Related papers: Nonlinear deterministic equations in biological ev…
We present a model for evolving population which maintains genetic polymorphism. By introducing random mutation in the model population at a constant rate, we observe that the population does not become extinct but survives, keeping…
Evolution occurs in populations of reproducing individuals. It is well known that population structure can affect evolutionary dynamics. Traditionally, natural selection is studied between mutants that differ in reproductive rate, but are…
A model for the evolution of a finite population in a rugged fitness landscape is introduced and solved. The population is trapped in an evolutionary loop, alternating periods of stasis to periods in which it performs adaptive walks. The…
We discuss linear autonomous evolution equations on function spaces which have the property that a positive initial value leads to a solution which initially changes sign, but then becomes - and stays - positive again for sufficiently large…
We consider the problem of determining the time evolution of a trait distribution in a mathematical model of non-uniform populations with parametric heterogeneity. This means that we consider only heterogeneous populations in which…
We discuss a simple model of co-evolution. In order to emphasise the effect of interaction between individuals the entire population is subjected to the same physical environment. Species are emergent structures and extinction, origination…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
The dynamical equation satisfied by the density matrix, when a quantum system is subjected to one or more constraints arising from conserved quantities, is derived. The resulting nonlinear motion of the density matrix has the property that…
Population dynamics in random ecological networks are investigated by analyzing a simple deterministic equation. It is found that a sequence of abrupt changes of populations punctuating quiescent states characterize the long time behavior.…
Biological organisms adapt to changes by processing informations from different sources, most notably from their ancestors and from their environment. We review an approach to quantify these informations by analyzing mathematical models of…
When predicting the fate and consequences of recurring deleterious mutations in self-fertilising populations most models developed make the assumption that populations have discrete non-overlapping generations. This makes them biologically…
Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Here we develop a general approach to modeling heterogeneous populations with discrete…
Due to the conventional distinction between ecological (rapid) and evolutionary (slow)timescales, ecological and population models to date have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has…
Large sets of genotypes give rise to the same phenotype because phenotypic expression is highly redundant. Accordingly, a population can accept mutations without altering its phenotype, as long as thegenotype mutates into another one on the…
It is described a nonlocal interaction between entangled quantum objects, which is initiated by a process different from the reduction of the wave function. The scheme of an experiment realizing a deterministic nonlocal quantum evolution is…
We analyze the morphological transition of a one-dimensional system described by a scalar field, where a flat state looses its stability. This scalar field may for example account for the position of a crystal growth front, an order…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
We investigate a simple quantitative genetics model subjet to a gradual environmental change from the viewpoint of the phylogenies of the living individuals. We aim to understand better how the past traits of their ancestors are shaped by…
The dynamics of recombination in genetics leads to an interesting nonlinear differential equation, which has a natural generalization to a measure valued version. The latter can be solved explicitly under rather general circumstances. It…
Transverse elastic waves behave differently in nonlinear isotropic and anisotropic media. Quadratically nonlinear coupling in the evolution equations for wave amplitudes is not possible in isotropic solids, but such a coupling may occur for…