Population Growth Models Flashcards

In the logistic growth equation dN/dt = rN((K-N)/K), what does the term (K-N)/K represent?

Answer: The fraction of carrying capacity still available

The term (K-N)/K represents the proportion of the carrying capacity that has not yet been used, acting as a brake on growth as N approaches K.

Which scenario best illustrates an Allee effect in population growth?

Answer: A population has a reduced per capita growth rate at very low densities

The Allee effect describes reduced fitness or growth rate at low population densities, often due to difficulties finding mates or cooperative defense failures.

Doubling time for a population growing exponentially at rate r is approximately:

Answer: 0.693 / r

Doubling time ≈ ln(2)/r ≈ 0.693/r, derived from the exponential growth equation N(t) = N₀e^(rt).

A population has K = 500 and N = 250. Under logistic growth, the growth rate is at what fraction of its maximum possible rate?

Answer: 50%

At N = K/2 = 250, the logistic braking term equals 0.5, so growth rate is 50% of its theoretical maximum rN.

What distinguishes a Leslie matrix model from simple exponential or logistic growth models?

Answer: It tracks age- or stage-structured survival and fecundity

Leslie matrix models track survival rates and fecundity for distinct age or stage classes, producing more realistic projections for structured populations.

In a metapopulation framework, a 'rescue effect' refers to:

Answer: Immigration that prevents local patch extinction

The rescue effect occurs when immigration from other patches supplements a declining local population and prevents its extinction.

A population growing according to the Gompertz model grows fastest when N equals:

Answer: K/e

In the Gompertz model, maximum growth rate occurs at N = K/e (approximately 37% of carrying capacity), unlike the logistic model where it occurs at K/2.