Related papers: Phase Transition in an Exactly Solvable Extinction…
Phenotypically structured equations arise in population biology to describe the interaction of species with their environment that brings the nutrients. This interaction usually leads to selection of the fittest individuals. Models used in…
The causes of major and rapid transitions observed in biological macroevolution as well as in the evolution of social systems are a subject of much debate. Here we identify the proximate causes of crashes and recoveries that arise…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
We study the extinction of epidemics in a simplicial susceptible-infected-susceptible model, where each susceptible individual becomes infected either by two-body interactions ($S+I \to 2I$) with a rate $\beta$ or by three-body interactions…
Microbial adaptation to extreme stress, such as starvation, antimicrobial exposure, or freezing often reveals fundamental trade-offs between survival and proliferation. Understanding how populations navigate these trade-offs in fluctuating…
Motivated as a null model for comparison with data, we study the following model for a phylogenetic tree on $n$ extant species. The origin of the clade is a random time in the past, whose (improper) distribution is uniform on $(0,\infty)$.…
The phase diagrams survival-extinction for the Penna model with parameters: (mutations rate)-(birth rate), (mutation rate)-(harmful mutations threshold), (harmful mutation threshold)-(minimal reproduction age) are presented. The extinction…
An important component in studying mathematical models in many biochemical systems, such as those found in developmental biology, is phase transition. The purpose of this work is to analyze the phase transition property of a…
Unlike many physical nonequilibrium systems, in biological systems, the coupling to external energy sources is not a fixed parameter but adaptively controlled by the system itself. We do not have theoretical frameworks that allow for such…
Many species see their range shifted poleward in response to global warming and need to keep pace in order to survive. To understand the effect of climate change on species ranges and its consequences on population dynamics, we consider a…
Here, we address the essential question of whether, in the context of evolving populations, ecosystems attain properties that enable persistence of the ecosystem itself. We use a simple ecosystem model describing resource, producer, and…
Understanding how species persist under interacting stressors is a central challenge in ecology. We develop a spatially explicit reaction-diffusion framework to investigate competing species in landscapes shaped by climate variability,…
We propose a generic model of eco-systems, with a {\it hierarchical} food web structure. In our computer simulations we let the eco-system evolve continuously for so long that that we can monitor extinctions as well as speciations over…
We show how highly-diverse ecological communities may display persistent abundance fluctuations, when interacting through resource competition and subjected to migration from a species pool. This turns out to be closely related to the ratio…
The ability of organisms to accurately sense their environment and respond accordingly is critical for evolutionary success. However, exactly how the sensory ability influences fitness is a topic of active research, while the necessity of a…
The evolution of cooperative behaviour is studied in the deterministic version of the Prisoners' Dilemma on a two-dimensional lattice. The payoff parameter is set at the critical region $1.8 < b < 2.0$ , where clusters of cooperators are…
This paper aims to introduce a concept of an equilibrium point of a dynamical system which will call it almost global asymptotically stable. A biological prey-predator model is also analyzed with a modification function growth in prey…
Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…
When three species compete cyclically in a well-mixed, stochastic system of $N$ individuals, extinction is known to typically occur at times scaling as the system size $N$. This happens, for example, in rock-paper-scissors games or…
We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady state mass…