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Understanding why we age is a long-lived open problem in evolutionary biology. Aging is prejudicial to the individual and evolutionary forces should prevent it, but many species show signs of senescence as individuals age. Here, I will…

We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population are governed by correlation…

Adaptation often involves the acquisition of a large number of genomic changes which arise as mutations in single individuals. In asexual populations, combinations of mutations can fix only when they arise in the same lineage, but for…

Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the…

The selection pressures that have shaped the evolution of complex traits in humans remain largely unknown, and in some contexts highly contentious, perhaps above all where they concern mean trait differences among groups. To date, the…

We derive a Poisson random field model for population site polymorphisms differences within and between two species that share a relatively recent common ancestor. The model can be either equilibrium or time inhomogeneous. We first consider…

Culture evolves following a process that is akin to biological evolution, although with some significant differences. At the same time culture has often a collective good value for human groups. This paper studies culture in an evolutionary…

We consider a stochastic individual-based model for the evolution of a haploid, asexually reproducing population. The space of possible traits is given by the vertices of a (possibly directed) finite graph $G=(V,E)$. The evolution of the…

The dynamical evolution of many economic, sociological, biological and physical systems tends to be dominated by a relatively small number of unexpected, large changes (`extreme events'). We study the large, internal changes produced in a…

We consider an exponentially growing population of cells undergoing mutations and ask about the effect of reproductive fluctuations (genetic drift) on its long-term evolution. We combine first step analysis with the stochastic dynamics of a…

We investigate the evolution of populations of random Boolean networks under selection for robustness of the dynamics with respect to the perturbation of the state of a node. The fitness landscape contains a huge plateau of maximum fitness…

The modeling of time series is becoming increasingly critical in a wide variety of applications. Overall, data evolves by following different patterns, which are generally caused by different user behaviors. Given a time series, we define…

We introduce and analyze a general model of a population evolving over a network of selectively neutral genotypes. We show that the population's limit distribution on the neutral network is solely determined by the network topology and…

Consider an arbitrary large population at the present time, originated at an unspecified arbitrary large time in the past, where individuals in the same generation reproduce independently, forward in time, with the same offspring…

Population genetic studies have found evidence for dramatic population growth in recent human history. It is unclear how this recent population growth, combined with the effects of negative natural selection, has affected patterns of…

Our understanding of the evolutionary process has gone a long way since the publication, 150 years ago, of "On the origin of species" by Charles R. Darwin. The XXth Century witnessed great efforts to embrace replication, mutation, and…

We are interested in the impact of natural selection in a prey-predator community. We introduce an individual-based model of the community that takes into account both prey and predator phenotypes. Our aim is to understand the phenotypic…

While generic competitive systems exhibit mixtures of hierarchy and cycles, real-world systems are predominantly hierarchical. We demonstrate and extend a mechanism for hierarchy; systems with similar agents approach perfect hierarchy in…

Evolution of genus density is calculated from Gaussian initial conditions using Zel'dovich approximation. A new approach is introduced which formulates the desired quantity in a rotationally invariant manner. It is shown that normalized…

Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…