Stochastic models for biological evolution

In this work, we deal with the problem of creating a model that describes a population of agents undergoing Darwinian Evolution, which takes into account the basic phenomena of this process. According to the principles of evolutionary biology, Evolution occurs if there is selection and adaptation of phenotypes, mutation of genotypes, presence of physical space. The evolution of a biological population is then described by a system of ordinary stochastic differential equations; the basic model of dynamics represents the trend of a population divided into different types, with relative frequency in a simplex. The law governing this dynamics is called Replicator Dynamics: the growth rate of type k is measured in terms of evolutionary advantage, with its own fitness compared to the average in the population. The replicator dynamics model turns into a stochastic process when we consider random mutations that can transform fractions of individuals into others. The two main forces of Evolution, selection and mutation, act on different layers: the environment acts on the phenotype, selecting the fittest, while the randomness of the mutations affects the genotype. This difference is underlined in the model, where each genotype express a phenotype, and fitness influences emerging traits, not explicitly encoded in genotypes. The presence of a potentially infinite space of available genomes makes sure that variants of individuals with characteristics never seen before can be generated. In conclusion, numerical simulations are provided for some applications of the model, such as a variation of Conway's Game of Lif

Cancer evolution: mathematical models and computational inference.

Cancer is a somatic evolutionary process characterized by the accumulation of mutations, which contribute to tumor growth, clinical progression, immune escape, and drug resistance development. Evolutionary theory can be used to analyze the dynamics of tumor cell populations and to make inference about the evolutionary history of a tumor from molecular data. We review recent approaches to modeling the evolution of cancer, including population dynamics models of tumor initiation and progression, phylogenetic methods to model the evolutionary relationship between tumor subclones, and probabilistic graphical models to describe dependencies among mutations. Evolutionary modeling helps to understand how tumors arise and will also play an increasingly important prognostic role in predicting disease progression and the outcome of medical interventions, such as targeted therapy.FM would like to acknowledge the support of The University of Cambridge, Cancer Research UK and Hutchison Whampoa Limited.This is the final published version. It first appeared at http://sysbio.oxfordjournals.org/content/early/2014/10/07/sysbio.syu081.short?rss=1

Information Geometry

This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience

Approximate Analysis of Large Simulation-Based Games.

Game theory offers powerful tools for reasoning about agent behavior and incentives in multi-agent systems. Traditional approaches to game-theoretic analysis require enumeration of all possible strategies and outcomes. This often constrains game models to small numbers of agents and strategies or simple closed-form payoff descriptions. Simulation-based game theory extends the reach of game-theoretic analysis through the use of agent-based modeling. In the simulation-based approach, the analyst describes an environment procedurally and then computes payoffs by simulation of agent interactions in that environment. I use simulation-based game theory to study a model of credit network formation. Credit networks represent trust relationships in a directed graph and have been proposed as a mechanism for distributed transactions without a central currency. I explore what information is important when agents make initial decisions of whom to trust, and what sorts of networks can result from their decisions. This setting demonstrates both the value of simulation-based game theory—extending game-theoretic analysis beyond analytically tractable models—and its limitations—simulations produce prodigious amounts of data, and the number of simulations grows exponentially in the number of agents and strategies. I propose several techniques for approximate analysis of simulation-based games with large numbers of agents and large amounts of simulation data. First, I show how bootstrap-based statistics can be used to estimate confidence bounds on the results of simulation-based game analysis. I show that bootstrap confidence intervals for regret of approximate equilibria are well-calibrated. Next, I describe deviation-preserving reduction, which approximates an environment with a large number of agents using a game model with a small number of players, and demonstrate that it outperforms previous player reductions on several measures. Finally, I employ machine learning to construct game models from sparse data sets, and provide evidence that learned game models can produce even better approximate equilibria in large games than deviation-preserving reduction.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113587/1/btwied_1.pd