MPE 2013+ Workshop on Management of Natural Resources

June 4 - 6, 2015
Howard University, Washington, DC

Jon Conrad, Cornell University, jmc16 at
Midge Cozzens, DIMACS, Rutgers University, midgec at
Avner Friedman, Ohio State/MBI, afriedman at
Suzanne Lenhart, University of Tennessee, Knoxville, NIMBioS, lenhart at
Catherine Roberts, College of the Holy Cross, croberts at
Fred Roberts, DIMACS, Rutgers University, froberts at
Abdul-Aziz Yakubu, Howard University, ayakubu at
Presented under the auspices of the DIMACS Special Program: Mathematics of Planet Earth 2013+.


Jon M. Conrad, Cornell University, and Daniel Rondeau, University of Victoria, Victoria, British Columbia, Canada

Title: Bioeconomics of a Marine Disease

We study the adaptive harvest of healthy stocks of shellfish that are faced with the risk of high natural mortality from a disease that is spreading along a coastline. This was the situation when Abalone Viral Ganglioneuritis (AVG) spread along the coast of Victoria, Australia in 2006. Abalone mortality on some reefs was thought to have been as high as 90%. In the face of an approaching virus, how should stocks at different reefs be managed? A stochastic, spatial bioeconomic model allows us to examine how optimal preemptive stock reductions are in uenced by (1) the probability of spread, (2) the mortality induced by AVG when it reaches a previously uninfected reef, (3) the form of the harvest cost function, and (4) a regime shift to lower biological productivity, post-AVG.

Keith R. Criddle, Juneau Center for Fisheries and Ocean Sciences, University of Alaska, Fairbanks

Title: La Machine InfernaleHow the Interplay of Social, Ecological, and Environmental Factors Influence the Observability and Controllability of Fishery Social Ecological Systems

The sustainability of fisheries and fishery dependent communities is dependent on the intrinsic characteristics of ecological and environmental systems that govern the response of fish stocks to environmental forcing and exploitation as well as the intrinsic characteristics social, economic, and legal systems that determine who is allowed to fish and how fishing takes place. Some fisheries and fishery dependent communities have proven resilient to changes in fish abundance and distribution, changes in exvessel prices, changes in the cost of factors of production, changes in macroeconomic conditions, changes living costs and employment opportunities within the community, and demographic changes. Factors that affect resilience are illustrated by reference to sub-Arctic fisheries that have weathered or recovered from the influence of adverse forcing and others that have not. Key factors are within the scope of fisheries policy include tradeoffs between economic efficiencies associated with specialized single species fisheries and heightened sensitivity to variations in the magnitude or unit value of that species. In contrast, generalist fleets trade reduced economic efficiency for reduced exposure to losses associated with variations in the abundance or value of any one species. Durable individual entitlements to shares of the allowable catch increase profitability and help fishermen adapt to modest adverse changes in stock abundance, exvessel prices, and input costs but these highly constrained management strategies reduce resilience to non-stationarities and large perturbations. In addition, while durable entitlements increase choice and therefore resilience from the perspective of individuals, they decrease the resilience of some fishery dependent communities.

Nina H. Fefferman, Rutgers University

Title: Incorporating Evolutionary Rescue into Population Viability Models

Population viability analysis (PVA) is one of the most commonly employed modeling tools for estimating extinction risks for populations of concern. While many populations are at risk from a confluence of adverse factors, there are also important exmaples in which the major risks are the result of a single novel challenge to the population. In these cases, the novel factor can act as an evolutionary selective pressure on the available genetic diversity to increase representation of genes that confer greater robustness to the challenge. This talk will explore how to incorporate these evolutionary effects into PVA estimates of extinction risks. We'll apply these models in the context of White Nose Syndrome in Little Brown Bats (a novel risk and a gravely threatened population) and compare our predictions both against models that do not incorporate evolution and against real-world population data.

Kathleen R. Fowler, Clarkson University

Title: A Simulation-based Optimization Approach to Decision Making in Farming Practices

Farmers in regions experiencing water stress or drought conditions can struggle to balance their crop portfolios. Periods of low precipitation often lead to increased, unsustainable reliance on groundwater-supplied irrigation. As a result, regional water management agencies place limits on the amount of water which can be obtained from groundwater, requiring farmers to reduce acreage for more water-intensive crops or remove them from the portfolio entirely. Real-time decisions must be made by the farmer to ensure viability of his operation and reduce the impacts associated with limited water resources. Evolutionary algorithms, coupled with accurate, flexible, realistic simulation tools, are ideal mechanisms to allow farmers to assess scenarios with regard to multiple, competing objectives. In this work, we couple a multi-objective genetic algorithm with the MODFLOW-OWHM simulation tool to assess the ability of these algorithms to generate feasible planting scenarios under various precipitation conditions and pumping restrictions. We discuss the strategy for utilizing the software in an optimization environment, and present numerical results for case studies related to decisions faced by farmers in regions experiencing water stress.

Avner Friedman, Ohio State University

Title: Mathematics to Promote Public Health and Biomedicine

In this talk I will give two examples where mathematical modeling and simulations of biological processes can promote public health and facilitate treatment of diseases. The first example is about the risk associated with high cholesterol. The mathematical model describes how LDL ("bad") cholesterol induces the development of a plaque in artery, and how HDL ("good") cholesterol helps reducing the plaque by a process known as "reverse cholesterol transport." The model develops a risk map which predicts whether a small plaque will decrease or increase, and at what percentage, over 300 days. This risk map could be used to provide more precise guidelines for the risk of atherosclerosis associated with cholesterol than the current guidelines of the American Heart Association.

The second example is concerned with the development of fibrosis in a kidney, a disease associated with autoimmune disorder, such as Lupus Nephritis. The mathematical model identifies two biomarkers that can determine the disease. These biomarkers can then be used to monitor the effect of potential drugs which could reduce or at least block the progression of fibrosis. Currently the only way to monitor the disease progression is by invasive biopsy, which cannot be frequently repeated.

Both mathematical models are represented by a system of partial differential equations. These models also suggest some new challenging problems in mathematics.

This work is joint with MBI postdoctoral fellow, Wenrui Hao.

Wayne M. Getz, University of California, Berkeley, Richard Salter, Oberlin College, and Oliver Muellerklein, University of California, Berkeley

Title: A Nova Model and Web App for Sustainable Harvesting and Population Viability Analyses in Teaching and Research

Highly valued animal and plant populations are declining worldwide as a result of overexploitation, poaching, global climate change, or the conversion of wildlands to anthropized environments. Their value comes from either ethical considerations (the conservation imperative) or resource utility considerations (the management imperative). For the past halfcentury, mathematical models have played a central role in both evaluating and devising population management programs, initially for exploitation and, more recently, conserving populations through creating protected areas, improving security or translocating individuals among areas. At the core of the most comprehensive and successful of these models lies the Leslie matrix formulation, which provides a way of incorporating population vital rates (mortality and natality) into both harvesting (sustainable management) and population viability analysis (conservation management) models. Initially, harvesting applications predominated, but over the past 20 years these models have found wide application in conservation biology, particularly in the context of population viability analyses (PVA). In this presentation, we discuss the application of the Nova software platform to constructing models and web apps for both harvesting and PVA analyses. Nova itself is a new Java-based modeling platform that naturally supports the creation of system dynamics, spatial, and agent-based models in a single desktop application. Nova uses a visual language to express model design, and provides automatic conversion of such models to script form for execution. Nova's architecture promotes hierarchical design, code reuse, and extensibility through the use of plug-ins. Nova's expressive power derives from strong design principles: modularity, abstraction and extensibility. Nova web apps use this Nova engine while retaining a purely graphical. The Nova PVA web app is run using life table data entered directly into the web app dashboard window and through the manipulation of parameter values using sliders. This app can be run in either deterministic or stochastic modes. The deterministic mode is most useful for evaluating management strategies implemented in large population. The stochastic mode is most useful for carrying out species extinction risk analyses, i.e. PVA. In this talk, the mathematical structure of the Nova model underlying the app will be presented as a two-sex Leslie matrix, age-structured model with nonlinear density-dependent survival in the youngest, oldest, and sexually-maturing-male ageclasses. The use of the app in studying Rhino conservation issues will also be discussed.

Alan Hastings, University of California, Davis

Title: Control of Invasive Species

I will set up a series of models for management of invasive species, focusing on eradication as the goal. I will cover ways of incorporating economic issues and include complications such as the role of other species. The mathematical tools will be drawn from approaches to constrained optimization. I will discuss both our recent work and open questions in the control of invasive species at various stages of an invasion.

Lea Jenkins, Clemson University

Title: Mathematics for Water Management Strategies

Managing existing water supplies has become critically important in recent years, as overuse, in conjunction with severe levels of drought, have placed aquifers in jeopardy. The imbalances in aquifer levels are especially dire in regions whose economies are heavily dependent on agriculture, as irrigation of crops accounts for more than 80% of the usage of groundwater resources. Aquifer replenishment can be supplemented through the creation of managed aquifer recharge networks, designed to capture storm water runoff for infiltration into the underlying aquifer. Mathematical modeling and optimization can aid in the analysis of the ability of such a network to meet a target infiltration goal.

In this talk, I will provide a background on water resource issues in the Pajaro Valley region of California. The effects of a several-year, severe drought are exacerbated by the heavy agriculture production throughout the state. In particular, farmers in this region produce more than 80% of the strawberries consumed throughout the U.S. Thus, water policy decisions, and limited availablity of water, have a drastic effect on the livelihood of local residents.

Our multidisciplinary research team, funded in part by the American Institute of Mathematics, has developed a simulation tool based on open source software to model basin networks and use alternative optimization algorithms to maximize the infiltration capacity of the network while minimizing the cost of network construction. We consider a problem formulation which incorporates constraints based on environmental regulations and physical limitations due to construction considerations. We implement cost-based rewards for meeting target infiltration and storm water capture rates, while penalizing based on land and construction costs. I will present summary information on our results along with our future reserach considerations.

I will also discuss questions to consider in case-based studies environments or creative inquiry classes, where groups of students can consolidate their diverse backgrounds to understand and study large, complex problems.

Suzanne Lenhart, University of Tennessee and NIMBioS

Title: Modeling Johne's Disease in the Dairy Industry

Johne's disease in dairy cattle is a chronic infectious disease in the intestines caused by the bacilli, Mycobacterium avium ssp. paratuberculosis. This disease affects the milk production in most dairy farms in the US. We will discuss epidemiological models at the dairy farm level to investigate the economic effects of control measures and diagnostic tests.

Andrew M. Liebhold, US Forest Service and Rebecca S. Epanchin-Niell, Resources for the Future

Title: Bioeconomics and the Efficiency of Invasive Species Surveillance and Eradication

Given trends of ever-increasing volumes of global trade, non-native species continue to be accidentally introduced in cargo and passenger baggage. Unfortunately, many of these species have considerable impact so there can be great benefit in preventing species from establishing by searching for newly colonized populations ("surveillance") and eradicating (total elimination) them. Here, we discuss several issues related to the search for more efficient strategies for accomplishing this. First, there is the problem of optimal allocation of resources between surveillance and eradication. There is an inherent tradeoff between concentrating resources on surveillance, which leads to early detection and consequently less expensive eradication, and allocating fewer resources on surveillance, which leads to detecting populations when they have grown quite large and are expensive to eradicate. We describe an approach for optimizing the allocation of resources between surveillance and eradication and demonstrate how this can be applied across heterogeneous landscapes where surveillance costs and colonization rates vary. A key determinant of the costs of typical surveillance programs is driving through the landscape. We develop a model that predicts driving times and distances among a network of surveillance sampling locations and we explore how these costs vary with road density, road network topology and surveillance grid density. Finally, we explore cost-efficient approaches for eradicating invading populations. These populations typically exist at low levels where their dynamics are strongly influenced by Allee effects. We show how Allee dynamics can be exploited to maximize the efficiency of eradication efforts.

Safa Motesharrei, SESYNC, Jorge Rivas and Eugenia Kalnay

Title: Human and Nature Dynamics (HANDY): Modeling Inequality and use of Resources in the Collapse or Sustainability of Societies

This paper became the most downloaded paper in the history if the Journal Ecological Economics within a few weeks from its publication in April 2014.

There are widespread concerns that current trends in resource-use are unsustainable, but possibilities of overshoot/collapse remain controversial. Collapses have occurred frequently in history, often followed by centuries of economic, intellectual, and population decline. Many different natural and social phenomena have been invoked to explain specific collapses, but a general explanation remains elusive.

In this paper, we build a human population dynamics model by adding accumulated wealth and economic inequality to a predator-prey model of human and nature. The model structure, and simulated scenarios that offer significant implications, are explained. Four equations describe the evolution of Elites, Commoners, Nature, and Wealth. The model shows Economic Stratification or Ecological Strain can independently lead to collapse, in agreement with the historical record.

The measure “Carrying Capacity” is developed and its estimation is shown to be a practical means for early detection of a collapse. Mechanisms leading to two types of collapses are discussed. The new dynamics of this model can also reproduce the irreversible collapses found in history. Collapse can be avoided, and population can reach a steady state at maximum carrying capacity if the rate of depletion of nature is reduced to a sustainable level and if resources are distributed equitably.

Michael Neubert, Woods Hole Oceanographic Institute

Title: Bioeconomics of Marine Reserves when Dispersal Evolves

Marine reserves are an increasingly used and potentially contentious tool in fisheries management. Depending upon the way that individuals move, no-take marine reserves can be necessary for maximizing equilibrium rent in some simple mathematical models. The implementation of no-take marine reserves often generates a redistribution of fishing effort in space. This redistribution of effort, in turn, produces sharp spatial gradients in mortality rates for the targeted stock. Using a two-patch model, we show that the existence of such gradients is a sufficient condition for the evolution of an evolutionarily stable conditional dispersal strategy. Thus, the dispersal strategy of the fish depends upon the harvesting strategy of the manager and vice versa. We find that an evolutionarily stable optimal harvesting strategy (ESOHS)---one which maximizes equilibrium rent given that fish disperse in an evolutionarily stable manner---never includes a no-take marine reserve. This strategy is economically unstable in the short run because a manager can generate more rent by disregarding the possibility of dispersal evolution. Simulations of a stochastic evolutionary process suggest that such a short-run, myopic strategy performs poorly compared to the ESOHS over the long run, however, as it generates rent that is lower on average and higher in variability.

David B. Shmoys, Cornell University

Title: Mathematical Programming Models and Algorithms in Computational Sustainability

Computational Sustainability is a newly emerging interdisciplinary research field with the overall goal of developing computational models, methods, and tools to help manage the balance between environmental, economic, and societal needs for a sustainable future. Many of the problems highlighted by this perspective can be viewed as optimization problems that can be addressed through mathematical programming models and algorithms. In this talk, we will focus on a few examples of this; specifically, we will discuss several issues involving land-management policy for wildlife preservation and biodiversity, as well as models for preventative treatment of forests to limit the impact of damage from fires. These problems give rise to challenging computational mathematical programming problems, which require new advances in algorithmic techniques to address them.

Carl Simon, James Breck, Bobbi Low, University of Michigan; Edward Rutherford, National Oceanic and Atmospheric Administration, Ann Arbor; P.J. Lamberson, Northwestern University; and David Swank, National Marine Fisheries Service, Santa Cruz

Title: When to Mature? New Answers from Life History Theory, with Applications to Great Lakes Salmonids

We use life history theory and Fisher's reproductive value to derive an expression that calculates the optimal age of first reproduction for iteroparous females in different environments -- the first such analytical expression. We use this formulation to describe the sensitivity of age of maturity to growth, survival, and reproduction parameters, and compare to real world data, in particular, for the more than a dozen life history paths for the iteroparous steelhead living in the Great Lakes. We show that age of maturity is especially sensitive to juvenile survivorship. We describe the corresponding reaction norms that relate age of maturity to growth rates, and compare and contrast the patterns we find to previously published reaction norms

Abdul-Aziz Yakubu, Howard University

Title: A Bovine Babesiosis Mathematical Model with Dispersion

Bovine Babesiosis (BB) is a tick borne parasitic disease with worldwide over 1.3 billion bovines at potential risk of being infected. An important factor in the spread of the disease is the dispersion or migration of cattle as well as ticks. In this talk, we will introduce a number, P, a “proliferation index,” which plays the same role as the basic reproduction number R0 with respect to the stability/instability of the disease-free equilibrium, and observe that P decreases as the dispersion coefficients increase. We will also consider the case where the birth rate of ticks undergoes seasonal oscillations. Based on data from Colombia, South Africa, and Brazil, we will use the model to determine the effectiveness of several intervention schemes to control the progression of BB.

Contributed talks and students:

Caitlin Augustin and Benjamin Galfond, University of Miami

Title: Simulation and Corroboration of Near-surface CO2 Leak Events Occurring at an Industrial CCS Site

Large subsurface carbon dioxide (CO 2) sources are a naturally occurring and highly prized resource by actors from such divergent industries as oil and gas, food and beverage, water purification. However, it is estimated that these natural deposits of CO 2 will be depleted by 2030. In stark contrast, ever-increasing quantities of anthropogenic CO 2 are of key environmental concern. Capture and subsurface storage of this anthropogenic CO 2 has been seen as a synergistic way of meeting both industry demand and ambitious CO 2 reduction targets set by multiple regulatory agencies. Significant policy programs support these objectives, such as the international Clean Development Mechanism, and the United States Federal Master Limited Partnership framework that allows tax exemptions for industry CO 2 usage.

However, the potential environmental, health, and commercial impacts of leak events from such subsurface sites prevent implementation of this anthropogenic CO 2 usage and reduction scheme. In this paper, we model three distinct scenarios to explain observed leak phenomena at an active site. We use a combination of spatio-temporal models and reaction-path models to demonstrate the interplay between leak migrations and material interactions.

These leak-event scenarios have implications for human and environmental health as released CO 2 can accumulate in toxic levels at the near surface. Additionally, any leakage event has economic implications; in a carbon constrained world, where companies are incentivized to reduce emissions , both the CO 2 stream as a commodity and the associated carbon credits have monetary value. Finally, anthropogenic CO 2 management is integral to natural resource stewardship and therefore comprehensive under standing of leakage events is paramount.

Philomena Chu, Rutgers University

Title: Duckweed as a Sustainable Bioenergy Crop

We are developing duckweed-a fast-growing, miniature, aquatic plant-as a renewable and sustainable feedstock for biofuels and bioplastics. In the lab of Dr. Eric Lam in the Department of Plant Biology and Pathology at Rutgers University, we are optimizing conditions for robust growth and high starch production. We study how municipal and agricultural wastewater can be used as cheap fertilizer for duckweed cultivation. As the plants grow and multiply, the wastewater is cleaned and can be recycled for crop irrigation. This approach obviates the need for expensive fertilizers and freshwater resources, which are becoming limited in supply.

In addition, we collaborate with a social biotechnology company in Argentina that aims to produce bioplastics from wastewater-grown duckweed. With the help of an expert in agricultural economics, we are evaluating the economic feasibility and environmental impact of this approach. The production of duckweed-derived ethanol and plastics may help reduce our reliance on petroleum-based products, creating a cleaner future.

Moussa Doumbia, Howard University

Title: Malaria Incidence and Anopheles Mosquito Density in Irrigated and Adjacent Non-Irrigated Villages of Niono in Mal

In this paper, we extend the mathematical model framework of Dembele et al. and use it to study malaria disease transmission dynamics and control in irrigated and non-irrigated villages of Niono in Mali. As case studies, we use our "fitted" models to show that in supp ort of the survey studies of Dolo et al., the mosquito density in irrigated villages of Niono is much higher than that of the adjacent non-irrigated villages. Many parasitological surveys have observed higher incidence of malaria in non-irrigated villages than in adjacent irrigated areas. Our "fitted" models support these observations. That is, there are more malaria cases in non-irrigated areas than the adjacent irrigated villages. In addition, we use the extended "fitted" models to determine the drug administration proto cols that lead to fewest first episode of malaria in both irrigated and adjacent non-irrigated villages of Niono during the wet season.

Christina Edholm, University of Nebraska-Lincoln

Title: Optimal Control Theory Approach to Diaprepes Root Weevils

Diaprepes Root Weevils are an invasive species having a substantial negative impact on citrus tree growth in regions, such as Florida and California. At the larva stage of the life cycle Diaprepes Root Weevils cause destruction of citrus trees at the root level resulting in destruction of citrus crops. The detrimental economic effect for farmers motivates research into how to stop the invasion. For our work, we used Optimal Control theory to determine levels of pesticide or biological control to apply to the Diaprepes Weevil to halt further destruction. We minimize a cost functional, which takes into account the cost of applying the control and the damage done by the weevils, determining how much control to apply over time.

Natali Hritonenko, Prairie View A&M University

Title: Modeling of Sustainable Forest Management under Climate Changes and Natural Disturbances

Mathematical modeling of rational management of natural resources involve complex features that interconnect natural systems with human demands t hat are critically linked and often modeled by combining ecological, economic, and sociological blocks. Climate change and natural disturbances can greatly affect research outcomes and should be considered.

Forests are a valuable natural, economic, and recreational resource that play one of the central roles in mi tigating negative environmental impacts. Although several mathematical models for management in forestry have been suggested during the last 50 years, there are still a number of open issues waiting for their solution. Challenges of modeling in forestry wi ll be discussed.

A model for the sustainable forest management is presented as a boundary value problem for nonlinear partial differential equations with integral terms and is flexible enough to consider benefits from carbon sequestration, production and m itigation costs, density effects, and revenue from lumber production. The model aims at determining the best strategy for obtaining maximum sustainable lumber harvesting under different climate scenarios and understanding how fluctuations in the environmen t impact the biological processes of the forest growth, carbon sequestration, and economic regimes of forest management. Determining effective pricing systems for carbon and logging and understanding the impact of a pricing system on the economic system an d on the ecology are other goals of the qualitative analysis. The outcomes are approbated on real data on forestry in Spain and can be implemented in corresponding long - term policies and regulations

Matthew P. Johnson, Lehman College, CUNY

Title: Joint Optimization of Hydroelectric Power Plants

We address optimization problems arising from the complex interactions of hydroelectric power plants with one another and with their riverine environment. A power plant's operations can a ect its surrounding environment, for example by raising water temperatures, which can be harmful to aquatic life, and so must comply with government regulation such as the Clean Water Act (CWA). There is growing recognition that the effects of power plants' operations can be much longer-reaching and subtler than this, however: this warmer water, if later used by a second power plant downstream, can reduce that plant's generation efficiency, perhaps causing it to extract more water or to shut down completely, in order to comply with the CWA. Because of such complex dynamics characterizing the joint effects of a region's power plants, Miara and Vorosmarty have urged that power plant management be approached on a regional level rather than a single-plant level. This analytical perspective prompts consideration of a huge variety of potential benefits to seek and costs to avoid, and so it is far from obvious just what should be optimized for when designing regional-level management policies or choosing sites for the development of new plants.

We approach this problem setting as an application area to be modeled using the tools of theoretical computer science, building on the existing analytical model TP2M. We aim to design formal problem definitions that both a) are abstract enough to make mathematical and algorithmic analysis tractable and b) maintain sufficient fidelity to (some) important aspects of the real-world setting that the resulting algorithmic solutions will provide valuable insight and translate into useful policy recommendations. We are concerned with two broad classes of problems: 1) computing optimal management policies for a region's existing collection of plants, and 2) computing an optimal set of (additional) plant locations within a given region. In ongoing work, we are designing optimal or approximation algorithms for these problems. Finally, using tools from algorithmic game theory, we attempt to quantify the size of the bene t of solving such problems centrally, on a regional level, rather than plant by plant, i.e., the Price of Anarchy.

Harry Kessels, Telfer School of Management, University of Ottawa

Title: Adaptive Management Strategies in Canada's Boreal Ecosystem

In forestry management, strategic planning involves the longterm vision and mission for an entity or area, where tactical planning deals with the actual steps needed to achieve that vision. Operational planning regulates the day-to-day output relative to sched ules, specifications, and costs. Decision support systems would ideally balance short -, medium-and long-term planning goals.

This research focuses on adaptive management strate gies in support of wildfire risk mit igation decisions in the Nechako Lakes District in central British Columbia, Canada. Community profiles are assessed in terms of their vulnerability to wildfires, by using the following methods:

1. Spatial Analysis using ArcGIS to quantify spatial correlations and probability distributions of wildfires based on historic data from the Canadian National Fire Database along with topographical and land use data.

2. Scenario simulations and optimizations to assess impacts and opportunity cost of various adaptive management strategies for wildfire risk mitigation.

Results of this research will serve to increase our und erstanding of historic data and to strengthen existing wildfire management strategies and decision support models to mitigate wildfire risks

Dubrava Kirievskaya, The University of Utah

Title: The Chukchi Sea Ecosystem: Assessment of Contemporary Conditions and Vulnerability to Extended Human Activities

The key threat for deterioration of conditions of Arctic sea ecosystems is anthropogenic impact as a result of developing oil and natural gas deposits and shipping. The aim of the research is to identify ecologically important areas in the Chukchi Sea for their future protection (minimize interference from any shipping and offshore oil activities).

The location of the Chukchi Sea between the Bering Sea and the Arctic Ocean determines the mixed character of its fauna [1]. Modern environmental conditions of numerous components of the Chukchi Sea ecosystem can be considered as being close to average long-term norms [2, 3]. However, the stability of biocenoses can be considered as vulnerable because in the eastern part of the sea and along the coast of the Chukchi Peninsula relatively favorable conditions for accumulation of pollutants are observed [3].

In this research, we conduct assessment of vulnerability from the potential oil impact for two parts of ecosystem: the coastal zone and water area. Vulnerability of ecosystem in water area from oil spills was connected to biotic components of the Chukchi Sea ecosystem such as zoo-plankton and phytoplankton, benthos, fish, marine mammals and birds. We showed that birds in cold climate are most vulnerable to oil pollution as well as marine mammals have the smallest vulnerable because they can be adapted to impact of oil spills. Also the base on relative vulnerability we indicate the regions of the Chukchi Sea which can be vulnerable from oil spills. Most of the determined vulnerable areas are located in coastal areas where there are human activities or potential human activities in the future. Analysis of relative vulnerability for various types of oil shows that film and dispersed oil are the most dangerous to the coastal part of the Chukchi Sea ecosystem. Birds are the most vulnerable to film oil impact because they are concentrated in the coastal part of the Chukchi Sea ecosystem.

1. Ushakov P.V., 1952. Chukchi Sea and its bottom fauna. In: The Far North-East of the USSR. Vol.2: 
Fauna and Flora of the Chukchi Sea. Publ. Academy of Sciences of USSR, Moscow, pp. 5-82. (in 
2. Studies of Ecosystems of the Bering and Chukchi Seas, Ed. by Yu. A. Izrael’ and A. V. Tsyban’ 
(Gidrometeoizdat, Leningrad, 1992) (in Russian).
3. Kirievskaya, D.V., Kiyko, O.A., Shilin, M.B. (2012) The assessment of contemporary condition of 
the bottom ecosystem of southeastern Chukchi Sea. Scientific Transactions of the Russian State 
Hydrometeorological University, Vol. 23, pp. 117-125 (in Russian).

Benjamin Levy, University of Tennessee

Title: Modeling Feral Hogs in Great Smoky Mountains National Park

Feral Hogs (Sus Scrofa) are an invasive species that have occupied the Great Smoky Mountains National Park since the early 1900s. Recent studies have revitalized interest in the pest and have produced useful data on vegetation, mast and harvest history. Using these data, a model with discrete time and space was formulated to represent the hog dynamics in the park. Estimation of actual total population and importance of a control program was investigated.

Co-Authors: Dr. Suzanne Lenhart, University of Tennessee; Dr. Charles Collins, University of Tennessee; Dr. Marguerite Madden, University of Georgia; Dr. Joseph Corn, University of Georgia; Dr. Rene Salinas, Appalachian State University; and Bill Stiver, Great Smoky Mountains National Park

Juan Lopez Arriaza, University of California, Santa Cruz

Title: A Semiparametric Bayesian Approach for Estimation of Individual Growth

In order to better understand the effects that rapidly changing environmental conditions will have on populations, it is becoming increasingly important to accurately describe the effects that these changes will have at the individual level. Fo r an individual, body size and growth are arguably the most important life history process due to their significant implications on survival and reproductive success. By accounting for a wide range of environmental factors, bioenergetic models provide us with a sophisticated framework to describe the growth of individuals. However, many of the parameters and functions of these models are borrowed from laboratory studies on other populations or species, or estimated based on costly measurements of a large number of individuals. While this approach has been adequate at elucidating mean population effects, it often fails to capture nuances present within populations. Incorporating a semiparametric Bayesian approach based on Gaussian processes to estimate th e effects that temperature has on individual consumption into the bioenergetics framework allows us to forgo many of these assumptions. Additionally this modeling framework captures the effects of temporal variation in environmental conditions (e.g. food availability and temperature) and provides us with a flexible tool to examine the effects that changes in these conditions may have on individual growth.

Bobbi S. Low, University of Michigan

Title: Largely-Unexplored Factors in Modeling Conservation

Issues of conservation, including protection of rare species, and management of commercially important and pest species, have far to go. Here I suggest that a major reason is the failure to recognize important aspects of both human and non-human species’ life history traits and their interactions. Life history, the temporal, spatial, and social patterns of growth, fertility and mortality, is central to the biology of all species. What in the environment shapes non-human life history? The particular variables of interest will differ: temperature, available water, salinity, cover… What matters about each of these variable reduces to a short list: extremeness, range of variation, spatial patchiness, and temporal predictability. The result is a hugely variablebut patternedarray of life histories. These patterns are predictive of a species’ vulnerability in the face of specific kinds of human impacts, and they interact with human life history and behavioral ecology. Humans are optimizers (e.g., in foraging), rather than “noble savages”; like other species, they seek short-term maximization. The characteristics of humans and the species they exploit interact, so that understanding the dynamics of relevant species should improve our ability to predict, and possibly manage, species. Examples are explored, including cod, lobster, and sea urchin fisheries.

Katherine Meyer, University of Minnesota, Twin Cities

Title: Modeling Resilience of Natural Systems

Climate change and intensive human land use are delivering widespread and often unpredictable disturbances to natural systems. In this context, promoting resilience - broadly defined as the capacity for a system to retain or recover its basic structure and functions in the face of change - has emerged as an important goal for natural resource management. Despite fast growing interest in resilience, efforts to quantify this concept using mathematical structures are in their infancy. In this paper, we develop some possible quantifiable definitions of resilience in a dynamical systems framework. We assume that a continuous dynamical system represents the undisturbed natural system, and we distinguish two possible types of disturbance. In the first case, we perturb the state space with a regular discrete disturbance. We examine the effect of this perturbation on equilibria, limit cycles, and basins of attraction. The second type of disturbance involves transient changes to parameter values near a bifurcation. In this case, parameters may return to their original values without the system returning to its original state. We consider (i) critical timescales of parameter variation and (ii) whether we can predict the final state of the system given a certain schedule of parameter change. For both types of disturbance, we will distinguish between this idea of resilience and standard Lyaponov stability, presenting metrics that can be used to understand this difference.

Holly V. Moeller, Woods Hole Oceanographic Institute

Title: Marine Reserve Economics and the Value of Spatial Knowledge

Marine reserves, are as closed to fishing, are often touted for their conservation benefits: protection of essential fish habitat, increases in fish population and biomass, etc. However, reserves are often viewed as economically costly because closures deny fishermen access to potentially valuable fishing grounds. To address this perceived conflict, we developed a spatially continuous bioeconomic model that accounts for fish stock population dynamics and the economic value of this stock. Our model includes an oft-neglected fishing feedback: that fishing gear can be damaging to fish habitat, thereby affecting fishery productivity. A profit-maximizing analysis of this model shows that marine reserve networks, which enclose up to 80% of fish habitat, emerge as part of an optimal management strategy.

This optimal management strategy is spatially complex, and would require a high degree of spatial knowledge (i.e., of the distribution of fishing effort) for implementation. However, when we compared the results of this optimal manageme nt strategy with reduced - knowledge alternatives, we found that full spatial knowledge can have significant value, and may as much as double fishery revenues. Furthermore, spatial knowledge can help to reconcile multiple uses (e.g., fishing and tourism) within a revenue-maximizing management strategy.

Nathan Pollesch, University of Tennessee-Knoxville

Title: Towards a Sustainability Assessment Tool for Bioenergy (STAT-B): Key Components and Requirement Specification

This research presents a conceptual framework for the construction of a bioenergy sustainability assessment tool that builds upon previous research in the field. Seven key components for multimetric sustainability assessment are presented and current methodological approaches associated with each component are highlighted. The key components are: (1) Identification of Goals and Scale, (2) Indicator selection and categorization, (3) Data normalization and weighting, (4) Aggregation, (5) Analysis of data quality, (6) Evaluation of assessment results, and (7) Visualization and reporting. The research results in the identification of specific approaches within each key component that are suitable for the construction of a Sustainability Target Assessment Tool for Bioenergy (STAT-B). The approaches selected are those that most satisfy the following research objectives: Adaptability for assessing diverse bioenergy production pathways, exibility to support a range of analyses that researchers and policymakers may seek to undertake, and mathematical robustness with respect to normalization, aggregation, and the quantification of data uncertainty.

Richard Rebarber, University of Nebraska - Lincoln

Title: Feedback Methods for Population Management

A common mathematical approach to population management is to manipulate the life history parameters to get a more desirable dominant eigenvalue, which corresponds to changing the conditions for the population. Another common approach is to use optimal control theory, which identifies a control that minimizes a cost functional balancing the cost of doing something and the cost of leaving things alone. In this talk we present an alternative theoretical management strategy, which requires limited information from the system, and has built-in robustness to parametric uncertainty, measurement errors, and disturbances. This strategy uses robust feedback control techniques such as tracking, universal adaptive control, and observers. These techniques are ubiquitous in engineering applications of control theory, but have not been fully exploited for population management. For conservation, control theory can be used to determine how to replant or restock the population, while for management of invasive species, control can be used to determine a robust way to eradicate the population using pesticide or biological control. Our goal is to develop a control method which is implemented using only access to specified, limited observations of the population, and in a manner that is both independent of the initial population distribution and robust to model uncertainty, measurement errors, and disturbances, all of which are common in population models.

We will focus on two types of feedback control, using examples from the ecological literature to illustrate the techniques. Low gain integral tracking (with fixed gain and adaptive gain) can be used to regulate a population to a desired density; we apply this to a wild boar population model and a Savannah grass model. High gain feedback control (also with fixed gain and adaptive gain) can be used to suppress an invasive population; we will apply this to a model for invasive species Diaprepes root weevil, an herivore which has invaded citrus-growing regions. In both cases the controller uses limited observations of the system, and we illustrate how the feedback control robustly regulates the population.

The mathematical models we look at include population projection matrix models and integral projection models. Most of our work so far has been for linear systems, but can be extended to some nonlinear systems. We will be using both off-the-shelf techniques and theorems, and new techniques and theorems tailored to he specifics of ecological systems.

Noam Ross, University of California, Davis

Title: Optimal Control Methods for Individual-based Models of Disease

Optimal control techniques can be used to derive cost-effective management strategies for forest and wildlife diseases, but require appropriate models for disease dynamics. Many fungal diseases, such as sudden oak death in forests, white nose syndrome in bats, and chytridmycosis in amphibians, exhibit common properties that affect these dynamics: hosts can be repeatedly infecte d, effects of disease are load-dependent, and disease can originate from persistent reservoirs in the environment or other, unaffected hosts. Fungal diseases can suppress host populations and lead to extinction, and management goals may include host conser vation and disease eradication. This combination of factors favors stochastic, individual-based models (IBMs), which can simulate individual variation in disease loads and extinction behavior.

Applying optimal control to IBMs is challenging due to IBMs' hi gh dimensionality, which precludes robust exploration of state space. "Multi-scale" or "equation-free" (EF) techniques can be used to reduce IBM states to a small number of variables. Here, I demonstrate use of EF methods in optimal control, applied to the problem of fungal disease management for conservation. I examine a management problem using a model based on sudden oak death dynamics. In the model, hosts provide an ecosystem service and disease control can be exerted, with cost, by eliminating environ mental spore loads or culling hosts.

EF techniques calculate artificial derivatives by simulating stochastic IBMs in short, repeated bursts, and averaging outcomes. These artificial derivatives are then used to estimate changes at the population scale. I use these derivatives to solve the management problem using Hamiltonian-style optimal control.

Nourridine Siewe, Howard University

Title: A Mathematical Model for the Population Dynamics of Disease Transmitting Vectors with Spatial Consideration

A deterministic model with spatial consideration for a class of human disease-transmitting vectors is presented and analyzed. The model takes the form of a nonlinear system of delayed ordinary di erential equations in a compartmental framework. Using the model, existence conditions of a non-trivial steady-state vector population are obtained when more than one breeding site and human habitat site are available. Model analysis con rms the existence of a non-trivial steady state, uniquely determined by a threshold parameter, R0, whose value depends on the distribution and distance of breeding site j to human habitats. Results are based on the existence of a globally and asymptotically stable non-trivial steady-state human population. The explicit form of the Hopf bifurcation, initially reported by Ngwa [On the population dynamics of the malaria vector, Bull. Math. Biol. 68 (2006), pp. 2161{2189], is also obtained and used to show that the vector population oscillates with time. The modeling exercise points to the possibility of spatialtemporal patterns and oscillatory behavior without external seasonal forcing

Gwen Spencer, Smith College

Title: Missing Constraints: Local Incentives May Sabotage Landscape-Scale Coordinated Management

A rule of thumb in optimization is that the more decisions which can be coordinated, the better. Is this principle suitable for considering problems in landscape-scale natural resource management? When jurisdiction is fragmented, and local land managers face substantial personal costs under globally optimal policies, implementation of "scientifically optimal policies" may be impossible. As an example, we discuss the case of improving preventive fuel reduction policies (to suppress wildfire spread). Can we move towards a richer set of constraints that re ect the true social-ecological nature of managing important natural resource systems? We open this inquiry by extending work in behavioral and environmental economics on conditional provision for the public good to heterogeneous networks. When knowledge that the global system will benefit is not enough to in uence local adoption, what can we learn about optimal ways to coordinate an extended landscape of self-interested decision makers? Departures from the theoretical work on the spread of innovation and contagion are substantial, as total adoption is no longer submodular.

Anthony Tongen, James Madison University

Title: A Periodic Matrix Population Model for Monarch Butterflies

The migration pattern of the monarch butterfly Danaus plexippus consists of a sequence of generations of butterflies that originate in Michoacan, Mexico each spring, travel as far north as Southern Canada, and ultimately return to the original location in Mexico the following fall. We use periodic population matrices to model the life cycle of the eastern monarch butterfly and find that, under this model, this migration is not currently at risk. We extend the model to address the three primary obstacles for the long-term survival of this migratory pattern: deforestation in Mexico, increased extreme weather patterns, and milkweed degradation.

Yuri Yatsenko, Houston Baptist University

Title: Environmentally Sustainable Management of Agricultural Production

Sustainable management of a natural resource requires preserving the resource so that it can be utilized in the future. While owners of the resource intend to save it in the long-run, producers, who have leased the resource, are less interested in preserving it and can exploit it beyond sustainable extraction limits. In the case of agricultural land as a natural resource, the landlord either cultivates the land him/herself or leases it out in form of a fixed-rent or sharecropping contract. Intensive agricultural production and continuous application of mineral fertilizers reduce the fertility of the soil. The degraded soil favors soil erosion and affects negatively environmental services provided by the waterways. Starting with a quite general dynamic setting, we focus on a specific agricultural production problem that involves one landlord and several identical tenants-producers who invest into organic fertilizer (farmyard manure) to improve soil quality and productivity. This is the most essential investment made by tenants in many African and Asian countries. The problem under study is interdisciplinary and combines various agricultural, economic, social, and environmental factors.

A hierarchical economic-environmental model is formulated to analyze the sustainable management of farming production in this agricultural landlord-tenant system. To maximize profit, a landlord chooses rental payment and the duration of a lease contract. Tenants apply farmyard manure in order to increase future crop growth and maximize their profit. Positive effect of manure is not immediate since the nutrients are released slowly, and, thus, the improvement of the soil structure (humus content) is a gradual process over time. This investment cannot be verified and is not compensated by the landlord. The qualitative analysis of the model leads to interesting managerial upshots and policy recommendations. We demonstrate that the qualitative behavior of optimal trajectories in the landlord-tenant problem is governed by environmental conditions rather than by the end-of-horizon and delay effects. It is shown that the quality of the resource approaches the first-best sustainable trajectory when the duration of lease contract increases.

Najat Ziyadi, Morgan State University

Title: A mathematical model of Nutrients-Phytoplankton-Oysters in a bay ecosystem

In this talk, we will introduce a simple mathematical model that describes the interactions of nutrients, phytoplankton and oysters in a bay ecosystem. Using the model, we will derive verifiable conditions for the persistence and extinction of phytoplankton and oysters in the bay system.

In addition, we will use sensitivity analysis and simulations to illustrate how human activities such as increased oyster harvesting and environmental factors such as increased nutrients inflow and increased oyster filtration can generate phytoplankton bloom with corresponding oscillations in the oyster biomass and nutrients level in the bay ecosystem.


Title: Ensuring Scientific Knowledge is Useful for Practical Decision Making


Richard Merrick, Chief Science Advisor, National Oceanic and Atmospheric Administration (NOAA) Fisheries (richard.merrick at
Keith Criddle, Professor in the School of Fisheries and Ocean Sciences at the University of Alaska (kcriddle at
Catherine A. Roberts, Editor-in-Chief of Natural Resource Modeling (croberts at, Chair of Department of Mathematics and Computer Science at College of the Holy Cross

Biographies of Panelists:

Richard is the Chief Science Advisor for NOAA Fisheries. He leads their efforts to provide the science needed to support sustainable fisheries and ecosystems. He leads NOAA's six regional Fisheries Science Centers. Keith is a marine policy expert. He is the Ted Stevens Distinguished Professor of Marine Policy. He is headquartered in Juneau, Alaska. He provides advice to government agencies and private entities on matters of ocean policy. Catherine is the editor-in-chief of Natural Resource Modeling, an international journal devoted to mathematical modeling of natural resource systems. The major theme for the journal is the development and analysis of mathematical models as tools for resource management and policy development.

Description of Panel:

How does scientific scholarship contribute to the conversations and deliberations of stakeholders making important choices about how to manage natural resources? How can science inform and support decision-making? The panelists will share some of their experiences of the challenges and opportunities in this arena. The audience will have the opportunity to ask questions and contribute to the discussion.

Previous: Program
Workshop Index
DIMACS Homepage
Contacting the Center
Document last modified on May 27, 2015.