Coexistence in competition models with density-dependent mortality

Shigui Ruan1, Ada Ardito, Paolo Ricciardi

  • 1Department of Mathematics, University of Miami, P.O. Box 249085, Coral Gables, FL 33124-4250, USA. ruan@math.miami.edu

Comptes Rendus Biologies
|December 11, 2007
PubMed

Related Concept Videos

Population Growth00:57

Population Growth

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.However, realistic environmental conditions limit the number of...
Competition02:34

Competition

When organisms require the same limited resources within an environment, they may have to compete for them. Competition is a net-negative interaction. Even if two competing individuals or populations do not interact directly, the overall fitness of both competitors is lowered as a result of not having full access to the limited resource.Intraspecific competition, which occurs between individuals of the same species, serves as a natural mechanism for regulating population size. Too much...
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
Microbial Interactions: Competition01:26

Microbial Interactions: Competition

Microbial competition is an ecological interaction in which microorganisms vie for limited resources within shared environments. These resources may include nutrients, space, or light, depending on the system. The intensity and outcome of competition are influenced by the environmental context, such as nutrient availability, spatial constraints, and the diversity of microbial species present. These competitive interactions significantly influence the structure, function, and resilience of...
Assumptions of Survival Analysis01:15

Assumptions of Survival Analysis

Survival models analyze the time until one or more events occur, such as death in biological organisms or failure in mechanical systems. These models are widely used across fields like medicine, biology, engineering, and public health to study time-to-event phenomena. To ensure accurate results, survival analysis relies on key assumptions and careful study design.