Computing Epistasis of Template Functions Through Walsh Transforms

Template functions have been introduced as a class of test functions, allowing to study the convergence behaviour of genetic algorithms. In this note, we show how to use Walsh transforms to calculate the normalized epistasis of these functions

Constructing dynamic test environments for genetic algorithms based on problem difficulty

This article is posted here with permission from IEEE - Copyright @ 2004 IEEEIn recent years the study of dynamic optimization problems has attracted an increasing interest from the community of genetic algorithms and researchers have developed a variety of approaches into genetic algorithms to solve these problems. In order to compare their performance, an important issue is the construction of standardized dynamic test environments. Based on the concept of problem difficulty, This work proposes a new dynamic environment generator using a decomposable trap function. With this generator, it is possible to systematically construct dynamic environments with changing and bounding difficulty and hence, we can test different genetic algorithms under dynamic environments with changing but controllable difficulty levels.This research was supported by UK EPSRC under Grant GR/S79718/01

Schemata as Building Blocks: Does Size Matter?

We analyze the schema theorem and the building block hypothesis using a recently derived, exact schemata evolution equation. We derive a new schema theorem based on the concept of effective fitness showing that schemata of higher than average effective fitness receive an exponentially increasing number of trials over time. The building block hypothesis is a natural consequence in that the equation shows how fit schemata are constructed from fit sub-schemata. However, we show that generically there is no preference for short, low-order schemata. In the case where schema reconstruction is favoured over schema destruction large schemata tend to be favoured. As a corollary of the evolution equation we prove Geiringer's theorem. We give supporting numerical evidence for our claims in both non-epsitatic and epistatic landscapes.Comment: 17 pages, 10 postscript figure

Statistical advances and challenges for analyzing correlated high dimensional SNP data in genomic study for complex diseases

Recent advances of information technology in biomedical sciences and other applied areas have created numerous large diverse data sets with a high dimensional feature space, which provide us a tremendous amount of information and new opportunities for improving the quality of human life. Meanwhile, great challenges are also created driven by the continuous arrival of new data that requires researchers to convert these raw data into scientific knowledge in order to benefit from it. Association studies of complex diseases using SNP data have become more and more popular in biomedical research in recent years. In this paper, we present a review of recent statistical advances and challenges for analyzing correlated high dimensional SNP data in genomic association studies for complex diseases. The review includes both general feature reduction approaches for high dimensional correlated data and more specific approaches for SNPs data, which include unsupervised haplotype mapping, tag SNP selection, and supervised SNPs selection using statistical testing/scoring, statistical modeling and machine learning methods with an emphasis on how to identify interacting loci.Comment: Published in at http://dx.doi.org/10.1214/07-SS026 the Statistics Surveys (http://www.i-journals.org/ss/) by the Institute of Mathematical Statistics (http://www.imstat.org

Instability of natural selection at candidate barrier loci underlying speciation in wood ants

doi: 10.1111/mec.15606Speciation underlies the generation of novel biodiversity. Yet, there is much to learn about how natural selection shapes genomes during speciation. Selection is assumed to act against gene flow at barrier loci, promoting reproductive isolation. However, evidence for gene flow and selection is often indirect and we know very little about the temporal stability of barrier loci. Here we utilize haplodiploidy to identify candidate male barrier loci in hybrids between two wood ant species. As ant males are haploid, they are expected to reveal recessive barrier loci, which can be masked in diploid females if heterozygous. We then test for barrier stability in a sample collected 10 years later and use survival analysis to provide a direct measure of natural selection acting on candidate male barrier loci. We find multiple candidate male barrier loci scattered throughout the genome. Surprisingly, a proportion of them are not stable after 10 years, natural selection apparently switching from acting against to favouring introgression in the later sample. Instability of the barrier effect and natural selection for introgressed alleles could be due to environment-dependent selection, emphasizing the need to consider temporal variation in the strength of natural selection and the stability of the barrier effect at putative barrier loci in future speciation work.Peer reviewe