In this paper we study the evolution of sequential dynamical systems $(\mathsf{SDS})$ as a result of the erroneous replication of the SDS words. An $\mathsf{SDS}$ consists of (a) a finite, labeled graph Y in which each vertex has a state, (b) a vertex labeled sequence of functions (Fvi,Y), and...

Many properties of organisms show great robustness against mutations. Whether this robustness is an evolved property or intrinsic to genetic systems is by and large unknown. An evolutionary origin of robustness would require a rethinking of key concepts in the field of molecular evolution, such...

We introduce and analyze a general model of a population evolving over a network of selectively neutral genotypes. We show that the population's limit distribution on the neutral network is solely determined by the network topology and given by the principal eigenvector of the network's...

Folding of RNA sequences into secondary structures is viewed as a map that assigns a uniquely defined base pairing pattern to every sequence. This mapping is non-invertible since many sequences fold into the same (secondary) structure or shape. The preimages of the map, called neutral networks,...

Bedau and Packard [7] devised an approach to quantifying the adaptive phenomena in artificial systems. We use this approach to define two statistics: cumulative evolutionary activity and mean cumulative evolutionary activity. Then we measure the dynamics of cumulative evolutionary activity, mean...

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 defined using three statistics: diversity, new evolutionary...

Understanding which phenotypes are accessible from which genotypes is fundamental for understanding the evolutionary process. This notion of accessibility can be used to define a relation of nearness among phenotypes, independently of their similarity. Because of neutrality, phenotypes denote...

Environmental and biotic factors regulate species abundance and the composition of ecological communities. However, it is difficult to demonstrate principles of community assembly in nature due to observational limitations and historical effects. Numerical simulation can be used to evaluate...