Related papers: Random matrices and localization in the quasispeci…
This paper investigates the coexistence of two competing species on random geometric graphs (RGGs) in continuous time. The species grow by occupying vacant sites according to Richardson's model, while simultaneously competing for occupied…
Species evolution is essentially a random process of interaction between biological populations and their environments. As a result, some physical parameters in evolution models are subject to statistical fluctuations. In this paper, two…
The quasispecies model describes processes related to the origin of life and viral evolutionary dynamics. We discuss how the error catastrophe that reflects the transition from localized to delocalized quasispecies population is affected by…
Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…
In this paper we study localized states in a monitored evolution on a finite graph and how they are distinguished from the delocalized states in terms of the transition probabilities and the mean transition times. Monitoring is performed by…
Evolutionary and ecosystem dynamics are often treated as different processes --operating at separate timescales-- even if evidence reveals that rapid evolutionary changes can feed back into ecological interactions. A recent long-term field…
Phenotypically structured equations arise in population biology to describe the interaction of species with their environment that brings the nutrients. This interaction usually leads to selection of the fittest individuals. Models used in…
The stable cooperation ratio of spatial evolutionary games has been widely studied using simulations or approximate analysis methods. However, sometimes such ``stable'' cooperation ratios obtained via approximate methods might not be…
Simple agent based exchange models are a commonplace in the study of wealth distribution of artificial societies. Generally, each agent is characterized by its wealth and by a risk-aversion factor, and random exchanges between agents allow…
The origin of diversification and coexistence of genes and species have been traditionally studied in isolated biological levels. Ecological and evolutionary views have focused on the mechanisms that enable or constrain species coexistence,…
We investigate the scaling limit of the seed bank diffusion when reproduction and migration (to and from the seed bank) happen on different time-scales. More precisely, we consider the case when migration is `slow' and reproduction is…
The adaptation of biological species to their environment depends on their traits. When various biological processes occur (survival, reproduction, migration, etc.), the trait distribution may change with respect to time and space. In the…
The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional…
Numerous experimental studies have demonstrated that the microenvironment is a key regulator influencing the proliferative and migrative potentials of species. Spatial and temporal disturbances lead to adverse and hazardous…
We study metanetworks arising in genotype and phenotype spaces, in the context of a model population of Boolean graphs evolved under selection for short dynamical attractors. We define the adjacency matrix of a graph as its genotype, which…
In this treatise I introduce the time dependent Generalized Born's Rule for the probabilities of quantum events, including conditional and consecutive probabilities, as the unique fundamental time evolution equation of quantum theory. Then…
We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e. how many neighbours are in…
The evolutionary origin of universal statistics in biochemical reaction network is studied, to explain the power-law distribution of reaction links and the power-law distributions of chemical abundances. Using cell models with catalytic…
This paper develops a simplified model for sexual replication within the quasispecies formalism. We assume that the genomes of the replicating organisms are two-chromosomed and diploid, and that the fitness is determined by the number of…
Evolutionary dynamics can be studied in well-mixed or structured populations. Population structure typically arises from the heterogeneous distribution of individuals in physical space or on social networks. Here we introduce a new type of…