We present forms of the classical Riesz–Kolmogorov theorem for compactness that are applicable in a wide variety settings. In particular, our theorems apply to classify precompact subsets Lebesgue space $$L^2$$ , Paley–Wiener spaces, weighted Bargmann–Fock and scale Besov–Sobolev spaces holomorphic functions includes Bergman general domains as well Hardy Dirichlet space. criteria characterize c...

Individual-based models (IBMs) of human populations capture spatio-temporal dynamics using rules that govern the birth, behavior, and death of individuals. We explore a stochastic IBM of logistic growth-diffusion with constant time steps and independent, simultaneous actions of birth, death, and movement that approaches the Fisher-Kolmogorov model in the continuum limit. This model is well-suit...

<p style='text-indent:20px;'>We study a periodic Kolmogorov system describing two species nonlinear competition. We discuss coexistence and extinction of one or both species, describe the domain attraction nontrivial solutions in axes, under conditions that generalise Gopalsamy conditions. Finally, we apply our results to model microbial growth phytoplankton competition effect toxins.<...

environmental factors mainly temperature are believed to determine the distribution and population dynamics of fusarium species in a natural ecosystem. species may be restricted in their distribution by adaptation to specific sets of soil environmental conditions. population dynamics of five fusarium species representative of different climatic conditions were studied at three levels of tem...

Understanding the influence of environmental variability on population dynamics is a fundamental goal of ecology. Theory suggests that, for populations in variable environments, temporal correlations between demographic vital rates (e.g., growth, survival, reproduction) can increase (if positive) or decrease (if negative) the variability of year-to-year population growth. Because this variabili...

Mate preferences shift according to contexts such as temporal duration of mateship sought and ecological prevalence of parasites. One important cross-cultural context that has not been explored is a country’s socioeconomic development. Because individuals in less developed countries are generally less healthy and possess fewer resources than those in more developed countries, displays of health...

In this technical section, we construct the Kolmogorov equations which determine the dynamics of the probability distribution function P (x, t). In order to do this, we first calculate the transition probabilities between the various states x ∈ {0, Let T ↑ (x) denote the probability that the system makes a transition from the state with a fraction x of mutators to the state with a fraction x + ...