Neutral Fitness Landscapes Research Articles

Success probability for selectively neutral invading species in the line model with a random fitness landscape

AbstractWe consider a spatial (line) model for invasion of a population by a single mutant with a stochastically selectively neutral fitness landscape, independent from the fitness landscape for nonmutants. This model is similar to those considered earlier. We show that the probability of mutant fixation in a population of size , starting from a single mutant, is greater than , which would be the case if there were no variation in fitness whatsoever. In the small variation regime, we recover precise asymptotics for the success probability of the mutant. This demonstrates that the introduction of randomness provides an advantage to minority mutations in this model, and shows that the advantage increases with the system size. We further demonstrate that the mutants have an advantage in this setting only because they are better at exploiting unusually favorable environments when they arise, and not because they are any better at exploiting pockets of favorability in an environment that is selectively neutral overall.

Recombination and mutational robustness in neutral fitness landscapes.

Mutational robustness quantifies the effect of random mutations on fitness. When mutational robustness is high, most mutations do not change fitness or have only a minor effect on it. From the point of view of fitness landscapes, robust genotypes form neutral networks of almost equal fitness. Using deterministic population models it has been shown that selection favors genotypes inside such networks, which results in increased mutational robustness. Here we demonstrate that this effect is massively enhanced by recombination. Our results are based on a detailed analysis of mesa-shaped fitness landscapes, where we derive precise expressions for the dependence of the robustness on the landscape parameters for recombining and non-recombining populations. In addition, we carry out numerical simulations on different types of random holey landscapes as well as on an empirical fitness landscape. We show that the mutational robustness of a genotype generally correlates with its recombination weight, a new measure that quantifies the likelihood for the genotype to arise from recombination. We argue that the favorable effect of recombination on mutational robustness is a highly universal feature that may have played an important role in the emergence and maintenance of mechanisms of genetic exchange.

Multiple phase transitions in an agent-based evolutionary model with neutral fitness.

Null models are crucial for understanding evolutionary processes such as speciation and adaptive radiation. We analyse an agent-based null model, considering a case without selection—neutral evolution—in which organisms are defined only by phenotype. Universal dynamics has previously been demonstrated in a related model on a neutral fitness landscape, showing that this system belongs to the directed percolation (DP) universality class. The traditional null condition of neutral fitness (where fitness is defined as the number of offspring each organism produces) is extended here to include equal probability of death among organisms. We identify two types of phase transition: (i) a non-equilibrium DP transition through generational time (i.e. survival), and (ii) an equilibrium ordinary percolation transition through the phenotype space (based on links between mating organisms). Owing to the dynamical rules of the DP reaction–diffusion process, organisms can only sparsely fill the phenotype space, resulting in significant phenotypic diversity within a cluster of mating organisms. This highlights the necessity of understanding hierarchical evolutionary relationships, rather than merely developing taxonomies based on phenotypic similarity, in order to develop models that can explain phylogenetic patterns found in the fossil record or to make hypotheses for the incomplete fossil record of deep time.

Lévy flights in neutral fitness landscapes

Regions of equal or close fitness are common in biological and artificial evolutionary systems. Customary hill-climbing optimizing paradigms turn out to be unsuitable to walk and search such large neutral networks. Here we propose a new technique to quickly jump out of neutral networks and to reach better fitness regions. The algorithm, based on Lévy flights, is compared to an established nearest neighbors random drift technique on two families of constructive neutral landscapes called the NKq and the NKp ensembles. The results of our numerical simulations clearly show that the new algorithm performs better than the nearest neighbors random drift for all studied landscapes. We conclude with some explanations of the observed behavior and some suggestions for the use of Lévy flights in more general search and optimization heuristics.

Evolutionary advantage via common action of recombination and neutrality

We investigate evolution models with recombination and neutrality. We consider the Crow-Kimura (parallel) mutation-selection model with the neutral fitness landscape, in which there is a central peak with high fitness A, and some of 1-point mutants have the same high fitness A, while the fitness of other sequences is 0. We find that the effect of recombination and neutrality depends on the concrete version of both neutrality and recombination. We consider three versions of neutrality: (a) all the nearest neighbor sequences of the peak sequence have the same high fitness A; (b) all the l-point mutations in a piece of genome of length l≥1 are neutral; (c) the neutral sequences are randomly distributed among the nearest neighbors of the peak sequences. We also consider three versions of recombination: (I) the simple horizontal gene transfer (HGT) of one nucleotide; (II) the exchange of a piece of genome of length l, HGT-l; (III) two-point crossover recombination (2CR). For the case of (a), the 2CR gives a rather strong contribution to the mean fitness, much stronger than that of HGT for a large genome length L. For the random distribution of neutral sequences there is a critical degree of neutrality ν(c), and for μ<μ(c) and (μ(c)-μ) is not large, the 2CR suppresses the mean fitness while HGT increases it; for ν much larger than ν(c), the 2CR and HGT-l increase the mean fitness larger than that of the HGT. We also consider the recombination in the case of smooth fitness landscapes. The recombination gives some advantage in the evolutionary dynamics, where recombination distinguishes clearly the mean-field-like evolutionary factors from the fluctuation-like ones. By contrast, mutations affect the mean-field-like and fluctuation-like factors similarly. Consequently, recombination can accelerate the non-mean-field (fluctuation) type dynamics without considerably affecting the mean-field-like factors.

Local Optima Networks of NK Landscapes With Neutrality

In previous work, we have introduced a network based model that abstracts many details of the underlying landscape and compresses the landscape information into a weighted, oriented graph which we call the local optima network. The vertices of this graph are the local optima of the given fitness landscape, while the arcs are transition probabilities between local optima basins. Here, we extend this formalism to neutral fitness landscapes, which are common in difficult combinatorial search spaces. The study is based on two neutral variants of the well-known NK family of landscapes (where N stands for the chromosome length, and K for the number of gene epistatic interactions within the chromosome). By using these two NK variants, probabilistic (NKp), and quantified NK (NKq), in which the amount of neutrality can be tuned by a parameter, we show that our new definitions of the optima networks and the associated basins are consistent with the previous definitions for the non-neutral case. Moreover, our empirical study and statistical analysis show that the features of neutral landscapes interpolate smoothly between landscapes with maximum neutrality and non-neutral ones. We found some unknown structural differences between the two studied families of neutral landscapes. But overall, the network features studied confirmed that neutrality, in landscapes with percolating neutral networks, may enhance heuristic search. Our current methodology requires the exhaustive enumeration of the underlying search space. Therefore, sampling techniques should be developed before this analysis can have practical implications. We argue, however, that the proposed model offers a new perspective into the problem difficulty of combinatorial optimization problems and may inspire the design of more effective search heuristics.

Neutral fitness landscapes in signalling networks.

Biological and technological systems process information by means of cascades of signals. Be they interacting genes, spiking neurons or electronic transistors, information travels across these systems, producing, for each set of external conditions, an appropriate response. In technology, circuits performing specific complex tasks are designed by humans. In biology, however, design has to be ruled out, confronting us with the question of how these systems could have arisen by accumulation of small changes. The key factor is the genotype-phenotype map. With the exception of RNA folding, not much is known about the exact nature of this mapping. Here, we show that structure of the genotype-phenotype map of simple feed-forward circuits is very close to the ones found in RNA; they have a large degree of neutrality, by which a circuit can be completely rewired keeping its input-output function intact, and there is a relatively small neighbourhood of a given circuit containing almost all the phenotypes.