Marc Harper

Escort evolutionary game theory

Abstract A family of replicator-like dynamics, called the escort replicator dynamic, is constructed using information-geometric concepts and generalized information divergences from information geometry and statistical thermodynamics. A single-formula Lyapunov function is given that covers the entire class of dynamics, which includes the replicator dynamic and the projection dynamic, as well as several new dynamics. A further class is discussed that allows for more variation, such as variable intensities of selection.

Phenotype Sequencing: Identifying the Genes That Cause a Phenotype Directly from Pooled Sequencing of Independent Mutants

Random mutagenesis and phenotype screening provide a powerful method for dissecting microbial functions, but their results can be laborious to analyze experimentally. Each mutant strain may contain 50–100 random mutations, necessitating extensive functional experiments to determine which one causes the selected phenotype. To solve this problem, we propose a “Phenotype Sequencing” approach in which genes causing the phenotype can be identified directly from sequencing of multiple independent mutants. We developed a new computational analysis method showing that 1. causal genes can be identified with high probability from even a modest number of mutant genomes; 2. costs can be cut many-fold compared with a conventional genome sequencing approach via an optimized strategy of library-pooling (multiple strains per library) and tag-pooling (multiple tagged libraries per sequencing lane). We have performed extensive validation experiments on a set of E. coli mutants with increased isobutanol biofuel tolerance. We generated a range of sequencing experiments varying from 3 to 32 mutant strains, with pooling on 1 to 3 sequencing lanes. Our statistical analysis of these data (4099 mutations from 32 mutant genomes) successfully identified 3 genes (acrB, marC, acrA) that have been independently validated as causing this experimental phenotype. It must be emphasized that our approach reduces mutant sequencing costs enormously. Whereas a conventional genome sequencing experiment would have cost

The art of war: beyond memory-one strategies in population games.

7,200 in reagents alone, our Phenotype Sequencing design yielded the same information value for only

Inherent randomness of evolving populations.

1200. In fact, our smallest experiments reliably identified acrB and marC at a cost of only

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

110–

Stationary Stability for Evolutionary Dynamics in Finite Populations

340.

Reinforcement learning produces dominant strategies for the Iterated Prisoner's Dilemma

We show that the history of play in a population game contains exploitable information that can be successfully used by sophisticated strategies to defeat memory-one opponents, including zero determinant strategies. The history allows a player to label opponents by their strategies, enabling a player to determine the population distribution and to act differentially based on the opponent’s strategy in each pairwise interaction. For the Prisoner’s Dilemma, these advantages lead to the natural formation of cooperative coalitions among similarly behaving players and eventually to unilateral defection against opposing player types. We show analytically and empirically that optimal play in population games depends strongly on the population distribution. For example, the optimal strategy for a minority player type against a resident TFT population is ALLC, while for a majority player type the optimal strategy versus TFT players is ALLD. Such behaviors are not accessible to memory-one strategies. Drawing inspiration from Sun Tzu’s the Art of War, we implemented a non-memory-one strategy for population games based on techniques from machine learning and statistical inference that can exploit the history of play in this manner. Via simulation we find that this strategy is essentially uninvadable and can successfully invade (significantly more likely than a neutral mutant) essentially all known memory-one strategies for the Prisoner’s Dilemma, including ALLC (always cooperate), ALLD (always defect), tit-for-tat (TFT), win-stay-lose-shift (WSLS), and zero determinant (ZD) strategies, including extortionate and generous strategies.

Lyapunov Functions for Time-Scale Dynamics on Riemannian Geometries of the Simplex

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 behaviors 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.

Evolution reinforces cooperation with the emergence of self-recognition mechanisms: An empirical study of strategies in the Moran process for the iterated prisoner’s dilemma

Discovering all the genetic causes of a phenotype is an important goal in functional genomics. We combine an experimental design for detecting independent 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.

Entropic Equilibria Selection of Stationary Extrema in Finite Populations

We demonstrate a vast expansion of the theory of evolutionary stability to finite populations with mutation, connecting the theory of the stationary distribution of the Moran process with the Lyapunov theory of evolutionary stability. We define the notion of stationary stability for the Moran process with mutation and generalizations, as well as a generalized notion of evolutionary stability that includes mutation called an incentive stable state (ISS) candidate. For sufficiently large populations, extrema of the stationary distribution are ISS candidates and we give a family of Lyapunov quantities that are locally minimized at the stationary extrema and at ISS candidates. In various examples, including for the Moran and Wright-Fisher processes, we show that the local maxima of the stationary distribution capture the traditionally-defined evolutionarily stable states. The classical stability theory of the replicator dynamic is recovered in the large population limit. Finally we include descriptions of possible extensions to populations of variable size and populations evolving on graphs.