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Bridging the gap between mathematical biology and undergraduate education using applicable natural resource modeling

Mathematical biology is a wide field of study with many venues that undergraduate students can access through research. However, the topics of study for these students can be overwhelming, and many topics of study yield either only trivial results or abstract outcomes that are nonintuitive and diffcult to understand. We have used natural resource modeling, and more specifically, a partnership between academic researchers and federal scientists, as a bridge between undergraduate research and mathematical biology. Our collaboration is an interdisciplinary team that combines biology, mathematics, and statistics professors with government research scientists. As a team, we have mentored students through opportunities such as a Research Experiences for Undergraduates and other projects. In this article, we provide an overview of how we develop questions for undergraduates and outline two case studies, both of which resulted in peer reviewed journal articles. Last, we describe how we also transfer the results from these undergraduate projects to resource managers so the results may be applied to real world problems.

Letters in Biomathematics

Selecting a landscape model for natural resource management applications

Purpose of Review: Climate change and associated ecological impacts have challenged many conventional, observation-based approaches for predicting ecosystem and landscape responses to natural resource management. Complex spatial ecological models provide powerful, flexible tools which managers and others can use to make inferences about management impacts on future, no-analog landscape conditions. However, land managers who wish to use ecosystem and landscape models for natural resource applications are faced with the difficult task of deciding among many models that differ in important ways. Here, we summarize a process to aid managers in the selection of an appropriate model for natural resource management. Recent Findings: To guide management planning, scientifically credible information on how landscapes will respond to management actions under changing climate is required. Landscape models are increasingly used in a management context to evaluate of impacts of changing climate and interacting stressors on ecosystems and to test effects of alternative management options on desired conditions. However, the wide range of available models makes selection of appropriate and viable models a complex process. Summary: We present a series of preliminary steps to define critical scales of time, space, and ecological organization to guide an experimental design for a modeling project and then list a set of criteria for selecting a landscape or ecological model. Material presented includes the preliminary steps (crafting modeling objective, designing modeling project), organizational concerns (resources available, expertise on hand, timelines), and modeling details (complexity, design, documentation) of model selection.

Current Landscape Ecology Reports

Assessing development pressure in the Chesapeake Bay watershed: An evaluation of two land-use change models

Natural resource lands in the Chesapeake Bay watershed are increasingly susceptible to conversion into developed land uses, particularly as the demand for residential development grows. We assessed development pressure in the Baltimore-Washington, DC region, one of the major urban and suburban centers in the watershed. We explored the utility of two modeling approaches for forecasting future development trends and patterns by comparing results from a cellular automata model, SLEUTH (slope, land use, excluded land, urban extent, transportation), and a supply/demand/allocation model, the Western Futures Model. SLEUTH can be classified as a land-cover change model and produces projections on the basis of historic trends of changes in the extent and patterns of developed land and future land protection scenarios. The Western Futures Model derives forecasts from historic trends in housing units, a U.S. Census variable, and exogenously supplied future population projections. Each approach has strengths and weaknesses, and combining the two has advantages and limitations. ?? 2004 Kluwer Academic Publishers.

Environmental Monitoring and Assessment

Multiple methods for multiple futures: Integrating qualitative scenario planning and quantitative simulation modeling for natural resource decision making

Scenario planning helps managers incorporate climate change into their natural resource decision making through a structured “what-if” process of identifying key uncertainties and potential impacts and responses. Although qualitative scenarios, in which ecosystem responses to climate change are derived via expert opinion, often suffice for managers to begin addressing climate change in their planning, this approach may face limits in resolving the responses of complex systems to altered climate conditions. In addition, this approach may fall short of the scientific credibility managers often require to take actions that differ from current practice. Quantitative simulation modeling of ecosystem response to climate conditions and management actions can provide this credibility, but its utility is limited unless the modeling addresses the most impactful and management-relevant uncertainties and incorporates realistic management actions. We use a case study to compare and contrast management implications derived from qualitative scenario narratives and from scenarios supported by quantitative simulations. We then describe an analytical framework that refines the case study’s integrated approach in order to improve applicability of results to management decisions. The case study illustrates the value of an integrated approach for identifying counterintuitive system dynamics, refining understanding of complex relationships, clarifying the magnitude and timing of changes, identifying and checking the validity of assumptions about resource responses to climate, and refining management directions. Our proposed analytical framework retains qualitative scenario planning as a core element because its participatory approach builds understanding for both managers and scientists, lays the groundwork to focus quantitative simulations on key system dynamics, and clarifies the challenges that subsequent decision making must address.

Climate Risk Management

U.S. Geological Survey Groundwater Modeling Software: Making Sense of a Complex Natural Resource

Computer models of groundwater systems simulate the flow of groundwater, including water levels, and the transport of chemical constituents and thermal energy. Groundwater models afford hydrologists a framework on which to organize their knowledge and understanding of groundwater systems, and they provide insights water-resources managers need to plan effectively for future water demands. Building on decades of experience, the U.S. Geological Survey (USGS) continues to lead in the development and application of computer software that allows groundwater models to address scientific and management questions of increasing complexity.

Fact Sheet

U.S. Geological Survey Activities Related to American Indians and Alaska Natives: Fiscal Year 2005

Introduction This report describes the activities that the U.S. Geological Survey (USGS) conducted with American Indian and Alaska Native governments, educational institutions, and individuals during Federal fiscal year (FY) 2005. Most of these USGS activities were collaborations with Tribes, Tribal organizations, or professional societies. Others were conducted cooperatively with the Bureau of Indian Affairs (BIA) or other Federal entities. The USGS is the earth and natural science bureau within the U.S. Department of the Interior (DOI). The USGS does not have regulatory or land management responsibilities. As described in this report, there are many USGS activities that are directly relevant to American Indians, Alaska Natives, and to Native lands. A USGS website, dedicated to making USGS more accessible to American Indians, Alaska Natives, their governments, and institutions, is available at www.usgs.gov/indian. This website includes information on how to contact USGS American Indian/Alaska Native Liaisons, training opportunities, and links to other information resources. This report and previous editions are also available through the website. The USGS realizes that Native knowledge and cultural traditions of living in harmony with nature result in unique Native perspectives that enrich USGS studies. USGS seeks to increase the sensitivity and openness of its scientists to the breadth of Native knowledge, expanding the information on which their research is based. USGS scientific studies include data collection, mapping, natural resource modeling, and research projects. These projects typically last 2 or 3 years, although some are parts of longer-term activities. Some projects are funded cooperatively, with USGS funds matched or supplemented by individual Tribal governments, or by the BIA. These projects may also receive funding from the U.S. Environmental Protection Agency (USEPA), the Indian Health Service (part of the Department of Health and Human Services), or other Federal agencies. The USGS routinely works with its sister bureaus in the Department of the Interior to provide the scientific information and expertise needed to meet the Department's science priorities. Some USGS activities described in this report are conducted as collateral tasks that result from USGS employees identifying and responding to perceived needs. These endeavors are usually prompted by employee interests and frequently involve educational activities. The education is often a reciprocal learning and teaching experience for USGS employees and for Native participants. Through these activities, USGS employees help to fulfill a mission of the USGS - to demonstrate scientific relevance - while helping their fellow citizens. Increasingly, some of the educational activities are becoming parts of formal USGS projects. USGS employees also take initiative in assisting American Indians and Alaska Natives by participating in several organizations that promote awareness of science career opportunities among Native peoples and help build support and communication networks. One such group is the American Indian Science and Engineering Society (AISES). USGS employees join this organization on a voluntary basis, bringing the benefits of this expanded network to the USGS, as many employees do with other professional organizations. The studies briefly described in this report span subsistence issues, wildlife health, water quality, mineral resources, monitoring and modeling to gather information and predict what may happen in the future. Although each project description relates to Native Americans in some way, the projects vary widely, including who conducted the work, the goals and products, the duration of the study, and whether it was local or covered a broad area. Each major organizational unit of the USGS has identified an American Indian/Alaska Native liaison. The USGS has a regional organizational structure, with Western, Central,

Circular

Digitized generalized areas where surface-water resources likely or potentially are susceptible to groundwater withdrawals in adjacent valleys, Great Basin National Park area, Nevada

Abstract Polygons delineate generalized areas in and around Great Basin National Park where surface-water resources likely or potentially are susceptible to groundwater withdrawals in adjacent valleys. Purpose This data set was created as part of a U.S. Geological Survey study, done in cooperation with the National Park Service, to characterize surface-water resources in and around Great Basin National Park. The intended uses of this data set include, but are not limited to, natural resource modeling, mapping, and visualization applications. Source Information SIR 2006-5099, Plate 1: Generalized areas where surface-water resources likely or potentially are susceptible to ground-water withdrawals in adjacent valleys, Great Basin National Park area, Nevada.

Nevada

An integrated hydrologic model to support the Central Platte Natural Resources District Groundwater Management Plan, central Nebraska

The groundwater and surface-water supply of the Central Platte Natural Resources District supports a large agricultural economy from the High Plains aquifer and Platte River, respectively. This study provided the Central Platte Natural Resources District with an advanced numerical modeling tool to assist with the update of their Groundwater Management Plan. An integrated hydrologic model, called the Central Platte Integrated Hydrologic Model, was constructed using the MODFLOW-One-Water Hydrologic Model code with the Newton solver. This code integrates climate, landscape, surface water, and groundwater-flow processes in a fully coupled approach. Model framework included 163 rows; 327 columns; 2,640 feet cell sides; and 3 vertical layers. A predevelopment model simulated steady-state hydrologic conditions prior to April 30, 1895, and a development period model discretized into 610 stress periods simulated transient hydrologic conditions from May 1, 1895, to December 31, 2016, using 170 biannual stress periods from 1895 to 1980, and monthly stress periods from May 1, 1980, to December 31, 2016. Calibration of the Central Platte Integrated Hydrologic Model involved two phases: a manual adjustment of parameters, followed by the automated calibration completed using BeoPEST that was facilitated by the employment of the singular value decomposition-assist features of PEST that specified 50 super parameters assembled from the 435 adjustable parameters and Tikhonov regularization. The average absolute groundwater-level residuals for model layers one, two, and three were 6.1, 12.4, and 7.4 feet, respectively. Calibrated horizontal hydraulic conductivity was about 70, 32, and 35 feet per day for layers 1, 2, and 3, respectively. The largest development period inflow to groundwater was recharge from deep percolation past the root zone, averaging 1,122,257 acre-feet per year (2.7 inches per year), and the largest outflow was to irrigation wells, averaging 693,171 acre-feet per year (10.2 inches per year for the Central Platte Natural Resources District). Other substantial groundwater outflows included evapotranspiration and base flow. For the total development period, there was a net change in storage of −122,393 acre-feet per year (−0.3 inch per year). The calibrated Central Platte Integrated Hydrologic Model was used to simulate eight different potential future climate and irrigation pumping conditions from January 1, 2017, to December 31, 2049. Simulated future groundwater levels within the Central Platte Natural Resources District varied significantly between scenarios and locally, from 13.8 feet below to 7.6 feet above baseline 1982 groundwater levels. Most areas exhibited groundwater-level declines for the drought scenarios and rises for the alternate irrigation scenarios. Changes in scenario groundwater levels correlated with the relations between farm net recharge and irrigation pumping. Linear “first order second moment” techniques indicated that the uncertainty in projected groundwater altitudes was reduced by 15.33 feet through model calibration.

Nebraska

Modeling and the management of migratory birds

Mathematical modeling of migratory bird populations is reviewed in the context of migratory bird management. We focus on dynamic models of waterfowl, since most management-oriented migratory bird models concern waterfowl species. We describe the management context for these modeling efforts, with a focus on large-scale operational data collection programs and on processes by which waterfowl harvest is regulated and waterfowl habitats are protected and managed. Through their impacts on key population parameters such as recruitment and survival rate, these activities can influence population dynamics, thereby providing managers some measure of control over the status of populations. Recent applications of the modeling of waterfowl are described in terms of objectives, mathematical structures, and contributions to management. Finally, we discuss research needs and data limitations in migratory bird modeling, and offer suggestions to increase the value to managers of future modeling efforts.

Natural Resource Modeling

Tag return models allowing for harvest and catch and release: Evidence of environmental and management impacts on striped bass fishing and natural mortality rates

Catch-and-release fisheries have become very important in the management of overexploited recreational fish stocks. Tag return studies, where the tag is removed regardless of fish disposition, have been used to assess the effectiveness of restoration efforts for these fisheries. We extend the instantaneous rate formulation of tag return models to allow for catch and release as well as harvest. The key point of our methods is that, given an estimate of the tag reporting rate, the fishing mortality rate (F) is separated into two components: the mortality on harvested fish and the "mortality" on tags (because the lags are removed) of fish released alive. The total fishing mortality rate for untagged fish is the sum of the Fs due to harvest and hooking mortality suffered by fish released alive. Natural mortality rates can also be estimated. Both age-independent models and age-dependent models are constructed, and the age-dependent models are illustrated by application to data from a study of striped bass Morone saxatilis in Chesapeake Bay from 1991 to 2003 by the Maryland Department of Natural Resources. By fitting models of the natural mortality rate with limited age and year dependence, we demonstrate an overall decrease in natural mortality rates as fish age and provide evidence of an increase in natural mortality beginning in the late 1990s, when an outbreak of the disease mycobacteriosis is thought to have begun. Our results indicate that fishing mortality is age dependent; selectivity increases up to age 6, when fish appear to be fully recruited to the fishery. There is also evidence of an increase in fishing mortality since 1995, when regulations were relaxed. ?? Copyright by the American Fisheries Society 2007.

North American Journal of Fisheries Management

Simulation of streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine, using watershed models

The U.S. Geological Survey (USGS) began a study in 2008 to investigate anticipated changes in summer streamflows and stream temperatures in four coastal Maine river basins and the potential effects of those changes on populations of endangered Atlantic salmon. To achieve this purpose, it was necessary to characterize the quantity and timing of streamflow in these rivers by developing and evaluating a distributed-parameter watershed model for a part of each river basin by using the USGS Precipitation-Runoff Modeling System (PRMS). The GIS (geographic information system) Weasel, a USGS software application, was used to delineate the four study basins and their many subbasins, and to derive parameters for their geographic features. The models were calibrated using a four-step optimization procedure in which model output was evaluated against four datasets for calibrating solar radiation, potential evapotranspiration, annual and seasonal water balances, and daily streamflows. The calibration procedure involved thousands of model runs that used the USGS software application Luca (Let us calibrate). Luca uses the Shuffled Complex Evolution (SCE) global search algorithm to calibrate the model parameters. The calibrated watershed models performed satisfactorily, in that Nash-Sutcliffe efficiency (NSE) statistic values for the calibration periods ranged from 0.59 to 0.75 (on a scale of negative infinity to 1) and NSE statistic values for the evaluation periods ranged from 0.55 to 0.73. The calibrated watershed models simulate daily streamflow at many locations in each study basin. These models enable natural resources managers to characterize the timing and amount of streamflow in order to support a variety of water-resources efforts including water-quality calculations, assessments of water use, modeling of population dynamics and migration of Atlantic salmon, modeling and assessment of habitat, and simulation of anticipated changes to streamflow and water temperature resulting from changes forecast for air temperature and precipitation.

Scientific Investigations Report

A comparison of the Trojan Y Chromosome strategy to harvesting models for eradication of nonnative species

The Trojan Y Chromosome strategy (TYC) is a promising eradication method for biological control of nonnative species. The strategy works by manipulating the sex ratio of a population through the introduction of supermales that guarantee male offspring. In the current study, we compare the TYC method with a pure harvesting strategy. We also analyze a hybrid harvesting model that mirrors the TYC strategy. The dynamic analysis leads to results on stability of solutions and bifurcations of the model. Several conclusions about the different strategies are established via optimal control methods. In particular, the results affirm that either a pure harvesting or hybrid strategy may work better than the TYC method at controlling a nonnative species population. Recommendations for resource managers Where harvesting is feasible, it is as effective if not more effective than the classical TYC method. Therein managers may attempt harvesting female fish while stocking males or harvesting both male and female fishes. Managers may attempt linear harvesting, saturating density‐dependent harvesting, and unbounded density‐dependent harvesting. Linear harvesting is seen to be the most effective. We caution against the outright use of harvesting due to various density‐dependent effects that may arise. To this end hybrid models that involve a combination of harvesting and TYC‐type methods might be a better strategy. One may also use harvesting as a tool in mesocosm settings to predict the efficacy of the TYC strategy in the wild.

Natural Resource Modeling

A full annual cycle modeling framework for American black ducks

American black ducks ( Anas rubripes ) are a harvested, international migratory waterfowl species in eastern North America. Despite an extended period of restrictive harvest regulations, the black duck population is still below the population goal identified in the North American Waterfowl Management Plan (NAWMP). It has been hypothesized that density-dependent factors restrict population growth in the black duck population and that habitat management (increases, improvements, etc.) may be a key component of growing black duck populations and reaching the prescribed NAWMP population goal. Using banding data from 1951 to 2011 and breeding population survey data from 1990 to 2014, we developed a full annual cycle population model for the American black duck. This model uses the seven management units as set by the Black Duck Joint Venture, allows movement into and out of each unit during each season, and models survival and fecundity for each region separately. We compare model population trajectories with observed population data and abundance estimates from the breeding season counts to show the accuracy of this full annual cycle model. With this model, we then show how to simulate the effects of habitat management on the continental black duck population.

Natural Resource Modeling

Assessing effects of variation in global climate data sets on spatial predictions from climate envelope models

Climate change poses new challenges for natural resource managers. Predictive modeling of species–environment relationships using climate envelope models can enhance our understanding of climate change effects on biodiversity, assist in assessment of invasion risk by exotic organisms, and inform life-history understanding of individual species. While increasing interest has focused on the role of uncertainty in future conditions on model predictions, models also may be sensitive to the initial conditions on which they are trained. Although climate envelope models are usually trained using data on contemporary climate, we lack systematic comparisons of model performance and predictions across alternative climate data sets available for model training. Here, we seek to fill that gap by comparing variability in predictions between two contemporary climate data sets to variability in spatial predictions among three alternative projections of future climate. Overall, correlations between monthly temperature and precipitation variables were very high for both contemporary and future data. Model performance varied across algorithms, but not between two alternative contemporary climate data sets. Spatial predictions varied more among alternative general-circulation models describing future climate conditions than between contemporary climate data sets. However, we did find that climate envelope models with low Cohen's kappa scores made more discrepant spatial predictions between climate data sets for the contemporary period than did models with high Cohen's kappa scores. We suggest conservation planners evaluate multiple performance metrics and be aware of the importance of differences in initial conditions for spatial predictions from climate envelope models.

Journal of Fish and Wildlife Management

Multispecies modeling for adaptive management of horseshoe crabs and red knots in the Delaware Bay

Adaptive management requires that predictive models be explicit and transparent to improve decisions by comparing management actions, directing further research and monitoring, and facilitating learning. The rufa subspecies of red knots ( Calidris canutus rufa ), which has recently exhibited steep population declines, relies on horseshoe crab ( Limulus polyphemus ) eggs as their primary food source during stopover in Delaware Bay during spring migration. We present a model with two different parameterizations for use in the adaptive management of horseshoe crab harvests in the Delaware Bay that links red knot mass gain, annual survival, and fecundity to horseshoe crab dynamics. The models reflect prevailing hypotheses regarding ecological links between these two species. When reported crab harvest from 1998 to 2008 was applied, projections corresponded to the observed red knot population abundances depending on strengths of the demographic relationship between these species. We compared different simulated horseshoe crab harvest strategies to evaluate whether, given this model, horseshoe crab harvest management can affect red knot conservation and found that restricting harvest can benefit red knot populations. Our model is the first to explicitly and quantitatively link these two species and will be used within an adaptive management framework to manage the Delaware Bay system and learn more about the specific nature of the linkage between the two species.

Delaware, New Jersey

A guide to calculating habitat-quality metrics to inform conservation of highly mobile species

Many metrics exist for quantifying the relative value of habitats and pathways used by highly mobile species. Properly selecting and applying such metrics requires substantial background in mathematics and understanding the relevant management arena. To address this multidimensional challenge, we demonstrate and compare three measurements of habitat quality: graph-, occupancy-, and demographic-based metrics. Each metric provides insights into system dynamics, at the expense of increasing amounts and complexity of data and models. Our descriptions and comparisons of diverse habitat-quality metrics provide means for practitioners to overcome the modeling challenges associated with management or conservation of such highly mobile species. Whereas previous guidance for applying habitat-quality metrics has been scattered in diversified tracks of literature, we have brought this information together into an approachable format including accessible descriptions and a modeling case study for a typical example that conservation professionals can adapt for their own decision contexts and focal populations. Considerations for Resource Managers Management objectives, proposed actions, data availability and quality, and model assumptions are all relevant considerations when applying and interpreting habitat-quality metrics. Graph-based metrics answer questions related to habitat centrality and connectivity, are suitable for populations with any movement pattern, quantify basic spatial and temporal patterns of occupancy and movement, and require the least data. Occupancy-based metrics answer questions about likelihood of persistence or colonization, are suitable for populations that undergo localized extinctions, quantify spatial and temporal patterns of occupancy and movement, and require a moderate amount of data. Demographic-based metrics answer questions about relative or absolute population size, are suitable for populations with any movement pattern, quantify demographic processes and population dynamics, and require the most data. More real-world examples applying occupancy-based, agent-based, and continuous-based metrics to seasonally migratory species are needed to better understand challenges and opportunities for applying these metrics more broadly.

Natural Resource Modeling

Tailoring point counts for inference about avian density: dealing with nondetection and availability

Point counts are commonly used for bird surveys, but interpretation is ambiguous unless there is an accounting for the imperfect detection of individuals. We show how repeated point counts, supplemented by observation distances, can account for two aspects of the counting process: (1) detection of birds conditional on being available for observation and (2) the availability of birds for detection given presence. We propose a hierarchical model that permits the radius in which birds are available for detection to vary with forest stand age (or other relevant habitat features), so that the number of birds available at each location is described by a Poisson-gamma mixture. Conditional on availability, the number of birds detected at each location is modeled by a beta-binomial distribution. We fit this model to repeated point count data of Florida scrub-jays and found evidence that the area in which birds were available for detection decreased with increasing stand age. Estimated density was 0.083 (95%CI: 0.060–0.113) scrub-jays/ha. Point counts of birds have a number of appealing features. Based on our findings, however, an accounting for both components of the counting process may be necessary to ensure that abundance estimates are comparable across time and space. Our approach could easily be adapted to other species and habitats.

Natural Resource Modeling

Management strategy evaluation of pheromone-baited trapping techniques to improve management of invasive sea lamprey

We applied a management strategy evaluation (MSE) model to examine the potential cost-effectiveness of using pheromone-baited trapping along with conventional lampricide treatment to manage invasive sea lamprey. Four pheromone-baited trapping strategies were modeled: (1) stream activation wherein pheromone was applied to existing traps to achieve 10 −12 mol/L in-stream concentration, (2) stream activation plus two additional traps downstream with pheromone applied at 2.5 mg/hr (reverse-intercept approach), (3) trap activation wherein pheromone was applied at 10 mg/hr to existing traps, and (4) trap activation and reverse-intercept approach. Each new strategy was applied, with remaining funds applied to conventional lampricide control. Simulating deployment of these hybrid strategies on fourteen Lake Michigan streams resulted in increases of 17 and 11% (strategies 1 and 2) and decreases of 4 and 7% (strategies 3 and 4) of the lakewide mean abundance of adult sea lamprey relative to status quo. MSE revealed performance targets for trap efficacy to guide additional research because results indicate that combining lampricides and high efficacy trapping technologies can reduce sea lamprey abundance on average without increasing control costs.

Natural Resource Modeling