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This chapter begins by discussing fitness landscape, an idea first introduced by evolutionary geneticist Sewall Wright and later extended by several other authors. The fitness landscape is defined in terms of some particular traits that are implicit in the virus particle phenotype and are usually described in terms of replication rate or infectivity. The landscape appears in most textbook plots as a multi-peaked surface. Local maxima represent optimal fitness values, which can be reached through mutation from a subset of lower-fitness neighbors. Given an initial condition defined by a quasi-species distribution localized somewhere in the sequence space, the population will evolve by exploring nearest positions through mutation. The remainder of the chapter deals with symmetric competition, epistasis in RNA viruses, experimental virus landscapes, the survival of the flattest effect, and virus robustness.

This chapter explores the benefits of restructuring search spaces and internal representations so as to make search more efficient. It begins by providing a formal definition of search, and proposes a method for shifting search between low- and high-dimensionality problem spaces. Consideration is given to how learning shapes the representations that help people search efficiently as well as on constraints that people face. Some constraints are considered biases necessary to make sense out of the world; others (e.g., working memory) are taken as both “limiters” to be overcome and “permitters” that make learning in a finite amount of time possible at all. Further constraints on search are tied to the physical structure of the world. The chapter concludes with a discussion of social search, where communication can promote exploration and exploitation in an environment that often consists of other agents searching for similar solutions.

This chapter describes what happens when one takes seriously the idea that adaptive landscapes are mathematical constructs of very high dimensionality and surprising properties, and reviews a theory of fitness landscapes and a theory of speciation. It describes two particular directions for theoretical studies on the origins of biodiversity that are especially important for the unification of different branches of the life sciences, and shows the theoretical developments of the theory of multidimensional fitness landscapes and the emergence of a dynamical theory of speciation and diversification.

This chapter examines various estimates of the fitness of an individual, focusing on statistical issues and potential sources of bias. With estimates of individual fitness in hand, one can then search for fitness-trait association, and this topic comprises the second half of the chapter. A number of metrics for describing how the phenotypic distribution of a trait is perturbed by selection are examined, again along with a discussion of statistical issues and sources of bias.

Evolutionary processes combine many features of complex systems: they are algorithmic; states co-evolve with interactions; they show power law statistics; they are selforganized critical; and they are driven non-equilibrium systems. Evolution is a dynamical process that changes the composition of large sets of interconnected elements, entities, or species over time. The essence of evolutionary processes is that, through the interaction of existing entities with each other and with their environment, they give rise to an open-ended process of creation and destruction of new entities. Evolutionary processes are critical, co-evolutionary, and combinatorial, meaning that thew entities are created from combinations of existing ones. We review the concepts of the replicator equation, fitness landscapes, cascading events, the adjacent possible. We review several classical quantitative approaches to evolutionary dynamics such as the NK model and the Bak–Snappen model. We propose a general and universal framework for evolutionary dynamics that is critical, co-evolutionary, and combinatorial.

Kauffman (1993, 1995; Kauffman and Levin 1987; Kauffman and Johnsen 1991) has proposed and studied in depth a class of models referred to as NK models, which are models of random fitness landscapes on which one can implement a variety of types of evolutionary dynamics and study the development and interaction of species. (The letters N and K do not stand for anything; they are the names of parameters in the model.) Based on the results of extensive simulations of NK models, Kauffman and co-workers have suggested a number of possible connections between the dynamics of evolution and the extinction rate. To a large extent it is this work which has sparked recent interest in biotic mechanisms for mass extinction. In this chapter we review Kauffman's work in detail. An NK model is a model of a single rugged landscape, which is similar in construction to the spin-glass models of statistical physics (Fischer and Hertz 1991), particularly p-spin models (Derrida 1980) and random energy models (Derrida 1981). Used as a model of species fitness the NK model maps the states of a model genome onto a scalar fitness W. This is a simplification of what happens in real life, where the genotype is first mapped onto phenotype and only then onto fitness. However, it is a useful simplification which makes simulation of the model for large systems tractable. As long as we bear in mind that this simplification has been made, the model can still teach us many useful things. The NK model is a model of a genome with N genes. Each gene has A alleles. In most of Kauffman's studies of the model he used A = 2, a binary genetic code, but his results are not limited to this case. The model also includes epistatic interactions between genes—interactions whereby the state of one gene affects the contribution of another to the overall fitness of the species. In fact, it is these epistatic interactions which are responsible for the ruggedness of the fitness landscape.

This chapter reviews and discusses the use of the landscape metaphor in development by analyzing its relationship with experimental work and theoretical modelling. Defining a landscape as a mathematical function of multiple variables, we show how this can be interpreted as a dynamical system. From the perspective of dynamical systems modelling, an analysis of Waddingto’s‘epigenetic landscap’ is proposed, as well as of other landscape representations occurring in current developmental biology literature. From this particular perspective, the problem of models and metaphorical representations in science is addressed. This problem stands out as a crux for assessing the use of landscapes in development. The somehow parallel stories of Wrigh’s fitness landscapes and Waddingto’s developmental landscapes is discussed. After considering some ideas on developmental landscapes in the context of visualization in science, with a focus on theoretical work in developmental biology, it is concluded that, overall, landscapes seem to be too limited a form of abstraction to stand as a pivotal metaphor in the search for a comprehensive theory of development.

In contrast to prevailing views Alexander Gerschenkron understood the development of backward countries as a contextual process that varied from country to country depending on which perquisites were present or absent. In this chapter we explore this view of development with the use of fitness landscapes. The landscapes are good representations of this view of development for they portray this process as an evolutionary search for good designs across a large, uncertain and not pre-statable set of possibilities. In such circumstances a controlled strategy of following predetermined stages is often not effective and what is required is an approach that uses creativity and imagination to find solution to specific problems faced by each country. This process is illustrated with a historical account of how Brazilian agriculture evolved from a backwardness and low productivity to become a current leader in the field.

After having discussed how life might have originated in the early Earth (chapter 6), chapter 7 looks at how living organisms evolve by natural selection. It does that from a quantitative perspective, appropriate in the context of Artificial Chemistries. It starts with an introduction to evolutionary dynamics, the mathematical modelling of evolutionary processes. Basic concepts in evolutionary dynamics such as replication, death, selection, fitness landscapes, resource limitations, neutrality, drift and mutations are briefly explained. The classical Lotka-Volterra system is illustrated as a chemistry involving these basic concepts. An early artificial chemistry called random catalytic reaction network is then discussed, which links to the final part of the chapter, where various artificial chemistries that model evolutionary processes are reviewed, together with a brief overview of some algorithms in this area.

The models discussed in the last chapter are intriguing, but present a number of problems. In particular, most of the results about them come from computer simulations, and little is known analytically about their properties. Results such as the power-law distribution of extinction sizes and the system's evolution to the "edge of chaos" are only as accurate as the simulations in which they are observed. Moreover, it is not even clear what the mechanisms responsible for these results are, beyond the rather general arguments that we have already given. In order to address these shortcomings, Bak and Sneppen (1993; Sneppen et al. 1995; Sneppen 1995; Bak 1996) have taken Kauffman's ideas, with some modification, and used them to create a considerably simpler model of large-scale coevolution which also shows a power-law distribution of avalanche sizes and which is simple enough that its properties can, to some extent, be understood analytically. Although the model does not directly address the question of extinction, a number of authors have interpreted it, using arguments similar to those of section 1.2.2.5, as a possible model for extinction by biotic causes. The Bak-Sneppen model is one of a class of models that show "self-organized criticality," which means that regardless of the state in which they start, they always tune themselves to a critical point of the type discussed in section 2.4, where power-law behavior is seen. We describe self-organized criticality in more detail in section 3.2. First, however, we describe the Bak-Sneppen model itself. In the model of Bak and Sneppen there are no explicit fitness landscapes, as there are in NK models. Instead the model attempts to mimic the effects of landscapes in terms of "fitness barriers." Consider figure 3.1, which is a toy representation of a fitness landscape in which there is only one dimension in the genotype (or phenotype) space. If the mutation rate is low compared with the time scale on which selection takes place (as Kauffman assumed), then a population will spend most of its time localized around a peak in the landscape (labeled P in the figure).

Evolutionary dynamics treats the growth and decay of populations under conditions that influence reproduction, competition, predation and selection. The Lotka–Volterra equations are population equations that describe population cycles between predators and prey. Symbiotic dynamics can lead to stable ecosystems among a wide variety of species. Natural selection operates through the principle of relative fitness among species. A simple frequency-dependent fitness model is the replicator equation, which follows a zero-sum game among multiple species whose total populations reside within a simplex. Many closely related species, connected by mutation, are called quasispecies. The quasispecies equation includes mutation among quasispecies through a mutation matrix that drives diffusion in a multidimensional fitness landscape. Adding frequency-dependent fitness to the quasispecies equation converts it to the replicator–mutator equation, which captures collective group dynamics. Game theory provides a different perspective on the adoption of strategies for species evolving on a fitness landscape.

Parallel evolution has been used as “proof” of a bewildering array of sometimes contradictory assertions: that Darwinism is wrong, that selection is all powerful, that the modern synthesis is incomplete, that chance matters, or that chance does not matter. Perhaps most importantly, parallel evolution is a source of fascination, as the evolution of a particular life form is seen as one of the least probable chains of events imaginable. Our stance is that both chance and history do matter in evolution. Beyond reasserting these well-known points, the central question is what parallel evolution (or the lack thereof) tells us about evolutionary processes. First, we argue that the topic of parallel evolution crystallizes a series of unsolved issues that have fueled recurrent debates throughout the history of evolutionary genetics. Second, we discuss the implications of parallel evolution at different biological levels. Third, we review the causes of genotypic and phenotypic parallel evolution. Fourth, we show how parallel evolution can be modeled and the additional insights brought by theory. We conclude with a series of questions for future work, and by stressing that using explicit phenotypic landscape models is a useful way to resolve controversies emerging from the observation of parallel evolution.

An agent- based model of social dynamics is introduced using a deformable fitness landscape, and it is shown that in certain clearly specifiable situations, strategies that are different from utility maximization outperform utility maximizers. Simulation results are presented and intuitive interpretations of the results provided. The situations considered occur when individuals' actions affect the outcomes for other agents and endogenous effects are dominant. The Tragedy of the Commons is merely a special case of this. Arguments are given that constraints are to be encouraged in some circumstances. The appropriate role of constraints in various types of society is assessed and their use justified in identifiable types of situations.

I continue to be surprised and pleased by the dramatic growth of interest in and applications of genetic algorithms (GAs) in recent years. This growth, in turn, has placed a certain amount of healthy "stress" on the field as current understanding and traditional approaches are stretched to the limit by challenging new problems and new areas of application. At the same time, other forms of evolutionary computation such as evolution strategies [50] and evolutionary programming [22], continue to mature and provide alternative views on how the process of evolution might be captured in an efficient and useful computational framework. I don't think there can be much disagreement about the fact that Holland's initial ideas for adaptive system design have played a fundamental role in the progress we have made in the past thirty years [23, 46]. So, an occasion like this is an opportunity to reflect on where the field is now, how it got there, and where it is headed. In the following sections, I will attempt to summarize the progress that has been made, and to identify critical issues that need to be addressed for continued progress in the field. The widespread availability of inexpensive digital computers in the 1960s gave rise to their increased use as a modeling and simulation tool by the scientific community. Several groups around the world including Rechenberg and Schwefel at the Technical University of Berlin [49], Fogel et al. at the University of California at Los Angeles [22], and Holland at the University of Michigan in Ann Arbor [35] were captivated by the potential of taking early simulation models of evolution a step further and harnessing these evolutionary processes in computational forms that could be used for complex computer-based problem solving. In Holland's case, the motivation was the design and implementation of robust adaptive systems, capable of dealing with an uncertain and changing environment. His view emphasized the need for systems which self-adapt over time as a function of feedback obtained from interacting with the environment in which they operate. This led to an initial family of "reproductive plans" which formed the basis for what we call "simple genetic algorithms" today, as outlined in figure 1.

Sibani and co-workers have proposed a model of the extinction process, which they call the "reset model" (Sibani et al. 1995,1998), which differs from those discussed in the preceding chapters in a fundamental way; it allows for, and indeed relies upon, nonstationarity in the extinction process. That is, it acknowledges that the extinction record is not uniform in time, is not in any sense in equilibrium, as it is assumed to be in the other models we have considered. In fact, extinction intensity has declined on average over time from the beginning of the Phanerozoic until the Recent. Within the model of Sibani et al., the distributions of section 1.2 are all the result of this decline, and the challenge is then to explain the decline, rather than the distributions themselves. In figure 1.9 we showed the number of known families as a function of time over the last 600 My. On the logarithmic scale of the figure, this number appears to increase fairly steadily and although, as we pointed out, some of this increase can be accounted for by the bias known as the "pull of the recent," there is probably a real trend present as well. It is less clear that there is a similar trend in extinction intensity. The extinctions represented by the points in figure 1.1 certainly vary in intensity, but on average they appear fairly constant. Recall however, that figure 1.1 shows the number of families becoming extinct in each stage, and that the lengths of the stages are not uniform. In figure 6.1 we show the extinction intensity normalized by the lengths of the stages—the extinction rate in families per million years—and on this figure it is much clearer that there is an overall decline in extinction towards the Recent. In order to quantify the decline in extinction rate, we consider the cumulative extinction intensity c(t) as a function of time. The cumulative extinction at time t is defined to be the number of taxa which have become extinct up to that time.