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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.

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.

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.

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.

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.

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.

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.