Population Growth Models: Density-Independent vs Density-Dependent

Vocabulary flashcards covering key terms and definitions from the lecture notes on density-independent (exponential) and density-dependent (logistic) population growth models.

N (Population size)

The number of individuals in the population.

t (Time)

The variable representing time in growth models.

r (Per-capita growth rate)

Average births minus deaths per individual at a given time; baseline growth rate in the exponential model.

r_{max}

The maximal per-capita growth rate under near-ideal conditions.

K (Carrying capacity)

The maximum number of individuals the habitat can sustain indefinitely given finite resources.

dN/dt (Population growth rate)

The rate of change of population size over time.

BIDE (Births, Immigration, Deaths, Emigration)

Factors determining population changes; simplified here to births and deaths.

Density-independent growth

Growth where the rate does not depend on population density; growth can be exponential.

Exponential growth

Growth with a constant per-capita rate, producing a J-shaped curve.

Logistic growth

Density-dependent growth with carrying capacity, producing an S-shaped curve.

dN/dt = rN (exponential form)

Population growth rate when growth is density-independent.

r{per acapita} = r(1 - N/K)

Per-capita growth rate in the logistic model, decreasing with density.

dN/dt = rN(1 - N/K)

Logistic growth equation expressing density dependence.

r{per acapita}

Growth contribution per individual; declines with density in logistic growth.

Carrying capacity (K) significance

When N ≪ K, growth is near exponential; as N → K, per-capita growth → 0.

Intraspecific competition

Competition for resources within the same species that slows growth.

Interspecific competition

Competition with other species that can affect growth and survival.

Cannibalism

Intra-specific predation that can reduce growth at high densities.

Disease and parasites at high density

Higher density facilitates spread, reducing reproduction and increasing mortality.

Sigmoidal (S-shaped) growth

Growth curve of logistic model: slow growth, rapid middle growth, then leveling off near K.

Maximum total growth rate (dN/dt peak) at N = K/2

The point where the logistic growth rate is greatest.

r_max variability

r_max is an average value and can vary due to genetics and environment.

Early-growth realism caveat

Exponential growth is a good approximation only when resources are abundant.

Model structure commonality

Both models follow dN/dt = (per-capita growth rate) × N.

J-curve vs S-curve

Exponential growth yields a J-curve; logistic growth yields an S-curve.

Immigration/Emigration

Migration processes ignored in these basic models; including them adds complexity.

r > 0 / r = 0 / r < 0 interpretations

r > 0: population grows; r = 0: remains constant; r < 0: declines.

r-selected (brief note)

A concept related to growth strategies; mentioned but not central to these simple models.