Biology subjects

Arne Traulsen

Publications and source records attributed to Arne Traulsen.

12 recordsLinked to original sources

bioRxiv2016

Chaotic provinces in the kingdom of the Red Queen

The interplay between parasites and their hosts is found in all kinds of species and plays an important role in understanding the principles of evolution and coevolution. Usually, the different genotypes of hosts and parasites oscillate in their abundances. The well-established theory of oscillatory Red Queen dynamics proposes an ongoing change in frequencies of the different types within each species. So far, it is unclear in which way Red Queen dynamics persists with more than two types of hosts and parasites. In our analysis, an arbitrary number of types within two species are examined in a deterministic framework with constant or changing population size. This general framework allows for analytical solutions for internal fixed points and their stability. For more than two species, apparently chaotic dynamics has been reported. Here we show that even for two species, once more than two types are considered per species, irregular dynamics in their frequencies can be observed in the long run. The nature of the dynamics depends strongly on the initial configuration of the system; the usual regular Red Queen oscillations are only observed in some parts of the parameter region.

Evolutionary Biology↗

bioRxiv2016

Should tissue structure suppress or amplify selection to minimize cancer risk?

BackgroundIt has been frequently argued that tissues evolved to suppress the accumulation of growth enhancing cancer inducing mutations. A prominent example is the hierarchical structure of tissues with high cell turnover, where a small number of tissue specific stem cells produces a large number of specialised progeny during multiple differentiation steps. Another well known mechanism is the spatial organisation of stem cell populations and it is thought that this organisation suppresses fitness enhancing mutations. However, in small populations the suppression of advantageous mutations typically also implies an increased accumulation of deleterious mutations. Thus, it becomes an important question whether the suppression of potentially few advantageous mutations outweighs the combined effects of many deleterious mutations.\n\nResultsWe argue that the distribution of mutant fitness effects, e.g. the probability to hit a strong driver compared to many deleterious mutations, is crucial for the optimal organisation of a cancer suppressing tissue architecture and should be taken into account in arguments for the evolution of such tissues.\n\nConclusionWe show that for systems that are composed of few cells reflecting the typical organisation of a stem cell niche, amplification or suppression of selection can arise from subtle changes in the architecture. Moreover, we discuss special tissue structures that can suppress most types of non-neutral mutations simultaneously.

Evolutionary Biology↗

bioRxiv2016

Haplotype block dynamics in hybrid populations

When species originate through hybridization, the genomes of the ancestral species are blended together. Over time genomic blocks that originate from either one of the ancestral species accumulate in the hybrid genome through genetic recombination. Modeling the accumulation of ancestry blocks can elucidate processes and patterns of genomic admixture. However, previous models have ignored ancestry block dynamics for chromosomes that consist of a discrete, finite number of chromosomal elements. Here we present an analytical treatment of the dynamics of the mean number of blocks over time, for continuous and discrete chromosomes, in finite and infinite populations. We describe the mean number of haplotype blocks as a universal function dependent on population size, the number of genomic elements per chromosome, the number of recombination events, and the initial relative frequency of the ancestral species.

Evolutionary Biology↗

bioRxiv2016

How life history can sway the fixation probability of mutants

In this work, we study the effects of demographic structure on evolutionary dynamics, when selection acts on reproduction, survival, or both. In contrast with the previously discovered pattern that the fixation probability of a neutral mutant decreases while population becomes younger, we show that a mutant with constant selective advantage may have a maximum or a minimum of the fixation probability in populations with an intermediate fraction of young individuals. This highlights the importance of life history and demographic structure in studying evolutionary dynamics. We also illustrate the fundamental differences between selection on reproduction and on survival when age structure is present. In addition, we evaluate the relative importance of size and structure of the population in determining the fixation probability of the mutant. Our work lays the foundation for studying also density and frequency dependent effects in populations when demographic structures cannot be neglected.

Evolutionary Biology↗

bioRxiv2016

Evolutionary games of multiplayer cooperation on graphs

There has been much interest in studying evolutionary games in structured populations, often modelled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering.\n\nAuthor SummaryCooperation can be defined as the act of providing fitness benefits to other individuals, often at a personal cost. When interactions occur mainly with neighbors, assortment of strategies can favor cooperation but local competition can undermine it. Previous research has shown that a single coefficient can capture this trade-off when cooperative interactions take place between two players. More complicated, but also more realistic models of cooperative interactions involving multiple players instead require several such coefficients, making it difficult to assess the effects of population structure. Here, we obtain analytical approximations for the coefficients of multiplayer games in graph-structured populations. Computer simulations show that, for particular instances of multiplayer games, these approximate coefficients predict the condition for cooperation to be promoted in random graphs well, but fail to do so in graphs with more structure, such as lattices. Our work extends and generalizes established results on the evolution of cooperation on graphs, but also highlights the importance of explicitly taking into account higher-order statistical associations in order to assess the evolutionary dynamics of cooperation in spatially structured populations.

Evolutionary Biology↗

bioRxiv2015

Modes of migration and multilevel selection in evolutionary multiplayer games

The evolution of cooperation in group-structured populations has received much attention, but little is known about the effects of different modes of migration of individuals between groups. Here, we have incorporated four different modes of migration that differ in the degree of coordination among the individuals. For each mode of migration, we identify the set of multiplayer games in which the cooperative strategy has higher fixation probability than defection. The comparison shows that the set of games under which cooperation may evolve generally expands depending upon the degree of coordination among the migrating individuals. Weak altruism can evolve under all modes of individual migration, provided that the benefit to cost ratio is high enough. Strong altruism, however, evolves only if the mode of migration involves coordination of individual actions. Depending upon the migration frequency and degree of coordination among individuals, conditions that allow selection to work at the level of groups can be established.

Evolutionary Biology↗

bioRxiv2015

Evolving synergetic interactions

The outcome of a major evolutionary transition is the aggregation of independent entities into a new synergetic level of organisation. Classical models involve either pairwise interactions between individuals or a linear superposition of these interactions. However, major evolutionary transitions display synergetic effects: their outcome is not just the sum of its parts. Multiplayer games can display such synergies, as their payoff can be different from the sum of any collection of two-player interactions. Assuming that all interactions start from pairs, how can synergetic multiplayer games emerge from simpler pairwise interaction? Here, we present a mathematical model that captures the transition from pairwise interactions to synergetic multiplayer ones. We assume that different social groups have different breaking rates. We show that non-uniform breaking rates do foster the emergence of synergy, even though individuals always interact in pairs. Our work sheds new light on the mechanisms underlying a major evolutionary transition.

Evolutionary Biology↗

bioRxiv2015

Ordering structured populations in multiplayer cooperation games

Spatial structure greatly affects the evolution of cooperation. While in two-player games the condition for cooperation to evolve depends on a single structure coefficient, in multiplayer games the condition might depend on several structure coefficients, making it difficult to compare different population structures. We propose a solution to this issue by introducing two simple ways of ordering population structures: the containment order and the volume order. If population structure [S]1 is greater than population structure [S]2 in the containment or the volume order, then [S]1 can be considered a stronger promoter of cooperation. We provide conditions for establishing the containment order, give general results on the volume order, and illustrate our theory by comparing different models of spatial games and associated update rules. Our results hold for a large class of population structures and can be easily applied to specific cases once the structure coefficients have been calculated or estimated.

Evolutionary Biology↗

bioRxiv2015

Stochastic evolutionary games in dynamic populations

Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on interactions between individuals within the population. This should be reflected in fluctuations of the population size even in constant environ ments. Here, we propose a stochastic model, which naturally combines these two evolutionary ingredients by assuming frequency dependent competition between different types in an individual-based model. In contrast to previous game theoretic models, the carrying capacity of the population and thus the population size is determined by pairwise competition of individuals mediated by evolutionary games and demographic stochasticity. In the limit of infinite population size, the averaged stochastic dynamics is captured by the deterministic competitive LotkaVolterra equations. In small populations, demographic stochasticity may instead lead to the extinction of the entire population. As the population size is driven by the fitness in evolutionary games, a population of cooperators is less prone to go extinct than a population of defectors, whereas in the usual systems of fixed size, the population would thrive regardless of its average payoff.

Evolutionary Biology↗

bioRxiv2015

Estimating stem cell fractions in hierarchically organized tumors

Cancers arise as a result of genetic and epigenetic alterations. These accumulate in cells during the processes of tissue development, homeostasis and repair. Many tumor types are hierarchically organized and driven by a sub-population of cells often called cancer stem cells. Cancer stem cells are uniquely capable of recapitulating the tumor and can be highly resistant to radio-and chemotherapy treatment. We investigate tumor growth patterns from a theoretical standpoint and show how significant changes in pre-and post-therapy tumor dynamics are tied to the dynamics of cancer stem cells. We identify two characteristic growth regimes of a tumor population that can be leveraged to estimate cancer stem cell fractions in vivo using simple linear regression. Our method is a mathematically exact result, parameter free and does not require any microscopic knowledge of the tumor properties. A more accurate quantification of the direct link between the sub-population driving tumor growth and treatment response promises new ways to individualize treatment strategies.\n\nSignificance StatementUnder the cancer stem cell hypothesis a tumor population is driven by a fraction of self-renewing cancer stem cells. Absolute and relative size of this population in human cancers at any stage of the disease remains unknown. We formulate a mathematical model that describes the tumor cell populations growth dynamics and response to therapy. This allows to estimate cancer stem cell fraction from longitudinal measurements of tumor size (often available from imaging). Such estimates are critical because treatment outcome and risk of relapse depend on the tumors capacity to self-renew. Ideally, by tailoring patient treatment strategies based on the relative abundance of cancer stem cells could lead to radically different therapeutic regime and to the successful eradication of the disease.

Cancer Biology↗

bioRxiv2014

Host-parasite coevolution in populations of constant and variable size

The matching-allele and gene-for-gene models are widely used in mathematical approaches that study the dynamics of host-parasite interactions. Agrawal and Lively (Evolutionary Ecology Research 4:79-90, 2002) captured these two models in a single framework and numerically explored the associated time discrete dynamics of allele frequencies. Here, we present a detailed analytical investigation of this unifying framework in continuous time and provide a generalization. We extend the model to take into account changing population sizes, which result from the antagonistic nature of the interaction and follow the Lotka-Volterra equations. Under this extension, the population dynamics become most complex as the model moves away from pure matching-allele and becomes more gene-for-gene-like. While the population densities oscillate with a single oscillation frequency in the pure matching-allele model, a second oscillation frequency arises under gene-for-gene-like conditions. These observations hold for general interaction parameters and allow to infer generic patterns of the dynamics. Our results suggest that experimentally inferred dynamical patterns of host-parasite coevolution should typically be much more complex than the popular illustrations of Red Queen dynamics. A single parasite that infects more than one host can substantially alter the cyclic dynamics.

Evolutionary Biology↗

bioRxiv2014

Evolutionary Multiplayer Games

Evolutionary game theory has become one of the most diverse and far reaching theories in biology. Applications of this theory range from cell dynamics to social evolution. However, many applications make it clear that inherent non-linearities of natural systems need to be taken into account. One way of introducing such non-linearities into evolutionary games is by the inclusion of multiple players. An example is of social dilemmas, where group benefits could e.g. increase less than linear with the number of cooperators. Such multiplayer games can be introduced in all the fields where evolutionary game theory is already well established. However, the inclusion of non-linearities can help to advance the analysis of systems which are known to be complex, e.g. in the case of non-Mendelian inheritance. We review the diachronic theory and applications of multiplayer evolutionary games and present the current state of the field. Our aim is a summary of the theoretical results from well-mixed populations in infinite as well as finite populations. We also discuss examples from three fields where the theory has been successfully applied, ecology, social sciences and population genetics. In closing, we probe certain future directions which can be explored using the complexity of multiplayer games while preserving the promise of simplicity of evolutionary games.

Evolutionary Biology↗