Natural Selection of Paths in Networks

We present a novel algorithm that exhibits natural selection of paths in a network. If each node and weighted directed edge has a unique identifier, a path in the network is defined as an ordered list of these unique identifiers. We take a population perspective and view each path as a genotype. If each node has a node phenotype then a path phenotype is defined as the list of node phenotypes in order of traversal. We show that given appropriate path traversal, weight change and structural plasticity rules, a path is a unit of evolution because it can exhibit multiplicative growth (i.e. change it’s probability of being traversed), and have variation and heredity. Thus, a unit of evolution need not be a spatially distinct physical individual. The total set of paths in a network consists of all possible paths from the start node to a finish node. Each path phenotype is associated with a reward that determines whether the edges of that path will be multiplicatively strengthened (or weakened). A pair-wise tournament selection algorithm is implemented which compares the reward obtained by two paths. The directed edges of the winning path are strengthened, whilst the directed edges of the losing path are weakened. Edges shared by both paths are not changed (or weakened if diversity is desired). Each time a node is activated there is a probability that the path will mutate, i.e. find an alternative route that bypasses that node. This generates the potential for a novel but correlated path with a novel but correlated phenotype. By this process the more frequently traversed paths are responsible for most of the exploration. Nodes that are inactive for some period of time are lost (which is equivalent to connections to and from them being broken). This network-based natural selection compares favourably with a standard pair-wise tournament-selection based genetic algorithm on a range of combinatorial optimization problems and continuous parametric optimization problems. The network also exhibits memory of past selective environments and can store previously discovered characters for reuse in later optimization tasks. The pathway evolution algorithm has several possible implementations and permits natural selection with unlimited heredity without template replication

Microbial community pattern detection in human body habitats via ensemble clustering framework

The human habitat is a host where microbial species evolve, function, and continue to evolve. Elucidating how microbial communities respond to human habitats is a fundamental and critical task, as establishing baselines of human microbiome is essential in understanding its role in human disease and health. However, current studies usually overlook a complex and interconnected landscape of human microbiome and limit the ability in particular body habitats with learning models of specific criterion. Therefore, these methods could not capture the real-world underlying microbial patterns effectively. To obtain a comprehensive view, we propose a novel ensemble clustering framework to mine the structure of microbial community pattern on large-scale metagenomic data. Particularly, we first build a microbial similarity network via integrating 1920 metagenomic samples from three body habitats of healthy adults. Then a novel symmetric Nonnegative Matrix Factorization (NMF) based ensemble model is proposed and applied onto the network to detect clustering pattern. Extensive experiments are conducted to evaluate the effectiveness of our model on deriving microbial community with respect to body habitat and host gender. From clustering results, we observed that body habitat exhibits a strong bound but non-unique microbial structural patterns. Meanwhile, human microbiome reveals different degree of structural variations over body habitat and host gender. In summary, our ensemble clustering framework could efficiently explore integrated clustering results to accurately identify microbial communities, and provide a comprehensive view for a set of microbial communities. Such trends depict an integrated biography of microbial communities, which offer a new insight towards uncovering pathogenic model of human microbiome.Comment: BMC Systems Biology 201

Simon-Ando decomposability and fitness landscapes

In this paper, we investigate fitness landscapes (under point mutation and recombination) from the standpoint of whether the induced evolutionary dynamics have a “fast-slow” time scale associated with the differences in relaxation time between local quasi-equilibria and the global equilibrium. This dynamical hevavior has been formally described in the econometrics literature in terms of the spectral properties of the appropriate operator matrices by Simon and Ando (Econometrica 29 (1961) 111), and we use the relations they derive to ask which fitness functions and mutation/recombination operators satisfy these properties. It turns out that quite a wide range of landscapes satisfy the condition (at least trivially) under point mutation given a sufficiently low mutation rate, while the property appears to be difficult to satisfy under genetic recombination. In spite of the fact that Simon-Ando decomposability can be realized over fairly wide range of parameters, it imposes a number of restriction on which landscape partitionings are possible. For these reasons, the Simon-Ando formalism does not appear to be applicable to other forms of decomposition and aggregation of variables that are important in evolutionary systems

Landscapes and Effective Fitness

The concept of a fitness landscape arose in theoretical biology, while that of effective fitness has its origin in evolutionary computation. Both have emerged as useful conceptual tools with which to understand the dynamics of evolutionary processes, especially in the presence of complex genotype-phenotype relations. In this contribution we attempt to provide a unified discussion of these two approaches, discussing both their advantages and disadvantages in the context of some simple models. We also discuss how fitness and effective fitness change under various transformations of the configuration space of the underlying genetic model, concentrating on coarse-graining transformations and on a particular coordinate transformation that provides an appropriate basis for illuminating the structure and consequences of recombination

Modelling Genetic Algorithms and Evolving Populations

A formalism for modelling the dynamics of genetic algorithms using methods from statistical physics, originally due to Pr¨ugel-Bennett and Shapiro, is extended to ranking selection, a form of selection commonly used in the genetic algorithm community. The extension allows a reduction in the number of macroscopic variables required to model the mean behaviour of the genetic algorithm. This reduction allows a more qualitative understanding of the dynamics to be developed without sacrificing quantitative accuracy. The work is extended beyond modelling the dynamics of the genetic algorithm. A caricature of an optimisation problem with many local minima is considered — the basin with a barrier problem. The first passage time — the time required to escape the local minima to the global minimum — is calculated and insights gained as to how the genetic algorithm is searching the landscape. The interaction of the various genetic algorithm operators and how these interactions give rise to optimal parameters values is studied

Evolvable Neuronal Paths: A Novel Basis for Information and Search in the Brain

We propose a previously unrecognized kind of informational entity in the brain that is capable of acting as the basis for unlimited hereditary variation in neuronal networks. This unit is a path of activity through a network of neurons, analogous to a path taken through a hidden Markov model. To prove in principle the capabilities of this new kind of informational substrate, we show how a population of paths can be used as the hereditary material for a neuronally implemented genetic algorithm, (the swiss-army knife of black-box optimization techniques) which we have proposed elsewhere could operate at somatic timescales in the brain. We compare this to the same genetic algorithm that uses a standard ‘genetic’ informational substrate, i.e. non-overlapping discrete genotypes, on a range of optimization problems. A path evolution algorithm (PEA) is defined as any algorithm that implements natural selection of paths in a network substrate. A PEA is a previously unrecognized type of natural selection that is well suited for implementation by biological neuronal networks with structural plasticity. The important similarities and differences between a standard genetic algorithm and a PEA are considered. Whilst most experiments are conducted on an abstract network model, at the conclusion of the paper a slightly more realistic neuronal implementation of a PEA is outlined based on Izhikevich spiking neurons. Finally, experimental predictions are made for the identification of such informational paths in the brain