EE 3- Carrying Capacity and Density Dependence Lecture Flashcards

This set of flashcards covers vocabulary related to carrying capacity, density-dependent and independent growth, the logistic equation, and types of intraspecific competition based on the lecture transcript.

Exponential Growth Assumptions

A model assuming that per capita growth rate ($r$ or $\lambda$) is constant, resources are plentiful, physical space is not limiting, and predation/disease rates are unchanged with population size.

Density-Independent Limitation

Factors, such as weather or environmental stress (e.g., drought), that alter population growth rates where per capita mortality does not depend on the population density.

Galapagos Finches Drought Example

An example of density-independent limitation where drought supports fewer individuals regardless of pre-drought numbers.

Density-Dependent Limitation

A process where the mortality rate (per capita) is higher at high population densities, such as viruses regulating phytoplankton populations.

Negative Density Dependence

Increased negative effects on a population at high density, such as more deaths, fewer births, and dispersal away from the group.

Carrying Capacity ($K$)

The population density where births balance deaths and the population neither grows nor shrinks ($dN/dt = 0$).

Density-Dependent Regulation

The stabilization of population size resulting from factors like disease and resource competition acting in a density-dependent manner.

Law of Constant Final Yield

A principle where plant biomass (yield) reaches a plateau due to intraspecific competition among plants regardless of planting density.

The Logistic Equation

A model for density dependence in continuous time expressed as $\frac{dN}{dt} = rN(1 - \frac{N}{K})$.

Per-Capita Growth Rate in Logistic Model

Expressed as $(\frac{dN}{dt}) / N = r(1 - \frac{N}{K})$, which decreases as the population size $N$ approaches the carrying capacity $K$.

Equilibrium (Logistic Growth)

A state defined as no change in population size over time ($dN/dt = 0$), which occurs when $N = K$.

Discrete Time Logistic Model

Models derived to look at density-dependent population growth in steps or generations, often represented by the relationship between $N_t$ and $N_{t+1}$.

Ricker Diagrams

Graphs used to predict future population size ($N_{t+1}$) based on current size ($N_t$), showing how parameters like $R$ influence oscillations.

Damped Oscillations

A pattern of population size returning to equilibrium observed in Ricker diagrams when 1 < R < 2.

2-point Limit Cycle

A type of population dynamic where the population size alternates between two specific values, typically occurring when R > 2.

Chaos (Population Dynamics)

Erratically fluctuating population size without a regular cycle, occurring at very high values of $R$ (e.g., $R = 2.9$).

Allee Effect

Nonlinearities at low densities where population growth is restricted by factors like mate limitation, inbreeding depression, or the lack of cooperative strategies.

Mate Limitation

A component of the Allee effect where individuals cannot find a mate because population densities are too low.

Intraspecific Competition

Competition between individuals of the same species for similar resources, leading to fewer resources per capita at high population densities.

Exploitation Competition

A type of intraspecific competition where individuals do not interact directly but respond to the level of a resource depressed by others.

Scramble Competition

A form of competition where a threshold is reached that prevents resource acquisition for many, often resulting in a population crash (boom and bust).

Contest Competition

A type of competition where individuals interact directly (e.g., territoriality) to prevent others from exploiting resources, providing dynamic stabilization.

Compensation

The degree to which larger population numbers are offset by higher mortality and lower fecundity.

Overcompensation

A scenario where so many more individuals die in a large population ($Y$) compared to a small one ($X$) that $Y$ ends up smaller than $X$ after a fixed period.

Undercompensation

A scenario where more individuals die in a large population than a small one, but the originally larger population still remains larger after a fixed period.

Exact Compensation

A state where a large population ends up exactly the same size as a small one after fixed mortality/fecundity rates; often called pure contest competition.

Pure Scramble Competition

The most extreme form of overcompensating density dependence where no competing individuals survive.

Bifurcation Diagram

A graph showing the onset of limit cycles and chaos as the growth parameter $R$ increases beyond 2.

Sentinel Behavior

An anti-predator behavior that relies on high population densities (numbers) to be effective, often cited in Allee effect studies.

Warders C. Allee

The scientist (1885–1955) who described nonlinearities and positive density dependence at low population densities.