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István Scheuring

Publications and source records attributed to István Scheuring.

10 recordsLinked to original sources
PubMed2006

Fixation of strategies for an evolutionary game in finite populations.

A stochastic evolutionary dynamics of two strategies given by 2x 2 matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire population. The process is discussed in the framework of a random walk with site dependent hopping rates. The time of fixation is found to be identical for both strategies in any particular game. The asymptotic behavior of the fixation time and fixation probabilities in the large population size limit is also discussed. We show that fixation is fast when there is at least one pure evolutionary stable strategy (ESS) in the infinite population size limit, while fixation is slow when the ESS is the coexistence of the two strategies.

Biological Evolution↗
PubMed2005

Rock-scissors-paper game in a chaotic flow: the effect of dispersion on the cyclic competition of microorganisms.

Laboratory experiments and numerical simulations have shown that the outcome of cyclic competition is significantly affected by the spatial distribution of the competitors. Short-range interaction and limited dispersion allows for coexistence of competing species that cannot coexist in a well-mixed environment. In order to elucidate the mechanisms that destroy species diversity we study the intermediate situation of imperfect mixing, typical in aquatic media, in a model of cyclic competition between toxin producing, sensitive and resistant phenotypes. It is found, that chaotic mixing, by changing the character of the spatial distribution, induces coherent oscillations in the populations. The magnitude of the oscillations increases with the strength of mixing, leading to the extinction of some species beyond a critical mixing rate. When mixing is non-uniform in space, coexistence can be sustained at much stronger mixing by the formation of partially isolated regions, that prevent global extinction. The heterogeneity of mixing may enable toxin producing and sensitive strains to coexist for very long time at strong mixing.

Animals↗
PubMed2005

The iterated continuous prisoner's dilemma game cannot explain the evolution of interspecific mutualism in unstructured populations.

The evolutionionary origin of inter- and intra-specific cooperation among non-related individuals has been a great challenge for biologists for decades. Recently, the continuous prisoner's dilemma game has been introduced to study this problem. In function of previous payoffs, individuals can change their cooperative investment iteratively in this model system. Killingback and Doebeli (Am. Nat. 160 (2002) 421-438) have shown analytically that intra-specific cooperation can emerge in this model system from originally non-cooperating individuals living in a non-structured population. However, it is also known from an earlier numerical work that inter-specific cooperation (mutualism) cannot evolve in a very similar model. The only difference here is that cooperation occurs among individuals of different species. Based on the model framework used by Killingback and Doebeli (2002), this Note proves analytically that mutualism indeed cannot emerge in this model system. Since numerical results have revealed that mutualism can evolve in this model system if individuals interact in a spatially structured manner, our work emphasizes indirectly the role of spatial structure of populations in the origin of mutualism.

Altruism↗
PubMed2005

Sturdy cycles in the chaotic Tribolium castaneum data series.

Because of the inherent discreteness of individuals, population dynamical models must be discrete variable systems. In case of strong nonlinearity, such systems interacting with noise can generate a great variety of patterns from nearly periodic behavior through complex combination of nearly periodic and chaotic patterns to noisy chaotic time series. The interaction of a population consisting of discrete individuals and demographic noise has been analyzed in laboratory population data Henson et al. (Science 294 (2001) 602; Proc. Roy. Soc. Ser. B 270 (2003) 1549). In this paper we point out that some of the cycles are fragile, i.e. they are sensitive to the discretization algorithm and to small variation of the model parameters, while others remain "sturdy" against the perturbations. We introduce a statistical algorithm to detect disjoint, nearly-periodic patterns in data series. We show that only the sturdy cycles of the discrete variable models appear in the data series significantly. Our analysis identified the quasiperiodic 11-cycle (emerging in the continuous model) to be present significantly only in one of the three experimental data series. Numerical simulations confirm that cycles can be detected only if noise is smaller than a certain critical level and population dynamics display the largest variety of nearly-periodic patterns if they are on the border of "grey" and "noisy" regions, defined in Domokos and Scheuring (J. Theor. Biol. 227 (2004) 535).

Algorithms↗
PubMed2004

Discrete and continuous state population models in a noisy world.

Simple ecological models operate mostly with population densities using continuous variables. However, in reality densities could not change continuously, since the population itself consists of integer numbers of individuals. At first sight this discrepancy appears to be irrelevant, nevertheless, it can cause large deviations between the actual statistical behaviour of biological populations and that predicted by the corresponding models. We investigate the conditions under which simple models, operating with continuous numbers of individuals can be used to approximate the dynamics of populations consisting of integer numbers of individuals. Based on our definition for the (statistical) distance between the two models we show that the continuous approach is acceptable as long as sufficiently high biological noise is present, or, the dynamical behaviour is regular (non-chaotic). The concepts are illustrated with the Ricker model and tested on the Tribolium castaneum data series. Further, we demonstrate with the help of T. castaneum's model that if time series are not much larger than the possible population states (as in this practical case) the noisy discrete and continuous models can behave temporarily differently, almost independently of the noise level. In this case the noisy, discrete model is more accurate [OR has to be applied].

Animals↗
PubMed2003

Competing populations in flows with chaotic mixing.

We investigate the effects of spatial heterogeneity on the coexistence of competing species in the case when the heterogeneity is dynamically generated by environmental flows with chaotic mixing properties. We show that one effect of chaotic advection on the passively advected species (such as phytoplankton, or self-replicating macro-molecules) is the possibility of coexistence of more species than that limited by the number of niches they occupy. We derive a novel set of dynamical equations for competing populations.

Competitive Behavior↗
PubMed2003

Spatial models of prebiotic evolution: soup before pizza?

The problem of information integration and resistance to the invasion of parasitic mutants in prebiotic replicator systems is a notorious issue of research on the origin of life. Almost all theoretical studies published so far have demonstrated that some kind of spatial structure is indispensable for the persistence and/or the parasite resistance of any feasible replicator system. Based on a detailed critical survey of spatial models on prebiotic information integration, we suggest a possible scenario for replicator system evolution leading to the emergence of the first protocells capable of independent life. We show that even the spatial versions of the hypercycle model are vulnerable to selfish parasites in heterogeneous habitats. Contrary, the metabolic system remains persistent and coexistent with its parasites both on heterogeneous surfaces and in chaotically mixing flowing media. Persistent metabolic parasites can be converted to metabolic cooperators, or they can gradually obtain replicase activity. Our simulations show that, once replicase activity emerged, a gradual and simultaneous evolutionary improvement of replicase functionality (speed and fidelity) and template efficiency is possible only on a surface that constrains the mobility of macromolecule replicators. Based on the results of the models reviewed, we suggest that open chaotic flows ('soup') and surface dynamics ('pizza') both played key roles in the sequence of evolutionary events ultimately concluding in the appearance of the first living cell on Earth.

Animals↗
PubMed2002

In silico simulations reveal that replicators with limited dispersal evolve towards higher efficiency and fidelity.

The emergence of functional replicases, acting quickly and with high accuracy, was crucial to the origin of life. Although where the first RNA molecules came from is still unknown, it is nevertheless assumed that catalytic RNA enzymes (ribozymes) with replicase function emerged at some early stage of evolution. The fidelity of copying is especially important because the mutation load limits the length of replicating templates that can be maintained by natural selection. An increase in template length is disadvantageous for a fixed digit copying fidelity, however, longer molecules are expected to be better replicases. An iteration for longer molecules with better replicase function has been suggested and analysed mathematically. Here we show that more efficient replicases can spread, provided they are adsorbed to a prebiotic mineral surface. A cellular automaton simulation reveals that copying fidelity, replicase speed and template efficiency all increase with evolution, despite the presence of molecular parasites, essentially because of reciprocal atruism ('within-species mutualism') on the surface, thus making a gradual improvement of replicase function more plausible.

Adsorption↗
PubMed2002

Species positions and extinction dynamics in simple food webs.

Recent investigations on the structure of complex networks have provided interesting results for ecologists. Being inspired by these studies, we analyse a well-defined set of small model food webs. The extinction probability caused by internal Lotka-Volterra dynamics is compared to the position of species. Simulations have revealed that some global properties of these food webs (e.g. the homogeneity of connectedness) and the positions of species therein (e.g. interaction pattern) make them prone to modelled biotic extinction caused by population dynamical effects. We found that: (a) homogeneity in the connectedness structure increases the probability of extinction events; (b) in addition to the number of interactions, their orientations also influence the future of species in a web. Since species in characteristic network positions are prone to extinction, results could also be interpreted as describing the properties of preferred states of food webs during community assembly. Our results may contribute to understanding the intimate relationship between pattern and process in ecology.

Animals↗