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The maximum population size that the environment can sustain indefinitely. Application in Ecology: Determines the ceiling for species population growth and informs conservation efforts.

A species-specific method of risk assessment used to determine the probability that a population will go extinct within a given number of years. Application in Ecology: Helps in formulating conservation strategies and understanding the effects of environmental change on species survival.

The measure of how much disturbance an ecological system can withstand without changing self-organized processes and structures. Application in Ecology: Guides the management of ecosystems to prevent regime shifts.

A group of spatially separated populations connected by dispersal of individuals or gametes. Application in Ecology: Helps in understanding and modeling the effects of habitat fragmentation on species survival.

A mathematical change in the number or stability of equilibrium points as a parameter is varied. Application in Ecology: It helps in identifying critical points where small changes can lead to drastic shifts in population dynamics.

A model that describes how a population grows rapidly at first then stabilizes as the population reaches the carrying capacity of the environment. Application in Ecology: Used to predict population sizes and growth rates within an ecosystem where resources are limited.

A branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions. Application in Ecology: Explains complex and seemingly random fluctuations in ecological systems.

A discrete population model that shows how populations may fluctuate widely due to strong density-dependent regulation. Application in Ecology: Used for managing harvested populations like fish or forest species.

A theory of how small changes in certain parameters can lead to sudden and dramatic changes in the system's behavior. Application in Ecology: Used to analyze cases where ecosystems experience abrupt changes due to gradual environmental stress.

The ability of an ecological system to return to its original state after being disturbed. Application in Ecology: Central to the study of ecosystem dynamics and the impact of external stressors.

The Lotka-Volterra equations represent the dynamics between predators and their prey, showing oscillations in the populations of both. Application in Ecology: Helps in understanding the interaction between predator and prey populations in an ecosystem.