arXiv subjects

Marc Harper

Publications and source records attributed to Marc Harper.

25 records · Page 2Linked to original sources

arXiv2013

The Inherent Randomness of Evolving Populations

The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation dependent on both short-run and long-run behavior, and allow the relationships between mutation, selection, and population size to be examined. Bounds for the entropy rate are given for the Moran process (independent of population size) and for the Wright-Fisher process (bounded for fixed population size). A generational Moran process is also presented for comparison to the Wright-Fisher Process. Results include analytic results and computational extensions.

math.DS↗

arXiv2013

Stability of Evolutionary Dynamics on Time Scales

We combine incentive, adaptive, and time-scale dynamics to study multipopulation dynamics on the simplex equipped with a large class of Riemmanian metrics, simultaneously generalizing and extending many dynamics commonly studied in dynamic game theory and evolutionary dynamics. Each population has its own geometry, method of adaptation (incentive), and time-scale (discrete, continuous, and others). Using an information-theoretic measure of distance we give a widely-applicable Lyapunov result for the dynamic. We include a wealth of examples leading up to and beyond the main results.

math.DS↗

arXiv2013

Comprehensive Detection of Genes Causing a Phenotype using Phenotype Sequencing and Pathway Analysis

Discovering all the genetic causes of a phenotype is an important goal in functional genomics. In this paper we combine an experimental design for multiple independent detections of the genetic causes of a phenotype, with a high-throughput sequencing analysis that maximizes sensitivity for comprehensively identifying them. Testing this approach on a set of 24 mutant strains generated for a metabolic phenotype with many known genetic causes, we show that this pathway-based phenotype sequencing analysis greatly improves sensitivity of detection compared with previous methods, and reveals a wide range of pathways that can cause this phenotype. We demonstrate our approach on a metabolic re-engineering phenotype, the PEP/OAA metabolic node in E. coli, which is crucial to a substantial number of metabolic pathways and under renewed interest for biofuel research. Out of 2157 mutations in these strains, pathway-phenoseq discriminated just five gene groups (12 genes) as statistically significant causes of the phenotype. Experimentally, these five gene groups, and the next two high-scoring pathway-phenoseq groups, either have a clear connection to the PEP metabolite level or offer an alternative path of producing oxaloacetate (OAA), and thus clearly explain the phenotype. These high-scoring gene groups also show strong evidence of positive selection pressure, compared with strictly neutral selection in the rest of the genome.

q-bio.QM↗

arXiv2012

Basic Experiment Planning via Information Metrics: the RoboMendel Problem

In this paper we outline some mathematical questions that emerge from trying to "turn the scientific method into math". Specifically, we consider the problem of experiment planning (choosing the best experiment to do next) in explicit probabilistic and information theoretic terms. We formulate this as an information measurement problem; that is, we seek a rigorous definition of an information metric to measure the likely information yield of an experiment, such that maximizing the information metric will indeed reliably choose the best experiment to perform. We present the surprising result that defining the metric purely in terms of prediction power on observable variables yields a metric that can converge to the classical mutual information measuring how informative the experimental observation is about an underlying hidden variable. We show how the expectation potential information metric can compute the "information rate" of an experiment as well its total possible yield, and the information value of experimental controls. To illustrate the utility of these concepts for guiding fundamental scientific inquiry, we present an extensive case study (RoboMendel) applying these metrics to propose sequences of experiments for discovering the basic principles of genetics.

cs.IT↗

arXiv2012

Escort Evolutionary Game Theory

A family of replicator-like dynamics, called the escort replicator equation, is constructed using information-geometric concepts and generalized information entropies and diverenges from statistical thermodynamics. Lyapunov functions and escort generalizations of basic concepts and constructions in evolutionary game theory are given, such as an escorted Fisher's Fundamental theorem and generalizations of the Shahshahani geometry.

math.DS↗

arXiv2010

The Replicator Equation as an Inference Dynamic

The replicator equation is interpreted as a continuous inference equation and a formal similarity between the discrete replicator equation and Bayesian inference is described. Further connections between inference and the replicator equation are given including a discussion of information divergences and exponential families as solutions for the replicator dynamic, using Fisher information and information geometry.

math.DS↗

arXiv2009

Information Geometry and Evolutionary Game Theory

The Shahshahani geometry of evolutionary game theory is realized as the information geometry of the simplex, deriving from the Fisher information metric of the manifold of categorical probability distributions. Some essential concepts in evolutionary game theory are realized information-theoretically. Results are extended to the Lotka-Volterra equation and to multiple population systems.

cs.IT↗