Two Modes of Evolution: Optimization and Expansion (original) (raw)
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Complexity, 2004
What features characterize complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analyzed to confirm this effect. The strain arises from local frustration. As the strain is released through "quakes," some system variable undergoes record statistics with accompanying log-Poisson statistics for the quake event times. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology and show how quantitative indications of aging can be found.
Physical Review E, 2009
The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the Random Energy Model (REM) and by a ferromagnetic version of the REM. The solution method uses the mapping of the evolutionary dynamics into a quantum Ising chain in a transverse field and the Suzuki-Trotter formalism to calculate the transition probabilities between configurations at different times. We find that in the case of the REM landscape the dynamics can exhibit three distinct regimes: pure diffusion or stasis for short times, depending on the fitness of the initial configuration, and a spin-glass regime for large times. The dynamic transition between these dynamical regimes is marked by discontinuities in the mean-fitness as well as in the overlap with the initial reference sequence. The relaxation to equilibrium is described by an inverse time decay. In the ferromagnetic REM, we find in addition to these three regimes, a ferromagnetic regime where the overlap and the mean-fitness are frozen. In this case, the system relaxes to equilibrium in a finite time. The relevance of our results to information processing aspects of evolution is discussed.
Evolution and non-equilibrium physics: A study of the Tangled Nature Model
EPL (Europhysics Letters), 2014
The stochastic dynamics of a network of interacting agents which replicate, mutate and die is described as a non-equilibrium physical process using simulational data from the Tangled Nature Model (TNM) of darwinian co-evolution. We characterize the metastable configurations transversed by the dynamics and show that they are hierarchically organized and separated by increasing entropy barriers. An approximate description based on the temporal statistics of quakes, the events leading from one component of the hierarchy to the next, accounts for the logarithmic growth of the population and shows the kinship of evolution dynamics with physical aging of complex materials. Finally, we question the role of fitness in large scale evolution models and speculate on the possible evolutionary role of rejuvenation and memory effects.
Evolution of evolvability via adaptation of mutation rates
Biosystems, 2003
We examine a simple form of the evolution of evolvability-the evolution of mutation rates-in a simple model system. The system is composed of many agents moving, reproducing, and dying in a two-dimensional resource-limited world. We first examine various macroscopic quantities (three types of genetic diversity, a measure of population fitness, and a measure of evolutionary activity) as a function of fixed mutation rates. The results suggest that (i) mutation rate is a control parameter that governs a transition between two qualitatively different phases of evolution, an ordered phase characterized by punctuated equilibria of diversity, and a disordered phase of characterized by noisy fluctuations around an equilibrium diversity, and (ii) the ability of evolution to create adaptive structure is maximized when the mutation rate is just below the transition between these two phases of evolution. We hypothesize that this transition occurs when the demands for evolutionary memory and evolutionary novelty are typically balanced. We next allow the mutation rate itself to evolve, and we observe that evolving mutation rates adapt to values at this transition. Furthermore, the mutation rates adapt up (or down) as the evolutionary demands for novelty (or memory) increase, thus supporting the balance hypothesis.
Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models
Theoretical Population Biology, 2006
A distinctive signature of living systems is Darwinian evolution, that is, a propensity to generate as well as self-select individual diversity. To capture this essential feature of life while describing the dynamics of populations, mathematical models must be rooted in the microscopic, stochastic description of discrete individuals characterized by one or several adaptive traits and interacting with each other. The simplest models assume asexual reproduction and haploid genetics: an ospring usually inherits the trait values of her progenitor, except when a mutation causes the ospring to take a mutation step to new trait values; selection follows from ecological interactions among individuals. Here we present a rigorous construction of the microscopic population process that captures the probabilistic dynamics over continuous time of birth, mutation, and death, as inuenced by the trait values of each individual, and interactions between individuals. A by-product of this formal construction is a general algorithm for ecient numerical simulation of the individual-level model. Once the microscopic process is in place, we derive dierent macroscopic models of adaptive evolution. These models dier in the renormalization they assume, i.e. in the limits taken, in specic orders, on population size, mutation rate, mutation step, while rescaling time accordingly. The macroscopic models also dier in their mathematical nature: deterministic, in the form of ordinary, integro-, or partial dierential equations, or probabilistic, like stochastic partial dierential equations or superprocesses.
Progressive evolution and a measure for its noise-dependent complexity
The second international conference on computing anticipatory systems, CASYS’98, 1999
A recently introduced model of macroevoluton is studied on two different levels of systems analysis. Firstly, the systems dynamics and properties, above all the growth of complexity of the evolutionary units during the long-term evolution, are discussed, and, secondly, the complexity of the model itself, i.e. the richness of its various features, is studied with regard to a control parameter representing a background noise within the systems dynamics. The same is done with a randomized version of the model.
Evolutionary dynamics and optimization
Lecture Notes in Computer Science, 1995
We view the folding of RNA-sequences as a map that assigns a pattern of base pairings to each sequence, known as secondary structure. These preimages can be constructed as random graphs (i.e. the neutral networks associated to the structure s). By interpreting the secondary structure as biological information we can formulate the so called Error Threshold of Shapes as an extension of Eigen's et al. concept of an error threshold in the single peak landscape 5]. Analogue to the approach of Derrida & Peliti 3] for a at landscape we investigate the spatial distribution of the population on the neutral network. On the one hand this model of a single shape landscape allows the derivation of analytical results, on the other hand the concept gives rise to study various scenarios by means of simulations, e.g. the interaction of two di erent networks 29]. It turns out that the intersection of two sets of compatible sequences (with respect to the pair of secondary structures) plays a key role in the search for " tter" secondary structures.
Dual phase evolution - a mechanism for self-organization in complex systems
A key challenge in complexity theory is to understand self-organization: how order emerges out of the interactions between elements within a system. Prigogine (1980) pointed out that in dissipative systems (open systems that exchange energy with their environment), order can increase. Rather then being suppressed, positive feedback allows local irregularities to grow into global features. introduced the idea of an order parameter and pointed out that critical behaviour (e.g. the firing of a laser) always occurs at some predictable value of the parameter. Nevertheless, many questions remain, especially about the ways in which different processes act in concert with one another. In particular, the relationships between self-organization, natural selection and the evolution of complexity remain unclear.
Sustained Evolution from Changing Interaction
We develop and analyze an agent-based simulation model aimed at achieving sustained evolution under sympatric conditions. Evolution is understood here in the form of speciation, ie. the emergence of reproductively isolated and functionally distinct populations. In our model, reproduction is a function of phenotype interaction. A population with given phenotypic interactions tends to adaptive stasis, whereas new species can emerge if the interaction space changes, so that new dimensions are added in the course of the process. We show that this behavior is stable and leads to a persistent production of new species.