Reaction-diffusion problems are often described at a macroscopic scale by partial derivative equations of the type of the Fisher or KolmogorovPetrovsky-Piscounov equation. These equations have a continuous family of front solutions, each of them corresponding to a different velocity of the front. By simulating systems of size up to N = 10 particles at the microscopic scale, where particles reac...

The Cockcroft-Gault (CG) equation has become perhaps the most popular practical approach for estimating renal function among health care professionals. Despite its widespread use, clinicians often overlook not only the limitations of the original serum creatinine (SCr) based equation, but also may not appreciate the validity of the many variations used to compensate for these limitations. For c...

We introduce and study a conserved version of the Fisher equation. Within a population biology context, this model describes spatially extended populations in which the total number of individuals is fixed due to either biotic or environmental factors. We find a rich spectrum of dynamical phases including a pseudotraveling wave and, in the presence of the Allee effect, a phase transition from a...

We investigate the phenomenon of extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state n=0 is a repelling (scenario A) or attracting (scenario B) point of the deterministic rate equation. In scenario A the metastable stochastic population resides in ...

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quant...

 The population structure of Aphanius anatoliae in Lake Eğirdir-Isparta-Turkey was studied, using 522 fish monthly in 2008. This study were observed in the number of individuals of each sex, age, weight and size compositions. In addition, the total length-weight relationship was calculated as well as the Von Bertalanffy growth equation. A study of the food uptake throughout the year h...

The forward diffusion equation for gene frequency dynamics is solved subject to the condition that the total probability is conserved at all times. This can lead to solutions developing singular spikes (Dirac delta functions) at the gene frequencies 0 and 1. When such spikes appear in solutions they signal gene loss or gene fixation, with the "weight" associated with the spikes corresponding to...