### Organizers

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

- Mon, Jul 25, 2011
- Tue, Jul 26, 2011
- Wed, Jul 27, 2011
- Thu, Jul 28, 2011
- Fri, Jul 29, 2011
- Sat, Jul 30, 2011
- Sun, Jul 31, 2011
- Mon, Aug 1, 2011
- Tue, Aug 2, 2011
- Wed, Aug 3, 2011
- Thu, Aug 4, 2011
- Fri, Aug 5, 2011
- Full Schedule

Monday, July 25, 2011 | |
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Time | Session |

09:00 AM 10:00 AM | - 2011 Summer Graduate Lecture I will start with a discussion of some real world examples, and then return to thinking about (relatively) simple population models that can exhibit dramatic shifts in dynamics either without external changes, or with small external changes. The mathematical tools will essentially be drawn from ordinary differential and difference equations (dynamical systems). I will discuss the extensions of these ideas to more complex systems. |

10:30 AM 12:00 PM | - 2011 Summer Graduate Lecture I will start with a discussion of some real world examples, and then return to thinking about (relatively) simple population models that can exhibit dramatic shifts in dynamics either without external changes, or with small external changes. The mathematical tools will essentially be drawn from ordinary differential and difference equations (dynamical systems). I will discuss the extensions of these ideas to more complex systems. |

02:00 PM 05:00 PM | - Computer Lab: Matlab Richard Gejji demostrates Matlab |

Tuesday, July 26, 2011 | |
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Time | Session |

09:00 AM 10:00 AM | - 2011 Summer Graduate Lecture A severe cholera outbreak began in Haiti in late October 2010 and continues to this day. We will use this situation to motivate and discuss some basic aspects of mathematical epidemiology. In particular, we will discuss the basic reproduction number, spatial "patch" models, and the effects of different patch properties and connectivity patterns on disease dynamics. |

10:30 AM 12:00 PM | - 2011 Summer Graduate Lecture A severe cholera outbreak began in Haiti in late October 2010 and continues to this day. We will use this situation to motivate and discuss some basic aspects of mathematical epidemiology. In particular, we will discuss the basic reproduction number, spatial "patch" models, and the effects of different patch properties and connectivity patterns on disease dynamics. |

Wednesday, July 27, 2011 | |
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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 | |
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Time | Session |

09:00 AM 10:00 AM | Chris Cosner - 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. |

10:30 AM 12:00 PM | Chris Cosner - 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. |

Friday, July 29, 2011 | |
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Time | Session |

09:00 AM 10:00 AM | Suzanne Lenhart - 2011 Summer Graduate Lecture (no description available) |

02:00 PM 05:30 PM | Suzanne Lenhart - 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. |

Saturday, July 30, 2011 | |
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Time | Session |

09:00 AM 10:00 AM | - 2011 Summer Graduate Lecture Natural selection favors traits that maximize fitness. However, the fitness effects of a particular behavioral strategy often depend on the behavior of other individuals. Evolutionary game theoretical models are used to model the evolution of strategic social behavior. A strategy is said to be a Nash equilibrium if it is a best response to itself, and an evolutionarily stable strategy (ESS) if it cannot be invaded by a rare, alternative tactic. I will present several game theoretical models used in evolutionary biology, including the Prisoner's Dilemma and Hawk-Dove game and games against the field. I will discuss a variety of methods to find Nash equilibriums and ESS and discuss the application of game theoretical models to biological problems of cooperation and conflict and the spatial distribution of organisms. |

10:30 PM 12:00 PM | - 2011 Summer Graduate Lecture Natural selection favors traits that maximize fitness. However, the fitness effects of a particular behavioral strategy often depend on the behavior of other individuals. Evolutionary game theoretical models are used to model the evolution of strategic social behavior. A strategy is said to be a Nash equilibrium if it is a best response to itself, and an evolutionarily stable strategy (ESS) if it cannot be invaded by a rare, alternative tactic. I will present several game theoretical models used in evolutionary biology, including the Prisoner's Dilemma and Hawk-Dove game and games against the field. I will discuss a variety of methods to find Nash equilibriums and ESS and discuss the application of game theoretical models to biological problems of cooperation and conflict and the spatial distribution of organisms. |

Sunday, July 31, 2011 | |
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Time | Session |

Monday, August 1, 2011 | |
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Time | Session |

09:00 AM 10:00 AM | Edward Allen - 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. |

10:30 AM 12:00 PM | Linda Allen - 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 dened 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). |

Tuesday, August 2, 2011 | |
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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 Computer Lab (no description available) |

Wednesday, August 3, 2011 | |
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Time | Session |

09:00 AM 10:00 AM | Fred Guichard - 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. |

10:30 AM 12:00 PM | Fred Guichard - 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. |

Thursday, August 4, 2011 | |
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Time | Session |

Friday, August 5, 2011 | |
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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 | 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 |

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.

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.

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.

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.