Generation time measures the trade-off between survival and reproduction in a life cycle

AbstractSurvival and fertility are the two most basic components of fitness, and they drive the evolution of a life cycle. A trade-off between them is usually present: when survival increases, fertility decreases?and vice versa. Here we show that at an evolutionary optimum, the generation time is a measure of the strength of the trade-off between overall survival and overall fertility in a life cycle. Our result both helps to explain the known fact that the generation time describes the speed of living in the slow-fast continuum of life cycles and may have implications for the extrapolation from model organisms of longevity to humans

A deterministic model for the occurrence and dynamics of multiple mutations in hierarchically organized tissues

We model a general, hierarchically organized tissue by a multi compartment approach, allowing any number of mutations within a cell. We derive closed solutions for the deterministic clonal dynamics and the reproductive capacity of single clones. Our results hold for the average dynamics in a hierarchical tissue characterized by an arbitrary combination of proliferation parameters.Comment: 4 figures, to appear in Royal Society Interfac

The evolution of strategic timing in collective-risk dilemmas

In collective-risk dilemmas, a group needs to collaborate over time to avoid a catastrophic event. This gives rise to a coordination game with many equilibria, including equilibria where no one contributes, and thus no measures against the catastrophe are taken. In this game, the timing of contributions becomes a strategic variable that allows individuals to interact and influence one another. Herein, we use evolutionary game theory to study the impact of strategic timing on equilibrium selection. Depending on the risk of catastrophe, we identify three characteristic regimes. For low risks, defection is the only equilibrium, whereas high risks promote equilibria with sufficient contributions. Intermediate risks pose the biggest challenge for cooperation. In this risk regime, the option to interact over time is critical; if individuals can contribute over several rounds, then the group has a higher chance to succeed, and the expected welfare increases. This positive effect of timing is of particular importance in larger groups, where successful coordination becomes increasingly difficul

Interacting cells driving the evolution of multicellular life cycles

Author summary Multicellular organisms are ubiquitous. But how did the first multicellular organisms arise? It is typically argued that this occurred due to benefits coming from interactions between cells. One example of such interactions is the division of labour. For instance, colonial cyanobacteria delegate photosynthesis and nitrogen fixation to different cells within the colony. In this way, the colony gains a growth advantage over unicellular cyanobacteria. However, not all cell interactions favour multicellular life. Cheater cells residing in a colony without any contribution will outgrow other cells. Then, the growing burden of cheaters may eventually destroy the colony. Here, we ask what kinds of interactions promote the evolution of multicellularity? We investigated all interactions captured by pairwise games and for each of them, we look for the evolutionarily optimal life cycle: How big should the colony grow and how should it split into offspring cells or colonies? We found that multicellularity can evolve with interactions far beyond cooperation or division of labour scenarios. More surprisingly, most of the life cycles found fall into either of two categories: A parent colony splits into two multicellular parts, or it splits into multiple independent cells

Probing the accretion processes in soft X-ray selected polars

High-energy data of accreting white dwarfs give access to the regime of the primary accretion-induced energy release and the different proposed accretion scenarios. We perform XMM-Newton observations of polars selected due to their ROSAT hardness ratios close to -1.0 and model the emission processes in accretion column and accretion region. Our models consider the multi-temperature structure of the emission regions and are mainly determined by mass-flow density, magnetic field strength, and white-dwarf mass. To describe the full spectral energy distribution from infrared to X-rays in a physically consistent way, we include the stellar contributions and establish composite models, which will also be of relevance for future X-ray missions. We confirm the X-ray soft nature of three polars.Comment: Accepted for publication in Acta Polytechnica, Proceedings of "The Golden Age of Cataclysmic Variables and Related Objects II

Evolutionary games in the multiverse

Evolutionary game dynamics of two players with two strategies has been studied in great detail. These games have been used to model many biologically relevant scenarios, ranging from social dilemmas in mammals to microbial diversity. Some of these games may in fact take place between a number of individuals and not just between two. Here, we address one-shot games with multiple players. As long as we have only two strategies, many results from two player games can be generalized to multiple players. For games with multiple players and more than two strategies, we show that statements derived for pairwise interactions do no longer hold. For two player games with any number of strategies there can be at most one isolated internal equilibrium. For any number of players $\boldsymbol{d}$ with any number of strategies n, there can be at most (d-1)^(n-1) isolated internal equilibria. Multiplayer games show a great dynamical complexity that cannot be captured based on pairwise interactions. Our results hold for any game and can easily be applied for specific cases, e.g. public goods games or multiplayer stag hunts

The pace of evolution across fitness valleys

How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a fitness advantage. We consider the time until a population has evolved from one fitness peak to another one with a higher fitness. The order of mutations can either be fixed or random. If the order of mutations is fixed, then the population follows a metaphorical ridge, a single path. If the order of mutations is arbitrary, then there are many ways to evolve to the higher fitness state. We address the time required for fixation in such scenarios and study how it is affected by the order of mutations, the population size, the fitness values and the mutation rate

Strategy abundance in 2x2 games for arbitrary mutation rates

We study evolutionary game dynamics in a well-mixed populations of finite size, N. A well-mixed population means that any two individuals are equally likely to interact. In particular we consider the average abundances of two strategies, A and B, under mutation and selection. The game dynamical interaction between the two strategies is given by the 2x2 payoff matrix [(a,b), (c,d)]. It has previously been shown that A is more abundant than B, if (N-2)a+Nb>Nc+(N-2)d. This result has been derived for particular stochastic processes that operate either in the limit of asymptotically small mutation rates or in the limit of weak selection. Here we show that this result holds in fact for a wide class of stochastic birth-death processes for arbitrary mutation rate and for any intensity of selection.Comment: version 2 is the final published version that contains minor changes in response to referee comment

Cooperation and control in multiplayer social dilemmas

Direct reciprocity and conditional cooperation are important mechanisms to prevent free riding in social dilemmas. However, in large groups, these mechanisms may become ineffective because they require single individuals to have a substantial influence on their peers. However, the recent discovery of zero-determinant strategies in the iterated prisoner’s dilemma suggests that we may have underestimated the degree of control that a single player can exert. Here, we develop a theory for zero-determinant strategies for iterated multiplayer social dilemmas, with any number of involved players. We distinguish several particularly interesting subclasses of strategies: fair strategies ensure that the own payoff matches the average payoff of the group; extortionate strategies allow a player to perform above average; and generous strategies let a player perform below average. We use this theory to describe strategies that sustain cooperation, including generalized variants of Tit-for-Tat and Win-Stay Lose-Shift. Moreover, we explore two models that show how individuals can further enhance their strategic options by coordinating their play with others. Our results highlight the importance of individual control and coordination to succeed in large groups

Extrapolating weak selection in evolutionary games

In evolutionary games, reproductive success is determined by payoffs. Weak selection means that even large differences in game outcomes translate into small fitness differences. Many results have been derived using weak selection approximations, in which perturbation analysis facilitates the derivation of analytical results. Here, we ask whether results derived under weak selection are also qualitatively valid for intermediate and strong selection. By ‘‘qualitatively valid’’ we mean that the ranking of strategies induced by an evolutionary process does not change when the intensity of selection increases. For two-strategy games, we show that the ranking obtained under weak selection cannot be carried over to higher selection intensity if the number of players exceeds two. For games with three (or more) strategies, previous examples for multiplayer games have shown that the ranking of strategies can change with the intensity of selection. In particular, rank changes imply that the most abundant strategy at one intensity of selection can become the least abundant for another. We show that this applies already to pairwise interactions for a broad class of evolutionary processes. Even when both weak and strong selection limits lead to consistent predictions, rank changes can occur for intermediate intensities of selection. To analyze how common such games are, we show numerically that for randomly drawn two-player games with three or more strategies, rank changes frequently occur and their likelihood increases rapidly with the number of strategies n. In particular, rank changes are almost certain for n§8, which jeopardizes the predictive power of results derived for weak selection