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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.

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.

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.

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 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.

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.

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.

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 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.

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 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.