Alan Hastings - US grants

The aim of this project is to understand better the role of selection in the genetics and evolution of natural populations through a study of the static and dynamic behavior of multilocus population genetic models. The models used in most of the analysis will be standard multilocus ones or quantitative genetics models as used in the study of mutation-selection balance. However, different methods of analysis will be used which will stress techniques and approaches which study the effects of weakening a prior assumptions made, such as the usual assumptions of normality of distributions and absence of epistasis in the study of the evolution of phenotypic characters. The static behavior of multilocus models with selection, both with and without mutation will be studied with the goal of understanding mechanisms underlying the maintenance of variability both at the phenotypic level and at the level of the single locus. Techniques based on bifurcation theory, perturbation theory and computer simulation will be used. Models where allele frequencies are explicitly included will be emphasized. The dynamics of multilocus systems will also be studied using perturbation techniques and computer simulation, again stressing phenotypic models based on underlying genetic models where allele frequencies are specified, with several goals. One aim will be to understand the role of disequilibrium in the transient behavior of multilocus systems. In the context of phenotypic models, the importance of and implications of deviations from normality for the dynamics of continuous characters will be determined. Moreover, the role of epistasis will be investigated. Additionally, dynamics and statics in finite populations will be studied using both computer simulations and analytic techniques. The results of this study will help in understanding mechanisms which maintain variability in both natural and human populations.

This special award will give Ph.D. student Katya Prince flexibility in pursuing her graduate studies and research initiation in Functional Morphology and Behavioral Ecology. This award will strengthen minority research participation in this area.

Dr. Botsford and collaborators will model and analyze the dynamic effects of spatially and temporally varying physical oceanographic conditions on spatially distributed, meroplanktonic marine populations with age or size structure and density- dependent recruitment. They will examine the effects of both: (1) large scale physical forcing on transport and survival between sub-populations during the planktonic larval stage, and (2) small scale physical forcing on life history rates in local sub-populations. Population behavior will be characterized in terms of persistence, stability, sensitivity to environmental variability, and spatial synchrony. These investigators will use their models and the results of their analyses to project changes in these populations due to projected changes in global climate. As specific examples for which to make these projections, they will focus on the Dungeness crab (Cancer magister) and the feeding interaction between sea urchins (Strongylocentrotus spp.) and macroalgae (Nereocystis leutkeana, Macrocystis pyrifera) in the California Current System. For these systems they will model larval transport based on idealized flows and small scale benthic flows computed from wave energy. Potential future changes in the physical environment will include changes in the level of upwelling and the frequency and magnitude of ENSO events.

The overall aim of this project is to understand better the role of selection in the genetics and evolution of natural populations through a study of the static and dynamic behavior of multilocus population genetic models, both in single populations and in models incorporating many sub-populations. The specific aim during this project period will be to examine the determination of processes, such as the relationship of phenotype to genotype, by the observation of patterns, such and response to selection Knowledge of the relationship between genotype and phenotype is important both in pure and applied genetics. Studies of dynamics, especially understanding the dynamics and causes of disequilibrium, such as found in the HLA complex, is also important for our understanding of human genetics. The models used for single populations will be standard multilocus ones. However, both the goals of the analysis and the techniques used will be quite different. The influence of epistasis and pleiotropy on predictions from population genetic models and on the maintenance of genetic variability in natural populations will be studied. Using techniques based on optimal control for finding minimum time solutions, the role of selection will be studied by specifying observable quantities such as the dynamics of mean, variances or covariances of characters under selection, and then trying to deduce information about the unobservable ones, such as the map from genotype to phenotype. The information about unobservable quantities will range from limits to behavior to estimates, depending on the input information provided. This will naturally lead to statistical questions concerning the detection of epistasis and or pleiotropy through the dynamics of gross observable characteristics such as means and variances. A similar approach based on optimal control theory will also be used to understand the evolution of genetic modifiers. A second specific aim will be to study the dynamics of genetic modifiers when selection is allowed to vary. Finally, the effects of spatial variation as well as temporal variation. on response to selection will be studied. Ways in which information about historical processes can be inferred by present day observations of hybrid zones and more generally spatial patterns of allele frequencies will be investigated.

This is a proposal to purchase six color computer workstation, a high speed graphic server a color laser printer, peripherals for storage and video graphics, and related software. Funds for a 50% computer services manager to manage the system and provide training and graphics consultation will be provided by the University. The facility would be available to all faculty and students with either theoretical or experimental research programs involving computational problems in biology. Use of the instrumentation will form a core feature of graduate research training in computational biology across the campus.

The overall aim of this project is to understand better the role of selection in the genetics and evolution of natural populations through a study of the static and dynamic behavior of multilocus population genetic models, both in single populations and in models incorporating many sub-populations. The specific aim during this project period will be to examine the determination of processes, such as the relationship of phenotype to genotype, by the observation of patterns, such and response to selection Knowledge of the relationship between genotype and phenotype is important both in pure and applied genetics. Studies of dynamics, especially understanding the dynamics and causes of disequilibrium, such as found in the HLA complex, is also important for our understanding of human genetics. The models used for single populations will be standard multilocus ones. However, both the goals of the analysis and the techniques used will be quite different. The influence of epistasis and pleiotropy on predictions from population genetic models and on the maintenance of genetic variability in natural populations will be studied. Using techniques based on optimal control for finding minimum time solutions, the role of selection will be studied by specifying observable quantities such as the dynamics of mean, variances or covariances of characters under selection, and then trying to deduce information about the unobservable ones, such as the map from genotype to phenotype. The information about unobservable quantities will range from limits to behavior to estimates, depending on the input information provided. This will naturally lead to statistical questions concerning the detection of epistasis and or pleiotropy through the dynamics of gross observable characteristics such as means and variances. A similar approach based on optimal control theory will also be used to understand the evolution of genetic modifiers. A second specific aim will be to study the dynamics of genetic modifiers when selection is allowed to vary. Finally, the effects of spatial variation as well as temporal variation. on response to selection will be studied. Ways in which information about historical processes can be inferred by present day observations of hybrid zones and more generally spatial patterns of allele frequencies will be investigated.

9520820 HASTINGS Population biologists have developed models of population growth that are designed to predict the fate of fragmented populations, but these models have not been tested. Such tests require data on the original conditions and the ultimate fates of real fragmented populations. If a set of populations that were fragmented in the past can be identified, and we can use models to predict whether each should be persisting today, a comparison of observed and predicted persistence can determine model reliability. According to fossil evidence, a set of at least 14 populations of pika (a small mammal) was isolated on mountaintops in the Great Basin at the end of the last ice age (about 7500 years ago). Since then, some of these populations have gone extinct. Pika live in a habitat created by freeze-thaw processes. With the retreat of the glaciers and the rising snowline, pika habitat within each mountain range was fragmented. Many aspects of this animal's ecology allow reasonable estimates of the condition of these populations when they were originally fragmented. Thus, models to predict the persistence of these populations can be developed. The proposed research will gather the data necessary to develop these models. The spatial distribution of pika habitat fragments on each mountain range and the movement of individuals between habitat fragments will be calculated. These data will be applied to models similar to those used in current conservation. Natural landscapes are being fragmented by development, often adversely affecting native populations. In order to plan development that it is compatible with the persistence of natural populations, we must be able to reliably predict population persistence under various patterns of habitat fragmentation.

The goal of the GLOBEC Northeast Pacific program is to gain an understanding of how variability in the physical environment, specifically changes that might result from climate change, affects populations of marine animals on the west coast of North America, specifically salmon and associated species. The PIs will formulate models spanning the individual level to the metapopulation level for two genera of interest to GLOBEC in the California Current System (CCS): (1) the two CCS salmon species identified by GLOBEC, coho salmon (Oncorhynchus kisutch) and chinook salmon (O. tshawytscha) and (2) Dungeness crab (Cancer magister), a species which covaries with salmon, is a significant prey of both species, and is subject to similar mesoscale circulation patterns. These models will link the different scales of variability and levels of ecological organization in the various retrospective, monitoring and process studies so that the effects of changes in the physical environment on populations can be projected.

ABSTRACT

Hastings, Alan M. , Susan L. Ustin, Edwin D. Grosholz, and Donald R. Strong

DEB 0083583

"Dynamics of an invasive non-native species and its biological, physical, and human impacts: Spartina alterniflora on the Pacific coast"

The PIs propose an integrative study of the dynamics of the invasive species, Spartina alterniflora (cordgrass), including a core mathematical/conceptual model, physical and biological feedbacks, and a study of the impacts on non-commercial human values. The core model is termed a "local-state, regional-state" model and the crucial innovation is the use of discrete time and continuous states and explicit inclusion of stochastically based on integro-difference equations, yielding substantial mathematical and computational advantages over reaction diffusion models. The state of the invasion will be a function of position along the shore, tidal height, age of Spartina, and densities of other species or human valuations in the system, and time. ENSO fluctuations, feedbacks, and non-reciprocal effects are included in the framework. Hypotheses concerning the biological bases of positive feedbacks, Allee effects, and density dependence will be tested experimentally and results integrated into the model.

Parameterization will be from a rich set of historical records and from remotely-sense images, references with GPS. Mixture analysis with data will inform the model of biochemical conditions of the cordgrass. Experiments will give data on demography, clonal growth, seed set, tide flow profile, sediment erodability, and shear stress. Sediment accretion will be quantified. Intensively studied sites will be extrapolated to the entire estuary using NASA's ASTER sensor on the Terra satellite. A map will be built of Pacific estuaries using daily MODIS satellite images. Food web and community effects will be studies experimentally. The ultimate faunal effects on the invasion will be measured in passerines and rallids. These observations will be combined with the overall model to develop long term prediction of the impact of Spartina on birds. Finally, these invasions are ideal for studying non-commercial values lost to the changes caused by Atlantic cordgrass. Integrating the valuation with the model will provide one of the first rigorous studies of invasive species on the value of ecosystem services.

The GLOBEC NEP Program will continue annual long term observations (2D) in two parts of the California Current System (CCS), along with mesoscale (3D) and process studies in two field years. Through those studies the program aims to achieve a quantitative understanding of how physical and biological processes drive zooplankton and salmon populations, on time scales ranging from multi-decadal to weekly, and spatial scales from the basin to mesoscale. Modeling is required to integrate over the many disciplines involved, scales of variability, and levels of ecological organization, both as a part of the scientific process, and as a prospective tool to predict the effects of future climate change on these populations. As part of the GLOBEC Program the PIs will: (1) add a swimming capability to their bioenergetic model of individual CCS salmon and embed that in GLOBEC and CoOP physical models to explain salmon distribution, growth and survival in early ocean life, (2) describe implications for CCS salmon population dynamics of well known, but poorly understood effects of the ocean environment on salmon size structure, and (3) assess retrospectively relationships between CCS salmon spawner and recruit data and physical data from the CCS from multidecadal scales to the mesoscale. In addition the PIs will use numerical. experiments to test explanations of observed distributions, to see whether they meet bioenergetic and swimming speed constraints, and to evaluate their consequences regarding distributions of food and predators. Individual level analyses and existing data indicate environmental influences on growth affect not just survival, but also maturity schedules, an effect whose consequences for population and metapopulation dynamics and for retrospective are not known. GLOBEC NEP conclusions regarding the response of this ecosystem and salmon populations to climate change will require consistency with past data. The PIs will refine their retrospective results by relating decadal and annual scales to seasonal, mesoscale mechanisms, using recruitment and spawner data (which are less confounded than catch) and accounting for freshwater conditions. As GLOBEC NEP reaches completion 4 or 5 years from now, the modeling and retrospective studies will be integrated to provide a prospective summary.

9910897
Botsford

This collaborative project, involving eleven investigators at five institutions is under the auspices of the Coastal Ocean Processes (CoOP) Program, and it focuses on the role of wind-driven transport in shelf productivity. Wind-driven continental shelves represent a paradox in that while they are characterized by high productivity due to upward fluxes of nutrients into the euphotic zone, wind forcing also represents negative physical and biological controls via offshore transport and deep (light-limiting) mixing of primary producers. Specifically, upwelling ecosystems along mid-latitude eastern boundaries of the ocean are well known for wind forcing and high productivity at lower trophic levels, with concomitant transport of near-surface plankton offshore.

The group of researchers will conduct an interdisciplinary study to examine the roles that wind-driven transport plays in productivity over the shelf off northern California. Research will focus on key processes to explain the integrated functioning of highly productive planktonic systems over eastern boundary shelves in response to wind-driven transport, and specifically, to determine the sensitivity of these processes to both wind intensity and the time scales of wind forcing. Work will also identify specific features of the nutrient-phytoplankton-zooplankton (NPZ) food web that lead to greater or lesser secondary productivity in response to changes in wind forcing.

To implement the study, part of the work will examine the 3-dimensional wind-driven circulation of water concurrently with size-structured distributions of phytoplankton and zooplankton species. Other efforts will study the key physical and biological processes that control primary production, zooplankton population responses, and offshore transport of plankton and nutrients over the strongly wind-driven shelf and slope off Bodega Bay. An integrated sampling scheme coupled with appropriate physical-biological models designed to synthesize and guide the fieldwork has been developed. The fieldwork will be comprised of fixed station time-series, ship surveys, drifter releases, and satellite remote sensing. There are two parts to the fieldwork - one focusing on the mooring array off Bodega Bay, and a second involving ship surveys and drifters. The mooring array places emphasis on eulerian measurements of cross-shelf circulation, aiming also to resolve up/downwelling fluxes. The surveys and drifters place emphasis on transformations in the water column, specifically the maturation of upwelled water as it moves away from the mooring site. By combining these data with the synoptic measurements available from satellites and the integrative aspects of the modeling, the project seeks to address all the important processes associated with wind-driven transport. This promises to unravel the paradox of how wind-driven transport supports high levels of productivity over eastern boundary shelf regions.

This particular component of the study addresses the modeling component, which includes physical (circulation) and biological (plankton) modeling objectives. The first general objective of modeling is to integrate and generalize research results - to formulate a model that integrates all of the important dynamic links between the physical and biological processes in such a way that all of the collaborators can make joint use of data and analyses from all disciplines. The second general objective is to develop increasingly efficient models that allow the inclusion of more complex dynamics in models that can be run on local workstations. For example, the exclusion of size or age structure may also exclude some of the stronger non-linear effects in plankton systems.

ABSTRACT


Pis: Arzberger, Peter and Hastings, Alan
University of California-San Diego

DEB-0092081

Title: "QEIB: Quantitative Environmental Biology Workshop, Fall 2000"

The PIs proposes to hold a workshop to bring together leading environmental biologists, mathematicians, and statisticians to identify research opportunities for collaboration in environmental sciences. Further, they will identify cultural inhibitions to collaboration, and possible programs to help foster collaboration. The workshop will be held at the San Diego Supercomputing Center on the University of California campus, on September 7-9,2000. The participants will produce a report and publication that will be broadly available to the community. These documents will discuss the research opportunities and new modes of interdisciplinary interactions that the participants identify.

Population density cycles that appear synchronous, or irin-phasel, over large geographic areas
are some of the most striking phenomena in population biology. In theory, such synchrony is
caused either by widespread meteorological factors, or by movement of individuals between
populations. Theory for predator-prey 'metapopulationsl' that extend over groups of patches
also links synchrony to regional persistence. The study of these phenomena in nature has been
hampered by difficulty in identifying both the cause of population cycles and the roles of
environmental factors and interpatch movement in modifying population fluctuations and
synchrony. The environmental forcing of metapopulations which is explored here is relevant to
biological control of pest species and conservation. Additionally, extreme weather events
caused by global warming have the potential to synchronize regional populations, which might
cut short regional persistence. The proposed work uses mathematical techniques focused on
phase dynamics to analyze synchrony and build precise links among environmental variability,
population dynamics and extinction. Phase dynamics have been widely used in neurobiology,
but their potential in ecology is only just beginning to be realized. This project develops new
analytic tools for an ecological audience and uses a model experimental system, bacteria and
protozoa in laboratory microcosms, to bridge the gap between populations and metapopulation
theory. The work starts with a classic model and then develops more precise and biologically
realistic models, which in turn will fuel further, more precise, experimental tests.
Two-patch predator-prey systems coupled by random dispersal will provide a link with
analytical solutions, which numerical simulations and experiments can build on to consider more
complex and realistic situations. Two patch models will be used to derive equations which relate
phase, the point in a predator-prey cycle, to population dynamic processes. The dynamics of
phase difference between two patches will be derived and used as a measure of synchrony,
which can be related to regional persistence and within-patch predator-prey dynamics. Phase
dynamics can also distinguish whether persistence is controlled not by deterministic equilibrium
dynamics (the focus of most theoretical studies), but instead by long-lived transient dynamics
which may dominate during ecologically relevant time scales; specifically regression of phase
difference through time will be used to calculate the duration of transient dynamics, when phase
difference becomes zero. Experimentally, the initial phase difference of predator-prey
oscillations in two linked patches will be manipulated by starting microcosms with different
predator and prey densities in each patch. Statistics will then quantify the phase difference
between patches and test its correlation with regional persistence time. Repeating this
procedure in microcosms with different movement rates between patches (lengths of corridors)
will test the prediction that increased movement rate between patches will reduce phase
differences and regional persistence time. Experiments with 1-8 patches will manipulate
environmental variability through temperature fluctuations and control whether this operates
uniformly across a region or just in a single patch. Quantification of regional persistence time
and phase differences between patches will then test the predictions that local variability
enhances regional persistence, but regional variability and increased movement reduce regional
variability.
This project will demonstrate how and why environmental variability influences dynamics
and extinction in regionally-distributed predator and prey systems. The techniques of phase
dynamics will be brought to a broader ecological audience, and two graduate students will be
trained with the necessary mathematical, modeling, statistical and experimental techniques that
are required to understand the links between the environment and populations. This work will
provide a paradigm on which future combined experimental and theoretical studies of population
synchrony and persistence can build.

Abstract

Knowledge about the spread of diseases is vitally important to health, agriculture, and to natural communities of organisms. We propose to experiment with an insect disease that offers great potential for learning general principles of spread. We will work with entomopathogenic nematodes (EPNs) that kill caterpillars that eat the roots of plants. These nematodes can protect the plants by killing root feeding caterpillars.
Our preliminary mathematical models lead us to propose that the EPN population is caught between the point of extinction due to overexploitation and a the point of extinction due to underexploitation Finding the biological factors that create the area between over exploitation and underexploitation is the major objective of this project. The spread and dispersal of the EPN among lupine bushes is central to the area of over and underexploitation biology. Immigrants can rescue EPN populations that have or are headed for extinction. The field experiments are designed to answer questions about the conditions that lead to stability of the EPN population EPNs are among the most important natural enemies of root feeding insects in both cultivated and natural settings and are of substantial interest to agriculture and management

Many of the traditional approaches in ecological theory are based on the paradigm that natural ecosystems return to stable states. Thus, traditional approaches to environmental problems draw on the large body of mathematical and statistical techniques for analyzing such systems. These approaches, however, have clear limitations. Just as ecologists emphasize that long-term experiments yield different results from short-term experiments, theory needs to take the role of time scales into account, and look beyond an emphasis on stability. In the context of this proposal, the PI's will develop the mathematical and statistical tools to understand the role of transient dynamics (as opposed to dynamics connected with stability) in ecological systems.

This study will both aid our basic understanding of real ecological systems, and refine old and open up new approaches to environmental management. To cope with the often sudden and large impacts that humans can have on ecosystems, there is growing interest in management strategies that change as managers learn and as an ecosystem is beset by new shocks. Implementing adaptive management, however, requires a far more sophisticated understanding of how short-term, observed dynamics of a system generate long-term patterns that ultimately determine sustainability. Students will also receive important interdisciplinary training.

How fast a species expands its range depends on characteristics of the species and on random variation in time and space. This is a difficult problem to study in nature because of the large time and space scales that may be involved, and the lack of repeatability. To address these limitation, this project examines the problem in the laboratory using the flour beetle, Tribolium castaneum, as a model system. The study will include many replicates of artificial landscapes and varying demographic parameters under controlled conditions in an incubator. The experimental work will be coordinated with the development of mathematical models that incorporate variability. The models will allow extension to other systems and the development of general principles.

The problem of spatial spread is of both great scientific and practical importance. The spread of invasive species is one of the most important and costly environmental issues facing the United States. Yet, there have been essentially no detailed, repeated experiments on how predictable spread is, and on how demographic parameters affect spread. As the current problem illustrates, progress in many ecological problems depends on the joint application of experimental and mathematical methods, so the training received by undergraduates during the course of this work will have very significant long term impacts.

A predictive understanding of salmon abundance is still lacking despite GLOBEC NEP's program of field sampling, retrospective analysis and modeling, a strong comparative component and observation of an environmental shift in 1999/2000. Although the physical/biological conditions associated with (1) annual variability in fish survival, and (2) the spatial distribution of juveniles, are amenable to description, neither the underlying mechanisms to explain them nor the link between two are known.

This proposal aims to achieve both understanding and predictability by using a comparative approach while synthesizing several data sets for coho salmon. This species was studied by GLOBEC in both Southeast Alaska (SEAK) and the California Current System (CCS), and its abundance covaries inversely in the two systems. The biological/physical conditions under which juvenile coho salmon were found in GLOBEC NEP-funded studies in SEAK and the variation of the juvenile salmon habitat over 8 years at one location and 4 years at another will be described. An individual-based model will be employed to assess the advantages of these habitats to growth and mortality of juvenile coho salmon, and to describe how individual salmon could interact with such spatial distributions. The findings of a GLOBEC-NEP funded retrospective study regarding potential predator buffering effects will be extended in time and space. Local indicators of biologically important physical conditions, based on local winds and general circulation, will be developed to study the response of individual stocks along the coast north of the bifurcation of the West Wind Drift (WWD). The coded wire tag data set, which spans both systems, will be used together with GLOBEC observations in the NEP to derive a model of coho salmon early life history that is consistent across the two systems, but can have different physical forcing in each.

The ultimate product of this project is an indicator of annual ocean conditions that affect salmon survival and age of spawning. This indicator will be directly useful in the short term in fishery management and in the long term by reducing the uncertainty and contentiousness surrounding management of factors influencing the freshwater phase of the salmon lifecycle. This project includes a graduate student and a postdoc.

This proposal is for a workshop that will discuss both the need for and design of a center that would promote interaction at the intersection of mathematics and biology that would focus on both proposals from the scientific community and the ability to respond to needs for expertise on relatively short time scales. The workshop will develop ideas that could be used in the future design of such a center. The overall product will be a report that will be available immediately on the web, as well as in a print version after a reasonable amount of time. The report will focus both on issues of the design of a center, the need for a center, what potential issues would arise in funding and operation and evaluation, as well as the kinds of needs that could be met both in terms of scientific advances and training and infrastructure.

It is becoming increasingly recognized that the solutions to many essential problems in biology require mathematical approaches. Past successes at combining mathematics and biology have ranged from improving basic theoretical understanding to developing practical solutions to problems of societal importance. Today, many pressing problems require the use of mathematical approaches, including important applied questions, such as the modeling of infectious diseases, ameliorating the effects of human activities on the environment, and understanding the basic biology underlying many animal and plant diseases.

In GLOBEC investigations, causality is often inferred from observed covariability between environmental indicators and populations, but mechanisms of action (e.g., an effect on individual growth rate or survival at a certain age) are seldom known, though they are frequently hypothesized. The population dynamic effects of the mechanism of action are seldom elucidated, and investigators are often not aware of the population dynamic differences between variability at different ages or between variability in survival or growth. However, research in population dynamics is increasing awareness of the differences these make in terms of sensitivity of populations to the environment and the time scales of variability of the environmental forcing and the response. Salmon and cod are two taxa that have been of interest to GLOBEC and they span the Pacific and the Atlantic Oceans in the Northern Hemisphere. Their populations vary spatially in development rates and the consequent distribution of spawning ages, and they experience inter-annual temporal variability in both survival at various ages and development rates (and spawning age distributions). The investigators will examine the role of the differences that population dynamics makes in structuring the different responses of various salmon and cod populations to environmental variability and climate change. Specifically, they will describe how the mechanism of action (variable growth rate or survival rate at age) influence population sensitivity to environmental fluctuations at various time scales, including expected time scales of population response. Examples of similar studies include out elucidation of the differences in population responses of coho and chinook salmon to the regime shift in the mid-1970s due to differences in spawning age distributions. Discovering that the expected differences were slight re-focused attention on other potential causes of the differences in response. Another example is identification of the causes of cohort resonance in cod and the drawing of attention to the fact that increasing resonance (sensitivity to specific time scales of environmental variability) also led to increasing sensitivity to variability at very low frequencies such as might be seen in climate change. Concern was expressed that this heightened sensitivity to random noise could interfere with attempts to detect slow climate change.

A societal benefit will be derived from this investigation of how the addition of fishing mortality rate changes the basic response of populations to environmentally induced variability in development rates and survival rates at various ages. This will aid in the risk analysis associated with fishery management. Also, description of the expected scales of variability to which populations will be sensitive will aid in the design and analysis of ocean observing systems. From a human resources point of view, this project will be train one student and two postdoctoral scholars.

The goal of this project is to develop a general theory for the dynamics of biological systems at intermediate time scales. At short time scales, the current state or the current direction of a biological system provides a good description of the future state. At very long time scales, systems settle into predictable patterns that are relatively easy to study. Intermediate time scales lie in between these two states and may include rapid, and harder to predict yet important, changes in system behavior. As a first step toward understanding intermediate time scales, specific case studies based on a) ecological models with a small number of interacting species, b) neural models with a few neurons or c) epidemic models will be studied numerically on a computer. These numerical results will then be generalized using mathematical theory based on the study of dynamical physical systems. The resulting generalizations will allow the determination of when phenomena like turbulence (apparently irregular changes in population size) or bursting (rapid, apparently random large changes in population size separated by periods without change) will arise in systems with interacting species distributed over space, and also in a variety of other biological systems.

The theory developed will be general and of wide applicability across levels of biological organization ranging from the cellular level to neuroscience to the dynamics of individual populations to ecosystems. A particular set of important applications will be fisheries management, the impact of global climate change on ecosystem services, and the dynamics of diseases, all of which will require prediction on scales appropriate for human dominated systems. In the course of this work postdoctoral scholars and graduate students will receive interdisciplinary training that will develop the human capital to meet future challenges in understanding complex biological systems.

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).

Although the distribution of every species is limited to a particular range, the fundamental ecological processes that determine species' range boundaries are not understood well enough to predict how species will respond to environmental change. This project will investigate three overarching questions. First, what determines range limits? Second, how variable are range limits and what factors determine this variability? Third, how do range limits respond to environmental change? That is, how quickly do they respond and how predictable or variable are their responses given the inherent variability arising from random population processes? These questions will be addressed using a laboratory based experimental system together with mathematical and statistical modeling.

Understanding what sets range limits and their variability is vital for understanding and forecasting how species will respond to climate change and to increasing variability in climate. This understanding is also vital for the management of species - both those that are undesirable and those that are endangered. Only a combination of manipulative experiments and mathematical modeling will yield the understanding needed by society over the available time before action is required. This approach has the additional benefit of providing real interdisciplinary training and experience for both graduate and undergraduate students, and plans are presented to include more than 40 undergraduate and 2 graduate students in the research. Both investigators have strong records of recruiting undergraduate assistants from groups typically underrepresented in biological research.

Many invasive species have strong negative impacts on biodiversity and ecosystem function and attempts to control or reverse their spread can be costly and require coordination among multiple institutions. This project integrates biological, mathematical, economic and political science tools to answer several critical and interrelated questions surrounding the invasive and high impact Eastern Smooth Cordgrass, Spartina spp, in San Francisco Bay. Two ways in which human intervention can mitigate the impact are to eradicate the invader and to restore the habitat. This is a complex problem with spatial linkages arising from the biology and impact of Spartina, and the spatial mosaic of governing agencies and responsible authorities. The project will focus on three questions: 1) What are the dynamics of eradication of an invasive species and subsequent restoration? 2) How can a program of eradication of an invasive species and subsequent restoration be designed taking into account both economics and ecology? 3) How do eradication and restoration policies depend on collective action on the part of multiple governmental and non-governmental stakeholders? This project will develop general models that will apply to a wide range of systems where an invasive species can have long lasting effects on the biotic and abiotic environment and to a much wider range of natural systems which are affected by humans and in which potential irreversibilities can occur.

The eradication of invasive Spartina is one of the top priorities recently identified in the West Coast Governor's Agreement on Ocean Health, which provides a mandate for its eradication from the Pacific Coast by 2018. The project will provide specific guidance for control and restoration efforts in San Francisco Bay, and in other west coast estuaries, and will provide interdisciplinary research training for several graduate and undergraduate students and postdoctoral scholars. Outreach will provide information to the public about Spartina and invasive species more generally. The tools developed and lessons learned can be applied broadly to the wide range of ecosystem management projects with feedbacks between natural and human systems, including invasive species management, fisheries, endangered species protection, forest management, and the provision of ecosystem services more broadly.

This INSPIRE award is partially funded by the Population and Community Ecology Program in the Division of Environmental Biology in the Directorate for Biological Sciences and by the Emerging Frontiers Program in the Directorate for Biological Sciences, by the Condensed Matter and Materials Theory Program in the Division of Materials Research and Office of Multidisciplinary Activities in the Directorate for Mathematics and Physical Sciences, and by the Office of Integrative Activities.

Spatial and temporal variability are common across many areas of study ranging from physics to ecology. In all areas, it is important to understand dynamics across space: under what conditions are dynamics synchronous across space and when is there a lack of spatial coherence? Ecologists have struggled to understand spatial synchrony for over a century, in part because lack of synchrony often promotes persistence of populations. Within physics, studies of magnetic materials or of crystal structures have posed similar questions about the coherence of states across space. This project will explain how broad-scale synchrony can arise from local couplings by mapping relevant ecological models to an equilibrium model developed in physics. The interdisciplinary team of researchers has preliminary data establishing a correspondence between ecological non-equilibrium models and the equilibrium properties of physical models. Research will build on these preliminary results to confirm the presence of phase transitions for a wide variety of systems, thus providing ways to unify approaches for understanding the dynamics of synchrony. The primary tools will be computer simulations that are complemented by analytic approximations that provide understanding of transitions. This combination will both provide a deep understanding of synchrony in ecological systems that is not model specific, and produce new models of interest within physics, thus benefitting both disciplines.

This novel interdisciplinary project will contribute basic, new theory to the disparate fields of ecology and condensed matter physics by developing a basic understanding of the dynamics of synchrony at different spatial scales. Understanding of the emergence of spatially and temporally synchronous behavior in agroecological systems could have tremendous impact on effective management of plant and animal diseases, control of pests, agricultural strategies, and ultimately on food security. It is very rare that a theoretical project spanning two disparate disciplines has such potential to address questions of food security, providing novel ways to address a problem that will grow in importance with time. The researchers plan to train students in interdisciplinary approaches and will hold workshops both at the National Institute for Mathematical and Biological Synthesis and the Santa Fe Institute to provide broad dissemination of the approaches developed.

This proposal will support U.S. participation in the activities of the Mathematics for Planet Earth 2013 thematic program in Canada focusing on Models and Methods in Ecology, Epidemiology and Public Health. U.S. researchers and students will participate in ten workshops and three summer schools. The first workshop will be held at the Centre de recherches mathématiques in Montréal in February 2013 and is entitled "Models and Methods in Ecology and Epidemiology." Mathematical models have a long tradition in exploring dynamical aspects of ecology and epidemiology on a number of different temporal and spatial scales. While ecological and epidemiological applications are often studied separately for historical reasons, both fields are faced with similar challenges of model complexity, model-data fitting and accurate predictions. Recently, advances in data collection (e.g. GIS), availability of large-scale simulation tools (e.g. agent-based modeling), development of statistical tools to fit mechanistic models, and new mathematical techniques (e.g. multiscale methods) have highlighted the many commonalities between ecological and epidemiological models. Successful applications of these models to pressing issues in population and ecosystem health combine techniques and insights from all fields.

The main goal of the pan-Canadian thematic year on Models and Methods in Ecology, Epidemiology and Public Health is to tackle pressing and emerging challenges in population and ecosystem health, to stimulate cross-disciplinary research between all the disciplines involved and to foster tighter links between the research community, government agencies and policy makers, and to train a new generation of researchers in this priority research area. The wide range of topics includes questions of how global change will impact vector-borne diseases and biodiversity, how aquatic ecosystems can be managed sustainably, or how modeling and surveillance can be integrated for public health decision-making. All of these questions are very active areas of research around the world; and the Canadian mathematics community plays a leadership role. The purpose of this pan-Canadian program is to bring together the international community of researchers who work on these topics in a series of workshops and to foster exchange between the different disciplines involved, to discuss perspectives and directions for future advances in the field, including new models and methods. In addition, several summer schools are aimed to train the next generation of researchers in the most recent tools and techniques and enable them to build novel tools in the future in these research areas. The funds from this grant will allow promising junior researchers from a diverse set of backgrounds, including early career professors, postdoctoral fellows and graduate students, from the United States to participate in the workshops and summer schools of this program. Understanding the mechanisms and effects of ecosystem function, ecosystem service, disease transmission and disease spread rests on mathematical models on different spatio-temporal scales. Effective and efficient management and policy decisions are based on these insights. Advancing research into the required tools, techniques and applications will provide us with better understanding and guidance for policy makers and management.

The spread of an invasive species is a poorly understood ecological phenomenon, yet it is of great practical importance causing an estimated $120 billion in damages per year. Current theory largely considers the situation of a single species invading into a stable habitat. Those models are inadequate to address the realistic situation of invasive species interacting with competitor species as the invasion front moves across the landscape. They also do not incorporate the fact that habitats themselves can shift on the landscape as a result of climatic and other environmental changes. For example, rapid movement of habitats toward the poles and higher elevations is a contemporary, global phenomenon. This research project will develop new theory, backed by experiments with model species in the laboratory, to explain how species invasions are shaped by the presence of competitor species, and the situation of habitats shifting on the landscape. This work will advance ecological science by providing a stronger theoretical basis for projections of species range shifts driven by invasive species and climate, and provide models useful to land managers, public health officials, and conservation biologists concerned with the spread of invasive species. This project will provide hands on training and experience to biologists from undergraduate students to postdoctoral scholars, enabling them to become the leaders of the next generation of scientists tackling complex problems in biology.

Important new phenomena for range dynamics emerge when two or more species are considered, and especially given that at the edge of any species range, densities are low, stochasticity must play an important role. Stochastic models will be developed together with highly replicated, microcosm experiments using a flour beetle model system. The research will determine 1) how interactions with a resident species modify the range expansion of an invader and its effect on the resident; 2) how species interactions and stochasticity set species ranges in stationary heterogeneous environments; and 3) how species interactions, stochasticity, and moving environments set species ranges and alter spatial community structure.

Oceans span over 70% of the Earth and play critical roles in almost all facets of human well-being, including regulating climate, biodiversity, and feeding the world's growing population. A grand challenge for society is to improve the scientific understanding of natural and human impacts on marine ecosystems to ensure that the oceans continue to provide for generations to come. To overcome this challenge, a segment of our nation's workforce must address an unmet and growing demand for hypothesis-driven research to inform the decisions of federal and state resource management agencies. This National Science Foundation Research Traineeship (NRT) award to the University of California, Davis will train the next generation of marine scientists under a new paradigm that puts the policy focus on the front-end of the research and training enterprise as a means of building more effective links between the science and decisions on sustainable use of living marine resources. The project anticipates training 60 PhD students, including 30 funded trainees, from ecology, conservation biology, economics, geology, physiology, biogeochemistry, and oceanography.

There is growing appreciation that the disconnect between the scientific and policy communities is due to the scientific research questions not aligning with the information that policymakers need to make informed decisions, and to the researchers rarely having the wide-angle lens necessary to understand how their disciplinary research integrates with other science to address policy questions. The basis for the training program's paradigm is a novel causal chain model that extends from a policy goal to the different types of scientific information needed to measure the impacts of management decisions. The practice of working through a causal chain, coupled with fieldtrips to stakeholders, basecamps (week-long workshops with decision-makers and stakeholders organized around marine management issues), internships, short-term visiting scientists, research symposium, data-model integration training, and immersion in marine science and policy will provide trainees with a deeper understanding of how their own STEM research, founded in the primary perspective of a single discipline, fits into a policy process. Trainees will be recruited from a diversity of populations, with special attention to students from natural resource-dependent communities (e.g., tribal nations in Northern California, rural and remote coastal towns). Recruitment, mentoring, and professional development skills are woven throughout all of the elements of the training program, including research partnerships with tribal nations and direct engagement with resource-dependent communities via the fieldtrips and basecamps. Elements of the training program are also open to California State University (CSU) masters students through our novel Scholars Program in partnership with CSU's Council on Ocean Affairs and Technology (COAST) program. The NRT program will help shape the future curriculum of a new Marine Science PhD program at UC Davis.

The NSF Research Traineeship (NRT) Program is designed to encourage the development and implementation of bold, new potentially transformative models for STEM graduate education training. The Traineeship Track is dedicated to effective training of STEM graduate students in high priority interdisciplinary research areas, through comprehensive traineeship models that are innovative, evidence-based, and aligned with changing workforce and research needs.

This project will develop a novel mathematical approach for describing the dynamics of ecological communities at large spatial scales, a description of dynamics called metacommunities. From a mathematical standpoint, the project will start with relatively simple descriptions of interactions among species, such as competition and predation, at small spatial scales, coupled with descriptions of connectivity, the way species move between locations. The mathematical descriptions will then be expanded to include more detailed and realistic descriptions of interactions among species and underlying environmental changes. The models will be analyzed to determine both long-term behavior and dynamics. The mathematical models will then be used to answer important ecological questions focused on how changes in habitat quality and availability and connectivity between different habitats will affect the composition and dynamics of these metacommunities. This, in turn, will provide information about how human activities that affect habitats and connectivity will affect species composition and dynamics and can provide guidance for both conservation and restoration efforts.

The mathematical models of metacommunities used will be primarily phrased in discrete time with a time step of one year, both to reflect dynamics in seasonal environments and how data is gathered. The simplest models will focus only on species presence or absence and will be difference equations, so a relatively complete analytical treatment will be possible. Equilibria and their stability can be calculated. The more complex descriptions will all be phrased as integro-difference equations where time is discrete, but the state space is continuous. The underlying dependent variables will be density functions for the abundance of the species under consideration, and the kernels in the integro-difference equations will describe the underlying ecological dynamics. Initial analyses will be numerical with the expectation that analytic treatment of conditions for persistence and coexistence will be possible, building on recent mathematical work on integro-difference equations. To treat changing conditions through time, the kernels will be modified to include explicit time dependence. The mathematical analyses will then be used to answer the underlying ecological questions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

This research will use ideas from statistical physics to examine the transitions to synchrony (events operating in unison) across space in biological systems. Tools in physics developed primarily to explain how magnetism arises at large scale from alignment at small scale will be employed to develop detail-independent explanations for the emergence of synchrony. The work aims to determine general rules that govern the propagation of information or changes in biological systems from short-range interactions to large scales, with an emphasis on ecological systems. Phenomena in this category range from synchrony across space of oscillations in predator and prey systems to synchrony in dynamics of neural activity in the brain. Synchrony is strongly linked to extinction risk, which may either be beneficial (as in epidemic burnout) or detrimental (as for threatened species). Similarly, synchronous neural dynamics may have large implications for human health. This work addresses several fundamental questions in the life sciences: What are general rules that determine patterns of synchrony in identical biological oscillators with nearest-neighbor coupling? How do heterogeneities and system size affect the rules governing the appearance and maintenance of synchrony in coupled biological oscillators? How do correlations in randomly-determined effects across space or time affect the appearance and maintenance of synchrony in coupled biological oscillators? The project will involve junior researchers at the undergraduate, graduate, and postdoctoral levels. The investigators plan to organize an interdisciplinary workshop that will include leading and junior researchers in ecology and physics as well as other areas of biology.

This project aims to build upon previous research demonstrating that the transitions in the two-dimensional Ising model of theoretical physics map onto models of spatial population dynamics on a lattice and can be used to explain data for the yield of individual trees across space and time in a pistachio orchard. The goal of the project is to elucidate a detail-independent explanation for the synchrony across space that is prevalent at many scales of biological systems. However, real biological systems have significant heterogeneities, so this work aims both to build on extensions and modifications of the Ising model as well as to investigate other models. The work will depend on extensive simulations and analysis of models from statistical physics. The overall goal of finding detail-independent universal explanations of large-scale synchronous dynamics will advance understanding of ecological systems as well as a range of other biological systems.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

Science advances through coordinated developments in theory, experimentation, and observation. In the field of ecology, theoretical advances have repeatedly guided experiments and observation, resulting in a mature, predictive discipline. Theory has provided the basis for management of invasive species and pests, guided conservation efforts, improved fisheries management, and contributed to the effective management of human, livestock and wildlife diseases. New challenges posed by unprecedented rates of environmental change, the dominant effects of human activity on climate and the environment, and the massive amounts of data now available highlight the need for new ecological theory that is invigorated by novel approaches, new collaborations, and the integration across relevant sub-disciplines. This workshop engages researchers at diverse career stages, with different theoretical backgrounds and skills, and from different geographical and cultural backgrounds. New theoretical directions and collaborations developed during the workshop will guide future research. New theoretical paths will provide the foundation for training future generations of ecologists and our workforce, ensuring they have the requisite skills to tackle emerging problems. Theory directly and indirectly resulting from the workshop will accelerate the advancement of a discipline that lies at the heart of global problems such as food security, public health, environmental change, and resource limitation.

Workshop activities and discussions will identify key areas in ecology that need reinvigorated theory; establish the approaches needed to advance these theories; identify emergent areas in need of new theory; and develop an agenda for advancing ecological theory. Initial workshop discussions tackle topics including theory that spans levels of ecological organization; theory of uncertainty, ecological variation, and the limits of prediction; and the role of transients and non-stationarity. Discussions in large and small groups will debate and determine the theoretical approaches needed to advance these and other critical contemporary ecological questions. Groups will determine when entirely new theory is needed and when hybridization of existing approaches may address a challenge. Simultaneously, entirely new areas in need of theory will emerge from group discussions. These may include disciplines that share common challenges, forging new or strengthening existing collaborations. Results will appear as publications in leading journals.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

Microorganisms inhabit almost every imaginable environment on Earth, playing integral roles in various ecosystem processes. Microbiomes, collections of microbes in specific habitats, change significantly from place to place and over time. Although rapid advances in genetic technologies have revolutionized our understanding of microbiomes, the rules governing microbiome function are yet to be learned. Research to understand these mechanisms in natural ecosystems can be difficult due to their open nature and extremely high diversity. Adequately capturing this complexity results in a need for extremely large datasets over long time scales. By contrast to open natural systems, engineered anaerobic digesters (ADs) are enclosed systems with controlled environments. AD systems are used globally for waste treatment and represent the largest engineering application of microbial biotechnology. As such, AD systems provide an ideal model system for understanding the rules governing microbiome function because of their microbial diversity, environmental significance, and the ability to control the environment. The goal of this research is to identify the rules controlling microbiome dynamics in ADs that can be used for other microbial ecosystems. This study will provide fundamental knowledge critical to predicting microbiome behavior in engineered and natural microbial ecosystems. Benefits to society resulting from this project will include improved science-based management of microbial ecosystems in both engineered and natural systems. Additional benefits include the training of the next generation of microbiome professionals with broad interdisciplinary expertise and skills to understand and control microbiome dynamics.

The overall goal of this project is to identify general ecological rules governing microbiome dynamics in different ecosystems with a focus on ADs as model microbial ecosystems. This will be achieved by examining whether general rules exist for species-area relationships as are known to exist in ecology. The four fundamental ecological processes of selection, dispersal, diversification, and drift will serve as a general theory to explain how microbial communities in microbiomes are assembled across space and time. Specific research objectives to achieve this goal include the following tasks: 1) Laboratory AD systems will be used to determine the short- (< 1 year) and long-term (>15 years) stability of microbiome biodiversity, structure, and function in responses to various environmental changes; 2) Advanced statistical tools will be used to elucidate underlying community assembly mechanisms in AD systems; 3) Novel mathematical approaches will be developed to detect the transient dynamics of AD microbiomes in response to environmental perturbations; and 4) Novel metagenomics-enabled anaerobic digestion models will be developed to provide effective frameworks for predicting and manipulating the dynamics of AD systems for desired functions. Resulting rules describing AD microbiome dynamics will be tested for their utility in describing other microbiomes from a variety of habitats including soils, marine, lacustrine, groundwater, gut, and other engineered systems. Cross-disciplinary training and workforce development will be achieved through research, training, and workshops to meet future needs for microbiome professionals.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.