A Classi cation of Long - Term Evolutionary Dynamics

We present empirical evidence that long-term evolutionary dynamics fall into three distinct classes, depending on whether adaptive evolutionary activity is absent (class 1), bounded (class 2), or unbounded (class 3). These classes are de ned using three statistics: diversity, new evolutionary activity (Bedau & Packard 1992), and mean cumulative evolutionary activity (Bedau et al. 1997). The three classes partition all the longterm evolutionary dynamics observed in Holland's Echo model (Holland 1992), in a random-selection adaptivelyneutral \shadow" of Echo, and in the biosphere as reected in the Phanerozoic fossil record. This classi cation provides quantitative evidence that Echo lacks the unbounded growth in adaptive evolutionary activity observed in the fossil record. Why Classify Evolutionary Dynamics? We present and illustrate a classi cation of long-term evolutionary dynamics. Classi cations of complex dynamical behavior are reasonably familiar, with Wolfram's classi cation of cellular automata rules being one well-known example (Wolfram 1984), but there are few attempts to classify the dynamics speci cally of adaptive evolution. Nevertheless, such a classi cation is at least implicitly presupposed by the debates in biology about such issues as the evolution of clay crystallites (Cairns-Smith 1982; 1985), the evolution of \memes" (Dawkins 1976), and the increasing complexity of life on Earth (Gould 1989; McShea 1996; Gould 1996). Likewise for claims in arti cial life about systems exhibiting \open-ended evolution" or \perpetual novelty" or operating \far from equilibrium" (Lindgren 1992; Ray 1992; Holland 1992; 1995; Bedau et al. 1997). Indeed, the de ning focus of the eld of arti cial life|simulating and synthesizing systems that behave essentially like living systems|implies such a classi cation. How can we tell whether arti cial systems behave relevantly like real living systems without using at least an implicit classi cation of system behavior? The classi cation question arises sharply only when we have many concrete instances to classify, so our inattention to the classi cation question was understandable when we had a sample size of only one|the biosphere. But the advent of arti cial life changes this. Scores of arti cial evolving systems are now generating many thousands of instances of long-term evolutionary dynamics. So we now have ample empirical data to tackle the classi cation question rigorously. On the basis of studying data from a variety of articial life models and from the biosphere, we have concluded that long-term evolutionary dynamics fall into three di erent classes. Our procedure here is to de ne statistics characterizing evolutionary dynamics and then use them to de ne three classes of long-term evolutionary trends. We then illustrate these classes of evolutionary dynamics in three systems: Holland's Echo model (Holland 1992; 1995), a random-selection model that shadows Echo's dynamics, and the Phanerozoic biosphere as reected in the fossil record. We choose these systems to illustrate the kinds of dynamics because (i) Echo, among arti cial life models, is an especially promising candidate for exhibiting complex adaptive evolutionary dynamics, (ii) Echo's random-selection shadow provides an adaptively-neutral null case which highlights adaptations in Echo, and (iii) the Phanerozoic fossil record presents our best evidence about long-term dynamics in natural evolving systems. We are in the process of classifying many other arti cial and natural evolving systems. Evolutionary Activity Statistics Our classi cation of evolutionary dynamics is based on statistics for quantifying adaptive evolutionary phenomena. These statistics have already been applied to various evolving systems in various ways for various purposes (Bedau & Packard 1992; Bedau 1995; Bedau et al. 1997; Bedau & Brown 1997). This section describes these statistics with maximal generality and then explains how they are applied here. Our evolutionary activity statistics are computed from data obtained by observing an evolving system. In our view an evolving system consists of a population of components, all of which participate in a cycle of birth, life and death, with each component largely determined by inherited traits. (We use this \component" terminology to maintain enough generality to cover a wide variety of entities, ranging from individuals alleles to taxonomic families.) Birth, however, creates the possibility of innovations being introduced into the population. If the innovation is adaptive, it persists in the population with a bene cial e ect on the survival potential of the components that have it. It persists not only in the component which rst receives the innovation, but in all subsequent components that inherit the innovation, i.e., in an entire lineage. If the innovation is not adaptive, it either disappears or persists passively. Our idea of evolutionary activity is to identify innovations that make a di erence. Generally we consider an innovation to \make a di erence" if it persists and continues to be used. Counters are attached to components for bookkeeping purposes, to update each component's current activity as the component persists and is used. If the components are passed along during reproduction, the corresponding counters are inherited with the components, maintaining an increasing count for an entire lineage. Two large issues immediately arise: 1. What should be counted as a component, and what counts as the addition or subtraction of a component from the system? In most evolving systems components may be identi ed on a variety of levels. Previous work has studied components on the level of individual alleles (Bedau & Packard 1992; Bedau 1995) as well as genotypes (Bedau et al. 1997; Bedau & Brown 1997) and taxonomic families (Bedau et al. 1997). Here we study entire genotypes and taxonomic families. The addition or subtraction of a given component consists of the origination or extinction of a given genotype or taxonomic family. It's natural to choose genotypes and taxonomic families as components because adaptive evolution can be expected to a ect the dynamics of those entities. 2. What should be a new component's initial contribution to the evolutionary activity of the system and how should it change over time? To measure activity contributions we attach a counter to each component of the system, ai(t), where i labels the component and t labels time. These activity counters are purely observational devices. A component's activity increases over time as follows, ai(t) = P k t i(k), where i(k) is the activity increment for component i at time k. Various activity incrementation functions i(t) can be used, depending on the nature of the components and the purposes at hand. Since genotypes and taxonomic families are components in the present context, it's natural to measure a component's contribution to the system's evolutionary activity simply by its age. Everything else being equal, the more adaptive an innovative genotype or taxonomic family continues to be, the longer it will persist in the system. So we choose an activity incrementation function that increases a component's activity counter by one unit for each time step that it exists: i(t) = 1 if component i exists at t 0 otherwise : (1) Though there are ways to re ne this simple counting method (Bedau & Packard 1992; Bedau 1995; Bedau et al. 1997), this version facilitates direct comparison with many other systems. In some contexts activity statistics indicate a system's adaptive evolutionary dynamics only after the activity increment i(t) is normalized with respect to a \neutral" model devoid of adaptive dynamics (Bedau 1995; Bedau et al. 1997; Bedau & Brown 1997). Here we address this issue in two di erent ways. With respect to taxonomic families in the Phanerozoic biosphere, we consider this normalization to be accomplished de facto by the fossil record itself. In our view, the mere fact that a family appears in the fossil record is good evidence that its persistence re ects its adaptive signi cance. Signi cantly maladaptive taxonomic families would likely go extinct before leaving a trace in the fossil record. But measuring evolutionary activity in Echo data is another matter, because we know maladaptive genotypes contribute to Echo's activity data. So, to screen o the activity of maladaptive Echo genotypes, we measure evolutionary activity in a \neutral shadow" of Echo. Then, by comparing the Echo and neutral shadow data we can tell how much (if any) of Echo's evolutionary activity is due to the genotypes' adaptive value. The details of this neutral screening are explained in subsequent sections. Now, we can de ne various statistics based on the components in a system and their activity counters. Perhaps the simplest statistic|because it ignores activity information|is the system's diversity, D(t), which is simply the number of components present at time t, D(t) = #fi : ai(t) > 0g ; (2) where #f g denotes set cardinality. The values of the activity counters of each component in the system over all time can be collected in the component activity distribution, C(t; a), as follows: