Complexity of evolutionary equilibria in static fitness landscapes

A fitness landscape is a genetic space -- with two genotypes adjacent if they differ in a single locus -- and a fitness function. Evolutionary dynamics produce a flow on this landscape from lower fitness to higher; reaching equilibrium only if a local fitness peak is found. I use computational complexity to question the common assumption that evolution on static fitness landscapes can quickly reach a local fitness peak. I do this by showing that the popular NK model of rugged fitness landscapes is PLS-complete for K >= 2; the reduction from Weighted 2SAT is a bijection on adaptive walks, so there are NK fitness landscapes where every adaptive path from some vertices is of exponential length. Alternatively -- under the standard complexity theoretic assumption that there are problems in PLS not solvable in polynomial time -- this means that there are no evolutionary dynamics (known, or to be discovered, and not necessarily following adaptive paths) that can converge to a local fitness peak on all NK landscapes with K = 2. Applying results from the analysis of simplex algorithms, I show that there exist single-peaked landscapes with no reciprocal sign epistasis where the expected length of an adaptive path following strong selection weak mutation dynamics is $e^{O(n^{1/3})}$ even though an adaptive path to the optimum of length less than n is available from every vertex. The technical results are written to be accessible to mathematical biologists without a computer science background, and the biological literature is summarized for the convenience of non-biologists with the aim to open a constructive dialogue between the two disciplines.Comment: 14 pages, 3 figure

Computational strategies for dissecting the high-dimensional complexity of adaptive immune repertoires

The adaptive immune system recognizes antigens via an immense array of antigen-binding antibodies and T-cell receptors, the immune repertoire. The interrogation of immune repertoires is of high relevance for understanding the adaptive immune response in disease and infection (e.g., autoimmunity, cancer, HIV). Adaptive immune receptor repertoire sequencing (AIRR-seq) has driven the quantitative and molecular-level profiling of immune repertoires thereby revealing the high-dimensional complexity of the immune receptor sequence landscape. Several methods for the computational and statistical analysis of large-scale AIRR-seq data have been developed to resolve immune repertoire complexity in order to understand the dynamics of adaptive immunity. Here, we review the current research on (i) diversity, (ii) clustering and network, (iii) phylogenetic and (iv) machine learning methods applied to dissect, quantify and compare the architecture, evolution, and specificity of immune repertoires. We summarize outstanding questions in computational immunology and propose future directions for systems immunology towards coupling AIRR-seq with the computational discovery of immunotherapeutics, vaccines, and immunodiagnostics.Comment: 27 pages, 2 figure

Analysis of adaptive walks on NK fitness landscapes with different interaction schemes

Fitness landscapes are genotype to fitness mappings commonly used in evolutionary biology and computer science which are closely related to spin glass models. In this paper, we study the NK model for fitness landscapes where the interaction scheme between genes can be explicitly defined. The focus is on how this scheme influences the overall shape of the landscape. Our main tool for the analysis are adaptive walks, an idealized dynamics by which the population moves uphill in fitness and terminates at a local fitness maximum. We use three different types of walks and investigate how their length (the number of steps required to reach a local peak) and height (the fitness at the endpoint of the walk) depend on the dimensionality and structure of the landscape. We find that the distribution of local maxima over the landscape is particularly sensitive to the choice of interaction pattern. Most quantities that we measure are simply correlated to the rank of the scheme, which is equal to the number of nonzero coefficients in the expansion of the fitness landscape in terms of Walsh functions.Comment: 29 pages, 9 figure

Fitness Landscape-Based Characterisation of Nature-Inspired Algorithms

A significant challenge in nature-inspired algorithmics is the identification of specific characteristics of problems that make them harder (or easier) to solve using specific methods. The hope is that, by identifying these characteristics, we may more easily predict which algorithms are best-suited to problems sharing certain features. Here, we approach this problem using fitness landscape analysis. Techniques already exist for measuring the "difficulty" of specific landscapes, but these are often designed solely with evolutionary algorithms in mind, and are generally specific to discrete optimisation. In this paper we develop an approach for comparing a wide range of continuous optimisation algorithms. Using a fitness landscape generation technique, we compare six different nature-inspired algorithms and identify which methods perform best on landscapes exhibiting specific features.Comment: 10 pages, 1 figure, submitted to the 11th International Conference on Adaptive and Natural Computing Algorithm

Visualisation of advanced search

This article presents investigation on visualisation of search processes. Existing evolutionary and adaptive algorithms for search and optimisation, in certain extent, may differ from each other in behaviour and in obtained results. An intention for future analysis of search algorithms, their behaviour and differences motivates the development of tools for visual representation of the search process. By developing a 3D graphical interface for Computational Intelligence Software such as Free Search [1] [2], Particle Swarm Optimisation [3], Differential Evolution [4] and Genetic Algorithm [5] [6] it is possible to build a scene with test function and individuals, moving on the landscape of that test function towards their goals

Society Functions Best with an Intermediate Level of Creativity

In a society, a proportion of the individuals can benefit from creativity without being creative themselves by copying the creators. This paper uses an agent-based model of cultural evolution to investigate how society is affected by different levels of individual creativity. We performed a time series analysis of the mean fitness of ideas across the artificial society varying both the percentage of creators, C, and how creative they are, p using two discounting methods. Both analyses revealed a valley in the adaptive landscape, indicating a tradeoff between C and p. The results suggest that excess creativity at the individual level can be detrimental at the level of the society because creators invest in unproven ideas at the expense of propagating proven ideas.Comment: 6 pages. arXiv admin note: text overlap with arXiv:1310.4086, arXiv:1310.378

LaDy: software for assessing local landscape diversity profiles of raster land cover maps using geographic windows

Landscape ecology starts from the assumption that diversity and spatial arrangement of ecosystem mosaics have ecological implications and tries to understand the interactions between diversity and structure of large spatially heterogeneous areas and their ecological functions. These assumptions imply effective use of earth observation techniques and geographic information systems, enabling a global view of the landscape mosaics. In this paper, a software, LaDy (Landscape Diversity Software), for computing Re´nyi’s local landscape diversity profile on raster land cover maps is presented. LaDy is based on the use of Merchant’s adaptive geographic window, which is designed to operate on a neighborhood of patches instead of a fixed rectangular neighborhood of pixels (the conventional approach in image analysis).L'articolo è disponibile sul sito dell'editore www.elsevier.co

Adaptation in tunably rugged fitness landscapes: The Rough Mount Fuji Model

Much of the current theory of adaptation is based on Gillespie's mutational landscape model (MLM), which assumes that the fitness values of genotypes linked by single mutational steps are independent random variables. On the other hand, a growing body of empirical evidence shows that real fitness landscapes, while possessing a considerable amount of ruggedness, are smoother than predicted by the MLM. In the present article we propose and analyse a simple fitness landscape model with tunable ruggedness based on the Rough Mount Fuji (RMF) model originally introduced by Aita et al. [Biopolymers 54:64-79 (2000)] in the context of protein evolution. We provide a comprehensive collection of results pertaining to the topographical structure of RMF landscapes, including explicit formulae for the expected number of local fitness maxima, the location of the global peak, and the fitness correlation function. The statistics of single and multiple adaptive steps on the RMF landscape are explored mainly through simulations, and the results are compared to the known behavior in the MLM model. Finally, we show that the RMF model can explain the large number of second-step mutations observed on a highly-fit first step backgound in a recent evolution experiment with a microvirid bacteriophage [Miller et al., Genetics 187:185-202 (2011)].Comment: 43 pages, 12 figures; revised version with new results on the number of fitness maxim