Evolutionary game theory in growing populations

Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model which combines the growth dynamics of the population and its internal evolution. Our model thereby accounts for the fact that both evolutionary and growth dynamics are based on individual reproduction events and hence are highly coupled and stochastic in nature. We exemplify our approach by studying the dilemma of cooperation in growing populations and show that genuinely stochastic events can ease the dilemma by leading to a transient but robust increase in cooperationComment: 4 pages, 2 figures and 2 pages supplementary informatio

Cooperation in Microbial Populations: Theory and Experimental Model Systems

Cooperative behavior, the costly provision of benefits to others, is common across all domains of life. This review article discusses cooperative behavior in the microbial world, mediated by the exchange of extracellular products called public goods. We focus on model species for which the production of a public good and the related growth disadvantage for the producing cells are well described. To unveil the biological and ecological factors promoting the emergence and stability of cooperative traits we take an interdisciplinary perspective and review insights gained from both mathematical models and well-controlled experimental model systems. Ecologically, we include crucial aspects of the microbial life cycle into our analysis and particularly consider population structures where an ensemble of local communities (sub populations) continuously emerge, grow, and disappear again. Biologically, we explicitly consider the synthesis and regulation of public good production. The discussion of the theoretical approaches includes general evolutionary concepts, population dynamics, and evolutionary game theory. As a specific but generic biological example we consider populations of Pseudomonas putida and its regulation and utilization of pyoverdines, iron scavenging molecules. The review closes with an overview on cooperation in spatially extended systems and also provides a critical assessment of the insights gained from the experimental and theoretical studies discussed. Current challenges and important new research opportunities are discussed, including the biochemical regulation of public goods, more realistic ecological scenarios resembling native environments, cell to cell signalling, and multi-species communities.Comment: Review article, 88 pages, 14 figure

Range expansion with mutation and selection: dynamical phase transition in a two-species Eden model

The colonization of unoccupied territory by invading species, known as range expansion, is a spatially heterogeneous non-equilibrium growth process. We introduce a two-species Eden growth model to analyze the interplay between uni-directional (irreversible) mutations and selection at the expanding front. While the evolutionary dynamics leads to coalescence of both wild-type and mutant clusters, the non-homogeneous advance of the colony results in a rough front. We show that roughening and domain dynamics are strongly coupled, resulting in qualitatively altered bulk and front properties. For beneficial mutations the front is quickly taken over by mutants and growth proceeds Eden-like. In contrast, if mutants grow slower than wild-types, there is an antagonism between selection pressure against mutants and growth by the merging of mutant domains with an ensuing absorbing state phase transition to an all-mutant front. We find that surface roughening has a marked effect on the critical properties of the absorbing state phase transition. While reference models, which keep the expanding front flat, exhibit directed percolation critical behavior, the exponents of the two-species Eden model strongly deviate from it. In turn, the mutation-selection process induces an increased surface roughness with exponents distinct from that of the classical Eden model

Spontaneous symmetry breaking in a two-lane model for bidirectional overtaking traffic

First we consider a unidirectional flux \omega_bar of vehicles each of which is characterized by its `natural' velocity v drawn from a distribution P(v). The traffic flow is modeled as a collection of straight `world lines' in the time-space plane, with overtaking events represented by a fixed queuing time tau imposed on the overtaking vehicle. This geometrical model exhibits platoon formation and allows, among many other things, for the calculation of the effective average velocity w=\phi(v) of a vehicle of natural velocity v. Secondly, we extend the model to two opposite lanes, A and B. We argue that the queuing time \tau in one lane is determined by the traffic density in the opposite lane. On the basis of reasonable additional assumptions we establish a set of equations that couple the two lanes and can be solved numerically. It appears that above a critical value \omega_bar_c of the control parameter \omega_bar the symmetry between the lanes is spontaneously broken: there is a slow lane where long platoons form behind the slowest vehicles, and a fast lane where overtaking is easy due to the wide spacing between the platoons in the opposite direction. A variant of the model is studied in which the spatial vehicle density \rho_bar rather than the flux \omega_bar is the control parameter. Unequal fluxes \omega_bar_A and \omega_bar_B in the two lanes are also considered. The symmetry breaking phenomenon exhibited by this model, even though no doubt hard to observe in pure form in real-life traffic, nevertheless indicates a tendency of such traffic.Comment: 50 pages, 16 figures; extra references adde

Growth dynamics and the evolution of cooperation in microbial populations

Microbes providing public goods are widespread in nature despite running the risk of being exploited by free-riders. However, the precise ecological factors supporting cooperation are still puzzling. Following recent experiments, we consider the role of population growth and the repetitive fragmentation of populations into new colonies mimicking simple microbial life-cycles. Individual-based modeling reveals that demographic fluctuations, which lead to a large variance in the composition of colonies, promote cooperation. Biased by population dynamics these fluctuations result in two qualitatively distinct regimes of robust cooperation under repetitive fragmentation into groups. First, if the level of cooperation exceeds a threshold, cooperators will take over the whole population. Second, cooperators can also emerge from a single mutant leading to a robust coexistence between cooperators and free-riders. We find frequency and size of population bottlenecks, and growth dynamics to be the major ecological factors determining the regimes and thereby the evolutionary pathway towards cooperation.Comment: 26 pages, 6 figure

Окончательные результаты рандомизированного исследования III фазы ABCSG-24

(Austrian Breast and Colorectal Cancer Study Group), в котором изучали эффективность неоадъювантной терапии пациенток с ранними стадиями рака молочной железы по схеме эпирубицин + доцетаксел + капецитабин (EDC) по сравнению со схемой эпирубицин + доцетаксел (ED), а также эффективность дополнительного назначения к этим схемам трастузумаба (Т) при Her2-положительных опухолях

Protein Pattern Formation

Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. A prominent example of intracellular patterns are the oscillatory pole-to-pole oscillations of Min proteins in \textit{E. coli} whose biological function is to ensure precise cell division. Cell polarization, a prerequisite for processes such as stem cell differentiation and cell polarity in yeast, is also mediated by a diffusion-reaction process. More generally, these functional modules of cells serve as model systems for self-organization, one of the core principles of life. Under which conditions spatio-temporal patterns emerge, and how these patterns are regulated by biochemical and geometrical factors are major aspects of current research. Here we review recent theoretical and experimental advances in the field of intracellular pattern formation, focusing on general design principles and fundamental physical mechanisms.Comment: 17 pages, 14 figures, review articl