Person:

Altrock, Philipp

Microbial communities display complex population dynamics, both in frequency and absolute density. Evolutionary game theory provides a natural approach to analyse and model this complexity by studying the detailed interactions among players, including competition and conflict, cooperation and coexistence. Classic evolutionary game theory models typically assume constant population size, which often does not hold for microbial populations. Here, we explicitly take into account population growth with frequency-dependent growth parameters, as observed in our experimental system. We study the in vitro population dynamics of the two commensal bacteria (Curvibacter sp. (AEP1.3) and Duganella sp. (C1.2)) that synergistically protect the metazoan host Hydra vulgaris (AEP) from fungal infection. The frequency-dependent, nonlinear growth rates observed in our experiments indicate that the interactions among bacteria in co-culture are beyond the simple case of direct competition or, equivalently, pairwise games. This is in agreement with the synergistic effect of anti-fungal activity observed in vivo. Our analysis provides new insight into the minimal degree of complexity needed to appropriately understand and predict coexistence or extinction events in this kind of microbial community dynamics. Our approach extends the understanding of microbial communities and points to novel experiments.

The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death events. The rates of these events may vary in time depending on the state of the environment, which follows an independent Markov process. We develop a general theory for the fixation probability of a mutant in a population of wild-types, and for mean unconditional and conditional fixation times. We apply our theory to evolutionary games for which the payoff structure varies in time. The mutant can exploit the environmental noise; a dynamic environment that switches between two states can lead to a probability of fixation that is higher than in any of the individual environmental states. We provide an intuitive interpretation of this surprising effect. We also investigate stationary distributions when mutations are present in the dynamics. In this regime, we find two approximations of the stationary measure. One works well for rapid switching, the other for slowly fluctuating environments.

SUMMARY Cancers arise through a process of somatic evolution that can result in substantial sub-clonal heterogeneity within tumors. The mechanisms responsible for the coexistence of distinct sub-clones and the biological consequences of this coexistence remain poorly understood. Here we used a mouse xenograft model to investigate the impact of sub-clonal heterogeneity on tumor phenotypes and the competitive expansion of individual clones. We found that tumor growth can be driven by a minor cell subpopulation, which enhances the proliferation of all cells within a tumor by overcoming environmental constraints and yet can be outcompeted by faster proliferating competitors, resulting in tumor collapse. We then developed a mathematical modeling framework to identify the rules underlying the generation of intratumor clonal heterogeneity. We found that non-cell autonomous driving, together with clonal interference, stabilizes sub-clonal heterogeneity, thereby enabling inter-clonal interactions that can lead to new phenotypic traits.

Weak selection, which means a phenotype is slightly advantageous over another, is an important limiting case in evolutionary biology. Recently, it has been introduced into evolutionary game theory. In evolutionary game dynamics, the probability to be imitated or to reproduce depends on the performance in a game. The influence of the game on the stochastic dynamics in finite populations is governed by the intensity of selection. In many models of both unstructured and structured populations, a key assumption allowing analytical calculations is weak selection, which means that all individuals perform approximately equally well. In the weak selection limit many different microscopic evolutionary models have the same or similar properties. How universal is weak selection for those microscopic evolutionary processes? We answer this question by investigating the fixation probability and the average fixation time not only up to linear but also up to higher orders in selection intensity. We find universal higher order expansions, which allow a rescaling of the selection intensity. With this, we can identify specific models which violate (linear) weak selection results, such as the one-third rule of coordination games in finite but large populations.

Recent advances in gene therapy and genome-engineering technologies offer the opportunity to correct sickle cell disease (SCD), a heritable disorder caused by a point mutation in the beta-globin gene. The developmental switch from fetal gamma-globin to adult beta-globin is governed in part by the transcription factor (TF) BCL11A. This TF has been proposed as a therapeutic target for reactivation of gamma-globin and concomitant reduction of beta-sickle globin. In this and other approaches, genetic alteration of a portion of the hematopoietic stem cell (HSC) compartment leads to a mixture of sickling and corrected red blood cells (RBCs) in periphery. To reverse the sickling phenotype, a certain proportion of corrected RBCs is necessary; the degree of HSC alteration required to achieve a desired fraction of corrected RBCs remains unknown. To address this issue, we developed a mathematical model describing aging and survival of sickle-susceptible and normal RBCs; the former can have a selective survival advantage leading to their overrepresentation. We identified the level of bone marrow chimerism required for successful stem cell-based gene therapies in SCD. Our findings were further informed using an experimental mouse model, where we transplanted mixtures of Berkeley SCD and normal murine bone marrow cells to establish chimeric grafts in murine hosts. Our integrative theoretical and experimental approach identifies the target frequency of HSC alterations required for effective treatment of sickling syndromes in humans. Our work replaces episodic observations of such target frequencies with a mathematical modeling framework that covers a large and continuous spectrum of chimerism conditions.