64
P.A. Whigharn . G.ß. Fogel
plant defenses. The work allowed an investigation of density dependence and
allowed several conclusions relating to coevolutionary patterns to be inferred.
4.4.6
Predator-Prey Algorithms
Following the traditional predator-prey models studied by Lotka and Volterra
(Lotka 1927) a number of works have studied competitive coevolution to model
predator-prey behaviour (Haynes et al. 1995; Cliff and Miller 1996; Haynes and
Sen 1996; Rosin and ßelew 1997). These models use competition between
evolving communities of predators and prey to demonstrate how survival
strategies and behaviour can coevolve. Since the complexity of real pursuitevasion are too difficult to code as a simple set of differential equations, the use of
evolving models affords more complex instances, such as perceptual
specialization, behaviour prediction and planning, to be studied.
The concept of evolutionary stable strategies (ESS) (Smith and Price 1973;
Smith 1982) has been commonly used to predict the behaviour and characteristics
of naturally evolved organisms (Dawkins 1989; Motro 1991; Visser et al. 1992;
Wolf and Waltz 1993). The behaviour of complex adaptive systems are
anticipated by examining an evolutionary garne with various possible strategies
for each player and prescribed payoffs dependent on the play of all participants.
The equilibrium conditions of the garne are deterrnined mathematically and it is
assumed that once the players' strategies have reached an equilibrium, they will
tend to remain in that condition, barring external influences. The hawk-dove garne
is a typical example of agame that can lead to an ESS condition given a variety of
assumptions regarding the population including an infinite population and payoffs
to competitors described only on the average. With these assumptions,
mathematics can be used to determine the ESS for the population. Evolutionary
computation has been applied to the hawk-dove garne in order to determine if the
ESS maintains value under the realization that in natural populations, the
assumptions mentioned above are not realistic (Fogel and Fogel 1995; Fogel and
Fogel 1997; Fogel et al. 1998). Under more realistic conditions of finite
populations and stochastic payoffs, the evolutionary simulations demonstrated that
populations may evolve in trajectories that are unrelated to an ESS, even in very
simple systems with small populations. This more realistic modelling of an
evolving system has therefore cast doubt on the utility of ESSs to provide useful
explanations of the behaviour of populations even at relatively low levels of
selection, even under persistent mixing.
P.A. Whigharn . G.ß. Fogel
plant defenses. The work allowed an investigation of density dependence and
allowed several conclusions relating to coevolutionary patterns to be inferred.
4.4.6
Predator-Prey Algorithms
Following the traditional predator-prey models studied by Lotka and Volterra
(Lotka 1927) a number of works have studied competitive coevolution to model
predator-prey behaviour (Haynes et al. 1995; Cliff and Miller 1996; Haynes and
Sen 1996; Rosin and ßelew 1997). These models use competition between
evolving communities of predators and prey to demonstrate how survival
strategies and behaviour can coevolve. Since the complexity of real pursuitevasion are too difficult to code as a simple set of differential equations, the use of
evolving models affords more complex instances, such as perceptual
specialization, behaviour prediction and planning, to be studied.
The concept of evolutionary stable strategies (ESS) (Smith and Price 1973;
Smith 1982) has been commonly used to predict the behaviour and characteristics
of naturally evolved organisms (Dawkins 1989; Motro 1991; Visser et al. 1992;
Wolf and Waltz 1993). The behaviour of complex adaptive systems are
anticipated by examining an evolutionary garne with various possible strategies
for each player and prescribed payoffs dependent on the play of all participants.
The equilibrium conditions of the garne are deterrnined mathematically and it is
assumed that once the players' strategies have reached an equilibrium, they will
tend to remain in that condition, barring external influences. The hawk-dove garne
is a typical example of agame that can lead to an ESS condition given a variety of
assumptions regarding the population including an infinite population and payoffs
to competitors described only on the average. With these assumptions,
mathematics can be used to determine the ESS for the population. Evolutionary
computation has been applied to the hawk-dove garne in order to determine if the
ESS maintains value under the realization that in natural populations, the
assumptions mentioned above are not realistic (Fogel and Fogel 1995; Fogel and
Fogel 1997; Fogel et al. 1998). Under more realistic conditions of finite
populations and stochastic payoffs, the evolutionary simulations demonstrated that
populations may evolve in trajectories that are unrelated to an ESS, even in very
simple systems with small populations. This more realistic modelling of an
evolving system has therefore cast doubt on the utility of ESSs to provide useful
explanations of the behaviour of populations even at relatively low levels of
selection, even under persistent mixing.