Claudia Neuhauser - US grants

The Department of Mathematics at the University of Southern California will purchase multiprocessing computation servers which will be dedicated to support research in the mathematical sciences. The equipment will be used for several research projects, including in particular: simulating biological neural networks, computing homological invariants of moduli space, interacting particle systems as models of catalytic surface reactions, nonparametric estimation of probability distributions from incomplete data.

There are a number of problems to be studied. Three problems concern percolation. The cluster size distribution and closely related aspects of the geometry of finite clusters will be examined for a continuous model in which the probability of a bond being occupied is a function of its length; the spread of th distribution of the passage time in first passage percolation will be studied; and finite clusters in the Fortuin-Kastelyn random cluster model will be examined and the results applied to the Ising model conditioned to be less magnetized thatn is typical. Research in interacting particle systems and cellular automata will center around four model which have applications in physics and biology: a catalytic surface reaction model, a threshold forest fire model, a cancellative system with mass extinction, and a model for the even-odd theory of food chains. Results to be sought concern the asymptotic behavior of these model and phase transitions. The investigator will study systems in which small-scale randomness produces large-scale phenomena which are essentially nonrandom. Such systems have long been an object of study in mathematical physics, and more recently also in biology. A standard physical example is a magnet, in which individual iron atoms have randomly aligned magnetic poles, with a slight tendency for nearby atoms to have parallel alignments. Depending on the temperature, this tendency may or may not be reflected in a large-scale nonrandom amount of magnetization of the chunk of iron.

9403644: Neuhauser Abstract. The first two parts of the research concern the investigation of several multispecies models from ecology and population biology. These models are formulated as complex spatial systems on the integer lattice in which each site is in one of a finite number of states indicating whether a certain species is present on that site. These systems evolve over time according to non-deterministic local rules which describe the dynamics of each species and how they interact with each other in this spatial environment. Models to be considered include host-parasitoid associations and a model for the study of genetic diversity of a species in a subdivided habitat in which local extinctions are frequent. These investigations are theoretical and experimental (computer simulations). The main goal is to study how the spatial component affects survival/coexistence of the species involved. In the third part, problems concerning DNA sequence comparisons are addressed. One project is to construct a statistical test that takes all types of mutations into account in order to assess the statistical significance of such comparisons. The other project is to investigate what happens when the sequences involved in the comparisons are very different. Current tests always assume that the frequencies with which letters in the sequences appear, are not too different. In the first two parts, the investigator will study several multispecies models from ecology and population biology. These models are formulated as complex spatial systems that evolve in time according to non-deterministic local rules. Examples include host-parasitoid associations and models for the study of genetic diversity of a species in a subdivided habitat in which local extinctions are frequent. Some of the proposed work is done in collaboration with researchers from the biology department at the University of Wisconsin - Madison and the USDA Forest Service. The main goal is to st udy ho w the spatial component affects survival/coexistence. In the third part, problems arising in DNA sequence comparisons are addressed. Such comparisons have revealed some unexpected sequence similarities and there is the need for statistical tests to assess statistical significance to such comparisons. Currently, there is no test available that takes all types of mutations into account that occur in DNA sequences. Furthermore, all available tests require the composition of the sequences (i.e., the frequencies with which the letters in the sequences appear) not to be too different. The proposed research addresses both problems.

9703694 Neuhauser The projects are divided into two primary research areas, the theoretical investigation of ecological models in the context of interacting particle systems, and genealogical processes in theoretical population genetics. Interacting particle systems are continuous time Markov processes on the integer lattice in which each site is in one of several states. Local rules determine the dynamics of the systems. They provide an ideal framework to investigate the role of the spatial structure in models in ecology. In joint work with Dr. Stephen Pacala (Princeton University) the principal investigator will consider the consequences of spatial structure in classical models in ecology, such as the Lotka-Volterra model of interspecific competition. The nonspatial version is very well understood. Including a spatial component will likely yield new phenomena. In joint work with Dr. Stephen Krone (University of Idaho) the principal investigator will study the spread of a population in a heterogeneous environment by using the two-dimensional contact process in a random environment. In theoretical population genetics, Dr. Neuhauser plans to study genealogies under various selection schemes, for instance, frequency-dependent selection and overdominant selection. It is planned to rigorously derive genealogies and to use them to investigate sample properties in both spatial and nonspatial settings. The causes and effects of spatial structure have long been central topics in population and community ecology. In joint work with Dr. Stephen Pacala (Princeton University) the principal investigator will study the effects of competition on the spatial structure of communities. Local interactions and competition in spatial communities can cause clumping of individuals of the same species which can lead to a reduction in biodiversity. In joint work with Dr. Stephen Krone (University of Idaho) the principal investigator will consider the spread of populations in heterogeneous environments and how habi tat destruction and subsequent restoration affects the ability of populations to recover. Genealogies are an important tool in population genetics to investigate properties of samples of genes. Dr. Neuhauser plans to investigate frequency-dependent and overdominant selection. Both modes of selection are known to be able to maintain a high degree of genetic diversity. Little is known about genealogies under such selection schemes which are important, for instance, in plant breeding systems or in the major histocompatibility complex.

Pacala
9807755
The primary goal of this project is to interpret
analytically the effects of spatial environmental heterogeneity
on the community dynamics and biodiversity of ecological systems.
Simulation models and experimental studies have convincingly
demonstrated the importance of endogenous and exogenous spatial
heterogeneity, such as variation in resource supply rate or
topography, to the coexistence and the maintenance of diversity
in ecological communities. However, both mathematicians and
ecologists still lack analytic understanding of the mechanisms
operating, particularly in fully spatial, stochastic
environments. The investigators extend existing analyses of the
effects of heterogeneity by using a wide range of models (from
metapopulation models to interacting particle systems and point
processes); they develop moment approximations, which express
spatial population dynamics in terms of mean densities and
covariances, to simplify the analysis while preserving both
exogenous and endogenous heterogeneity. The study uses moment
approximations, and more standard techniques, to analyze the
effects of environmental heterogeneity, endogenous heterogeneity,
and their interaction on population dynamics and competitive
outcomes in ecological models of plant and marine intertidal
communities.
Field ecologists have long known that small-scale
variability in environmental factors such as soils or temperature
can affect the structure and diversity of ecological communities
--- which and how many species can live together in a region.
Ecological modellers, however, have often found simple
explanations for small-scale spatial patterns of biodiversity,
caused by interactions between plants or animals (such as
competition or predation), that ignore environmental variability.
Computer simulation models have recently gone a long way toward
reconciling these two camps, but (1) simulations show that
patterns occur, but do not always explain why; and (2) even
powerful computers have limits (it could be foolhardy, for
example, to attempt to simulate every tree on a continent in
order to predict the effects of global climate change). This
study develops simple mathematical models that combine spatial
variability caused by interactions between organisms with spatial
variability caused by the environment to explore how these two
kinds of variability affect the structure and diversity of
communities. The results from these simple models will eventually
show how to build more complex and realistic models that can
predict patterns of biodiversity and ecosystem productivity, and
will provide a much more general understanding of how variability
in the environment leads to diversity in ecological communities.

Perturbation of biological communities, exemplified by habitat loss and the invasion of novel taxa is well documented. Economic development, new technologies, and population pressure have escalated the scale, frequency, and severity of such perturbations. As a result, evolutionary and ecological dynamics may be driven so far from their equilibria that the linear approximations used for understanding and predicting consequences of subtle perturbations are inappropriate and probably misleading. To elucidate the consequences of massive perturbations in biological communities, a spatially explicit model whose dynamics are complicated by ecological, genetic, and historical factors, is proposed. Studies on (i) corn smut and corn, (ii) rhizobia associated with common bean, (iii) corn borer and genetically modified Bt and non-Bt corn, and (iv) prairie plants and their pollinators provide the empirical basis that are framed by the general model of interactions between hosts and their associates. A hierarchy of models at different spatial scales will determine the evolutionary and ecological role of different factors at the different spatial scales. In addition, statistical tools are used to develop and analyze data of genetic diversity under non-equilibrium conditions using both temporal and spatial information.

Understanding the complex interactions between the members of communities undergoing such massive perturbations and their evolutionary and ecological consequences requires the integration of empirical work and mathematical models across temporal and spatial scales. The empirical studies represent examples of large perturbations that occurred either in the past (as in (i) and (ii)) or in the present (as in (iii) and (iv)). The historical studies allow testing the predictability of the theoretical models to assess the accuracy of the predictions for the consequences of massive perturbations that occur presently. The perturbations consist (1) of the introduction of novel organisms or (2) of habitat destruction, both at a large spatial scale: Corn and beans were moved from South and Central America to North America in the past carrying with them microorganism that, after introduction, competed with already present microorganisms. Bt corn is currently being introduced in North America as a control mechanism for the European corn borer, a devastating pest of corn; Bt corn is introduced at a large spatial scale that introduces large selection pressure on the evolution of resistance to Bt corn, which will make this control mechanism ineffective. Habitat destruction is an ongoing process affecting nearly every natural community in North America and in other parts of the world leading to loss in biodiversity. The goal is to predict the evolutionary and ecological consequences of large range expansions and contractions of plants on their associated biological communities in order to better manage natural and agricultural systems.

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Neuhauser
This research of Dr. Neuhauser covers three areas: (1) community ecology, (2) evolutionary ecology, and (3) population genetics. Mathematical tools will be developed to address questions of (i) the causes and effects of spatial structure on plant communities, in particular the question of how explicit space affects diversity and stability of plant communities; (ii) the evolution of resistance to insecticide and the spread of resistant alleles, in particular for a genetically engineered crop that expresses chemicals that are toxic to its insect pests; (iii) how mating structure affects spatial structuring in gynodioecious plants; and (iv) how temporal variability affects genealogies. The spatial processes will be modeled using the framework of interacting particle systems, which are continuous time Markov processes on the infinite D dimensional lattice, characterized by local interactions between sites. The genealogical processes will be investigated using the ancestral selection graph as a modeling framework.
The motivation for the proposed research is to gain a better understanding of how spatial and temporal factors affect the outcome of interactions in plant communities. Most of ecological and agricultural modeling traditionally did not take into account effects of explicit space due to the difficulties encountered in the analysis of such models. More recently, tools have been developed that allow rigorous analysis of spatial models. This research of Dr. Neuhauser is intended to shed light on how space affects plant communities; this is important in understanding the structure of both natural and managed (agricultural) communities. Her results should help devise management strategies for maintaining biodiversity in natural communities and for slowing the spread of resistance genes in crop systems of genetically engineered crop.

The investigators organize the Gordon Research Conference on
Theoretical Biology and Biomathematics. The conference has nine
formal sessions, each consisting of 2-3 oral presentations with
an introduction by a leading scientist in the area, and two
afternoon poster sessions. A wide variety of topics, ranging
from global environmental models to mathematical neuroscience to
genetic regulation networks, are represented. The unifying theme
of the conference is quantitative modeling of complex biological
networks. Invited speakers are selected on the basis of their
expertise in the respective areas, at the same time emphasizing
gender balance, minority representation, and incorporating
promising junior researchers.
The primary goal of this conference is to bring together
established and young investigators from the field of
quantitative biology to share their approaches and progress and
to discuss the perspectives. Such a multidisciplinary conference
is very important for identifying challenges in biology,
biotechnology, and medicine that require quantitative modeling
and computational approach. Moreover, the participation of
students and postdocs helps to increase the number of people
working in areas of quantitative biology.

Lakes and oceans are important regions on the Earth's surface in terms of carbon storage. One of the important regulators of the ability of aquatic systems to store carbon is the balance between plant and decomposer (bacterial) growth. This balance is strongly affected by the availability of nutrients in the water. Plant diversity is known to play an important role in the ability of ecosystems to produce biomass in ecosystems but little is known of the importance of bacterial diversity in decomposing the material produced by plants. This study will examine the importance of bacterial diversity to nutrient cycling and organic matter production in lakes in the north-central United States. Recent studies suggest that bacterial communities in lakes may not be particularly "species rich" but there is considerable variability among different lakes. Lakes that are species-rich are hypothesized to recycle nutrients very efficiently, and perhaps store carbon very inefficiently, whereas, species-poor lakes should recycle nutrient inefficiently while storing carbon very efficiently. These hypotheses will be examined by studying the behavior of both individual strains of bacteria isolated from lakes in the laboratory and intact communities of bacteria. Strains and intact communities will be characterized with respect to their ability to recycle nutrients and the importance of community diversity to nutrient recycling will be evaluated and modeled mathematically.
This study will promote teaching and training goals including: working with a middle school math teacher, high school science fair students, training of graduate students, and a post-doctoral fellow. The PIs will participate in summer undergraduate research programs focused on minority students.

Organisms that cause disease often possess features that make evolutionary change likely over relatively short periods of time. The rise of multi-drug resistant bacteria and the switching of hosts (e.g., diseases shifting from animals to humans) are particularly notable examples. Despite the importance of evolutionary change, most epidemiological models assume that pathogens do not change. This project combines mathematical and experimental approaches to study the evolutionary dynamics of pathogens in subdivided populations (i.e., metapopulations). Using a model host-pathogen system (bacteria as hosts and viruses infecting bacteria as pathogens'), the pattern of host/pathogen movement between a large set of subpopulations will be experimentally manipulated and evolution of the pathogen monitored. Pairing these experiments with empirically-based mathematical models will allow an assessment of how the structure of the host-pathogen population influences the evolution of the pathogen. In particular, virulence in the pathogen (i.e., how quickly it kills its host) will be the focus of the research, as the evolution of virulence may depend intimately on the manner by which hosts contact one another.

This work has a range of broader impacts. One goal is the use of this system as an educational tool for postdoctoral, graduate and undergraduate students. In addition, the experimental system will be adapted to serve as a teaching tool within upper-level undergraduate courses. Underrepresented minorities and women will be actively recruited for involvement in the proposed research. Finally, the proposed work may highlight how subtle aspects of population structure could favor different evolutionary paths in human pathogens. Such information would carry important implications for public health management.

This research aims to improve the efficiency, accuracy, and usability of online systems supporting citizen science, in which communities organized around serious scientific research projects combine the contributions of amateurs and professionals. In order to respond most efficiently to the increasing data deluge across multiple domains, citizen science platforms need to be more dynamic and complex - incorporating intelligent task assignment and machine learning strategies. Systems that make use of both human and machine intelligence are of interest to scientists from a wide range of disciplines. Whether viewed as social machines or as active learning systems in which progressive input from humans improves machine learning, these hybrid systems exhibit complex behavior which needs to be understood for effective system design. For example, machine learning researchers have concentrated on using the large training sets produced by citizen science projects in order to train algorithms that are later applied to a full dataset. Yet this serial processing may not be the most efficient use of the human or machine effort. The main research goal of this project is to investigate how the overall efficiency of the combined human-machine system is impacted by the separate components and their related properties and what the implications are for either human or machine classifiers or both. This process will test the hypothesis that improved overall efficiency will actually reduce the load on expert human classifiers instead of, as currently required, needing larger expert training sets for machines.

This project will investigate the dynamic combination of human and machine classifiers, gaining for the first time knowledge of how load can be optimally shared in a real, flexible citizen science platform. This research effort will be supported by building and deploying software modules on the existing Zooniverse infrastructure, the world-leading platform for online citizen science. It will (1) carry out efficient and dynamic task assignment, distinguishing in near-real time between experienced and inexperienced, and between skilled and less skilled classifiers; and (2) combine human and machine classifications dynamically, periodically training automatic classification routines on the increasing volume of training data produced by volunteers. This new software will then be utilized in a novel "cascade filtering" mode that reduces complex classification problems into a series of single binary tasks. The software developed in this project will provide domain scientists and social machine researchers who wish to exploit the new infrastructure with a fully flexible suite of functions appropriate to the needs defined by their specific problems.

The University of Wisconsin proposes to build a prototype for an online, open Crowdsourcing Innovation Platform to develop roadmaps for the solution of pressing societal issues through articulation of long-term goals and germination of transformative research ideas and questions. A diverse group of doctoral students and postdocs will participate in a year-long workshop course, further developing their skills gained in a Summer Institute, learning about how the U.S. sets research priorities, and developing an innovative environment. In this environment, problem definition and rapid prototyping alternate, and groups of researchers and stakeholders constructively critique approaches. The platform will be a ?living network? that links ideas and people in a dynamic way to keep people intellectually and socially engaged. Through the process, a complex problem will continue to be divided into smaller sub-problems until they are amenable to solutions.

The next generation (the 'millennials') has already embraced that the future of scientific research will need to be more open, accessible, and democratic and that solutions to the pressing societal issues will come from making many small contributions to big projects collaboratively. This pilot project tests the hypothesis that crowdsourcing pressing societal problems to the global research community and stakeholders (i) meshes well with the value system of the next generation of researchers; (ii) lets us look at the problems simultaneously from different angles, and thus, in essence, increases the number of potential pathways to solutions, and (iii) increases the willingness to take risks and pursue novel research paths as large, complex problems are subdivided into smaller, more manageable problems by a group connected within a social network. If successful, it will provide a novel way to find solutions to the pressing societal problems of today's society. Additionally, through jointly exploring problem posing, the teams will gain confidence and the skills to tackle complex problems and uncover barriers to collaborating on complex, interdisciplinary problems that are of national and international importance. The potential for scalability and the transferability of this approach into other domains could contribute to a long-term change in how the research community interacts with itself and stakeholders to build pathways to solutions that respect social and behavioral constraints.