Ecology Population Growth Models 2 ā Questions and Answers
Question 1: In the logistic growth equation dN/dt = rN((K-N)/K), what does the term (K-N)/K represent?
- The intrinsic rate of increase
- The fraction of carrying capacity still available (Correct answer)
- The per capita death rate
- The population density at equilibrium
Correct 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.
Question 2: Which scenario best illustrates an Allee effect in population growth?
- A population grows fastest at low density
- A population declines when density exceeds carrying capacity
- A population has a reduced per capita growth rate at very low densities (Correct answer)
- A population oscillates regularly around carrying capacity
Correct 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.
Question 3: Doubling time for a population growing exponentially at rate r is approximately:
- r / 0.693
- 0.693 / r (Correct answer)
- r Ć K
- K / r
Correct answer: 0.693 / r
Doubling time ā ln(2)/r ā 0.693/r, derived from the exponential growth equation N(t) = Nāe^(rt).
Question 4: A population has K = 500 and N = 250. Under logistic growth, the growth rate is at what fraction of its maximum possible rate?
- 100%
- 25%
- 75%
- 50% (Correct answer)
Correct answer: 50%
At N = K/2 = 250, the logistic braking term equals 0.5, so growth rate is 50% of its theoretical maximum rN.
Question 5: What distinguishes a Leslie matrix model from simple exponential or logistic growth models?
- It incorporates predator-prey interactions
- It tracks age- or stage-structured survival and fecundity (Correct answer)
- It models spatial dispersal across habitat patches
- It accounts for stochastic random events only
Correct 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.
Question 6: In a metapopulation framework, a 'rescue effect' refers to:
- Immigration that prevents local patch extinction (Correct answer)
- A sudden increase in carrying capacity after disturbance
- Emigration that reduces competition in overcrowded patches
- Rapid evolution of higher birth rates in declining populations
Correct 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.
Question 7: A population growing according to the Gompertz model grows fastest when N equals:
- K
- K/2
- K/e (Correct answer)
- 0
Correct 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.
Ecology Population Growth Models 2
In the logistic growth equation dN/dt = rN((K-N)/K), what does the term (K-N)/K represent?