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Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…
In many systems we can describe emergent macroscopic behaviors, quantitatively, using models that are much simpler than the underlying microscopic interactions; we understand the success of this simplification through the renormalization…
In large asexual populations, multiple beneficial mutations arise in the population, compete, interfere with each other, and accumulate on the same genome, before any of them fix. The resulting dynamics, although studied by many authors, is…
Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness…
A stochastic model for intermittent fluctuations due to a super-position of uncorrelated Lorentzian pulses is presented. For constant pulse duration, this is shown to result in an exponential power spectral density for the stationary…
A new model ecosystem consisting of many interacting species is introduced. The species are connected through a random matrix with a given connectivity. It is shown that the system is organized close to a boundary of marginal stability in…
When studying the dynamics of trait distribution of populations in a heterogeneous environment, classical models from quantitative genetics choose to look at its system of moments, specifically the first two ones. Additionally, in order to…
We present significantly advanced studies of the previously introduced physical growth mechanism and unite it with biochemical growth factors. Obtained results allowed formulating the general growth law which governs growth and evolutional…
Sex chromosomes have independently evolved in species with separate sexes in most lineages across the tree of life. However, the well-accepted canonical model of sex chromosome evolution is not universally supported. There is no single…
We build a general framework which establishes a one-to-one correspondence between species abundance distribution (SAD) and species accumulation curve (SAC). The appearance rates of the species and the appearance times of individuals of…
We study the length distribution of a particular class of DNA sequences known as 5'UTR exons. These exons belong to the messanger RNA of protein coding genes, but they are not coding (they are located upstream of the coding portion of the…
Species sharing a prey or a predator species may go extinct due to exploitative or apparent competition. We examine whether evolution of the shared species acts as a coexistence mechanism and to what extent the answer depends on the genetic…
We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness…
Understanding the causes and effects of spatial vegetation patterns is a fundamental problem in ecology, especially because these can be used as early predictors of catastrophic shifts such as desertification processes. Empirical studies of…
We have used the Monte Carlo based computer models to show that selection pressure could affect the distribution of recombination hotspots along the chromosome. Close to critical crossover rate, where genomes may switch between the…
A model of $s$ interacting species is considered with two types of dynamical variables. The fast variables are the populations of the species and slow variables the links of a directed graph that defines the catalytic interactions among…
Power law scaling is observed in many physical, biological and socio-economical complex systems and is now considered as an important property of these systems. In general, power law exists in the central part of the distribution. It has…
Consider a haploid population which has evolved through an exchangeable reproduction dynamics, and in which all individuals alive at time $t$ have a most recent common ancestor (MRCA) who lived at time $A_t$, say. As time goes on, not only…
The rate at which individual bacterial cells grow depends on the concentrations of cellular components such as ribosomes and proteins. These concentrations continuously fluctuate over time and are inherited from mother to daughter cells,…
A density-dependent branching process is a particle system in which individuals reproduce independently, but in a way that depends on the current population size. This feature can model a wide range of ecological interactions at the cost of…