From multi-cellular organisms to social structures, cooperation is the pillar of the high level of organization observed in biological world. However, as cooperation incurs a cost to the cooperator for others to benefit, its evolution seems to contradict natural selection. How evolution has resolved this obstacle, and how high level of cooperation has evolved, have been among the most intensely studied problems in the evolutionary theory, in recent decades. In this presentation, I will introduce this problem in the framework of evolutionary game theory, and discuss different mechanisms, using which evolution can promote cooperation. In this regards, after briefly discussing well-established mechanisms, I discuss how strategic signaling, democratic decision making, and competition between resources can provide novel roads to the evolution of cooperation. In addition, I will discuss closely related problems, such as the evolution of language, the evolution of community structure and leadership, the evolution of moral norms, and the evolution of sanctioning institutions, and discuss how such institutions can evolve and help cooperation to flourish. Finally, I discuss how this problem can more subtly arise in a broader context. For this purpose, I consider the evolution of collective information acquisition, in a context where information production has a cost. I show, despite the temptation to free-ride by not producing information, collective information acquisition can evolve in a structured population due to network reciprocity, and discuss how such collective sensing population can make optimal use of information in a changing environment.
Naive reasoning suggests that the ascending family tree of any individual is a binary tree, which would imply that this individual has ancestors generations back. Such an exponential growth is however not compatible with the size of the world population at that time. This apparent paradox is explained by the presence of inbred unions, which effectively reduces the number of distinct ancestors. We propose a stochastic model to study this phenomenon, in the form of an oriented acyclic random graph. We present conditions under which the family tree "collapses", i.e. has a diamond shape rather than the pyramid shape of the binary tree. These criteria on the random graph parameters are then translated into conditions on the studied population, in particular on the proportion of unions between cousins in each generation.
Competitive capacity of living organisms depends on two factors: their genetic information and the environmental conditions under which that genetic information encodes their functioning. When either genetics or environment changes randomly, the competitive capacity, if initially maximized, will most probably decline. Conversely, living organisms (or their coordinated structures) that exert control over their preferred environment preventing its spontaneous degradation can persistently enjoy high competitive capacity. Moreover, as far as the efficiency of natural selection for a given genotype also depends on environmental conditions, a stable environment allows for maximization of the selection efficiency and thus minimizes the probability of genetic degradation. According to the concept of the biotic regulation of the environment (https://bioticregulation.ru ), natural ecological communities of biological species stabilize their genetically encoded environment by compensating its random perturbations of both biotic and abiotic nature. Genetic and environmental stability are mutually guaranteed rather than arise by happenstance. In this talk we consider how this premise is reflected in key observed quantitative characteristics of oceanic and terrestrial life and its environment.
We also discuss how whether life regulates the environment or not is not an academic issue of little relevance to current global change problems. If the stability of the Earth’s environment favorable for life is maintained by natural ecosystems, then, even in the absence of direct environmental disturbances like e.g. carbon emissions, degradation of these regulatory mechanisms presents a major threat to the humanity, and the more so, the longer our species remains unaware of this fact. For the biosphere to preserve a global stabilizing function, the self-sustainable natural ecosystems must be globally protected from exploitation. The biota should be preserved not in biodiversity hotspots, advanced agricultural systems or zoos, but on large territories, such that the stabilizing power of these natural ecosystems would compensate the violation of natural processes that humans perform elsewhere.
Joint work with Andrei V. Nefiodov
The classic question of statistical physics – what is different when some parameter is large? - acquires a whole new life in the study of evolution. Most of our intuition about evolution and ecology comes from analysis of low-dimensional models, with few environments or few factors determining fitness. What novel phases might arise when evolution is examined in the realistic regime of many environments as opposed to a few? I will describe one minimally structured toy model for these intriguing general questions, and will discuss a few avenues we are investigating in my group. In particular, I will argue that, generically, in high dimensions one no longer expects a direct exposure to some environment to be the most effective way of achieving highest fitness in it.
Whenever an ecological system adapts, it affects its environment, which in turn tends to modify the selection pressures acting on it: such eco-evolutionary feedback therefore lies at the heart of understanding processes of adaptation in natural systems. The theory of adaptive dynamics is geared to analyzing evolutionary dynamics in realistically complex ecological settings. Adaptive-dynamics models are derived from considering ecological interactions and phenotypic variation at the level of individuals: extending classical birth-and-death processes, these models keep track, over time, of the phenotypic composition of a population or community in which offspring phenotypes are allowed to differ from those of their parents. Adaptive-dynamics theory formally integrates four widely used classes of evolutionary processes – individual-based models, random walks, gradient-ascent dynamics, and reaction-diffusion systems – into a single conceptual and mathematical framework, facilitating switching back and forth between alternative descriptions as research questions require. Adaptive-dynamics theory extends classical evolutionary game theory in several key dimensions: evolving traits are continuous, trait dynamics are explicitly described, mutational covariances and constraints can be examined, arbitrary forms of density dependence and frequency dependence are allowed, multi-species evolution is integrated, structured population dynamics and non-equilibrium population dynamics can be investigated, and – most importantly – fitness landscapes are derived from first principles. Novel phenomena revealed by the theory of adaptive dynamics include evolutionary slowing down, evolutionary branching, and evolutionary cycling. This presentation will provide an overview of adaptive-dynamics theory for a mathematically trained audience.Suggested readings:
Evolution and Ecology Program (EEP)
Homepage Ulf Dieckmann
Google Scholar Ulf Dieckmann
Paper for section 2
Paper for section 1-3
A brief introduction to elements of C-valued analysis over Qp will the theory of generalized functions on Qp, Fourier analysis, the theory of pseudo-differential operators, and, as an ultimate goal with applications in mind, elements of diffusion and Schrödinger-like equations on Qp. Most results will simply be announced without demonstration.
The seminar will take form of a very brief introduction to p-adic numbers themselves and to some basic facts on the topology and other geometric features of Qp, the space of p-adic numbers. A brief introduction to elements of C-valued analysis over Qp will follow touching the theory of generalized functions on Qp, Fourier analysis, the theory of pseudo-differential operators, and, as an ultimate goal with applications in mind, elements of diffusion and Schrödinger-like equations on Qp. The number theoretic aspects, algebraic aspects, or Qp-valued analysis will not be touched at all. Most results will simply be announced without demonstration.
Natural selection operates on phenotypes. In contrast, Modern Synthesis (the most formalized evolutionary theory) is essentially gene-centered or, more generally, genotype-centered. The organism's phenotype is considered, at best, as an image of the underlying genotype by a fixed mapping. General biology, however, knows examples where the genotype-phenotype dependence (mainly via ontogenesis and behavior) is very nontrivial and depends on external factors. This is traditionally captured by the notions of phenotypic plasticity and norm of reaction. Their effect on the evolutionary process is currently poorly understood due to the lack of a concise formalization. In this talk I will review the history of the question starting from the work of Baldwin, the stabilizing selection of Schmalhausen, and the epigenetics/genetic assimilation of Waddington, and ending with the modern Evo-Devo, Extended Evolutionary Synthesis, and Epigenetic Theory of Evolution. Finally, I will make an overview of attempts on mathematical conceptualization and computational modeling of the subject. Some parallels with results on computational RNA folding will be discussed, too.
We present a standard model of evolution by natural selection and mutation in integro-pde form. We show that Fourier transform of the model reduces to a variant of the transport equation and admits exact solution. We employ this solution, together with empirical characteristic functions, to estimate the distribution of fitness effects (DFE) of newly-arising mutations, given fitness measurements of random samples taken from evolving populations. We derive non-parametric methods to determine when the DFE undergoes major changes. We apply our methods to evolving populations of E coli.
Beerenwinkel et al.(2007) suggested studying fitness landscapes via regular subdivisions of convex polytopes. Building on their approach we propose cluster partitions and cluster filtrations of fitness landscapes as a new mathematical tool. In this way, we provide a concise combinatorial way of processing metric information from epistatic interactions. Using existing Drosophila microbiome data, we demonstrate similarities with and differences to the previous approach. As one outcome we locate interesting epistatic information where the previous approach is less conclusive.
The application of age structure, the temporal ordering of events in a life cycle, is a subtle matter: there are risks in neglecting it, but also in relying on it without regard to the underlying biology. In modeling aging, the risk of relying on age structure is that the biological chain of events that is supposed to lead to the timing of events remains unclear. On the other hand, neglecting age structure can lead to impossible results/hypotheses: Peto’s paradox and the proposed association between lifetime number of stem cell and lifetime cancer risk are examples. Ironically, if cancer is the result of the accumulation of cellular mutations, it is perhaps the only cause of death that seems to fit the classical theory that aging follows simply from age structure; ironically, because whether cancer can justly be called a “senescent” (i.e., resultant of the aging process) cause of death has been contested. Perhaps the idea of non-genetic instability in tumor progression can be of some help here?
Biological systems comprise processes on time and length scales ranging over many orders of magnitude; from chemical reactions with characteristic time scales in the order of nanoseconds to changes in gene expression requiring several hours. Modern experimental techniques enable high temporal and spatial resolutions in the measurements of single cells and suggest that both spatial and temporal domains in between the two mentioned extremes are densely filled with processes and structures. Such experiments are discussed as a motivation for the theoretical work. In particular, they demand possibilities of coarse-graining over several scales.
We develop a formalism for biochemical reaction networks using finite semigroups. It emphasizes the catalytic function of reactants within the networks thus can be used to decide whether the network is self-sustaining. Then, a correspondence between coarse-graining procedures and semigroup congruences respecting the functional structure is established. A family of congruences that leads to a rather unusual coarse-graining procedure is discussed: Thereby, the network is covered with local patches in a way that the local information on the network is fully retained, but the environment of each patch is no longer resolved. Whereas classical coarse-graining procedures would fix a particular local patch and delete detailed information about the environment, the algebraic approach keeps the structure of all local patches and allows the interaction of functions within distinct patches. Possible extensions of this work are sketched.
A growing number of experimental evidence shows that it is general for an enzyme to perform a conformational change upon binding to its substrate and during the release of its product. In addition, enzymes generically have in common allosteric and evolutionary potential. O. Rivoire has recently proposed an evolutionary scenario that explains these properties as a generic byproduct of selection for exquisite discrimination between very similar targets upon binding (between the substrate and the product in enzymes). The initial claim was supported by two classes of basic examples: continuous protein models with small numbers of degrees of freedom, on which the development of a conformational switch is established, and a 2D spin glass model. This work aimed to clarify the implication of the exquisite discrimination for smooth models with large number of degrees of freedom, the situation closer to real biological systems. With the help of differential geometry, jet-space analysis, and transversality theorems, it is shown that the claim holds true for any generic flexible system that can be described in terms of smooth manifolds. The result suggests that, indeed, a conformational change upon binding does not require a special explanation, rather its absence indicates on special circumstances. Furthermore, the evolutionary solutions to the exquisite discrimination problem, if exist, are located near a codimension 1 subspace of an appropriate genotypical space.
The emerging field of compartmentalized in vitro evolution, where selection is carried out by differential reproduction in each compartment, is a promising new approach to protein engineering. From practical point of view, it is important to know the effect of the increase in the average number of genotype bearing agents per compartment. This effect is also interesting on its own in the context of primordial evolution in the hypothetical RNA world. The question is important as genotypes with different phenotypes in the same compartment share their fitness (the number of produced copies) rendering the selection frequency-dependent. I will show the results of a theoretical investigation of this problem in the context of selection dynamics for a simple model with an infinite population that is periodically redistributed among infinite number of identical compartments, inside which all molecules are copied without distinction with the success rate as a function of the total genomic composition in the compartment. Surprisingly, with a linear selection function, the selection process is slowed down only approximately inversely proportional to the average number of individuals per compartment. I will also demonstrate exact forms of the governing equations for some nonlinear selection functions, as well as an apparent phase transition for an exponential selection seen in numerical experiments. Finally, I will discuss an application of the theory to the problem of comparison of different protocols in directed evolution experiments.
Bacterial quorum sensing (QS) is a mechanism used by bacteria to coordinate gene expression. Among QS-regulated processes are motility, biofilm formation and virulence. In this talk, I present some ways to model quorum sensing mathematically. The examples vary through bacterial strains and modeling approaches. As QS is basically a cooperation system, it is subjected to exploitation by members of the population which do not contribute. Although non-cooperators, in theory, can potentially invade the cooperative strain population, this is not observed in nature. We briefly discuss on how to approach the issue of the evolutionary stability of QS from a mathematical viewpoint.
