@phdthesis{7196,
abstract = {In this thesis we study certain mathematical aspects of evolution. The two primary forces that drive an evolutionary process are mutation and selection. Mutation generates new variants in a population. Selection chooses among the variants depending on the reproductive rates of individuals. Evolutionary processes are intrinsically random – a new mutation that is initially present in the population at low frequency can go extinct, even if it confers a reproductive advantage. The overall rate of evolution is largely determined by two quantities: the probability that an invading advantageous mutation spreads through the population (called fixation probability) and the time until it does so (called fixation time). Both those quantities crucially depend not only on the strength of the invading mutation but also on the population structure. In this thesis, we aim to understand how the underlying population structure affects the overall rate of evolution. Specifically, we study population structures that increase the fixation probability of advantageous mutants (called amplifiers of selection). Broadly speaking, our results are of three different types: We present various strong amplifiers, we identify regimes under which only limited amplification is feasible, and we propose population structures that provide different tradeoffs between high fixation probability and short fixation time.},
author = {Tkadlec, Josef},
issn = {2663-337X},
pages = {144},
publisher = {IST Austria},
title = {{A role of graphs in evolutionary processes}},
doi = {10.15479/AT:ISTA:7196},
year = {2020},
}
@article{7343,
abstract = {Coinfections with multiple pathogens can result in complex within‐host dynamics affecting virulence and transmission. While multiple infections are intensively studied in solitary hosts, it is so far unresolved how social host interactions interfere with pathogen competition, and if this depends on coinfection diversity. We studied how the collective disease defences of ants – their social immunity – influence pathogen competition in coinfections of same or different fungal pathogen species. Social immunity reduced virulence for all pathogen combinations, but interfered with spore production only in different‐species coinfections. Here, it decreased overall pathogen sporulation success while increasing co‐sporulation on individual cadavers and maintaining a higher pathogen diversity at the community level. Mathematical modelling revealed that host sanitary care alone can modulate competitive outcomes between pathogens, giving advantage to fast‐germinating, thus less grooming‐sensitive ones. Host social interactions can hence modulate infection dynamics in coinfected group members, thereby altering pathogen communities at the host level and population level.},
author = {Milutinovic, Barbara and Stock, Miriam and Grasse, Anna V and Naderlinger, Elisabeth and Hilbe, Christian and Cremer, Sylvia},
issn = {1461-023X},
journal = {Ecology Letters},
publisher = {Wiley},
title = {{Social immunity modulates competition between coinfecting pathogens}},
doi = {10.1111/ele.13458},
year = {2020},
}
@article{7212,
abstract = {The fixation probability of a single mutant invading a population of residents is among the most widely-studied quantities in evolutionary dynamics. Amplifiers of natural selection are population structures that increase the fixation probability of advantageous mutants, compared to well-mixed populations. Extensive studies have shown that many amplifiers exist for the Birth-death Moran process, some of them substantially increasing the fixation probability or even guaranteeing fixation in the limit of large population size. On the other hand, no amplifiers are known for the death-Birth Moran process, and computer-assisted exhaustive searches have failed to discover amplification. In this work we resolve this disparity, by showing that any amplification under death-Birth updating is necessarily bounded and transient. Our boundedness result states that even if a population structure does amplify selection, the resulting fixation probability is close to that of the well-mixed population. Our transience result states that for any population structure there exists a threshold r⋆ such that the population structure ceases to amplify selection if the mutant fitness advantage r is larger than r⋆. Finally, we also extend the above results to δ-death-Birth updating, which is a combination of Birth-death and death-Birth updating. On the positive side, we identify population structures that maintain amplification for a wide range of values r and δ. These results demonstrate that amplification of natural selection depends on the specific mechanisms of the evolutionary process.},
author = {Tkadlec, Josef and Pavlogiannis, Andreas and Chatterjee, Krishnendu and Nowak, Martin A.},
issn = {15537358},
journal = {PLoS computational biology},
publisher = {PLoS},
title = {{Limits on amplifiers of natural selection under death-Birth updating}},
doi = {10.1371/journal.pcbi.1007494},
volume = {16},
year = {2020},
}
@article{6918,
abstract = {We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge of the network is operable with its associated probability and the problem is to determine the probability of having at least one source-to-target path that is entirely composed of operable edges. This problem is known to be NP-hard.
We provide a novel scalable algorithm to solve the Network Reliability problem when the treewidth of the underlying network is small. We also show our algorithm’s applicability for real-world transit networks that have small treewidth, including the metro networks of major cities, such as London and Tokyo. Our algorithm leverages tree decompositions to shrink the original graph into much smaller graphs, for which reliability can be efficiently and exactly computed using a brute force method. To the best of our knowledge, this is the first exact algorithm for Network Reliability that can scale to handle real-world instances of the problem.},
author = {Goharshady, Amir Kafshdar and Mohammadi, Fatemeh},
issn = {09518320},
journal = {Reliability Engineering and System Safety},
publisher = {Elsevier},
title = {{An efficient algorithm for computing network reliability in small treewidth}},
doi = {10.1016/j.ress.2019.106665},
volume = {193},
year = {2020},
}
@inproceedings{7346,
abstract = {The Price of Anarchy (PoA) is a well-established game-theoretic concept to shed light on coordination issues arising in open distributed systems. Leaving agents to selfishly optimize comes with the risk of ending up in sub-optimal states (in terms of performance and/or costs), compared to a centralized system design. However, the PoA relies on strong assumptions about agents' rationality (e.g., resources and information) and interactions, whereas in many distributed systems agents interact locally with bounded resources. They do so repeatedly over time (in contrast to "one-shot games"), and their strategies may evolve. Using a more realistic evolutionary game model, this paper introduces a realized evolutionary Price of Anarchy (ePoA). The ePoA allows an exploration of equilibrium selection in dynamic distributed systems with multiple equilibria, based on local interactions of simple memoryless agents. Considering a fundamental game related to virus propagation on networks, we present analytical bounds on the ePoA in basic network topologies and for different strategy update dynamics. In particular, deriving stationary distributions of the stochastic evolutionary process, we find that the Nash equilibria are not always the most abundant states, and that different processes can feature significant off-equilibrium behavior, leading to a significantly higher ePoA compared to the PoA studied traditionally in the literature. },
author = {Schmid, Laura and Chatterjee, Krishnendu and Schmid, Stefan},
booktitle = {Proceedings of the 23rd International Conference on Principles of Distributed Systems},
location = {Neuchâtel, Switzerland},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{The evolutionary price of anarchy: Locally bounded agents in a dynamic virus game}},
doi = {10.4230/LIPIcs.OPODIS.2019.21},
volume = {153},
year = {2020},
}