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PubMed2006

Evolutionary game dynamics in a Wright-Fisher process.

Evolutionary game dynamics in finite populations can be described by a frequency dependent, stochastic Wright-Fisher process. We consider a symmetric game between two strategies, A and B. There are discrete generations. In each generation, individuals produce offspring proportional to their payoff. The next generation is sampled randomly from this pool of offspring. The total population size is constant. The resulting Markov process has two absorbing states corresponding to homogeneous populations of all A or all B. We quantify frequency dependent selection by comparing the absorption probabilities to the corresponding probabilities under random drift. We derive conditions for selection to favor one strategy or the other by using the concept of total positivity. In the limit of weak selection, we obtain the 1/3 law: if A and B are strict Nash equilibria then selection favors replacement of B by A, if the unstable equilibrium occurs at a frequency of A which is less than 1/3.

Algorithms↗
PubMed2004

Simulating protein evolution in sequence and structure space.

Naturally occurring proteins comprise a special subset of all plausible sequences and structures selected through evolution. Simulating protein evolution with simplified and all-atom models has shed light on the evolutionary dynamics of protein populations, the nature of evolved sequences and structures, and the extent to which today's proteins are shaped by selection pressures on folding, structure and function. Extensive mapping of the native structure, stability and folding rate in sequence space using lattice proteins has revealed organizational principles of the sequence/structure map important for evolutionary dynamics. Evolutionary simulations with lattice proteins have highlighted the importance of fitness landscapes, evolutionary mechanisms, population dynamics and sequence space entropy in shaping the generic properties of proteins. Finally, evolutionary-like simulations with all-atom models, in particular computational protein design, have helped identify the dominant selection pressures on naturally occurring protein sequences and structures.

Algorithms↗
PubMed2002

The adaptiveness of defence strategies against cuckoo parasitism.

Host bird species of the Eurasian Cuckoo, Cuculus canorus, often display egg-discrimination behaviour but chick-rejection behaviour has never been reported. In this paper, we analyse a host-cuckoo association in which both population dynamics and evolutionary dynamics are explored in a discrete-time model. We introduce four host types, each with their own defence behaviour, displaying either egg or chick rejection, neither or both, We also introduce fitness functions for each of these host types. Although we can characterize the long term behaviour in many cases by a simple heuristic argument which is in accordance with common views in ecology, there are a number of other phenomena that are not explained within this framework: we describe stable oscillatory behaviour and coexistence of two defensive host types. We analyse the scenarios in which chick rejection may establish itself and give a first explanation as to why this defence trait has never been recorded in nature. We find that chick rejectors generally are at an intrinsic disadvantage with respect to a host type that rejects eggs. Hosts benefit more from rejecting cuckoo eggs than cuckoo chicks, and our model suggests that this is chiefly responsible for the absence of chick rejection. Moreover, even though it seems that chick rejection must be useful as an extra defence, it is shown that hosts with both defence strategies are less likely to establish themselves in competition with egg-rejectors than hosts which reject chicks only. These results provide insight in the extent to which adaptations may be perfected by natural selection.

Adaptation, Biological↗
PubMed2004

Evolutionary tradeoff and equilibrium in an aquatic predator-prey system.

Due to the conventional distinction between ecological (rapid) and evolutionary (slow) timescales, ecological and population models have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has been recently established and may be critical to understanding how populations persist in changing environments. In this paper we examine the relationship between ecological and evolutionary dynamics, focusing on a well-studied experimental aquatic predator-prey system (Fussmann et al., 2000, Science, 290, 1358-1360; Shertzer et al., 2002, J. Anim. Ecol., 71, 802-815; Yoshida et al., 2003, Nature, 424, 303-306). Major properties of predator-prey cycles in this system are determined by ongoing evolutionary dynamics in the prey population. Under some conditions, however, the populations tend to apparently stable steady-state densities. These are the subject of the present paper. We examine a previously developed model for the system, to determine how evolution shapes properties of the equilibria, in particular the number and identity of coexisting prey genotypes. We then apply these results to explore how evolutionary dynamics can shape the responses of the system to 'management': externally imposed alterations in conditions. Specifically, we compare the behavior of the system including evolutionary dynamics, with predictions that would be made if the potential for rapid evolutionary change is neglected. Finally, we posit some simple experiments to verify our prediction that evolution can have significant qualitative effects on observed population-level responses to changing conditions.

Animals↗
PubMed2002

Population genetics of duplicated disease-defense genes, hm1 and hm2, in maize (Zea mays ssp. mays L.) and its wild ancestor (Zea mays ssp. parviglumis).

Plant defense genes are subject to nonneutral evolutionary dynamics. Here we investigate the evolutionary dynamics of the duplicated defense genes hm1 and hm2 in maize and its wild ancestor Zea mays ssp. parviglumis. Both genes have been shown to confer resistance to the fungal pathogen Cochliobolus carbonum race 1, but the effectiveness of resistance differs between loci. The genes also display different population histories. The hm1 locus has the highest nucleotide diversity of any gene yet sampled in the wild ancestor of maize, and it contains a large number of indel polymorphisms. There is no evidence, however, that high diversity in hm1 is a product of nonneutral evolution. In contrast, hm2 has very low nucleotide diversity in the wild ancestor of maize. The distribution of hm2 polymorphic sites is consistent with nonneutral evolution, as indicated by Tajima's D and other neutrality tests. In addition, one hm2 haplotype is more frequent than expected under the equilibrium neutral model, suggesting hitchhiking selection. Both defense genes retain >80% of the level of genetic variation in maize relative to the wild ancestor, and this level is similar to other maize genes that were not subject to artificial selection during domestication.

Ascomycota↗
PubMed2005

Coevolutionary dynamics: from finite to infinite populations.

Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics in finite populations. However, the relationship between deterministic and stochastic approaches remained unclear. Here we solve this problem by explicitly considering large populations. In particular, we identify different microscopic stochastic processes that lead to the standard or the adjusted replicator dynamics. Moreover, differences on the individual level can lead to qualitatively different dynamics in asymmetric conflicts and, depending on the population size, can even invert the direction of the evolutionary process.

Animals↗
PubMed2001

Effects of population size and metapopulation dynamics on a mating-system polymorphism.

The evolutionary dynamics of neutral alleles under the Wright-Fisher model are well understood. Similarly, the effect of population turnover on neutral genetic diversity in a metapopulation has attracted recent attention in theoretical studies. Here we present the results of computer simulations of a simple model that considers the effects of finite population size and metapopulation dynamics on a mating-system polymorphism involving selfing and outcrossing morphs. The details of the model are based on empirical data from dimorphic populations of the annual plant Eichhornia paniculata, but the results are also of relevance to species with density-dependent selfing rates in general. In our model, the prior selfing rate is determined by two alleles segregating at a single diploid locus. After prior selfing occurs, some remaining ovules are selfed through competing self-fertilisation in finite populations as a result of random mating among gametes. Fitness differences between the mating-system morphs were determined by inbreeding depression and pollen discounting in a context-dependent manner. Simulation results showed evidence of frequency dependence in the action of pollen discounting and inbreeding depression in finite populations. In particular, as a result of selfing in outcrossers through random mating among gametes, selfers experienced a "fixation bias" through drift, even when the mating-system locus was selectively neutral. In a metapopulation, high colony turnover generally favoured the fixation of the outcrossing morph, because inbreeding depression reduced opportunities for colony establishment by selfers through seed dispersal. Our results thus demonstrate that population size and metapopulation processes can lead to evolutionary dynamics involving pollen and seed dispersal that are not predicted for large populations with stable demography.

Alleles↗
PubMed1995

Body surface adaptations to boundary-layer dynamics.

Evolutionary processes have adapted nektonic animals to interact efficiently with the water that surrounds them. Not all these adaptations serve the same purpose. This paper concentrates on reduction of drag due to friction in the boundary layer close to the body surface. Mucus, compliant skins, scales, riblets and roughness may influence the flow velocity gradient, the type of flow and the thickness of the boundary layer around animals, and may seriously affect their drag in a positive or negative way. The long-chain polymers found in mucus decrease the pressure gradient and considerably reduced drag due to friction. The effect is probably due to channelling of the flow particles in the direction of the main flow, resulting in a reduction of turbulence. Compliant surfaces could probably reduce drag by equalising and distributing pressure pulses. However, the existing evidence that drag reduction actually occurs is not convincing. There is no indication that instantaneous heating, reducing the viscosity in the boundary layer, is used by animals as a drag-reducing technique. Small longitudinal ridges on rows of scales on fish can reduce shear stress in the boundary by a maximum of 10% compared with the shear stress of a smooth surface. The mechanism is based on the impedance of cross flow under well-defined conditions. The effect has been visualized with the use of particle image velocimetry techniques. The function of the swords and spears of several fast, pelagic, predatory fish species is still enigmatic. The surface structure of the sword of a swordfish is shown to be both rough and porous. The height of the roughness elements on the tip of the sword is close to the critical value for the induction of a laminar-to-turbulent flow transition at moderate cruising speeds. A flow tank is described that is designed to visualize the effects of surface imperfections on flow in the boundary layer in direct comparison with a smooth flat wall. The flow in a 1 m long, 10 cm high and 1 cm wide channel is visualized by illuminating the particles in a thin laser light sheet. The first results show that a rough surface increases the shear stress in the boundary layer and makes it thinner. The function of the roughness on the sword of a swordfish is probably to reduce the total drag by generating premature turbulence and by boundary layer thinning, despite an increased friction over the surface of the sword. The function of the porous surface structures on the sword, and of the porous skins of sharks and of the castor oil fish, will probably be discovered soon using new particle image velocimetry techniques applied under strong magnification to visualize the local behaviour of the flow.

Adaptation, Physiological↗
PubMed2006

Ecosystem engineers as selective agents: the effects of leaf litter on emergence time and early growth in Impatiens capensis.

By physically modifying the abiotic environment, ecosystem engineers can have dramatic effects on the distribution and abundance of species in a community. However, ecosystem engineering can also change the selective environment and evolutionary dynamics of affected species, although this remains relatively understudied. Here, we examine the potential for an ecosystem engineer - oak trees - to affect the evolutionary dynamics of the herbaceous, understory annual, Impatiens capensis, through leaf litter deposition. Using a quantitative genetic experimental approach, we found that: (i) the presence of leaf litter significantly affected a suite of germination, growth and phenological traits in I. capensis; (ii) I. capensis does not exhibit performance trade-offs across litter and bare soil environments in the form of negative across-environment genetic correlations; (iii) the presence or absence of leaf litter significantly alters the pattern of natural selection germination timing and hypocotyl length; and (iv) the frequency of leaf litter environments can dramatically change which combinations of hypocotyl length lead to highest mean fitness across both bare soil and leaf litter environments. More generally, our results demonstrate the potential for ecosystem engineers to alter both the ecological and the evolutionary dynamics of the species they affect.

Ecosystem↗
PubMed2025

Fluctuating DNA methylation tracks cancer evolution at clinical scale.

Cancer development and response to treatment are evolutionary processes1,2, but characterizing evolutionary dynamics at a clinically meaningful scale has remained challenging3. Here we develop a new methodology called EVOFLUx, based on natural DNA methylation barcodes fluctuating over time4, that quantitatively infers evolutionary dynamics using only a bulk tumour methylation profile as input. We apply EVOFLUx to 1,976 well-characterized lymphoid cancer samples spanning a broad spectrum of diseases and show that initial tumour growth rate, malignancy age and epimutation rates vary by orders of magnitude across disease types. We measure that subclonal selection occurs only infrequently within bulk samples and detect occasional examples of multiple independent primary tumours. Clinically, we observe faster initial tumour growth in more aggressive disease subtypes, and that evolutionary histories are strong independent prognostic factors in two series of chronic lymphocytic leukaemia. Using EVOFLUx for phylogenetic analyses of aggressive Richter-transformed chronic lymphocytic leukaemia samples detected that the seed of the transformed clone existed decades before presentation. Orthogonal verification of EVOFLUx inferences is provided using additional genetic data, including long-read nanopore sequencing, and clinical variables. Collectively, we show how widely available, low-cost bulk DNA methylation data precisely measure cancer evolutionary dynamics, and provides new insights into cancer biology and clinical behaviour.

Humans↗
PubMed2004

Structure and evolution of protein interaction networks: a statistical model for link dynamics and gene duplications.

BACKGROUND: The structure of molecular networks derives from dynamical processes on evolutionary time scales. For protein interaction networks, global statistical features of their structure can now be inferred consistently from several large-throughput datasets. Understanding the underlying evolutionary dynamics is crucial for discerning random parts of the network from biologically important properties shaped by natural selection. RESULTS: We present a detailed statistical analysis of the protein interactions in Saccharomyces cerevisiae based on several large-throughput datasets. Protein pairs resulting from gene duplications are used as tracers into the evolutionary past of the network. From this analysis, we infer rate estimates for two key evolutionary processes shaping the network: (i) gene duplications and (ii) gain and loss of interactions through mutations in existing proteins, which are referred to as link dynamics. Importantly, the link dynamics is asymmetric, i.e., the evolutionary steps are mutations in just one of the binding parters. The link turnover is shown to be much faster than gene duplications. Both processes are assembled into an empirically grounded, quantitative model for the evolution of protein interaction networks. CONCLUSIONS: According to this model, the link dynamics is the dominant evolutionary force shaping the statistical structure of the network, while the slower gene duplication dynamics mainly affects its size. Specifically, the model predicts (i) a broad distribution of the connectivities (i.e., the number of binding partners of a protein) and (ii) correlations between the connectivities of interacting proteins, a specific consequence of the asymmetry of the link dynamics. Both features have been observed in the protein interaction network of S. cerevisiae.

Biological Evolution↗
PubMed2026

Genomic and phenotypic diversification of Pseudomonas aeruginosa during sustained exposure to a ciliate predator.

UNLABELLED: Predator-mediated selection is an important ecological force shaping bacterial evolution, but its effects on genomic adaptation and virulence in opportunistic pathogens are not fully understood. Here, we used experimental evolution to study how exposure to the ciliate predator Tetrahymena thermophila affects Pseudomonas aeruginosa. Replicate populations were evolved for 60 days with or without the predator, followed by whole-genome shotgun metagenomic sequencing and phenotypic analyses. Both treatments showed strong selection and evidence of parallel evolution at gene and nucleotide levels, indicating constrained adaptation. However, predator exposure altered evolutionary dynamics. Predator-evolved populations showed a wider distribution of mutation frequencies, with many mutations persisting at intermediate frequencies, consistent with increased clonal interference and ongoing competition among lineages. In contrast, populations evolved without predators showed more high-frequency mutations, consistent with selective sweeps, although some low-frequency variants remained. Despite substantial genomic change, phenotypic outcomes were variable. Virulence in an invertebrate host model did not consistently increase. Instead, evolved isolates showed context-dependent changes, including modest decreases or occasional increases. Competition assays also showed no consistent fitness advantage for predator-evolved isolates, suggesting trade-offs between predator resistance and growth in other environments. Overall, predator-mediated selection reshaped evolutionary dynamics by maintaining diversity and altering the balance of lineages rather than producing uniform increases in virulence. These results highlight how ecological complexity influences adaptive evolution and the context-dependent nature of pathogen traits. IMPORTANCE: Opportunistic pathogens such as Pseudomonas aeruginosa often evolve in environmental settings before infecting hosts, raising questions about how ecological interactions influence virulence. Predator-mediated selection has been suggested to increase virulence via coincidental evolution, but evidence is inconsistent. Here, we show that exposure to a eukaryotic predator does not consistently elevate virulence but does reshape evolutionary dynamics by altering how mutations spread in populations. Predator-exposed populations retained more intermediate-frequency mutations, consistent with increased clonal interference and ongoing competition among lineages, whereas non-predator populations were dominated by selective sweeps. These differences were also reflected in functional targets of adaptation, with predator exposure favoring mutations in genes involved in environmental sensing and interaction. Together, these findings suggest that ecological complexity shapes the dynamics of adaptation rather than driving a single evolutionary outcome, highlighting that virulence is an emergent property influenced by underlying evolutionary processes.

Pseudomonas aeruginosa↗
PubMed2002

Consequences of plant-herbivore coevolution on the dynamics and functioning of ecosystems.

The potential consequences of plant-herbivore coevolution for ecosystem functioning are investigated using a simple nutrient-limited ecosystem model in which plant and herbivore traits are subject to adaptive dynamics. Although the ecological model is very simple and always reaches a stable equilibrium in the absence of evolution, coevolution can generate a great diversity of dynamical behaviors. The evolutionary dynamics can lead to a stable equilibrium. If the evolution of plants is fast enough, certain values of the trade-off parameters lead to complex evolutionary cycles bounded by physiological constraints. The dynamical behavior of the model is very different when the dynamics of inorganic nutrient is ignored and plant competition is modeled by a logistic growth function. This emphasizes the importance of including explicit nutrient dynamics in studies of plant-herbivore coevolution.

Adaptation, Biological↗
PubMed2006

Divergent evolution of a structural proteome: phenomenological models.

We develop models of the divergent evolution of genomes; the elementary object of sequence dynamics is the protein structural domain. To identify patterns of organization that reflect mechanisms of evolution, we consider the individual genomes of many procaryote species, studying the arrangement of protein structural domains in the space of all polypeptide structures. We view the network of structural similarities as a graph, called the organismal Protein Domain Universe Graph (oPDUG); vertices represent types of structural domains and edges represent strong structural similarity. As observed before, each oPDUG is a highly nonrandom graph, as evidenced in the vertex degree distribution, which resembles a Pareto law (which has a power-law asymptotic). To explain this and other peculiar properties of the oPDUGs, we construct an evolving-graph model for the long-timescale evolutionary dynamics of oPDUGs, containing only divergent mechanisms of domain discovery. The model generates degree distributions (resembling Pareto laws) and clustering-coefficient distributions that are characteristic of the oPDUGs. In the infinite-graph limit, we analytically compute the exponent for specific biological parameters, as well as the complete phase diagram of the model, finding two distinct regimes of domain innovation dynamics. Thus, divergent evolutionary dynamics quantitatively explains the nonrandom organization of oPDUGs.

Bacterial Proteins↗
PubMed2004

Reactive strategies in indirect reciprocity.

Evolution of reactive strategy of indirect reciprocity is discussed, where individuals interact with others through the one-shot Prisoner's Dilemma game, changing their partners in every round. We investigate all of the reactive strategies that are stochastic, including deterministic ones as special cases. First we study adaptive dynamics of reactive strategies by assuming monomorphic population. Results are very similar to the corresponding evolutionary dynamics of direct reciprocity. The discriminating strategy, which prescribes cooperation only with those who cooperated in the previous round, cannot be an outcome of the evolution. Next we examine the case where the population includes a diversity of strategies. We find that only the mean 'discriminatoriness' in the population is the parameter that affects the evolutionary dynamics. The discriminating strategy works as a promoter of cooperation there. However, it is again not the end point of the evolution. This is because retaliatory defection, which was prescribed by the discriminating strategy, is regarded as another defection toward the society. These results caution that we have to reconsider the role of retaliatory defection much more carefully.

Altruism↗
PubMed1994

Dynamics and evolution: evolutionarily stable attractors, invasion exponents and phenotype dynamics.

We extend the ideas of evolutionary dynamics and stability to a very broad class of biological and other dynamical systems. We simultaneously develop the general mathematical theory and a discussion of some illustrative examples. After developing an appropriate formulation for the dynamics, we define the notion of an evolutionary stable attractor (ESA) and give some samples of ESAS with simple and complex dynamics. We discuss the relationship between our theory and that for ESSS in classical linear evolutionary game theory by considering some dynamical extensions. We then introduce and develop our main mathematical tool, the invasion exponent. This allows analytical and numerical analysis of relatively complex situations, such as the coevolution of multiple species with chaotic population dynamics. Using this, we introduce the notion of differential selective pressure which for generic systems is nonlinear and characterizes internal ESAS. We use this to analytically determine the ESAS in our previous examples. Then we introduce the phenotype dynamics which describe how a population with a distribution of phenotypes changes in time with or without mutations. We discuss the relation between the asymptotic states of this and the ESAS. Finally, we use our mathematical formulation to analyse a non-reproductive form of evolution in which various learning rules compete and evolve. We give a very tentative economic application which has interesting ESAS and phenotype dynamics.

Animals↗
PubMed1995

A genetical theory of species selection.

Species selection, differential rates of speciation or extinction resulting from species level characters, is often invoked as the main mechanism of macroevolution that is not simply an extension of microevolutionary processes. So long as we are careful in defining "species", the logic of species selection is sound. This does not mean, however, that this process can influence evolutionary dynamics under realistic conditions. The principal challenge to the efficacy of species selection as an evolutionary mechanism is the idea that selection between individuals within species will be so much more efficient as to swamp out any effects of selection between species. To assess this, a genetic model is constructed that includes simultaneous selection within and between species, and this is used to ask: under what conditions could species selection influence evolutionary dynamics, even in the face of opposing selection between individuals? The model shows that the efficacy of species selection is strongly determined by the time between speciation events (measured in individual generations), the mutation rate of the character under consideration, and the initial size of a newly formed reproductively isolated population. Data indicate that a few studied lineages have shown sufficiently high speciation rates to make species selection an important mechanism in the evolution of characters with mutation rates on the order of 10(-6) per generation. Quantitative characters, such as body size, generally change too readily for species selection to be relevant to their evolution. Complex characters, however, may be good candidates to be influenced by species selection. The interaction of selection within and between species can be subtle, with individual selection looking, from the standpoint of a species, very much like development of an individual. Furthermore, selection between individuals may be the main process assembling complex adaptations, while species selection allows them to persist over long periods of time.

Animals↗
PubMed2025

ScITree: Scalable Bayesian inference of transmission tree from epidemiological and genomic data.

Phylodynamic models capture joint epidemiological-evolutionary dynamics during an outbreak, providing a powerful tool to enhance understanding and management of disease transmission. Existing phylodynamic approaches, however, mostly rely on various non-mechanistic or semi-mechanistic approximations of the underlying epidemiological-evolutionary process. Previous work by Lau and colleagues has shown that full Bayesian mechanistic models, without relying on these approximations, can enable highly accurate joint inference of the epidemiological-evolutionary dynamics including the unobserved transmission tree. However, the Lau method faces major computational bottlenecks. As the volume of genomic data collected during outbreaks continues to grow, it is crucial to develop scalable yet accurate phylodynamic methods. Here we propose a new Bayesian phylodynamic model, overcoming the major scalability issue in the previous method and enabling a readily deployable, yet accurate, phylodynamic modeling framework. Specifically, we develop a scalable spatio-temporal phylodynamic framework for inferring the transmission tree (ScITree) and other key epidemiological parameters considering the infinite sites assumption in modeling mutation on the sequence level, in contrast to the Lau method in which mutation was modeled explicitly on the nucleotide level. Our approach features full Bayesian implementation utilizing an exact likelihood to mechanistically integrate epidemiological and evolutionary processes. We develop a computationally-efficient data-augmentation Markov Chain Monte Carlo algorithm, inferring key model parameters and unobserved dynamics including the transmission tree. We assess performance of our method using multiple simulated outbreak datasets. Our results indicate that our method can achieve high inference accuracy, comparable to the performance of the Lau method. Additionally, our method scales significantly more efficiently for large outbreaks, with computing time increasing linearly with outbreak size, compared to the exponential scaling of the Lau method. We also demonstrate our method's utility by applying our validated modeling framework to a dataset describing a foot-and-mouth disease outbreak in the UK. Our results show that our method is able to generate estimates of the transmission dynamics consistent with those from the prior method, further demonstrating the robustness of our new approach. In summary, our method provides a computationally-efficient, highly scalable, accurate modeling framework for inferring the joint spatio-temporal dynamics of epidemiological and evolutionary processes, facilitating timely and effective outbreak responses in space and time. Our method is implemented in our R package ScITree.

Bayes Theorem↗