CTW: Evolutionary Game Theory

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  Maynard Smith & Parker's (1976) Rule Book for Animal Contests, Mostly
  Susan Riechert

  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.

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  Plants play games too: How the tragedy of the commons explains much about the vegetation we see
  Joel Brown

  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 over-produce roots to pre-empt each others access to water and nitrogen. Second, the plants do the same with their leaves to pre-empt 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 Cobb-Douglas 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.

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  Foraging games between gerbils and their predators
  Burt Kotler
  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 lock-step with predator activity and the apprehensiveness of the gerbils. Furthermore, a complete theory the predator-prey 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 density-dependent 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
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  Using game theory as a first order approximation to cancer evolution
  David Basanta

  Abstract not submitted.

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  Playing games in the mud: interactions between shorebirds and their benthic prey
  Jan van Gils

  Abstract not submitted.

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  The habitat selection game
  Vlastimil Krivan
  In my talk I will discuss the Habitat selection game, a game-theoretical concept aiming to describe animal distributions in space. This concept generalizes the Ideal Free Distribution of Fretwell and Lucas in several directions. For a single population, it provides characterization under which the IFD is evolutionarily stable. I will briefly discuss examples with the Allee type population growth, cost of dispersal and some applications for optimal harvesting. Extensions for two species (either competing or in predator-prey relation) will be discussed too.
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  Strategy dependent time delays in replicator dynamics
  Jacek Miekisz

  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 strategy-dependent. 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.