significant amount of progress was made, more work is necessary before the system is ready for commercial production.
Software Environment for Fuzzy Arithmetic
Software: RAMAS/GIS
Funding: Deutscher Akademischer Austasch Dienst
Published:Ferson, S. 1990. Ecological and environmental risk analysis: using computers to estimate impacts and uncertainties. CPSR Newsletter 8:25-28.
Ferson, S. and R. Kuhn. 1992. Propagating uncertainty in ecological risk analysis using interval and fuzzy arithmetic. Computer Techniques in Environmental Studies IV, P. Zannetti (ed.), pp. 387-401, Elsevier Applied Science, London.
Ferson, S. 1993. Using fuzzy arithmetic in Monte Carlo simulation of fishery populations. Proceedings of the International Symposium on Management Strategies for Exploited Fish Populations. Alaska Sea Grant College Program Report No. 93-02, University of Alaska, Fairbanks.
Ferson, S. and R. Kuhn. 1994. Interactive microcomputer software for fuzzy arithmetic. Proceedings of the High Consequence Operations Safety Symposium. J.A. Cooper (ed.), Sandia National Laboratories, SAND94-2364, pp. 493-506. Albuquerque, New Mexico.
Authors: Ruediger Kuhn, Scott Ferson
Project description
There are uncertainty propagation problems which are poorly suited for traditional methods such as Monte Carlo simulation because of extremely sparse data sets, ignorance about correlations among variables, or graded definitions of important quantities (how many children have high body burdens of an environmental contaminant depends on what you consider "high"). Fuzzy arithmetic was a developed for such situations as a way to make rigorous calculations without requiring subjective decisions. The Risk Calc software was developed as a part of this project.
Cluster Analysis in Space and Time
Software: RAMAS/GIS
Funding: National Institutes of Health (NIH) and the Electric Power Research Institute (EPRI)
Published: Jacquez, G.M. and L.I. Kheifets.1993. Synthetic cancer variables and the construction and testing of synthetic risk maps. Statistics in Medicine 12: 1931-1942.
Applied Biomathematics. 1993.
Oden, N. 1995. Adjusting Moran's I for population density. Statistics in Medicine 15: 783-806.
Oden, N. and G. Jacquez. 1996. Realistic power simulations compare point- and area-based disease cluster tests. Statistics in Medicine 15: 783-806.
Authors: N. Oden, G. Jacquez, L.I. Kheifets
Location of study: southern California
Project description
Diseases such as cancer are often clumped together in terms of their incidence in time or their distribution across space in ways that suggest a common environmental cause or a particular etiology or contagion process. However, humans are likely to perceive clusters even in purely randomly distributed data. The statistical problem is to determine whether there exists an excess of disease incidence--a cluster--above what might be expected by chance alone.
Some diseases may be clustered in time, so that most cases occur at a particular time of year. Other diseases, like those caused by a point release of toxic chemicals, may be clustered in space, so that most cases occur in the same place. There may also be space-time interaction, like an epidemic wave, so that pairs of cases are close both in time and space.
Statistical analysis can detect whether cases are clustered in space, in time, or whether there is space-time interaction. Useful statistical analyses include location/date methods such as Mantel's test, Knox test, Cuzick and Edwards case-control spatial clustering test, nearest neighbor statistics, and others. Complementary analyses include area/time-interval methods such as Dat's 0-1 matrix test, the Scan Test, Moran's I and Moran's I adjusted for population size, the empty cells test for rare events, Grimson's proximity test for binary events, Larsen's unimodal clustering test and the Ederer-Myers-Mantel test. Software is needed that brings all of these tests to the health professional in a convenient environment that also supports displaying of disease incidence information in multiple dimensions.
