Related papers: Coevolution Maintains Diversity in the Stochastic …
This paper is concerned with existence, non-existence and uniqueness of positive (coexistence) steady states to a predator-prey system with density-dependent dispersal. To overcome the analytical obstacle caused by the cross-diffusion…
We study a stochastic spatial model of biological competition in which two species have the same birth and death rates, but different diffusion constants. In the absence of this difference, the model can be considered as an off-lattice…
Species coexistence is one of the central themes in modern ecology. Coexistence is a prerequisite of biological diversity. However, the question arises how biodiversity can be reconciled with the statement of competition theory, which…
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…
Despite the general acknowledgment of the role of niche and fitness differences in community dynamics, species abundance has been coined as a relevant feature not just regarding niche perspectives, but also according to neutral…
A central goal in ecology is to understand how biodiversity is maintained. Previous theoretical works have employed the rock-paper-scissors (RPS) game as a toy model, demonstrating that population mobility is crucial in determining the…
Community ecology has traditionally relied on the competitive exclusion principle, a piece of common wisdom in conceptual frameworks developed to describe species assemblages. Key concepts in community ecology, such as limiting similarity…
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…
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…
Camouflage in nature seems to arise from competition between predator and prey. To survive, predators must find prey, and prey must avoid being found. This work simulates an abstract model of that adversarial relationship. It looks at…
This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on…
Two density-dependent branching processes are considered to model predator-prey populations. For both models, preys are considered to be the main food supply of predators. Moreover, in each generation the number of individuals of each…
Deterministic evolutionary theory robustly predicts that populations displaying altruistic behaviours will be driven to extinction by mutant cheats that absorb common benefits but do not themselves contribute. Here we show that when…
Predator-prey coevolution is commonly thought to result in reciprocal arms races that produce increasingly extreme and complex traits. However, such directional change is not inevitable. Here, we provide evidence for a previously…
Explaining biodiversity in nature is a fundamental problem in ecology. An outstanding challenge is embodied in the so-called Competitive Exclusion Principle: two species competing for one limiting resource cannot coexist at constant…
We analyze an interacting particle system with a Markov evolution of birth-and-death type. We have shown that a local competition mechanism (realized via a density dependent mortality) leads to a globally regular behavior of the population…
This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper we study the coexistence of competing species at the fixed point of population dynamic…
As part of a generalized "prisoners' dilemma", is considered that the evolution of a population with a full set of behavioral strategies limited only by the depth of memory. Each subsequent generation of the population successively loses…
We consider a predator-prey population model with prey gathering together for defense purposes. A transmissible unrecoverable disease affects the prey. We characterize the system behavior, establishing that ultimately either only the…
Exploiting the mathematical curiosity of intransitive dice, we present a simple theoretical model for co-evolution that captures scales ranging from the genome of the individual to the system-wide emergence of species diversity. We study a…