This paper studies various algorithmic issues in reconstructing a species tree from gene trees under the duplication and the mutation cost model. This is a fundamental problem in computational molecular biology. Our main results are as follows. 1. A linear time algorithm is presented for computing all the losses in duplications associated with the least common ancestor mapping from a gene tree to a species tree. This answers a problem raised recently by Eulenstein et al. (1998). 2. The complexity of finding an optimal species tree from gene trees is studied. The problem is proved to be NP-hard for the duplication cost and for the mutation cost. Further, the concept of reconciled trees was introduced by Goodman et al. and formalized by Page for visualizing the relationship between gene and species trees. We show that constructing an optimal reconciled tree for gene trees is also NP-hard. Finally, we consider a general reconstruction problem and show it to be NP-hard even for the well-kn...

Evolution can be mathematically modelled by a stochastic process that operates on the DNA of species. Such models are based on the established theory that the DNA sequences, or genomes, of all extant species have been derived from the genome of the common ancestor of all species by a process of random mutation and natural selection. A stochastic model...

A conjecture of Mirkin, Muchnik and Smith is answered affirmatively which connects the inconsistency function, a biologically meaningful similarity/dissimilarity measure for a gene tree and a species tree, to the mutation cost function, a combinatorial measure based on the mapping of trees. A linear-time algorithm for computing the mutation cost function is also derived from the conjecture. 1

The majority of current genetic algorithms (GAs), while inspired by natural evolutionary systems, are seldom viewed as biologically plausible models. This is not a criticism of GAs, but rather a reflection of choices made regarding the level of abstraction at which biological mechanisms are modeled, and a reflection of the more engineering-oriented goals of the evolutionary computation community. Understanding better and reducing this gap between GAs and genetics has been a central issue in an interdisciplinary project whose goal is to build GA-based computational models of viral evolution. The result is a system called VIV that incorporates a number of more biologically plausible mechanisms including a more flexible genotype-to-phenotype mapping; in VIV the genes are independent of position, and genomes can vary in length and may contain non-coding regions, as well as duplicative or competing genes. Initial computational studies with VIV have already revealed several emergent phenomen...

The genetic algorithm (GA) is a problem solving method that is modelled after the process of natural selection. We are interested in studying a specific aspect of the GA: the effect of non-coding segments on GA performance. Non-coding segments are segments of bits in an individual that provide no contribution, positive or negative, to the fitness of that individual. Previous research on non-coding segments suggests that including these structures in the GA may improve GA performance. Understanding when and why this improvement occurs will help us to use the GA to its full potential. In this article, we discuss our hypotheses on non-coding segments and describe the results of our experiments. The experiments may be separated into two categories: testing our program on problems from previous related studies, and testing new hypotheses on the effect of non-coding segments. Keywords: genetic algorithms, non-coding segments, non-coding DNA, introns, Royal Road function. 1 Introduction Na...

Phylogenetic reconstruction is a fast-growing field that is enriched by different statistical approaches and by findings and applications in a broad range of biological areas. Fundamental to these are the mathematical models used to describe the patterns of DNA base substitution and amino acid replacement. These may become some of the basic models for comparative genome research. We discuss these models, including the analysis of observed DNA base and amino acid mutation patterns, the concept of site heterogeneity, and the incorporation of structural biology data, all of which have become particularly important in recent years. We also describe the use of such models in phylogenetic reconstruction and statistical methods for the comparison of different models. PCR has deeply transformed and boosted phylogenetic studies. At the same time, the statistical analysis of evolutionary relationships among species has recently revealed important biotechnological uses. For example, the understanding of viral quasispecies variation allows us to trace routes of infectious disease transmission. The analysis of the host–

The coalescent process is a powerful modeling tool for population genetics. The allelic states of all homologous gene copies in a population are determined by the genealogical and mutational history of these copies. The coalescent approach is based on the realization that the genealogy is usually easier to model backward in time, and that selectively neutral mutations can then be superimposed afterwards. A wide range of biological phenomena can be modeled using this approach. Whereas almost all of classical population genetics considers the future of a population given a starting point, the coalescent considers the present, while taking the past into account. This allows the calculation of probabilities of sample configurations under the stationary distribution of various population genetic models, and makes full likelihood analysis of polymorphism data possible. It also leads to extremely efficient computer algorithms for generating simulated data from such distributions, data which can then be compared with observations as a form of exploratory data analysis.

This article compares the traditional, fixed problem representation style of a genetic algorithm (GA) with a new floating representation in which the building blocks of a problem are not fixed at specific locations on the individuals of the population. In addition, the effects of non-coding segments on both of these representations is studied. Non-coding segments are a computational model of non-coding DNA and floating building blocks mimic the location independence of genes. The fact that these structures are prevalent in natural genetic systems suggests that they may provide some advantages to the evolutionary process. Our results show that there is a significant difference in how GAs solve a problem in the fixed and floating representations. GAs are able to maintain a more diverse population with the floating representation. The combination of non-coding segments and floating building blocks appears to encourage a GA to take advantage of its parallel search and recombination abiliti...

The process of reconstructing evolutionary trees can be viewed formally as an optimization problem. Recently, decision problems associated with the most commonly used approaches to reconstructing such trees have been shown to be NP-complete [Day87, DJS86, DS86, DS87, GF82, Kri88, KM86]. In this thesis, a framework is established that incorporates all such problems studied to date. Within this framework, the NP-completeness results for decision problems are extended by applying theorems from [CT91, Gas86, GKR92, JVV86, KST89, Kre88, Sel91] to derive bounds on the computational complexity of several functions associated with each of these problems, namely ffl evaluation functions, which return the cost of the optimal tree(s), ffl solution functions, which return an optimal tree, ffl spanning functions, which return the number of optimal trees, ffl enumeration functions, which systematically enumerate all optimal trees, and ffl random-selection functions, which return a random...

. A brief survey of biological research on non-coding DNA is presented here. There has been growing interest in the effects of noncoding segments in evolutionary algorithms (EAs). To better understand and conduct research on non-coding segments and EAs, it is important to understand the biological background of such work. This paper begins with a review of basic genetics and terminology, describes the different types of non-coding DNA, and then surveys recent intron research. 1 Introduction There has been growing interest in the effects of non-coding segments in evolutionary algorithms (EAs). Non-coding segments, also called non-coding material or introns in the literature, is a computational model of what is known as noncoding DNA in biological systems. Simply put, non-coding segments refer to the portions of an individual that make no contribution to its fitness value. In genetic programming (GP) systems, non-coding material is a natural by-product of the evolutionary process...