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Solving the recombination equation has been a long-standing challenge of \emph{deterministic} population genetics. We review recent progress obtained by introducing ancestral processes, as traditionally used in the context of…

Families form the basis of society, and anthropologists have characterised various family systems. This study developed a multi-level evolutionary model of pre-industrial agricultural societies to simulate the evolution of family systems…

Crossover and mutation are the two main operators that lead to new solutions in evolutionary approaches. In this article, a new method of performing the crossover phase is presented. The problem of choice is evolutionary decision tree…

The provision of intergenerational care, via the Grandmother Hypothesis, has been implicated in the evolution of post-fertile longevity, particularly in humans. However, if grandmothering does provide fitness benefits, a key question is why…

The transition from a normal to cancerous cell requires a number of highly specific mutations that affect cell cycle regulation, apoptosis, differentiation, and many other cell functions. One hallmark of cancerous genomes is genomic…

How mutations accumulate in genomes is the central question of molecular evolution theories, however our understanding of this process is far from complete. Drake's rule is a notoriously universal property of genomes from microbes to…

Star-shaped branching patterns of genealogies are common in marine species. High-fecundity marine populations are characterized by low ratios of effective to actual population size, which reflect high variance in reproductive success among…

We consider a biological population in which a beneficial mutation is undergoing a selective sweep when a second beneficial mutation arises at a linked locus and we investigate the probability that both mutations will eventually fix in the…

Genetic and comparative genomic studies indicate that extant genomes are more properly considered to be a fusion product of random mutations over generations and genomic material transfers between individuals of different lineages. This has…

We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…

Using Monte Carlo model of biological evolution we have discovered that populations can switch between two different strategies of their genomes' evolution; Darwinian purifying selection and complementing the haplotypes. The first one is…

Resource are often not uniformly distributed within a population. Spatial variations of concentration of a resource, change the fitness of competing strategies locally. The notion of fitness varying with respect to both genotype and…

A tumor often consists of multiple cell subpopulations (clones). Current chemo-treatments often target one clone of a tumor. Although the drug kills that clone, other clones overtake it and the tumor reoccurs. Genome sequencing and…

Biological tools such as genetic lineage tracing, three dimensional confocal microscopy and next generation DNA sequencing are providing new ways to quantify the distribution of clones of normal and mutated cells. Population-wide clone size…

We critically review several recent approaches to solving the two cosmological constant problems. The "old" problem is the discrepancy between the observed value of $\Lambda$ and the large values suggested by particle physics models. The…

Biological time can be measured in two ways: in generations and in physical (chronological) time. When generations overlap, these two notions diverge, which impedes our ability to relate mathematical models to real populations. In this…

The variant of phenomenological theory of humankind future existence after time of demographic transition based on treating the time of demographic transition as a point of phase transition and taking into account an appearing of the new…

Some species exhibit very high levels of DNA sequence variability; there is also evidence for the existence of heritable epigenetic variants that experience state changes at a much higher rate than sequence variants. In both cases, the…

We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…

The RNA world hypothesis, that RNA genomes and catalysts preceded DNA genomes and genetically-encoded protein catalysts, has been central to models for the early evolution of life on Earth. A key part of such models is continuity between…