2011 Summer Graduate Program

(July 25,2011 - August 5,2011 )

Organizers


Fred Guichard
Department of Biology, McGill University
Suzanne Lenhart
Applied Mathematics, Instituto de Matematica, Estatistica e Computacao Cientifica
Yuan Lou
Department of Mathematics, The Ohio State University
Libby Marschall
Evolution, Ecology and Organismal Biology, The Ohio State University

Joint 2011 MBI-NIMBioS-CAMBAM Summer Graduate Program Mathematical Ecology and Evolution The 2011 Summer Graduate Program will be held at the Mathematical Biosciences Institute from July 25 to August 5, 2011. Summer school topics will include infectious disease, resource management, invasive species and evolution biology. Members of the organizing committee are: Fred Guichard (McGill University); Suzanne Lenhart (University of Tennessee at Knoxville); Yuan Lou (Ohio State University); and Libby Marschall (Ohio State University).

The Program will feature a number of researchers from the mathematical and biological sciences, each of them will work with the students for one day. The speakers will lecture in the mornings, followed by afternoon computer and analysis activity including work on projects. During the summer program each student is expected to work on one research project in a team of four or five participants. The following is a partial list of speakers:

* Linda Allen and Ed Allen, Texas Tech

* Chris Cosner, University of Miami

* Fred Guichard, McGill University

* Ian Hamilton, Ohio State University

* Alan Hastings, University of California at Davis

* Suzanne Lenhart, University of Tennessee at Knoxville

* Lea Popovic, Concordia University

* Joe Tien, Ohio State University

Graduate students from the mathematical, physical and life sciences are encouraged to apply. Application link will be posted soon. You will be asked to submit the following three items:

1. CV

2. Statement of your research interests (up to one page).

3. At least one letter of recommendation, addressing your academic background and suitability for the program.

Applications received by March 15, 2011 will receive full consideration. The Joint 2011 MBI-NIMBioS-CAMBAM Summer Graduate Program is a satellite summer school of ICIAM 2011, Vancouver BC, July 18-22, 2011 (http://www.iciam2011.com/).

Accepted Speakers

Linda Allen
Department of Mathematics and Statistics, Texas Tech University
Edward Allen
Mathematics and Statistics, Texas Tech University
Chris Cosner
Department of Mathematics, University of Miami
Lea Popovic
Dept of Mathematics and Statistics, Concordia University
Robin Snyder
Biology, Case Western Reserve University
Monday, July 25, 2011
Time Session
09:00 AM
10:00 AM
- The Alan Hastings Project Teacups, Transients, and Regime Shifts
(no description available)
10:30 AM
12:00 PM
- The Alan Hastings Project Teacups, Transients, and Regime Shifts
(no description available)
02:00 PM
05:00 PM
- Computer Lab: Matlab
Richard Gejji demostrates Matlab
Tuesday, July 26, 2011
Time Session
09:00 AM
10:00 AM
- Modeling the Cholera Outbreak in Haiti: A Multi-patch Disease Model
(no description available)
10:30 AM
12:00 PM
- Modeling the Cholera Outbreak in Haiti: A Multi-patch Disease Model
(no description available)
Wednesday, July 27, 2011
Time Session
09:00 AM
10:00 AM
Robin Snyder - 2011 Summer Graduate Lecture
Transfer functions are a useful tool for analyzing the effects of moderate spatial and/or temporal variation in model parameters. By the end of the day, you should have a grasp of basic Fourier analysis and be able to "read" transfer functions to tell how changes in parameters amplify or damp population response to variation and increase or decrease any response lags or spatial shifts. If there is time, we will consider stochastic environments, defined only by their spatial and/or temporal autocorrelation functions.
10:00 AM
12:00 PM
Robin Snyder - 2011 Summer Graduate Lecture
Transfer functions are a useful tool for analyzing the effects of moderate spatial and/or temporal variation in model parameters. By the end of the day, you should have a grasp of basic Fourier analysis and be able to "read" transfer functions to tell how changes in parameters amplify or damp population response to variation and increase or decrease any response lags or spatial shifts. If there is time, we will consider stochastic environments, defined only by their spatial and/or temporal autocorrelation functions.
Thursday, July 28, 2011
Time Session
09:00 AM
10:00 AM
Chris Cosner - Numerical Exploration to a System w Reaction, Diffusion, and Advection
(no description available)
10:30 AM
12:00 PM
Chris Cosner - Numerical Exploration to a System w Reaction, Diffusion, and Advection
(no description available)
Friday, July 29, 2011
Time Session
09:00 AM
10:00 AM
Suzanne Lenhart - Optimal Strategy for Controlling the Severity of Wildlife Disease Epidemics Due to Harvesting
(no description available)
02:00 PM
05:30 PM
Suzanne Lenhart - Optimal Strategy for Controlling the Severity of Wildlife Disease Epidemics Due to Harvesting
(no description available)
Saturday, July 30, 2011
Time Session
09:00 AM
10:00 AM
- Live Together or Eat Alone
(no description available)
10:30 PM
12:00 PM
- Live Together or Eat Alone
(no description available)
Sunday, July 31, 2011
Time Session
Monday, August 1, 2011
Time Session
09:00 AM
10:00 AM
Edward Allen - Deterministic and Stochastic Models for Multi-Patch SIS Epidemics
(no description available)
10:30 AM
12:00 PM
Linda Allen - Deterministic and Stochastic Models for Multi-Patch SIS Epidemics
(no description available)
Tuesday, August 2, 2011
Time Session
09:00 AM
10:00 AM
Lea Popovic - 2011 Summer Graduate Lecture
Macroevolution is the study of evolution or biodiversity on a long time scale, in other words, the evolutionary history of speciations and extinctions. In order to incorporate the stochastic effects of evolutionary events, one often uses branching models that generate the new speciation events and the extinction of species. Mathematical models used to describe these events are branching processes, in particular birth and death processes. The ultimate goal of using mathematical models for macroevolution is to identify which features of the observed data may have arisen by chance and which require a biological explanation.

In this lecture we will cover the basics of stochastic processes needed for such models, and describe the distribution of various quantities that will help us make a correspondence between these models and data. In addition to the one dimensional population size process, we will also discuss the more complicated aspects of phylogenetic tree structures, such as tree shape, generated by such models. We will begin with a review on birth and death processes and branching processes in general. We will discuss the random trees generated by these models and discuss various relevant statistics. Finally, if time permits, we will conclude with a discussion of hierarchical models on random trees that describe the grouping of species trees into trees of genera, families, etc.
10:30 AM
12:00 PM
Lea Popovic - 2011 Summer Graduate Lecture
Macroevolution is the study of evolution or biodiversity on a long time scale, in other words, the evolutionary history of speciations and extinctions. In order to incorporate the stochastic effects of evolutionary events, one often uses branching models that generate the new speciation events and the extinction of species. Mathematical models used to describe these events are branching processes, in particular birth and death processes. The ultimate goal of using mathematical models for macroevolution is to identify which features of the observed data may have arisen by chance and which require a biological explanation.

In this lecture we will cover the basics of stochastic processes needed for such models, and describe the distribution of various quantities that will help us make a correspondence between these models and data. In addition to the one dimensional population size process, we will also discuss the more complicated aspects of phylogenetic tree structures, such as tree shape, generated by such models. We will begin with a review on birth and death processes and branching processes in general. We will discuss the random trees generated by these models and discuss various relevant statistics. Finally, if time permits, we will conclude with a discussion of hierarchical models on random trees that describe the grouping of species trees into trees of genera, families, etc.
02:00 PM
05:30 PM
Lea Popovic - 2011 Summer Graduate Lecture
Macroevolution is the study of evolution or biodiversity on a long time scale, in other words, the evolutionary history of speciations and extinctions. In order to incorporate the stochastic effects of evolutionary events, one often uses branching models that generate the new speciation events and the extinction of species. Mathematical models used to describe these events are branching processes, in particular birth and death processes. The ultimate goal of using mathematical models for macroevolution is to identify which features of the observed data may have arisen by chance and which require a biological explanation.

In this lecture we will cover the basics of stochastic processes needed for such models, and describe the distribution of various quantities that will help us make a correspondence between these models and data. In addition to the one dimensional population size process, we will also discuss the more complicated aspects of phylogenetic tree structures, such as tree shape, generated by such models. We will begin with a review on birth and death processes and branching processes in general. We will discuss the random trees generated by these models and discuss various relevant statistics. Finally, if time permits, we will conclude with a discussion of hierarchical models on random trees that describe the grouping of species trees into trees of genera, families, etc.
Wednesday, August 3, 2011
Time Session
09:00 AM
10:00 AM
Fred Guichard - Spatial is Special: Coupling and Intraguild Predation
(no description available)
10:30 AM
12:00 PM
Fred Guichard - Spatial is Special: Coupling and Intraguild Predation
(no description available)
Thursday, August 4, 2011
Time Session
Friday, August 5, 2011
Time Session
09:00 AM
09:20 AM
, Leah Campbell, Steven Fassino, Kyle Frank, Shishi Luo, Rachel Taylor, Michael Kelly - Modeling the Cholera Outbreak in Haiti: A Multi-patch Disease Model
(no description available)
09:25 AM
09:45 AM
Suzanne Lenhart, Md. Haider Ali Biswas, Suzanne Doig, Moussa Doumbia, Wenrui Hao, Nianpeng Li, Fang Yu - Optimal Strategy for Controlling the Severity of Wildlife Disease Epidemics Due to Harvesting
(no description available)
09:50 AM
10:10 AM
Chris Cosner, Kanadpriya Basu, Ting Gao, Yen Ting Lin, Audrey Smith - Numerical Exploration to a System w Reaction, Diffusion, and Advection
(no description available)
10:15 AM
10:35 AM
Linda Allen, Edward Allen, Noah Brostoff, Lixian Chen, Glenn Lahodny, Marco Martinez, Samantha Tracht, Ilker Tunc - Deterministic and Stochastic Models for Multi-Patch SIS Epidemics
(no description available)
10:40 AM
11:00 AM
, Qianqian Ma, Andrew Bate, Theodore Galanthay, Lee Lerner - The Alan Hastings Project Teacups, Transients, and Regime Shifts
(no description available)
11:25 AM
11:45 AM
Fred Guichard, Shanshan Chen, Samuel Discua, Monica Granados, Justin Marleau, Holly Moeller, Eric Pedersen - Spatial is Special: Coupling and Intraguild Predation
(no description available)
12:15 PM
12:35 PM
, Fatih Olmez, Alicia Prieto Langarica, Oyita Udiani, Evan Lancaster - Live Together or Eat Alone
(no description available)
Name Email Affiliation
Allen, Linda linda.j.allen@ttu.edu Department of Mathematics and Statistics, Texas Tech University
Allen, Edward edward.allen@ttu.edu Mathematics and Statistics, Texas Tech University
Basu, Kanadpriya basuk@mailbox.sc.edu Mathematics, University of South Carolina
Bate, Andrew amb28@bath.ac.uk Department of Mathematical Sciences, University of Bath
Biswas, Md. Haider Ali mhabiswas@yahoo.com Mathematics Discipline, Khulna University, Khulna, Bangladesh
Brostoff, Noah NaBrostoff@gmail.com math bio, The Ohio State University
Bulut, Ummugul gul.bulut@ttu.edu Mathematics and statistics, Texas Tech University
Campbell, Leah campbell@math.ohio-state.edu Mathematics, The Ohio State University
Carrillo-Rubio, Eduardo ec278@cornell.edu Natural Resources, Cornell University
Chen, Shanshan chenshanshan221@gmail.com Mathematics, College of William and Mary
Chen, Lixian chen_lix@hotmail.com Department of Mathematics, California State University, San Marcos
Cook, Geoffrey geoffrey.cook@mail.mcgill.ca Biology, McGill University
Cosner, Chris gcc@math.miami.edu Department of Mathematics, University of Miami
Discua, Samuel discua.1@osu.edu Entomology, OSU-OARDC
Doig, Suzanne s.doig.1@research.gla.ac.uk Mathematics and Statistics, University of Glasgow
Doucet Beaupré, Philippe philippe.doucet-beaupre@mail.mcgill.ca Department of Biology, McGill University
Doumbia, Moussa doumbiassa@yahoo.fr Dept. of Mathematics, Howard University
Fassino, Steven sfassino@utk.edu Mathematics, University of Tennessee
Frank, Kyle frank@math.ohio-state.edu Mathematics, The Ohio State University
Galanthay, Theodore theodore.galanthay@colorado.edu Applied Mathematics, University of Colorado
Gao, Ting tgao5@iit.edu Applied Math, Illinois Institute of Technology
Granados, Monica monica.granados@mail.mcgill.ca Department of Biology, McGill University
Guichard, Fred fred.guichard@mcgill.ca Department of Biology, McGill University
Hao, Wenrui whao@nd.edu Department of Applied and Computational Mathematics and Statistics, University of Notre Dame
Kelly, Michael mkelly14@utk.edu Mathematics, University of Tennessee
Kraakmo, Kristina KKraakmo@yahoo.com Mathematics, University of Central Florida
Kramer, Sean kramersj@clarkson.edu Mathematics and Computer Sciences, Clarkson University
Lahodny, Glenn glenn.lahodny@ttu.edu Mathematics & Statistics, Texas Tech University
Lancaster, Evan lancaster@math.utk.edu Mathematics, University of Tennessee
Lerner, Lee lee.w.lerner-1@ou.edu Department of Mathematics, University of Oklahoma
Li, Nianpeng sylnp@hotmail.com Department of Mathematics, Howard University
Lin, Yen Ting yentingl@umich.edu Physics, University of Michigan
Lundy, Eric lundy.29@osu.edu The Ohio State University
Luo, Shishi szl@math.duke.edu Mathematics, Duke University
Ma, Qianqian maqian12@uga.edu Department of biological and agricultural engineering, University of Georgia
Marleau, Justin justin.marleau@mail.mcgill.ca Biology, McGill University
Martinez, Marco mmarti52@utk.edu Mathematics, University of Tennessee
Moeller, Holly hollyvm@alum.mit.edu Biology, Stanford University
Olmez, Fatih folmez@gmail.com Mathematics, The Ohio State University
Patra, Pintu pintu.patra@mpikg.mpg.de Theory & Bio-Systems, Max Planck Institute of Colloids and Interfaces
Pedersen, Eric eric.pedersen@mail.mcgill.ca Biology, McGill University
Popovic, Lea lpopovic@mathstat.concordia.ca Dept of Mathematics and Statistics, Concordia University
Prieto Langarica, Alicia alicia.prietolangarica@mavs.uta.edu Mathematics, University of Texas
Rivas, Mariolys mariolysrivas07@gmail.com Mathematics., Concordia University.
Smith, Audrey audrey.smith@aggiemail.usu.edu Mathematics, Utah State University
Snyder, Robin res29@case.edu Biology, Case Western Reserve University
Taylor, Rachel rat3@hw.ac.uk Mathematics, Heriot-Watt University
Tracht, Samantha samantha.tracht@gmail.com Mathematics, University of Tennessee
Tunc, Ilker itunc@email.wm.edu Applied Science Department, College of William and Mary
Udiani, Oyita udiani.1@osu.edu Mathematics, The Ohio State University
Yu, Fang yufang77@gmail.com Math & Stats department, University of New Brunswick
Deterministic and Stochastic Models for Multi-Patch SIS Epidemics
(no description available)
Deterministic and Stochastic Models for Multi-Patch SIS Epidemics
(no description available)
2011 Summer Graduate Lecture
Stochastic differential equations are introduced and some of their properties are described. Equivalence of SDE systems is explained. Commonly used numerical proce- dures are discussed for computationally solving systems of stochastic differential equations. A procedure is described for deriving stochastic differential equation (SDEs) from associated discrete stochastic models for randomly-varying problems in biology. The SDEs are derived from basic principles, i.e., from the changes in the system which occur in a small time interval. In the derivation procedure, a discrete stochastic model is rst constructed. As the time interval decreases, the discrete stochastic model leads to a system of It^o stochastic differential equations. Several examples illustrate the procedure. In particular, stochastic differential equations are derived for predator- prey, competition, and epidemic problems. In addition, for certain problems such as a size-structured population, it is shown how stochastic partial differential equations can be derived through replacing Wiener processes in the SDE system with appropriate Brownian sheets.
2011 Summer Graduate Lecture: Mathematical Modeling of Infectious Diseases: Deterministic and Stochastic Models
A brief introduction is presented to basic stochastic epidemic models. Several useful epidemiological concepts such as the basic reproduction number, herd immunity, and the final size of an epidemic are de ned in term of deterministic epidemic models. Then three well-known stochastic modeling formulations are introduced, discrete-time Markov chains (DTMC), continuous-time Markov chains (CTMC), and stochastic differential equations (SDE). Some of the important differences between deterministic and stochastic models and between the stochastic modeling formulations are discussed in relation to SIS and SIR epidemic models. Computation of the quasistationary distribution, probability of an outbreak, and the final size distribution are illustrated in stochastic epidemic models. In addition, methods for derivation, analysis, and numerical simulation are discussed for stochastic models. As a final example, an SDE epidemic model with vaccination is formulated, which has applications to pertussis (whooping cough).
Numerical Exploration to a System w Reaction, Diffusion, and Advection
(no description available)
The Alan Hastings Project Teacups, Transients, and Regime Shifts
(no description available)
Optimal Strategy for Controlling the Severity of Wildlife Disease Epidemics Due to Harvesting
(no description available)
Deterministic and Stochastic Models for Multi-Patch SIS Epidemics
(no description available)
Modeling the Cholera Outbreak in Haiti: A Multi-patch Disease Model
(no description available)
Deterministic and Stochastic Models for Multi-Patch SIS Epidemics
(no description available)
Spatial is Special: Coupling and Intraguild Predation
(no description available)
Numerical Exploration to a System w Reaction, Diffusion, and Advection
(no description available)
2011 Summer Graduate Lecture
Mathematical models predict that in environments that are heterogeneous in space but constant in time, there will be selection for slower rates of unconditional dispersal, including specifically random dispersal by diffusion. However, some types of unconditional dispersal may be unavoidable for some organisms, and some organisms may disperse in ways that depend on environmental conditions. In some cases, models predict that certain types of conditional dispersal strategies may be evolutionarily stable within a given class of strategies. For environments that vary in space but not in time those strategies are often the ones that lead to an ideal free distribution of the population using them, provided that such strategies are available within the class of feasible strategies.

Problems in the evolution of dispersal have been addressed from two complementary mathematical viewpoints, namely game theory and mathematical population dynamics. This talk will describe some results and open problems from the viewpoint of spatially explicit models in population dynamics, specifically reaction-diffusion-advection models. Some of the results and problems are related to the evolutionary stability of dispersal strategies leading to an ideal free distribution and the mechanisms that might allow organisms to realize such strategies.
2011 Summer Graduate Lecture
Mathematical models predict that in environments that are heterogeneous in space but constant in time, there will be selection for slower rates of unconditional dispersal, including specifically random dispersal by diffusion. However, some types of unconditional dispersal may be unavoidable for some organisms, and some organisms may disperse in ways that depend on environmental conditions. In some cases, models predict that certain types of conditional dispersal strategies may be evolutionarily stable within a given class of strategies. For environments that vary in space but not in time those strategies are often the ones that lead to an ideal free distribution of the population using them, provided that such strategies are available within the class of feasible strategies.

Problems in the evolution of dispersal have been addressed from two complementary mathematical viewpoints, namely game theory and mathematical population dynamics. This talk will describe some results and open problems from the viewpoint of spatially explicit models in population dynamics, specifically reaction-diffusion-advection models. Some of the results and problems are related to the evolutionary stability of dispersal strategies leading to an ideal free distribution and the mechanisms that might allow organisms to realize such strategies.
Spatial is Special: Coupling and Intraguild Predation
(no description available)
Optimal Strategy for Controlling the Severity of Wildlife Disease Epidemics Due to Harvesting
(no description available)
Optimal Strategy for Controlling the Severity of Wildlife Disease Epidemics Due to Harvesting
(no description available)
Modeling the Cholera Outbreak in Haiti: A Multi-patch Disease Model
(no description available)
Modeling the Cholera Outbreak in Haiti: A Multi-patch Disease Model
(no description available)
The Alan Hastings Project Teacups, Transients, and Regime Shifts
(no description available)
Numerical Exploration to a System w Reaction, Diffusion, and Advection
(no description available)
Spatial is Special: Coupling and Intraguild Predation
(no description available)
Spatial is Special: Coupling and Intraguild Predation
(no description available)
2011 Summer Graduate Lecture: Spatiotemporal dynamics ecosystems
Ecological systems can be studied as ensembles of locally interacting individuals within heterogeneous environments. Because many ecological interactions are nonlinear, they can promote spatial and temporal heterogeneity in the distribution of abundance over scales ranging from individuals to whole continents. Understanding patterns of heterogeneity is key to understanding the response of key ecosystem services (e.g. productivity of commercial species) to stressors (e.g. climate change, harvesting). The lecture will provide a survey of the main quantitative formalisms used in ecology to predict the onset of spatiotemporal patterns of abundance, with an emphasis on their ecological relevance. I will cover concepts of self-organization, criticality and synchrony, and link individual characteristics to emergent spatial structures over large spatial scales. I will then apply these concepts to marine ecosystems where spatiotemporal dynamics can be captured through the analysis of spatial synchrony. I will detail some recent work showing how asynchrony can be maintained over continental scales in an ensemble of locally coupled ecological oscillators. Such regional asynchrony can be tested in natural systems and provide important insights for the design of marine reserve networks.
2011 Summer Graduate Lecture
Ecological systems can be studied as ensembles of locally interacting individuals within heterogeneous environments. Because many ecological interactions are nonlinear, they can promote spatial and temporal heterogeneity in the distribution of abundance over scales ranging from individuals to whole continents. Understanding patterns of heterogeneity is key to understanding the response of key ecosystem services (e.g. productivity of commercial species) to stressors (e.g. climate change, harvesting). The lecture will provide a survey of the main quantitative formalisms used in ecology to predict the onset of spatiotemporal patterns of abundance, with an emphasis on their ecological relevance. I will cover concepts of self-organization, criticality and synchrony, and link individual characteristics to emergent spatial structures over large spatial scales. I will then apply these concepts to marine ecosystems where spatiotemporal dynamics can be captured through the analysis of spatial synchrony. I will detail some recent work showing how asynchrony can be maintained over continental scales in an ensemble of locally coupled ecological oscillators. Such regional asynchrony can be tested in natural systems and provide important insights for the design of marine reserve networks.
Optimal Strategy for Controlling the Severity of Wildlife Disease Epidemics Due to Harvesting
(no description available)
Modeling the Cholera Outbreak in Haiti: A Multi-patch Disease Model
(no description available)
Deterministic and Stochastic Models for Multi-Patch SIS Epidemics
(no description available)
Live Together or Eat Alone
(no description available)
Optimal Strategy for Controlling the Severity of Wildlife Disease Epidemics Due to Harvesting
(no description available)
2011 Summer Graduate Lecture
(no description available)
2011 Summer Graduate Computer Lab
Optimal control of ordinary differential equations will be introduced. Formulation of a system with control, choosing an objective functional, control analysis and numerical solutions will be included. Some epidemic, immunology and other population models will be illustrated. Practice with a simple control problem to be calculated by hand will given as a class exercise. Numerical solutions and solution dependence on parameters will be illustrated in the afternoon lab work.
The Alan Hastings Project Teacups, Transients, and Regime Shifts
(no description available)
Optimal Strategy for Controlling the Severity of Wildlife Disease Epidemics Due to Harvesting
(no description available)
Numerical Exploration to a System w Reaction, Diffusion, and Advection
(no description available)
Modeling the Cholera Outbreak in Haiti: A Multi-patch Disease Model
(no description available)
The Alan Hastings Project Teacups, Transients, and Regime Shifts
(no description available)
Spatial is Special: Coupling and Intraguild Predation
(no description available)
Deterministic and Stochastic Models for Multi-Patch SIS Epidemics
(no description available)
Spatial is Special: Coupling and Intraguild Predation
(no description available)
Live Together or Eat Alone
(no description available)
Spatial is Special: Coupling and Intraguild Predation
(no description available)
2011 Summer Graduate Lecture
Macroevolution is the study of evolution or biodiversity on a long time scale, in other words, the evolutionary history of speciations and extinctions. In order to incorporate the stochastic effects of evolutionary events, one often uses branching models that generate the new speciation events and the extinction of species. Mathematical models used to describe these events are branching processes, in particular birth and death processes. The ultimate goal of using mathematical models for macroevolution is to identify which features of the observed data may have arisen by chance and which require a biological explanation.

In this lecture we will cover the basics of stochastic processes needed for such models, and describe the distribution of various quantities that will help us make a correspondence between these models and data. In addition to the one dimensional population size process, we will also discuss the more complicated aspects of phylogenetic tree structures, such as tree shape, generated by such models. We will begin with a review on birth and death processes and branching processes in general. We will discuss the random trees generated by these models and discuss various relevant statistics. Finally, if time permits, we will conclude with a discussion of hierarchical models on random trees that describe the grouping of species trees into trees of genera, families, etc.
2011 Summer Graduate Lecture
Macroevolution is the study of evolution or biodiversity on a long time scale, in other words, the evolutionary history of speciations and extinctions. In order to incorporate the stochastic effects of evolutionary events, one often uses branching models that generate the new speciation events and the extinction of species. Mathematical models used to describe these events are branching processes, in particular birth and death processes. The ultimate goal of using mathematical models for macroevolution is to identify which features of the observed data may have arisen by chance and which require a biological explanation.

In this lecture we will cover the basics of stochastic processes needed for such models, and describe the distribution of various quantities that will help us make a correspondence between these models and data. In addition to the one dimensional population size process, we will also discuss the more complicated aspects of phylogenetic tree structures, such as tree shape, generated by such models. We will begin with a review on birth and death processes and branching processes in general. We will discuss the random trees generated by these models and discuss various relevant statistics. Finally, if time permits, we will conclude with a discussion of hierarchical models on random trees that describe the grouping of species trees into trees of genera, families, etc.
2011 Summer Graduate Computer Lab
(no description available)
Live Together or Eat Alone
(no description available)
Numerical Exploration to a System w Reaction, Diffusion, and Advection
(no description available)
2011 Summer Graduate Lecture
Transfer functions are a useful tool for analyzing the effects of moderate spatial and/or temporal variation in model parameters. By the end of the day, you should have a grasp of basic Fourier analysis and be able to "read" transfer functions to tell how changes in parameters amplify or damp population response to variation and increase or decrease any response lags or spatial shifts. If there is time, we will consider stochastic environments, defined only by their spatial and/or temporal autocorrelation functions.
2011 Summer Graduate Lecture
Transfer functions are a useful tool for analyzing the effects of moderate spatial and/or temporal variation in model parameters. By the end of the day, you should have a grasp of basic Fourier analysis and be able to "read" transfer functions to tell how changes in parameters amplify or damp population response to variation and increase or decrease any response lags or spatial shifts. If there is time, we will consider stochastic environments, defined only by their spatial and/or temporal autocorrelation functions.
Modeling the Cholera Outbreak in Haiti: A Multi-patch Disease Model
(no description available)
Deterministic and Stochastic Models for Multi-Patch SIS Epidemics
(no description available)
Deterministic and Stochastic Models for Multi-Patch SIS Epidemics
(no description available)
Live Together or Eat Alone
(no description available)
Optimal Strategy for Controlling the Severity of Wildlife Disease Epidemics Due to Harvesting
(no description available)