Organizers
Evolutionary game theory, along with replicator equations, has been applied successfully to modeling evolution of various biological or social systems, ranging from virus infection to bacteria development, from plant succession to animal breeding, and from trace of evolutionary history to study of biodiversity and ecology. Applications in areas such as population genetics, animal behaviors, and evolution of social cooperation have especially seen great developments and impacts. In evolutionary game theory, species are considered as if they are players in a game, competing for resources, for survival, and for reproduction. A mathematical (game) model can then be established for study of any given population of competing species, and for analysis of population changes and prediction of equilibrium states and their stabilities. The theory involves such mathematical branches as game theory, optimization theory, and ordinary differential equations, and further extends to graph theory, stochastic processes, and partial differential equations as appropriate. Although emerged as a powerful mathematical tool for evolutionary and ecological modeling, the evolutionary game theory is still in the stage of early development. Theoretical issues remain to be addressed and computational methods need to be developed, for equilibrium computation, dynamic simulation, and stability analysis. Application problems are arising and yet to be investigated in many critical fields of biology such as development of energyefficient or nutritionrich plants and animals, analysis of human microbiome genomic data, control of infectious diseases, modeling immunedefense systems of biological species, etc. This workshop is to bring an interdisciplinary group of experts as well as biologists and mathematicians who are interested in evolutionary game modeling, to have an extensive discussion on current and future development of evolutionary game theory and applications. Topics include reviews or reports on recent theoretical or computational developments, or critical applications. The goal of the workshop is to increase communications among researchers and especially between biologists and mathematicians, in order to have a better understanding of the theory, to identify challenges and applications of the field, to promote interdisciplinary collaborations, and to accelerate future developments of the field.
Accepted Speakers
Monday, April 27, 2015  

Time  Session 
08:00 AM  Shuttle to MBI 
08:15 AM 09:00 AM  Breakfast 
09:00 AM 09:15 AM  Greetings and info from MBI  Marty Golubitsky 
09:15 AM 09:30 AM  Welcome and Overview  The Organizers 
09:30 AM 10:15 AM  Susan Riechert  Maynard Smith & Parker's (1976) Rule Book for Animal Contests, Mostly Maynard Smith & Parker' 1976 paper on asymmetric games offered animal behaviorists and behavioral ecologists a theoretical framework/guide to understanding animal behavior in competitive contexts. In this essay I trace the influence of this 'contest rule book' from the factors that led the two researchers to develop a treatise on the logic of the asymmetric game to empirical tests of the contest rules and theoretical additions made to the basic model and its underlying assumptions. Over a thousand studies cite this paper directly and thousands more cite work spurred by the original paper. The vast majority of these studies confirm the evolutionarily stable strategy (ESS) predictions made by Maynard Smith & Parker. Theoretical and empirical deviations from EES can largely be explained by the need for further structuring of the analyses into sub games and investigation of less obvious asymmetries than apparent size and resource value. To date, much progress has been made in three areas of interest to behaviorists: (1) understanding of the strategic nature of contests between conspecifics over limited resources; (2) modelling developments that deal with how information about potential asymmetries is gained; and (3) evaluation of the question of honest signaling with specific reference to threat displays. I propose suggestions for future work, much of which will either require collaboration with mathematicians, or require that students interested in animal behavior obtain a strong foundation in biomathematics. My preference is for the latter strategy. 
10:15 AM 10:45 AM  Break 
10:45 AM 11:30 AM  Joel Brown  Plants play games too: How the tragedy of the commons explains much about the vegetation we see Plant communities offer conspicuous displays of woody stems, masses of leaves, and often several layers of such vegetation. Plants in their quest to compete and reproduce seem to produce a lot of biomass.Plant’ play games for nutrients (belowground) and light (aboveground). The solutions to these games result from three sources of a tragedy of the commons. First, the plants overproduce roots to preempt each others access to water and nitrogen. Second, the plants do the same with their leaves to preempt access to light.And third, the plants may invest heavily in stems because the lion’s share of light goes to the tallest plant. We begin with a simple game of belowground root production, we can then examine how asymmetric competition for light amplifies the tragedy of the commons, and finally using a CobbDouglas production function we can integrate roots, leaves and stem into a single model of resource allocation in response to competition. Such models can be placed within the context of population dynamics, plant number, total plant biomass and ultimately new avenues for species coexistence. Not only does evolutionary game theory assist in understanding plants, arguable a game theoretic approach may be the only way to understand some of the most important features of plants and their communities. 
11:30 AM 12:15 PM  Burt Kotler  Foraging games between gerbils and their predators Sand dune dwelling gerbils interact with foxes, owls, and horned vipers in an environment in which resource patches renew and deplete daily. There, gerbils face tradeoffs of food and safety and must use the tools of time allocation and vigilance to manage risk. Predators must contend with gerbil behavior and manage fear using the tools of time allocation and daring. For gerbils, this means optimal patch use and optimal vigilance levels in a depleting environment over the course of the night, i.e, their harvest rates in resource patches must balance energetic, predation, and missed opportunity costs throughout the night, and their vigilance levels must balance predator encounter rate, predator lethality, and the effectiveness of vigilance and decline throughout the night as resources deplete. For predator, this means that they must choose their activity to equalize opportunity throughout the night. The consequences of these are that gerbil activity declines throughout the night in lockstep with predator activity and the apprehensiveness of the gerbils. Furthermore, a complete theory the predatorprey foraging game in gerbils needs to account for the following. 1. Foraging decisions of gerbils are responsive to their own state and that of their predators; owls are responsive only to their own state. 2. The state of a gerbil affects it foraging decisions, and it foraging decisions affect its state. This feedback is necessary to understand risk management by gerbils over a lunar cycle. 3. Gerbils enjoy safety in numbers, and gerbils show densitydependent patch use and habitat selection. This creates a 'risk pump' across habitats as gerbils carry safety with them as they alter habitat use. 4. Sight lines affect the quality of vigilance and risk management in response to different predators. Mechanism of species coexistence with GP???

12:15 PM 02:00 PM  Lunch Break 
02:00 PM 02:45 PM  Amos Bouskila  Different approaches to modeling foraging and predatorprey games among animals Understanding principles and processes in ecology and evolution is not easy. Generating hypotheses and predictions in these disciplines is often not intuitive due, in part, to the many factors that may affect the outcomes of processes. Moreover, some of the situations involve games among various organisms that may lead to unintuitive results. Theoretical models may not provide proofs that we reached full understanding of the system, but they can generate testable hypotheses and predictions and can assist in the understanding of experimental results. Here I describe different modeling approaches we have used to investigate animal decisions in regard to foraging under the risk of predation in two systems. In the first, we interpret the escape strategy of a lizard from an avian predator with a simple decision tree model. The second system describes games among rodents and between rodents and their predators. This system begs for a game theoretic model, and two approaches will be exemplified. A static game has the advantage of simplicity. It can often be solved analytically and its results are relatively easy to interpret. Nevertheless, the simplicity has its costs in terms of realism. Some simplifications embedded in the static approach can be relaxed in a dynamic statevariable game model. These models provide refined insights and more specific predictions, taking into consideration variation in the state of the animals and its temporal dynamics. 
02:45 PM 03:30 PM  Bill Mitchell  Game theory of interactions among predators and groups of prey Abstract not submitted. 
03:30 PM 03:55 PM  Break 
03:55 PM 04:40 PM  Jeff Gore  Cooperation, cheating, and collapse in biological populations Natural populations can suffer catastrophic collapse in response to small changes in environmental conditions, and recovery can be difficult even after the environment is restored to its original condition. We have used laboratory microbial ecosystems to directly measure theoretically proposed early warning signals of impending population collapse based on critical slowing down. Our experimental yeast populations cooperatively break down sugar the sugar sucrose, meaning that below a critical size the population cannot sustain itself. The cooperative nature of yeast growth on sucrose makes the population susceptible to "cheater" cells, which do not contribute to the public good and reduce the resilience of the population. 
04:40 PM 05:15 PM  General Discussion 
05:15 PM 06:45 PM  Reception and Poster Session 
06:45 PM  Shuttle pickup from MBI 
Tuesday, April 28, 2015  

Time  Session 
08:00 AM  Shuttle to MBI 
08:15 AM 09:00 AM  Breakfast 
09:00 AM 09:45 AM  Douglas Morris  Testing predictions from games of habitat selection Abstract not submitted. 
09:45 AM 10:30 AM  Ted Galanthay  Optimal information use in habitat selection How might organisms constrained by perceptual limitations or imperfect information use available information optimally in habitat selection? To begin to answer this question, we study a general ordinary differential equation model of a single species in a twopatch heterogeneous environment in which organisms have access to resource information. There exists a global evolutionarily stable strategy, which depends on the magnitude of the constraints and the heterogeneity of the resources, which leads to the ideal free distribution (IFD). When organisms pay a cost to travel between patches, this strategy is no longer evolutionarily stable, but a strategy that incorporates these costs and does not lead to the IFD is convergent stable. 
10:30 AM 11:00 AM  Break 
11:00 AM 11:45 AM  Barry Sinervo  The rockpaperscissors game is everywhere in nature Abstract not submitted. 
11:45 AM 12:30 PM  Andrew Belmonte  Spatial patterns and interactions in public goods games Abstract not submitted. 
12:30 PM 02:00 PM  Lunch Break 
02:00 PM 02:45 PM  Rick Durrett  Spatial Evolutionary Games Evolutionary games first arose in the work of Maynard Smith and Price in the 70s, who introduced the concept into ecology in order to explain why conflicts over territory between male animals of the same species are usually of the “limited war” type and do not cause serious damage. A second important application, which involves the famousPrisoner's dilemma game, is to understand the persistence of altruistic behavior. There are many other applications, including recent work seeking to understand the competition (and cooperation) of different types of cells in cancer. Most of the analyses of evolutionary game dynamics assume a homogeneously mixing population. However twenty years ago, Nowak and May, and Durrett and Levin showed that space could drastically change the outcome of evolutionary games, for instance allowing cooperators to persist in Prisoner's dilemma. There is now an extensive literature on spatial games, but much of it is based on heuristic principles or approximate analyses. In this talk we will explain how recent work of Cox, Durrett, and Perkins for voter model perturbations can be applied to study spatial evolutionary games in which all relative fitness are close to 1, a situation which covers many applications to cancer. The main result is that the effect of space is equivalent to (i) changing the entries of the game matrix and (ii) replacing the replicator ODE by a related PDE. The first idea is due to Ohtsuki and Nowak (for the pair approximation) while the second is well known in the theory of stochastic spatial processes. A remarkable aspect of our result is that the limiting PDE depends on the kernel which dictates the interaction between players only through the values of two simple probabilities associated with it (an idea initially proposed by Corina Tarnita et al. Due to results of Aronson and Weinberger, and Fife and McLeod, we can analyze any 2x2 game. However, when there are three strategies the limiting object is a system of reaction diffusion equations. Many results can be derived using techniques from my AMS Memoir “Mutual Invadability implies Coexistence” but it is important open problem to understand what happens in the spatial game when the replicator dynamics show bistability. 
02:45 PM 03:30 PM  Yuan Lou  Evolution of dispersal in heterogeneous environments Abstract not submitted. 
03:30 PM 03:45 PM  Break 
03:45 PM 04:30 PM  Kateřina Staňková  Understanding the occurrence of crywolf plants in a tritrophic system This talk will focus on modeling a tritrophic system consisting of plants, herbivores and predators, in which plants release herbivoryinduced chemical signals betraying herbivores to their predators. In this system, socalled “cry wolf” plants occur, which produce signals even when they harbor no or only few herbivores. Initially, these cheating plants enjoy being protected even when they are not attacked, but the predators gradually learn to avoid these plants because they produce a different signal from the other, “honest” plants. This can then be followed by a change of signal of the “crywolf” plants, so that they are again visited by the predators. We propose to model the system in two ways: i. a differential game of a LotkaVolterra type with timevarying decisions of plants having a timevarying probability of being cheaters or honest, and decisions of the predators having a timevarying probability of visiting cheating plants; ii. A local dynamic game played on a finite lattice, described by the same set of equations as model i., where each cell can be inhabited by plants, herbivores, carnivores or empty spaces with certain probability. We analyze both models and compare their predictions with field and laboratory data. We then hypothesize which elements are important for coexistence of cheating and honest plants in the system and discuss (among others) whether spatial models are necessary to explain this coexistence. 
04:30 PM 05:00 PM  General Discussion 
05:00 PM  Shuttle pickup from MBI 
Wednesday, April 29, 2015  

Time  Session 
08:00 AM  Shuttle to MBI 
08:15 AM 09:00 AM  Breakfast 
09:00 AM 09:45 AM  Johan Metz  Evolutionary branching in the multivariate case Over the last two decades evolutionary branching has emerged as a possible mathematical paradigm for explaining the origination of phenotypic diversity. Although branching is well understood for onedimensional trait spaces, a similarly detailed understanding for higher dimensional trait spaces was still lacking. However, we recently arrived at some, surprising, first insights. In particular, we have shown that, as long as the evolutionary trajectory stays within the reign of the local quadratic approximation of the fitness function, any initial small scale polymorphism around an attracting invadable evolutionarily singular strategy (ess) will evolve towards a dimorphism. That is, if the trajectory does not pass the boundary of the domain of dimorphic coexistence and falls back to monomorphism (after which it moves again towards the singular strategy and from there on to a small scale polymorphism, etc.). To reach these results we analyzed in some detail the behaviour of the solutions of the coupled Landeequations purportedly satisfied by the phenotypic clusters of a quasi$n$morphism, and give a precise characterisation of the local geometry of the set $mathcal D$ in traitspace squared harbouring protected dimorphisms. Another matter is that in higher dimensional trait spaces an attracting invadable ess needs not connect to $mathcal D$ at all. However, for the practically important subset of strongly attracting esses (i.e., esses that robustly locally attract the (quasi)monomorphic evolutionary dynamics for all possible nondegenerate mutational (or genetic) covariance matrices) invadability implies that the ess connects to $mathcal D$, however without the guarantee that the polymorphic evolutionary trajectory will not revert to monomorphism still within the reign of the local quadratic approximation for the invasion fitnesses. 
09:45 AM 10:30 AM  Christoph Hauert  Origin and Structure of Social Networks Based on Cooperative Actions Abstract not submitted. 
10:30 AM 11:00 AM  Break 
11:00 AM 11:45 AM  Mark Broom  Modelling evolution in structured populations involving multiplayer interactions Within the last ten years, models of evolution have begun to incorporate structured populations, including spatial structure, through the modelling of evolutionary processes on graphs (evolutionary graph theory). One limitation of this otherwise quite general framework is that interactions are restricted to pairwise ones, through the edges connecting pairs of individuals. Yet many animal interactions can involve many individuals, and theoretical models also describe such multiplayer interactions. We shall discuss a more general modelling framework of interactions of structured populations, including the example of competition between territorial animals. Depending upon the behaviour concerned, we can embed the results of different evolutionary games within our structure, as occurs for pairwise games such as the Prisoner's Dilemma or the HawkDove game on graphs. For a population to evolve we also need an evolutionary dynamics, and we demonstrate a birthdeath dynamics for our framework. Finally we discuss some examples together with some important differences between this approach and evolutionary graph theory. 
11:45 AM 12:30 PM  Chris Cannings  Evolution of Animal Networks Joint work with Prof Mark Broom, City University, London. Consider a populations of individuals with pairwise relationships between those individuals. We represent this population by a simple graph G = (V, E), where V is the set of vertices representing the individuals and E ⊆ V ∗ V representing the existing relationships. The degree of a vertex x, d(x), is the number of vertices to which x is linked. We suppose that, labeling the vertices as {x1,x2,...,xn}, vertex xi has a target ti, which represents the degree which individual xi would ideally possess.A sequence {t1,t2,...,tn} is said to be graphic if there exists a simple graph which has precisely those degrees. In that case each individual could satisfy its target. On the other hand in general there will be some deviation from the set of targets. We consider the evolution of the network with the the following Markov Chain; at time t pick a vertex i with probability 1/n (independently of previous picks), if the vertex has degree equal to its target (a Neutral) then nothing happens, if the vertex has degree less than its target (a Joiner) then an edge (i,j) is added picking a possible j with equal probabilities over those available, while if the vertex has degree greater than its target (a Breaker) an edge (i,j) is removed picking a j with equal probability from those available. A graph G has deviation d(G) = Σi ∈ {1, 2, . . . , n}d(xi) − t(xi). It is proved that the set of graphs with minimal deviation is connected under the above Markov Chain, and that the chain converges to that set. The Markov Chain over that minimal set is reversible, so satisfies the complete balance condition. Some examples are given. In a further model we allow the individuals to select the change they induce when selected so that they improve their total payoff, (d(x) − t(x)), over the resulting stationary distribution compared with the current one. Variants of this model will be considered and some examples given. 
12:30 PM 02:00 PM  Lunch Break 
02:00 PM 02:45 PM  Sebastian Schreiber  Evolution and coevolution of habitat choice in stochastic environments Habitat selection by individuals can profoundly influence population persistence in heterogenous landscapes, stability of predatorprey interactions, and geographical shifts in species distributions in response to climate change. While there are significant and extensive advances in the evolutionary theory of habitat selection for populations living in spatially heterogeneous environments, the combined effects of temporal and spatial variation on the evolution of habitat selection is less well understood. Given the ubiquity of temporal variation and its notable impacts on demography, I will introduce a multispecies framework for studying evolutionarily stable strategies (ESSs) for habitat selection using systems of stochastic differential equations (SDEs). I will illustrate how spatialtemporal variation can select for sink populations, opposing habitat preferences for predators and their prey, and niche overlap for competing species. Part of this work is in collaboration with Steve Evans (UC Berkeley) and Alex Hening (Oxford). 
02:45 PM 03:30 PM  Zhijun Wu  Evolution of Social Cliques Species make social contacts and form social networks. The latter may have great impacts on the evolution of a population, such as preserving certain genetic features, sharing knowledge and information, preventing invasions, etc. In this talk, we show that the evolution of a population over a social network can be modeled as a symmetric evolutionary game. Its equilibrium states can therefore be obtained and analyzed by solving an optimization problem called the generalized knapsack problem. We show that an equilibrium state often corresponds to a social clique, when the population is distributed evenly on the clique. However, an equilibrium state may or may not be evolutionarily stable, whether it is on a clique or not. Only those stable ones may be observable or sustainable in nature. We analyze several different types of equilibrium states and prove a set of conditions for their stabilities. We show in particular that the equilibrium states on cliques are evolutionarily stable except for special circumstances, while nonclique equilibrium states are unstable in general. Therefore, the optimal clique strategies should have an evolutionary advantage over the nonclique ones. 
03:30 PM 03:45 PM  Break 
03:45 PM 04:30 PM  Kalle Parvinen  Evolutionary suicide and the adaptive dynamics of cooperation and dispersal Abstract not submitted. 
04:30 PM 05:00 PM  General Discussion 
05:00 PM  Shuttle pickup from MBI 
Thursday, April 30, 2015  

Time  Session 
08:00 AM  Shuttle to MBI 
08:00 AM 08:15 AM  Banquet at Crowne Plaza 
08:15 AM 09:00 AM  Breakfast 
09:00 AM 09:45 AM  Robert Austin  Cancer and Evolutionary Game Theory Abstract not submitted. 
09:45 AM 10:30 AM  Athena Aktipis  Needbased transfers and cooperation in uncertain environments Abstract not submitted. 
10:30 AM 11:00 AM  Break 
11:00 AM 11:45 AM  John Nagy  Coevolving Cancer Hallmarks Abstract not submitted. 
11:45 AM 12:30 PM  Jim Cushing  Some bifurcation theorems for evolutionary game theoretic versions of matrix models for structured population dynamics I’ll describe some theorems concerning the fundamental bifurcations that can occur as r (or R0) increases through 1 for evolutionary versions of matrix models for structured population dynamics. I’ll illustrate the theorems with applications motivated by recent observations from field studies of nesting colonies of gulls on Protection Island National Wildlife Refuge in the Strait Juan de Fuca (between Vancouver Island and the state of Washington). These observations concern changes in life history strategies (such as a rise in egg cannibalism and changes in the timing of egg laying) which have been correlated with an increase in mean sea temperature in the Strait. 
12:30 PM 02:00 PM  Lunch Break 
02:00 PM 02:45 PM  Tim Reluga  Challenges in the unification of life history theory and evolutionary game theory In my talk, I'll review the approach to population games my collaborators and I have used to study epidemic games over the last 10 years. I'll review the basic derivations, highlight the strengths and weaknesses of the approach, and discuss some of the current mathematical challenges we face in generalizing the results obtained so far. 
02:45 PM 03:30 PM  Rosalyn Rael  Multiscale Evolutionary Game Theory Modeling of Food Webs Abstract not submitted. 
03:30 PM 05:00 PM  General Discussion / Working in groups 
05:00 PM  Shuttle pickup from MBI 
06:00 PM 09:00 PM  Banquet at Crowne Plaza 
Friday, May 1, 2015  

Time  Session 
08:00 AM  Shuttle to MBI 
08:15 AM 09:00 AM  Breakfast 
09:00 AM 09:45 AM  Priyanga Amarasekare  Evolution of thermal reaction norms in response to climate warming: a game theoretical perspective Abstract not submitted. 
09:45 AM 10:30 AM  Jacek Miekisz  Strategy dependent time delays in replicator dynamics It is usually assumed that interactions between individuals immediately affect the state of population. In reality, in biological models, results of interactions may appear in the future, and in social models, individuals or players may act, that is choose appropriate strategies, on the basis of the information concerning events in the past. It is well known that time delays may cause oscillations in dynamical systems. We will show that the presence of oscillations in such systems depends on particular causes of time delays. In particular, we will discuss two evolutionary game models with the same payoff matrix and with a stable and unstable interior stationary point. We modify above models to allow time delays to be strategydependent. They exhibit a novel behavior: after transient oscillations, the population settles at an equilibrium which depends on time delays. We will discuss stability of stationary states in stochastic models of finite populations with time delays. 
10:30 AM 11:00 AM  Break 
11:00 AM 11:45 AM  Vlastimil Krivan  The habitat selection game In my talk I will discuss the Habitat selection game, a gametheoretical concept aiming to describe animal distributions in space. This concept generalizes the Ideal Free Distribution of Fretwell andLucas in several directions. For a single population, it providescharacterization under which the IFD is evolutionarily stable. I willbriefly discuss examples with the Allee type population growth, costof dispersal and some applications for optimal harvesting. Extensionsfor two species (either competing or in predatorprey relation) willbe discussed too. 
11:45 AM 12:30 PM  General Discussion / Working in groups 
12:30 PM  Shuttle pickup from MBI (One to airport and one back to hotel) 
Name  Affiliation  

Aktipis, Athena  aktipis@asu.edu  Psychology, Arizona State University 
Amarasekare, Priyanga  amarasek@ucla.edu  Ecology and Evolutionary Biology, University of California Los Angeles 
Austin, Robert  austin@princeton.edu  Physics, Princeton University 
Baetens, Jan  Jan.baetens@ugent.be  Mathematical Modelling, Statistics and Bioinformatics, Ghent University 
Belmonte, Andrew  andrew.belmonte@gmail.com  Department of Mathematics, Pennsylvania State University 
Bouskila, Amos  bouskila@bgu.ac.il  Life Sciences, BenGurion Univ. of the Negev 
Broom, Mark  mark.broom.1@city.ac.uk  Department of Mathematics, City University London 
Brown, Joel  squirrel@uic.edu  Biological Sciences, University of Illinois at Chicago 
Cannings, Chris  C.Cannings@shef.ac.uk  school of maths and stats, university 
Dall, Sasha  S.R.X.Dall@exeter.ac.uk  Centre for Ecology & Conservation, University of Exeter 
deForest, Russ  russell.f.deforest@gmail.com  Mathematics, Pennsylvania State University 
Durrett, Rick  rtd@math.duke.edu  Department of Mathematics, Duke University 
Galanthay, Ted  tgalanthay@ithaca.edu  Mathematics, Ithaca College 
Ghim, CheolMin  cmghim@unist.ac.kr  School of Life Sciences, Ulsan National Institute of Science and Technology 
Gore, Jeff  gore@mit.edu  Physics, MIT 
Griffin, Christopher  griffinch@ieee.org  Applied Research Laboratory, The Pennsylvania State University 
Halloway, Abdel  abdel.halloway@gmail.com  Biological sciences, University of Illinois at Chicago 
Hauert, Christoph  christoph.hauert@math.ubc.ca  Department of Mathematics, University of British Columbia 
Hayat, Muhammad  mqasimhayat@hotmail.com  Department of Plant Biotechnology, National Univeristy of Sciences and Technology, H12 Islamabad, Pakistan 
Hilbe, Christian  hilbe@fas.harvard.edu  Program for Evolutionary Dynamics, Harvard University 
Kang, Yun  yun.kang@asu.edu  Applied Sciences and Mathematics, Arizona State University 
Kotler, Burt  kotler@bgu.ac.il  Mitrani Department of Desert Ecology, BenGurion University 
Krivan, Vlastimil  vlastimil.krivan@gmail.com  Mathematics and Biomathematics, Faculty of Science, University of South Bohemia 
Lou, Yuan  lou@math.ohiostate.edu  Department of Mathematics, The Ohio State University 
Metz, Johan  j.a.j.metz@biology.leidenuniv.nl  Plant Ecology and Phytochemistry, Analysis and Dynamical Systems, Institute of Biology, Mathematical Institute 
Miekisz, Jacek  miekisz@mimuw.edu.pl  Institute of Applied Mathematics, University of Warsaw 
Mitchell, Bill  William.Mitchell@indstate.edu  Biology, Indiana State University 
Morris, Douglas  douglas.morris@lakeheadu.ca  Biology, Lakehead University 
Munther, Daniel  danielsmunther@gmail.com  Mathematics, Cleveland State University 
Nagy, John  john.nagy@scottsdalecc.edu  Life Sciences, Scottsdale Community College 
Parvinen, Kalle  kalle.parvinen@utu.fi  Department of Mathematics and Statistics, University of Turku 
Rael, Rosalyn  Rosalyn.rael@gmail.com  Center for Bioenvironmental Research, Tulane University 
Reluga, Tim  treluga@math.psu.edu  Department of Mathematics, Pennsylvania State University 
Riechert, Susan  sriecher@utk.edu  Department of Ecology and Evolutionary Biology, University of Tennessee 
Robertson, Suzanne  srobertson7@vcu.edu  Department of Mathematics and Applied Mathematics, Virginia Commonwealth University 
Schreiber, Sebastian  sschreiber@ucdavis.edu  Department of Evolution and Ecology, University of California, Davis 
Sinervo, Barry  lizardrps@gmail.com  Ecology and Evolutionary Biology, UC Santa Cruz 
Stankova, Katerina  k.stankova@maastrichtuniversity.nl  Department of Knowledge Engineering, Maastricht University 
Toupo, Danielle  Dpt35@cornell.edu  Applied mathematics, Cornell University 
van Gils, Jan  Jan.van.Gils@nioz.nl  Marine Ecology, NIOZ Royal Netherlands Institute for Sea Research 
Ventura, Rafael  rhv3@duke.edu  Philosophy Department, Duke University 
Vital, Dieff  dieff.vital001@mymdc.net  Engineering, Miami Dade College 
Wang, Min  mwang@iastate.edu  Mathematics & Statistics, Iowa State University 
Wu, Zhijun  zhijun@iastate.edu  Math, Bioinformatics, & Computational Biology, Iowa State University 
Zhou, Wen (Rick)  rickzhouwen@gmail.com  Statistics, Colorado State University 
Zimmerman, Mark  zimmermanmp@vcu.edu  Mathematics and Applied Mathematics, Virginia Commonwealth University 
Abstract not submitted.
Abstract not submitted.
Abstract not submitted.
Abstract not submitted.
Understanding principles and processes in ecology and evolution is not easy. Generating hypotheses and predictions in these disciplines is often not intuitive due, in part, to the many factors that may affect the outcomes of processes. Moreover, some of the situations involve games among various organisms that may lead to unintuitive results. Theoretical models may not provide proofs that we reached full understanding of the system, but they can generate testable hypotheses and predictions and can assist in the understanding of experimental results. Here I describe different modeling approaches we have used to investigate animal decisions in regard to foraging under the risk of predation in two systems. In the first, we interpret the escape strategy of a lizard from an avian predator with a simple decision tree model. The second system describes games among rodents and between rodents and their predators. This system begs for a game theoretic model, and two approaches will be exemplified. A static game has the advantage of simplicity. It can often be solved analytically and its results are relatively easy to interpret. Nevertheless, the simplicity has its costs in terms of realism. Some simplifications embedded in the static approach can be relaxed in a dynamic statevariable game model. These models provide refined insights and more specific predictions, taking into consideration variation in the state of the animals and its temporal dynamics.
Within the last ten years, models of evolution have begun to incorporate structured populations, including spatial structure, through the modelling of evolutionary processes on graphs (evolutionary graph theory). One limitation of this otherwise quite general framework is that interactions are restricted to pairwise ones, through the edges connecting pairs of individuals. Yet many animal interactions can involve many individuals, and theoretical models also describe such multiplayer interactions. We shall discuss a more general modelling framework of interactions of structured populations, including the example of competition between territorial animals. Depending upon the behaviour concerned, we can embed the results of different evolutionary games within our structure, as occurs for pairwise games such as the Prisoner's Dilemma or the HawkDove game on graphs. For a population to evolve we also need an evolutionary dynamics, and we demonstrate a birthdeath dynamics for our framework. Finally we discuss some examples together with some important differences between this approach and evolutionary graph theory.
Plant communities offer conspicuous displays of woody stems, masses of leaves, and often several layers of such vegetation. Plants in their quest to compete and reproduce seem to produce a lot of biomass.Plant’ play games for nutrients (belowground) and light (aboveground). The solutions to these games result from three sources of a tragedy of the commons. First, the plants overproduce roots to preempt each others access to water and nitrogen. Second, the plants do the same with their leaves to preempt access to light.And third, the plants may invest heavily in stems because the lion’s share of light goes to the tallest plant. We begin with a simple game of belowground root production, we can then examine how asymmetric competition for light amplifies the tragedy of the commons, and finally using a CobbDouglas production function we can integrate roots, leaves and stem into a single model of resource allocation in response to competition. Such models can be placed within the context of population dynamics, plant number, total plant biomass and ultimately new avenues for species coexistence. Not only does evolutionary game theory assist in understanding plants, arguable a game theoretic approach may be the only way to understand some of the most important features of plants and their communities.
Joint work with Prof Mark Broom, City University, London.
Consider a populations of individuals with pairwise relationships between those individuals. We represent this population by a simple graph G = (V, E), where V is the set of vertices representing the individuals and E ⊆ V ∗ V representing the existing relationships. The degree of a vertex x, d(x), is the number of vertices to which x is linked. We suppose that, labeling the vertices as {x1,x2,...,xn}, vertex xi has a target ti, which represents the degree which individual xi would ideally possess.A sequence {t1,t2,...,tn} is said to be graphic if there exists a simple graph which has precisely those degrees. In that case each individual could satisfy its target. On the other hand in general there will be some deviation from the set of targets. We consider the evolution of the network with the the following Markov Chain; at time t pick a vertex i with probability 1/n (independently of previous picks), if the vertex has degree equal to its target (a Neutral) then nothing happens, if the vertex has degree less than its target (a Joiner) then an edge (i,j) is added picking a possible j with equal probabilities over those available, while if the vertex has degree greater than its target (a Breaker) an edge (i,j) is removed picking a j with equal probability from those available. A graph G has deviation d(G) = Σi ∈ {1, 2, . . . , n}d(xi) − t(xi). It is proved that the set of graphs with minimal deviation is connected under the above Markov Chain, and that the chain converges to that set. The Markov Chain over that minimal set is reversible, so satisfies the complete balance condition. Some examples are given. In a further model we allow the individuals to select the change they induce when selected so that they improve their total payoff, (d(x) − t(x)), over the resulting stationary distribution compared with the current one. Variants of this model will be considered and some examples given.
Evolutionary games first arose in the work of Maynard Smith and Price in the 70s, who introduced the concept into ecology in order to explain why conflicts over territory between male animals of the same species are usually of the “limited war” type and do not cause serious damage. A second important application, which involves the famousPrisoner's dilemma game, is to understand the persistence of altruistic behavior. There are many other applications, including recent work seeking to understand the competition (and cooperation) of different types of cells in cancer.
Most of the analyses of evolutionary game dynamics assume a homogeneously mixing population. However twenty years ago, Nowak and May, and Durrett and Levin showed that space could drastically change the outcome of evolutionary games, for instance allowing cooperators to persist in Prisoner's dilemma. There is now an extensive literature on spatial games, but much of it is based on heuristic principles or approximate analyses. In this talk we will explain how recent work of Cox, Durrett, and Perkins for voter model perturbations can be applied to study spatial evolutionary games in which all relative fitness are close to 1, a situation which covers many applications to cancer.
The main result is that the effect of space is equivalent to (i) changing the entries of the game matrix and (ii) replacing the replicator ODE by a related PDE. The first idea is due to Ohtsuki and Nowak (for the pair approximation) while the second is well known in the theory of stochastic spatial processes. A remarkable aspect of our result is that the limiting PDE depends on the kernel which dictates the interaction between players only through the values of two simple probabilities associated with it (an idea initially proposed by Corina Tarnita et al. Due to results of Aronson and Weinberger, and Fife and McLeod, we can analyze any 2x2 game. However, when there are three strategies the limiting object is a system of reaction diffusion equations. Many results can be derived using techniques from my AMS Memoir “Mutual Invadability implies Coexistence” but it is important open problem to understand what happens in the spatial game when the replicator dynamics show bistability.
How might organisms constrained by perceptual limitations or imperfect information use available information optimally in habitat selection? To begin to answer this question, we study a general ordinary differential equation model of a single species in a twopatch heterogeneous environment in which organisms have access to resource information. There exists a global evolutionarily stable strategy, which depends on the magnitude of the constraints and the heterogeneity of the resources, which leads to the ideal free distribution (IFD). When organisms pay a cost to travel between patches, this strategy is no longer evolutionarily stable, but a strategy that incorporates these costs and does not lead to the IFD is convergent stable.
Natural populations can suffer catastrophic collapse in response to small changes in environmental conditions, and recovery can be difficult even after the environment is restored to its original condition. We have used laboratory microbial ecosystems to directly measure theoretically proposed early warning signals of impending population collapse based on critical slowing down. Our experimental yeast populations cooperatively break down sugar the sugar sucrose, meaning that below a critical size the population cannot sustain itself. The cooperative nature of yeast growth on sucrose makes the population susceptible to "cheater" cells, which do not contribute to the public good and reduce the resilience of the population.
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Sand dune dwelling gerbils interact with foxes, owls, and horned vipers in an environment in which resource patches renew and deplete daily. There, gerbils face tradeoffs of food and safety and must use the tools of time allocation and vigilance to manage risk. Predators must contend with gerbil behavior and manage fear using the tools of time allocation and daring. For gerbils, this means optimal patch use and optimal vigilance levels in a depleting environment over the course of the night, i.e, their harvest rates in resource patches must balance energetic, predation, and missed opportunity costs throughout the night, and their vigilance levels must balance predator encounter rate, predator lethality, and the effectiveness of vigilance and decline throughout the night as resources deplete. For predator, this means that they must choose their activity to equalize opportunity throughout the night. The consequences of these are that gerbil activity declines throughout the night in lockstep with predator activity and the apprehensiveness of the gerbils. Furthermore, a complete theory the predatorprey foraging game in gerbils needs to account for the following. 1. Foraging decisions of gerbils are responsive to their own state and that of their predators; owls are responsive only to their own state. 2. The state of a gerbil affects it foraging decisions, and it foraging decisions affect its state. This feedback is necessary to understand risk management by gerbils over a lunar cycle. 3. Gerbils enjoy safety in numbers, and gerbils show densitydependent patch use and habitat selection. This creates a 'risk pump' across habitats as gerbils carry safety with them as they alter habitat use. 4. Sight lines affect the quality of vigilance and risk management in response to different predators.
Mechanism of species coexistence with GP???
 Empirical field behavior from Kotler et al 2002
 Numbered List of experimental results a complete theory must include
 Feedback of state and behavior
 Full state. Gerbils respond to own state and that of the owls; owls respond only to own
 Temporal month, night
 Spatial including risk pump
 Sight lines
 Owls and activity
In my talk I will discuss the Habitat selection game, a gametheoretical concept aiming to describe animal distributions in space. This concept generalizes the Ideal Free Distribution of Fretwell andLucas in several directions. For a single population, it providescharacterization under which the IFD is evolutionarily stable. I willbriefly discuss examples with the Allee type population growth, costof dispersal and some applications for optimal harvesting. Extensionsfor two species (either competing or in predatorprey relation) willbe discussed too.
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Over the last two decades evolutionary branching has emerged as a possible mathematical paradigm for explaining the origination of phenotypic diversity. Although branching is well understood for onedimensional trait spaces, a similarly detailed understanding for higher dimensional trait spaces was still lacking. However, we recently arrived at some, surprising, first insights. In particular, we have shown that, as long as the evolutionary trajectory stays within the reign of the local quadratic approximation of the fitness function, any initial small scale polymorphism around an attracting invadable evolutionarily singular strategy (ess) will evolve towards a dimorphism. That is, if the trajectory does not pass the boundary of the domain of dimorphic coexistence and falls back to monomorphism (after which it moves again towards the singular strategy and from there on to a small scale polymorphism, etc.). To reach these results we analyzed in some detail the behaviour of the solutions of the coupled Landeequations purportedly satisfied by the phenotypic clusters of a quasi$n$morphism, and give a precise characterisation of the local geometry of the set $mathcal D$ in traitspace squared harbouring protected dimorphisms. Another matter is that in higher dimensional trait spaces an attracting invadable ess needs not connect to $mathcal D$ at all. However, for the practically important subset of strongly attracting esses (i.e., esses that robustly locally attract the (quasi)monomorphic evolutionary dynamics for all possible nondegenerate mutational (or genetic) covariance matrices) invadability implies that the ess connects to $mathcal D$, however without the guarantee that the polymorphic evolutionary trajectory will not revert to monomorphism still within the reign of the local quadratic approximation for the invasion fitnesses.
It is usually assumed that interactions between individuals immediately affect the state of population. In reality, in biological models, results of interactions may appear in the future, and in social models, individuals or players may act, that is choose appropriate strategies, on the basis of the information concerning events in the past.
It is well known that time delays may cause oscillations in dynamical systems. We will show that the presence of oscillations in such systems depends on particular causes of time delays. In particular, we will discuss two evolutionary game models with the same payoff matrix and with a stable and unstable interior stationary point.
We modify above models to allow time delays to be strategydependent. They exhibit a novel behavior: after transient oscillations, the population settles at an equilibrium which depends on time delays.
We will discuss stability of stationary states in stochastic models of finite populations with time delays.
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In my talk, I'll review the approach to population games my collaborators and I have used to study epidemic games over the last 10 years. I'll review the basic derivations, highlight the strengths and weaknesses of the approach, and discuss some of the current mathematical challenges we face in generalizing the results obtained so far.
Maynard Smith & Parker' 1976 paper on asymmetric games offered animal behaviorists and behavioral ecologists a theoretical framework/guide to understanding animal behavior in competitive contexts. In this essay I trace the influence of this 'contest rule book' from the factors that led the two researchers to develop a treatise on the logic of the asymmetric game to empirical tests of the contest rules and theoretical additions made to the basic model and its underlying assumptions. Over a thousand studies cite this paper directly and thousands more cite work spurred by the original paper. The vast majority of these studies confirm the evolutionarily stable strategy (ESS) predictions made by Maynard Smith & Parker. Theoretical and empirical deviations from EES can largely be explained by the need for further structuring of the analyses into sub games and investigation of less obvious asymmetries than apparent size and resource value. To date, much progress has been made in three areas of interest to behaviorists: (1) understanding of the strategic nature of contests between conspecifics over limited resources; (2) modelling developments that deal with how information about potential asymmetries is gained; and (3) evaluation of the question of honest signaling with specific reference to threat displays. I propose suggestions for future work, much of which will either require collaboration with mathematicians, or require that students interested in animal behavior obtain a strong foundation in biomathematics. My preference is for the latter strategy.
Habitat selection by individuals can profoundly influence population persistence in heterogenous landscapes, stability of predatorprey interactions, and geographical shifts in species distributions in response to climate change. While there are significant and extensive advances in the evolutionary theory of habitat selection for populations living in spatially heterogeneous environments, the combined effects of temporal and spatial variation on the evolution of habitat selection is less well understood. Given the ubiquity of temporal variation and its notable impacts on demography, I will introduce a multispecies framework for studying evolutionarily stable strategies (ESSs) for habitat selection using systems of stochastic differential equations (SDEs). I will illustrate how spatialtemporal variation can select for sink populations, opposing habitat preferences for predators and their prey, and niche overlap for competing species. Part of this work is in collaboration with Steve Evans (UC Berkeley) and Alex Hening (Oxford).
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This talk will focus on modeling a tritrophic system consisting of plants, herbivores and predators, in which plants release herbivoryinduced chemical signals betraying herbivores to their predators. In this system, socalled “cry wolf” plants occur, which produce signals even when they harbor no or only few herbivores. Initially, these cheating plants enjoy being protected even when they are not attacked, but the predators gradually learn to avoid these plants because they produce a different signal from the other, “honest” plants. This can then be followed by a change of signal of the “crywolf” plants, so that they are again visited by the predators.
We propose to model the system in two ways: i. a differential game of a LotkaVolterra type with timevarying decisions of plants having a timevarying probability of being cheaters or honest, and decisions of the predators having a timevarying probability of visiting cheating plants; ii. A local dynamic game played on a finite lattice, described by the same set of equations as model i., where each cell can be inhabited by plants, herbivores, carnivores or empty spaces with certain probability.
We analyze both models and compare their predictions with field and laboratory data. We then hypothesize which elements are important for coexistence of cheating and honest plants in the system and discuss (among others) whether spatial models are necessary to explain this coexistence.
Species make social contacts and form social networks. The latter may have great impacts on the evolution of a population, such as preserving certain genetic features, sharing knowledge and information, preventing invasions, etc. In this talk, we show that the evolution of a population over a social network can be modeled as a symmetric evolutionary game. Its equilibrium states can therefore be obtained and analyzed by solving an optimization problem called the generalized knapsack problem. We show that an equilibrium state often corresponds to a social clique, when the population is distributed evenly on the clique. However, an equilibrium state may or may not be evolutionarily stable, whether it is on a clique or not. Only those stable ones may be observable or sustainable in nature. We analyze several different types of equilibrium states and prove a set of conditions for their stabilities. We show in particular that the equilibrium states on cliques are evolutionarily stable except for special circumstances, while nonclique equilibrium states are unstable in general. Therefore, the optimal clique strategies should have an evolutionary advantage over the nonclique ones.