Workshop 1: Mathematical modelling of plant development

Mathematical Biosciences Institute http://mbi.osu.edu

2010-2011 Program in Evolution, Synchronization, and Environmental Interactions: Insights from Plants and Insects

Organizing Committee: Vincent Gutschick, vince@nmsu.edu; David Rand, david_rand@mac.com; Daniel Forger, forger@umich.edu; Karl Niklas, kjn2@cornell.edu; David Sumpter, david@math.uu.se, Mark Lewis, mlewis@math.ualberta.ca; Scott Nuismer, snuismer@uidaho.edu

Preamble for the entire year

Myriad influences shape the patterns of evolution, timing, behavior and ecology of living organisms. These influences range from biochemical cues to configurations of temperature, space and light, to interactions with other organisms. This one-year program focuses on connecting influence to pattern for processes involving plants and insects.

How do biotic and abiotic influences affect patterns of plants and insects? We investigate this complex question quantitatively, by focusing on specific areas where there has been recent growth, simultaneously in mathematical and statistical theories and in biological data and experiment. We propose to couple the mathematics and biology in new ways, allowing for innovative growth of both science and mathematics.

The year is based around six workshops: (i) Mathematical modeling of plant development, (ii) Circadian clocks in plants and fungi, (iii) Resource acquisition and allocation in plants, (iv) Insect self-organization and swarming, (v) Ecology and control of invasive species, including insects, and (vi) Coevolution and the ecological structure of plant-insect communities. Our mathematical investigation of these processes will rely upon a diverse array of quantitative theory, including geometry, control, optimization, pattern formation, spatial dynamics, evolution and data-model interaction.

The plant development workshop will connect biochemical mechanisms to geometric patterns, while simultaneously investigating the selection pressure for the geometric patterns. Circadian clocks will be evaluated both from the perspective of design features for feedback and control, and of robustness of these features to perturbation. Resource acquisition will focus both on mechanisms for acquisition, and on the trade-offs and optimization involved in plant growth. Insect self-organization and swarming will employ dual perspectives of emergent self-organization properties arising from individual interactions, and optimal design of artificial swarms using diffuse (decentralized) information with implications for robotics and decentralized computer algorithms. Biological invasions will be understood, not only in terms of predictable forecasting of future invasions, but in terms of optimal control of the invasion processes. Finally, the physical and behavioral mechanisms involved in coevolution of plant-insect communities will be understood in terms of fitness advantages incurred evolution and adaptation.

Thus the underlying feature throughout the workshops is simultaneous investigation of mechanism and optimality: What mechanisms give rise to observed patterns? What is the fitness or optimality associated with observed patterns? It is through this simultaneous study of mechanism and optimality in plants and insects that the workshops will provide general insight to the processes of evolution, synchronization and environmental interactions.

The goals of the year program are (i) to develop, analyze and apply new mathematical models for processes of evolution, timing, behavior and ecology of living organisms that are tailored to investigate both mechanisms underlying the processes and optimality of associated patterns; and (ii) train interdisciplinary quantitative researchers at a variety of levels (graduate, postdoctoral and faculty) in the area of evolution, synchronization and environmental interactions for biological systems.

Workshop 1: Mathematical modelling of plant development

Organizer: Vincent Gutschick (co-organizers to be determined) <-- since this proposal was submitted, several of you have offered to be co-organizers: Karine Chenu, Lyn Jones, Kate McCulloh, Michaël Chelle

： agrilya@tx.technion.ac.il; chelle@grignon.inra.fr; dme9@psu.edu; Thomas.Vogelmann@uvm.edu; tmdejong@ucdavis.edu; tom_buckley@alumni.jmu.edu; wksilk@ucdavis.edu; xs127127@sohu.com

as_komarov@rambler.ru, Ylo.Niinemets@emu.ee

Preamble

Plant development can be considered far beyond the original context of timing and elementary topology of organ development. We may explore its process origins in biochemistry; its mutual coupling to the environment as in energy balance and organ microclimate; the geometry of resources (rectilinear radiation, patchy and diffusive nutrients) that in turn conditions the necessary geometry of plant organs; the selection pressures that drive the evolution of diverse patterns of geometry and timing, and the population-genetic and phylogenetic constraints on such evolution; the ecological interactions with conspecifics as both competitors and mates, other resource competitors, herbivores, pollinators, diseases, and other biota that condition timing and geometry and the responsiveness of both. Exploration of these topics offers opportunities for biologists and mathematicians to meet in modes of modelling from first principles, inverse modelling, empirical modelling and data analysis, and to inform not only each other's major disciplines but also to link subfields within each discipline. Forward models may originate as functional models from basic levels of biochemistry and biophysics. One may also formulate models that begin with selection pressures to estimate how plants "should" function – simple optimization models, which must be generalized to address constraints that are variously functional, population-genetic, or phylogenetic.

The workshop has a goal of addressing these topics as items of intrinsic interest. Furthermore, it has a goal of involving young researchers to continue the development of mathematical biology and to take it in new directions. Finally, the workshop should engage us in defining the major challenges that remain. As an example of this last item, we may consider the problem of non-extinction: What is the geometry of the high-dimensional niche space that allows individual species to persist despite great numbers of extreme events in abiotic and biotic conditions, and how does this particularly relate to their biology, both physiological and developmental?

Here is the list of participants, without any attribution of being a speaker or co-organizer at this time:

Tom Buckley, CSIRO, Australia thomas.buckley@csiro.au Optimal architecture and resource allocation; stomatal control

Eric Casella, UK Forestry Commission, Farnham, Surrey, England eric.casella@forestry.gsi.gov.uk Architectural modelling; L-systems, light interception, growth / resource use

Michaël Chelle, INRA, Thiveral-Grignon, France chelle@grignon.inra.fr. Plant/canopy microclimate – radiative transport, energy balance, as determined by architecture; computationally efficient models, including nested radiosity

Karine Chenu, INRA/ENSA-M, Montpellier, France and CSIRO, Canberra ( ?), Australia, chenu@supagro.inra.fr. Leaf development in response to environment (light, temperature, water status) ; genetic control of these responses

DA Coomes, Plant Science, University of Cambridge, UK dac18@cam.ac.uk Competitive growth ; mortality relation to size; scaling relationships

Ted DeJong, Pomology, Univ. of California, Davis, CA, USA. tmdejong@ucdavis.edu. Plant architecture and attendant resource use and resource-use efficiencies; hydraulic architecture

David Eissenstat, Graduate Program in Ecology, Pennsylvania State University, College Park, PA, USA dme9@psu.edu Root development, turnover; growth and ecological effects

Vince Gutschick (myself, i.e.). Recently of the Dept. of Biology, New Mexico State University, Las Cruces, NM, USA. vince.gutschick@gmail.com Overall growth, allometry, resource use, functional balance, nutrient balance

Ilya Ioslovich, Civil and Environmental Engineering, Technion, Haifa, Israel. agrilya@tx.technion.ac.il. Plant-to-population models; inverse modelling to derive plant growth parameters

H. G. (Lyn) Jones, Plant Research Unit, University of Dundee, Scotland h.g.jones@dundee.ac.uk inverse modelling of plant architecture and energy balance; theory and data analysis

David King, Arnold Arboretum, Harvard University, Cambridge, MA, USA. dkingaz@yahoo.com Allometry and growth of plants; dynamic models of extreme events

AS Komarov, Institute of Physicochemical and Biological Problems in Soil Science, Russian Academy of Sciences, Moscow, Russia komarov@issp.serpukhov.su Cellular automata models of plant development

Jan Kozlowski, Jagiellonian Univ, Krakow, Poland kozlo@eko.uj.edu.pl Optimization and scaling models in biology

Hai Tao Li, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, China haitaoli@public.bta.net.cn Metabolic scaling in plants; isotopic tracers of processes

Annikki Makela, Forest Ecology, University of Helsinki, Finland annikki.makela@helsinki.fi Individual-tree models; GPP; allometry of water transport and light interception

Kate McCulloh, Wood Science and Engineering, Oregon State University, Corvallis, OR, USA kate.mcculloh@oregonstate.edu Hydraulic architecture of plants

Brenda Medlyn, Biological Science, Macquarie University, North Ryde, NSW, Australia b.medlyn@unsw.edu.au Individual-tree models of water use and carbon uptake

Karl Niklas, Plant Biology, Cornell University, Ithaca, NY, USA kjn2@cornell.edu Evolutionary ecology of plant structure, biomechanics; organizer of a companion workshop for the MBI

Przemyslaw Prusinkiewicz, Computer Science, University of Calgary, Canada. pwp@cpsc.ucalgary.ca . Geometrical and biochemical models of plant development

Ed Rastetter, Marine Biological Laboratory, Woods Hole, MA, USA erastett@mbl.edu

Evolution of plant structure and function, as coupled to nutrient cycles

Feike Schieving, Dept. of Biology, Univ. of Utrecht, Netherlands. F.Schieving@uu.nl Functional-structural plant growth models; models of competition and evolution based on structure

Wendy Kuhn Silk, Land, Air, and Water Resources, University of California, Davis, USA. wksilk@ucdavis.edu Functional and developmental models, physicochemically-based; growth and function of roots

Thierry Simonneau, Laboratoire d'Ecophysiologie des Plantes sous Stresses Environnementaux, INRA, Montpellier, France simonnea@ensam.inra.fr Leaf expansion, cell-cycle regulation, thermal time, environmental control of development

Tom Vogelmann, Botany and Agricultural Biochemistry, University of Vermont, Burlington, VT, USA Thomas.Vogelmann@uvm.edu Light distribution in leaves; optimzation models for metabolic processes

Sa Xiao, Laboratory of Arid Agroecology, Lanzhou University, China. xs127127@sohu.com . Game-theoretic models of plant height in competition

Most recent contacts:

Tadaki Hirose, Graduate School of Life Sciences, Sendai University, Miyagi, Japan hirose@mail.tains.tohoku.ac.jp Leaf structure and consequences for photosynthetic function; optimal allocation

Stephen P Long, Crop Science, University of Illinois, Urbana, IL, USA stevel@life.uiuc.edu Growth and yield analysis; photosynthetic models

Bill Shipley, Biologie, Université de Sherbrooke, Quebec, Canada Bill.Shipley@Usherbrooke.ca Mechanistic links of leaf traits to growth; statistical and statistical-mechanical models of communities and biodiversity

Mark Westoby, Biological Sciences, Macquarie University, North Ryde, NSW, Australia mwestoby@bio.mq.edu.au Evolutionary ecology; climatic driving of performance; strategies of height competition and leaf traits

Workshop 2: Circadian clocks in plants and fungi

Organizers: David Rand, Daniel Forger (co-organizers to be determined)

Preamble

Circadian (~24-hour) rhythms control the timing of many biological processes including leaf movements in plants and sporulation in fungi. Advances in understanding the biological mechanism of plant and fungal clocks have also helped inspire clock research in higher organisms. This workshop brings together theorists and experimentalists to better understanding timekeeping in plants and fungi and how they relate to clocks in higher organisms.

We plan to organize this workshop around the following themes:

1) How do multiple feedback loops within the Neurospora and aribidopsis clocks interact? How do individual feedback loops regulate circadian behavior?

2) How do circadian clocks keep a near constant period despite a widely changing environmental conditions?

3) How can mathematical models be matched to time series data?

4) How do circadian rhythms synchronize to the external world and the circadian clocks of other cells?

The goals of this workshop are to bring together theorists and experimentalists, some of whom are new to mathematical modelling or circadian rhythms, to foster interdisciplinary collaborations. The workshop will begin with a 2 day tutorial focusing on theory for experimentalists one day and the basics of circadian timekeeping for theorists on the second.

Key topics

Recent research results on Arabidopsis and Neurospora clocks

Design principles and multiple loop/oscillator structures

Robustness, flexibility and sensitivity

Linking clock models and time-series data

Temperature regulation of clocks and other regulatory networks

The clock's role in regulating flowering and other outputs

Implications for general regulatory networks

Proposed key participants (depending on funding)

Bell-Pedersen, Deborah (Texas A&M, Neurospora clock)

Brody, Stuart (UCSD, Neurospora clock)

Carre, Isabelle (Warwick, UK, plant clocks)

Doyle, Frank (UCSB, theorist)

Dunlap, Jay (Dartmouth Med. School, Neurospora clock)

Forger, Daniel (Univ. of Michigan, theorist)

Goldbeter, Albert (Univ. Bruxelles, theorist)

Gonze, Didier (Univ. Bruxelles, theorist)

Hall, Antony (plant clocks; Liverpool)

Harmer, Stacey (UCD, plant clocks)

Herzog, Erik (WA Univ in St. Louis, mammalian clock)

Johnson, Carl (plant clocks, Vanderbilt University)

Kay, Steve (UCSD, plant clocks)

Merrow, Martha (fungal clocks, Groeningen)

Millar, Andrew (Edinburgh, UK, plant clocks)

Rand, David (Warwick, UK, theorist)

Roenneberg, Till (fungal clocks, Munich);

Ruoff, Peter (University of Stavanger, theorist)

Tyson, John (Virginia Polytechnic, theorist)

Ueda, Hiro (Riken, Japan)

Webb, Alex (plant clocks, Cambridge)

Workshop structure

Morning: 4 40 minute talks in morning

9 - 9.40, 9.50 - 10.30, 11.00 – 11.40, 11.50-12.30

Afternoon:1 40 minute talk setting scene for 1.5 hr discussion session one of

topics above or a coherent combination of two of them (2-2.40); tea break; practical workshop session addressing topic (2.50-4.20); 1 hour talk/demonstration session e.g. demos of software, data analysis tools, experimental or theoretical technologies (5 – 6).

Summary of Discussions at 2/4 meeting (in a random order)

1) We should being with a 2 day tutorial with one day summarizing theory and another summarizing experiments

2) Steve Strogatz would be a good person to give an introduction to synchronization.

3) Have no more than about 4 hours of talks in a day

4) These can be divided into 4 ~1 hour talks or 8 ~ half hour talks

5) The workshop could have 30 or more people

6) We should organize sessions within the workshop around mathematical ideas or processes (e.g. synchronization).

7) Two possible organizing principles of our workshop could be synchronization and adaptation to the environment

8) There should be 2 other people on the organizing committee besides Forger and Rand.

9) Diversity and inclusion of women and underrepresented minorities are particularly important for NSF, it would be good to have a woman or underrepresented minority on our organizing committee

10) It would be good to invite mathematicians (especially dynamical systems researchers) who might not have previously worked in but would be interested in clocks

Suggestions for long term visitors:

Laura Miller (UNC) (David please provide)

Other potential speakers:

John Guckenheimer (Cornell), David Summers (OSU), Richard Rand (Cornell), Steve Strogatz (Cornell)

Workshop 3: Resource Acquisition and Allocation

Organizer: Karl J. Niklas (co-organizers to be determined)

Prospectus and Objectives

All plants must acquire light energy, atmospheric gases (carbon dioxide and oxygen), water, essential nutrients (e.g., phosphorus and nitrogen), and physical space to accomplish annual growth in biomass. They must also reproduce sexually to evolve. Thus, each individual must not only acquire resources but it must also allocate these resources to the production of the three primary vegetative organs (leaves, stems, and roots) and reproductive structures (e.g., spores, seeds, flowers, or cones). Biomass allocation patterns at the level of the individual plant necessitate optimization in how mass and energy are distributed among the three vegetative and reproductive organs. This aspect of plant biology has been an area of extensive experimental and theoretical work, but a synthesis of this work is lacking in large part because individual workers have focused on one or at most a few of the resources required for vegetative and reproductive growth. The objective of this workshop is to bring researchers in diverse areas of plant resource acquisition and allocation to examine from a mathematical perspective the various trade-offs and optimization strategies manifested by different plant life forms that are required to achieve growth and successful reproduction.

Key Topics

Water acquisition and conservation

Phosphorus/nitrogen acquisition and allocation

Carbon acquisition and allocation

Acquisition of space (space-filling)

Reproductive allocation patterns

Proposed Participants (suggested co-organizers indicated in bold)

J. H. C. Cornelissen (Department of Systems Ecology, Institute of Ecological

Science, Faculty of Earth and Life Sciences, Vrije Universiteit, De Boelelaan 1085, 1081 HV Amsterdam, The Netherlands)

James H. Brown (Biology Department, University of New Mexico,

Albuquerque, NM)

James J. Elser (School of Life sciences, University of California, Davis)

Brian J. Enquist (Department of Ecology and Evolutionary Biology,

University of Arizona, Tucson, Arizona)

Sabine Güsewell (Institut für integrative Biologie Universitätstrasse 16 CHN

H 68 8092 Zürich)

Michelle Holbrook (Biological Laboratory, Harvard University)

Andrew J. Kerkhoff (Departments of Biology and Mathematics

Kenyon College, Gambier, OH 43022)

Mimi Koehle (University of California, Berkeley)

Robert W. Pearcy (Division of Biological Sciences. Section of Evolution and

Ecology. University of California. Davis, CA 95616)

Peter B. Reich (Department of Forest Resources, University of Minnesota)

Bill Shipley (Département de Biologie, Université de Sherbrooke, Sherbrooke, Québec, J1K 2R1, CANADA)

Robert W. Sterner (Department of ecology, evolution and Behavior,

University of Minnessota)

Sean C. Thomas (College of Forest Research, University of Washington, Seattle)

Mel Tyree (Centre for Enhanced Forest Management, University of Alberta)

Jacob Weiner (Department of Ecology, The Royal Veterinary and Agricultural University, Rolighedsvej 21. DK-1958 Frederiksberg, Denmark)

Insect self-organisation and swarming

David Sumpter

Preamble

Insect groups generate a wide range of interesting collective patterns and behaviours, for example the formation of ant trails, the building of elaborate nests, collective movement of honey bee swarms and marching locust bands, to name just a few. The complex non-linear nature of the mechanisms underlying such collective behaviour has generated a great deal of theoretical interest from mathematicians and physicists. Collective insect behaviour is one area where mathematical modelling and experiment have lived well side by side.

Collective insect behaviour is interesting from the point of view of evolution because understanding the non-linear dynamics provides insights into self-organization in natural systems which in turn serves as an inspiration for computer algorithms and robots. Many of the emergent collective phenomena involve synchronization where large numbers of individuals move in the same direction or co-ordinate their activities. Lastly, mass movement of insects such as grasshoppers and crickets involve large-scale interactions with the environment, whereby feedback between individuals within a group and their environment determine collective patterns.

Target audience and aims

There are currently three key communities involved in the study of insect swarming and self-organization.

1. The social insect community, who build mathematical models and conduct experiments to see how insect societies function effectively.

2. The biologically inspired computing people, who use inspiration from insect societies and insect swarming to design robots and computer algorithms.

3. The applied mathematics and theoretical physics community with an interest in self-organization and self-propelled particle models both from a mathematical viewpoint and with an application to insect swarms, bird flocks and cell movement.

The workshop should provide something in all three of these areas, aiming in particular to bring individuals with different backgrounds together.

Organizing committee

The organizing committee is

Social insect community: Madeleine Beekman (Sydney); Stephen Pratt (Arizona State)

Computer science: Vijay Kumar (Penn State)

Applied mathematics: David Sumpter (Uppsala); Chad Topaz (Macalester)

Participants

Experimentalists and biologists:

Madeleine Beekman (Sydney); Honey bee organization.

Audrey Dussutour (Sydney) Ant foraging.

Jennifer Fewell (Arizona) division of labour in insects.

Graham Taylor (Oxford) Insect locomotion.

Deborah Gordon (Stanford) Ant organisation.

Laura Miller (North Carolina) Insect aerodynamics.

Stephen Pratt (Arizona State) Collective decision-making by ants.

Steve Simpson (Sydney) Locust swarming.

Iain Couzin (Princeton) Group behaviour of animals.

Jean-Louis Deneubourg (Brussels) Self-organization in social insects.

Tom Seeley (Cornell) Honey bees

Guy Theraulaz (Toulouse) Insect societies.

Jane Wang (Cornell) Insect flight

Computer Scientists and engineers:

Vijay Kumar (Pennsylvania) Robots

Tucker Balch (Georgia Tech) Autonomous robots.

Marco Dorigo (Brussels) Ant colony optimization.

Dario Floreano (Lausanne) Insect inspired robot groups.

Naomi Leonard (Princeton) Control systems and collective motion

Bernd Meyer (Monash) Natural computation.

Martin Middendorf (Leipzig) Ant algrothims and swarm optimization.

Kevin Passino (Ohio State) Bio-inspired engineering.

Applied mathematicians:

Maximino Aldana (UNAM) Phase transistions in SPP models

Andy Bernoff (Harvey Mudd) Fluid mechanics and swarming of insects.

Andrea Bertozzi (UCLA) Cooperative motion and swarming.

Maria D'Orsogna (CSUN) Self-propelled particle models

Leah Edelstein-Keshet (University of British Columbia) Modelling swarms.

Nina H. Fefferman (DIMACS/Princeton) Mathematical modelling of social insects.

Raymond Goldstein (Cambridge) Fluid dynamics of complex systems.

Cristian Huepe (independent researcher) Phase transistions in SPP models

Mark Lewis (Alberta) PDE’s and group pattern formation.

Mary Myerscough (Sydney) Modelling of insect societies.

Michael Shelley (NYU) Fluid dynamics of complicated bodies.

David Sumpter (Uppsala) Modelling animal groups.

Chad Topaz (Macalester) Modelling of swarms.

Tamas Vicsek (Budapest) Self-propelled particle models.

Those in bold are proposed to be on organizing committee. I have chosen them to reflect a broadness of interests, coming from each of the key communities listed below.

Key topics

The main talks will set the overall tone for the workshop. That is, how can we use mathematical models to understand insect (and other animal) societies and swarms. Afternoon practical workshops will take these themes and discuss them in more detail.

Specific topics for practical workshops:

The dynamics of moving swarms: theory and experiment (chair: Chad Topaz). Self-propelled particle models of swarms, but with a special emphasis on interactions within real insect swarms, such as locust and honey bee swarms. Speakers with a background in fluid dynamics will interact with experimentalists and try to come up with explanations of the structure of moving animal groups.

Group decision-making (chair: Stephen Pratt). This session will look at decision-making by animal groups. How do ants and bees choose a new nest site? How do moving animal groups decide which direction to go? How can we design artificial systems of interacting agents which can make decisions?

Complicated interactions within insect societies (chair: Madeleine Beekman) Many researchers of insect societies believe that the devil is in the detail when it comes to understand how they function: ‘simple’ particle models can’t capture that detail and explain what is going on. This session will discuss how we might develop mathematical theory which includes these important details, and how such an approach ties in to other areas of systems biology.

Designing artificial swarms (chair: Vijay Kumar) Much of the research in swarms and self-organization has spilled over to inspire the design of robots and decentralized computer algorithms. This workshop will take up these applications and discuss future developments.

Workshop structure

Workshop will take place over 5 days.

Morning: Four 30 minute talks, each with general interest although themed along the lines of the afternoon’s workshop.

9 - 9.30, 9.30 - 10.00, (one hour coffee break) 11.00 – 11.30, 11.30-12.00

Afternoon: Practical workshops. One each afternoon apart from the middle afternoon (afternoon off). Each workshop will start with a talk giving an overview of the area (30 minutes); then splitting in to smaller groups to discuss important issues in the field (1 hour); then a tea break (30 minutes) followed by discursive presentations by group members (1 hour). If the session organizers want they can add short contributed talks to this format.

Poster session take place after the workshop on the first day, along with welcome drinks.

Tutorial

In the week before the workshop we will have a two day tutorial. One day on biology and one on mathematical models. The biology day will look at the behavioural ecology of animal groups, why do animal groups form, why do some animals co-operate and others don’t. The modelling day will discuss modelling of insect societies, including some of the classic models of self-organization and the Vicsek model of self-propelled particles. The modelling day will be a hands on play about with some of the simulation models.

Workshop 5: Ecology and control of invasive species, including insects

Organizer: Mark Lewis (co-organizers to be determined)

Proposed Co-organizers: Ottar Bjornstadt (Penn State) onb1@psu.edu; Subhash Lele (Alberta) slele@ualberta.ca; Sergei Petrovskii (Leicester) sp237mcs.le.ac.uk

The spread of invasive species is a key applied problem in ecology. In North America, invasive exotic species are widespread, ranging from gyspy moth to Asian longhorn beetle to weedy plants. The associated costs are immense, by some estimates exceeding

$100 billion US per year. While many invasive species are introduced from Asia or Europe, others, like mountain pine beetle, are simply spreading into new areas of North America, due to processes such as climatic change.

Early models for invasive species were nonlinear reaction diffusion equations such as Fisher's equation, which describes quadratic growth coupled to Brownian motion. Here the analysis of traveling waves and of the convergence of initial data to wave solutions has been a fruitful area of classical mathematical research. The traveling wave

speed, interpreted biologically as the rate of spread of the introduced population, has successfully predicted spread rates of many introduced species, but has failed dramatically with others. Modifications of these equations to include long-distance dispersal, stage structure, spatial heterogeneity, stochasticity, Allee effects, and nonlinear interactions with resident species (eg, competition or predation) have driven new advances in the theory of nonlinear dynamical systems, while, at the same time, providing a more realistic framework for the study of invasions.

In parallel with the development of new mathematical models, has been increasing availability of detailed spatio-temporal datasets that can be used to track actual invasion processes. These datasets can be accessed via Geographic Information Systems (GIS), and, in some cases, they show yearly changes in the extent of invaders. Classic data sets include those for mountain pine beetle in western Canada and US, gypsy moth in the eastern US and Spartina in coastal California (Ottar or others, can you add some verbiage here on other ones? I can work on this too).

At the same time, new powerful statistical methods for estimating functions and composite likelihood, coupled to computer algorithms, make it possible to interface the detailed data sets with the new realistic dynamical system models. This interface allows the models to be assessed, tested and validated against the real data for the invasions. Hypotheses regarding key factors governing invasions can be evaluated, and the means for controlling the invasions/adapting to the invasions can be investigated. This coupling that the nonlinear dynamical systems models are no longer simply mathematical abstractions of key processes. They are the quantitative formulation of underlying hypotheses, and they provide the means for testing the hypotheses against data.

This interface between nonlinear dynamical systems, large datasets and statistical and computer methods has only become possible recently, with the growth of large data sets via remote sensing, with the advent of new powerful computers, and with the development of new statistical methods. This interface provides fertile ground for new mathematical, statistical and scientific advances.

The purpose of the MBI workshop on invasive species is to bring together researchers from different groups: mathematicians, biologists and statisticians to develop the new interdisciplinary approaches to biological invasions described above. Possible participants are given below.

Biologists:

Ottar Bjornstadt (Penn State)

James Bullock (NERC)

Hal Caswell (Woods Hole Oceanographic Institute)

Jim Clark (Duke)

Kim Cuddington

Greg Dwyer (Chicago)

Bill Fagan (Maryland)

Bryan Grenfell (Penn State)

Alan Hastings (Davis)

Carol Horvath (Miami)

Sandy Leibhold (US Dept Agriculture)

Mike Neubert (Woods Hole Oceanographic Institute)

Hugh MacIssac (Windsor)

Kat Shea (Penn State)

Mathematicians:

Britta Basse (Canterbury)

Frank Hilker (Lisbon)

Mark Kot (Washington)

Mark Lewis (Alberta)

Frithjof Lutscher (Ottawa)

Horst Malchow (Osnabrueck)

Sergei Petrovskii (Leicester)

Michael Plank (Canterbury)

Hugh Possingham (Adelaide)

Jim Powell (Utah State)

Nanako Shigesada (Tokyo)

Horst Thieme (Arizona State)

James Watmough (New Brunswick)

Statisticians:

Noel Cressie (Ohio State)

Brian Dennis (Idaho)

Subhash Lele (Alberta)

Mark Taper (Montana State)

Workshop 6: Coevolution and the ecological structure of plant-insect communities

Organizer(s): Scott L. Nuismer; Sharon Strauss? (co-organizers to be determined)

BACKGROUND: Plant-insect interactions have played a pivotal role in the development of modern coevolutionary theory, beginning with Darwin’s initial insights into reciprocal adaptation between plants and pollinators. When Ehrlich and Raven published their now classic study of coevolution between butterflies and plants in 1964, the link between the development of coevolutionary theory and plant-insect interactions was cemented. Since this time, numerous studies of plant-insect interactions have revealed an important role for coevolution, even as the perceived importance of coevolution for the overall structure of plant-insect communities has waxed and waned. Currently, much of the research on the ecology and evolution of plant-insect interactions is organized around two partially overlapping conceptual frameworks: community genetics and the geographic mosaic theory.

Community Genetics

Community genetics focuses on the role the genetic structure of component species plays in shaping the ecological structure and dynamics of biological communities. Thus, community genetics represents a marriage of the traditional disciplines of quantitative genetics, population genetics, and community ecology. As it is usually articulated, community genetics does not explicitly integrate the process of coevolution, although its potential importance is generally acknowledged.

Empirical studies of community genetics have relied heavily on interactions between insects and plants. For instance, the long running studies of interactions between cottonwoods and insects conducted by Thomas Whitham and colleagues have clearly demonstrated that host genetics strongly influence the community of associated insect species. A wide variety of other studies, conducted in a diverse array of taxa, support the basic argument of community genetics – that integrating the genetic structure of the interacting species is important for any cohesive theory of community ecology. From a theoretical perspective, work in community genetics has been somewhat piecemeal, although excellent models have been developed and analyzed to address particular topics (e.g., see Neehauser et al. for a particularly nice collection of examples). The development of a general theoretical framework for community genetics is an important goal, and essential for interpreting rapidly accumulating empirical data.

The Geographic Mosaic Theory

The geographic mosaic theory focuses on how spatial variability in the abiotic and biotic environment shapes ecological and evolutionary dynamics of interspecific interactions. Unlike community genetics, which is largely agnostic regarding the importance of coevolution, the geographic mosaic theory explicitly identifies coevolution as the driving force underlying the ecological dynamics and structure of biological communities.

Much of the empirical work motivated by the geographic mosaic theory has focused on quantifying patterns of trait matching or local adaptation in interacting species, with plant-insect interactions representing several of the best studied cases. A general result that has emerged from this work is that species interactions exhibit a complex mix of local adaptation, local maladaptation, trait matching, and trait mismatching as predicted by the verbal theory. A substantial body of mathematical theory has been developed to elucidate whether these patterns are consistent with a geographic mosaic process, and if so, whether such a process is more likely than other simpler processes. As with community genetics, the development of a robust mathematical framework for the geographic mosaic is essential for interpreting existing data and designing future empirical studies.

Synthesis

Although community genetics and the geographic mosaic differ with respect to the perceived importance of coevolution, both attempt to explain similar phenomena. For instance, both seek to understand how complex biological communities are assembled, what factors contribute to their stability or instability, and why the structure of such communities is often spatially variable. Discussing profitable avenues for the development of a mathematical framework which unifies community genetics and the geographic mosaic theory will be an important focus of this workshop. An additional focus will be the development of statistical tools that can be used to evaluate the importance of reciprocal selection and ongoing coevolution for the composition, structure, and stability of plant-insect communities.

GOALS OF THE WORKSHOP:

1) To discuss metrics (e.g., network structure, local adaptation, community heritability) with robust theoretical/statistical underpinnings that can be used elucidate the importance of coevolutionary processes in structuring plant-insect communities at local and regional scales.

2) To discuss statistical techniques (e.g., path analysis; selective source analysis, etc.) for evaluating the importance of ongoing coevolutionary selection in multi-specific communities of plants and insects.

3) To discuss profitable avenues for the development of a cohesive theoretical framework that incorporates coevolution, multiple interacting species, spatial structure, and variable abiotic environments. This framework will thus formally link community genetics and the geographic mosaic.

PARTICIPANTS:

Empiricists

1. Anurag A. Agrawal

2. Thomas G. Witham

3. Marc T.J. Johnson

4. Sharon Y. Strauss

5. Kari A. Segraves

6. John Stinchcombe

7. David Althoff

8. Jordi Bascompte (E&T)

9. PW de Jong

10. Robert S. Fritz

11. John N. Thompson

12. Timothy Craig

13. Rebecca Irwin

Theoreticians

1. Mike Wade

2. Michael Doebeli

3. Richard Gomulkiewicz

4. Benjamin Ridenhour

5. Ulf Dieckman

6. Michael Hochberg

7. Marc Rausher (E&T)

8. Jordi Bascompte

9. Peter Abrams

10. Sarah P. Otto

11. Norio Yamamura

12. Tadezius Kawecki

13. Mark C. Urban (E&T)

14. Sylvain Gandon

15. Claudia Neehauser

Other Applied mathematicians?