Three Illustrations of Artificial Life's Working Hypothesis

Arti cial life uses computer models to study the essential nature of the characteristic processes of complex adaptive systems| proceses such as self-organization, adaptation, and evolution. Work in the eld is guided by the working hypothesis that simple computer models can capture the essential nature of these processes. This hypothesis is illustrated by recent results with a simple population of computational agents whose sensorimotor functionality undergo open-ended adaptive evolution. These might illuminate three aspects of complex adaptive systems in general: punctuated equilibrium dynamics of diversity, a transition separating genetic order and disorder, and a law of adaptive evolutionary activity. 1 Arti cial Life's Working Hypothesis Arti cial life studies computer models of the processes characteristic of complex adaptive systems|processes like self-organization, self-reproduction, adaptation, and evolution. Complex adaptive systems take many forms, each of which di ers from the others in myriad ways. By abstracting away from the diverse details, arti cial life hopes to reveal fundamental principles governing broad classes of complex adaptive systems. This hope rests on arti cial life's working hypothesis that simple computer models can capture the essential nature of complex adaptive systems [1]. I propose to pursue arti cial life's working hypothesis by applying a \thermodynamic" methodology [5, 6, 3, 4, 2, 7]. Recently it has been suggested that there is a close, intrinsic connection between the content of evolution and thermodynamics (e.g., Brooks and Wiley [8]). By contrast, I envisage the two elds as sharing the methodology of developing and investigating statistical macrovariables. Thermodynamics investigates macrovariables like temperature, pressure, and speci c heat, and the fruits of this method include simple, basic laws and classi cations (like the ideal gas law and the phase transition separating the solids and liquids). By analogy, the \thermodynamic" approach in arti cial life seeks to identify statistical macrovariables that capture the distinctive features of complex adaptive systems. The most straightforward sign that this methodology is bearing fruit would be the demonstration that appropriate macrovariables can be used to frame simple, basic laws and classi cations that apply to broad classes of complex adaptive systems. This methodology involves formulating statistical macrovariables that are general enough to apply across a wide variety of systems, and then using these variables to search for underlying quantitative order unifying di erent systems. It is natural to begin this endevour with simple models, for macrovariables are easiest to formulate initially in simple models and simple models are easiest to study. Furthermore, simple models can reveal the essential nature of complex adaptive systems in general|at least, that is arti cial life's working hypothesis. This working hypothesis might be false, of course. It is at odds with the conclusions often drawn from the historicity, contingency, and variety of evolving biological systems (e.g., [25, 16]). One should bear in mind though that processes rife with historicity, complexity, and variety may well still fall under simple, basic laws and classi cations, especially if these laws and classi cations emerge through the application of statistical macrovariables. The \thermodynamic" methodology applied to simple computer models is a promising way to identify such laws and classi cations, if they exist. 2 A Simple Model of Evolution The model studied here is designed to be simple yet able to capture the essential features of an evolutionary process [27, 5, 6, 3, 4, 2, 7]. This model is motivated by the view that evolving life is typi ed by a population of agents whose continued existence depends on their sensorimotor functionality, i.e., their success at using local information to nd and process the resources needed to survive and ourish. Thus, information processing and resource processing are the two internal processes that dominate agents' lives, and their primary goal|whether they know this or not|is to enhance their sensorimotor functionality by suitably coordinating these two internal processes. Since the requirements of sensorimotor functionality typically alter as the contingencies of evolution change, continued viability and vitality calls for sensorimotor functionality to adapt in an openended, autonomous fashion. The present model attempts to create agents with sensorimotor functionality that can undergo this open-ended, autonomous evolutionary adaptation. The model consists of agents residing in a two-dimensional world, sensing their local environment, moving, and ingesting resources. All that exists in the world besides the agents are heaps of resources that are concentrated at particular locations, with levels decreasing with distance from a central location. The resource is refreshed periodically in time and randomly in space. Agents interact with the resource eld at each time step by extracting any found at their current site and storing it in their internal resource reservoir. Agents must continually replenish their internal resource supply to survive. Agents pay a resource tax just for living and a movement tax proportional to the distance traveled. If an agent's internal resource supply drops to zero, it dies and disappears from the world. On the other hand, an agent can remain alive inde nitely if it can continue to nd su cient resources. An agent's movement is governed by its genetically hardwired sensorimotor strategy. A sensorimotor strategy is simply a map taking sensory data from a local neighborhood (the ve site von Neumann neighborhood) to a vector indicating a magnitude and direction for movement: S : (s1; :::; s5)! v = (r; ) : (1) A agent's sensory data has two bits of resolution for each site, allowing the agents to recognize four resource levels (minimal resources, somewhat more resources, much more resources, maximal resources). Its behavioral repertoire is also nite, with four bits of resolution for magnitude r (zero, one, ..., fteen steps), and three bits for direction (north, northeast, east, ...). A unit step in the NE, SE, SW, or NW direction is de ned as movement to the next diagonal site, so its magnitude is p 2 times greater than a unit step in the N, E, S, or W direction. Each movement vector v thus produces a displacement (x; y) in a square space of possible spatial destinations from an agent's current location. The graph of the strategy map S may be thought of as a look-up table with 2 entries, each entry taking one of 2 possible values. This look-up table represents an agent's overall sensorimotor strategy. The entries are input-output pairs that link each sensory state (input) that an agent could possibly encounter with a speci c behavior (output). The di erent entries in the look-up table represent genetic loci, and the movement vectors assigned to them represent alleles. Since agents have 1024 loci, each containing one out of a possible 128 alleles, the total number of di erent genotypes is 128. Although nite, this space of genotypes allows for evolution in a huge space of genetic possibilities, which simulates the much larger number of possibilities in the biological world. In order to investigate how adaptation a ects the evolutionary dynamics of this model, I introduce a behavioral noise parameter, B0, de ned as the probability that an agent's behavior is chosen at random from the 2 possible behaviors, rather than determined by the agent's genetically encoded sensorimotor strategy. Thus, behavioral noise severs the link between genotype and phenotype. If B0 = 1, then agents survive and reproduce di erentially, and children inherit their parents' strategy elements (except for mutations), but the inherited strategies re ect only random genetic drift rather than the process of adaptation. Sensorimotor strategies evolve over generations. An agent reproduces (asexually) when its internal resource supply crosses a threshold. The parent produces one child, which is given half of its parent's supply of resources. Parental allele values are inherited except when a point mutation at a locus gives a child a randomly chosen allele value. The mutation rate determines the probability with which individual locus mutate during reproduction. At the limit of = 1, every allele value will mutate and thus each allele of child is chosen completely randomly. It is important to note that selection and adaptation in the model are \intrinsic" or \indirect" in the sense that survival and reproduction are determined solely by the contingencies involved in each agent's nding and expending resources. No externally-speci ed tness function governs the evolutionary dynamics [27, 5]. Good strategies for ourishing in this model would allow agents to acquire and manage resources e ciently. However, it is an open question which speci c strategies would e ciently acquire and manage resources, and there might be no universally optimal strategy. A strategy's worth is relative to the environment; a strategy might be optimal in one environment and suboptimal in another. The environment of the present model consists of the uctuating resource eld and the competing strategies possessed by the agents in the population. Both of these environmental components change during the course of evolution. The strategies directly evolve, and the resource eld indirectly changes because di erent populations of strategies a ect it di erently. For this reason, the model has the potential to show an open-ended evolutionary dynamic consisting of the perpetual creation of adaptive novelty. This potential for an unpredictably shifting adaptive landscape is one reason the model resists treatment by the analytical methods used in traditional mathematical population genetics [9, 14, 15]. Not only are there thousands of loci and hundreds of alleles per locus, but the vicissitudes of natural selection indirectly cause unpredictable uctuations in the nite population's size, age structure, and genotype distribution. In general, the only way to discern any underlying order in the model's behavior is through extensive computer simulation focussed on appropriate statistical macrovariables. These complications notwithstanding, the model is an unabashedly abstract and idealized representation of a population of evolving agents, lacking many of the features often emphasized in the biological literature. For example, the environment lacks the spatial structure required for migration e ects, there are no explicit interactions (such as predation) among organisms, there is no intron/exon distinction in the chromosome, and there is no \continuity" of mutation (mutated allele values are not \near" previous values). Nevertheless, my working hypothesis is that this model captures the fundamental features of complex adaptive systems, and is thus a useful model for investigating the essential aspects of more realistic systems. 3 Measurement of Population Diversity Population diversity is one plausible statistical macrovariable for arti cial life to investigate. But how might population diversity be measured? My proposal, very roughly, is to represent the population as a cloud of points in an abstract genetic space, and then de ne the population's diversity as the spread of that cloud. In the present model, an allele is a movement vector, a spatial displacement, and an agent's genotype is a set of spatial displacements. To capture the total population diversity, D, then, collect all the displacements of all agents in all environments into a cloud, and measure the spread or variance of that cloud. We can divide this total diversity D into two components. First, collect the spatial displacements of each agent in the population in a given environment, i.e., the traits encoded across the population at a given locus, and calculate the spread of this locus's cloud. The average spread or variance of all such locus distributions is a population's within-locus diversity, W . Now, form another, second-order collection of the centroid each locus's cloud, i.e., a cloud of the \mean" displacement at each locus. The spread or variance of this second-order cloud is the population's between-locus diversity, B; it measures the diversity of the di erent mean population responses. More formally, I de ne total diversity as the mean squared deviation between the average movement of the whole population, averaged over all agents and over all environmental conditions, and the individual movements of particular agents subject to particular conditions, i.e.,