Generalist, Specialist, K-Selected and r-Selected Species：練習問題

Consider a population of rabbits introduced to an island. The growth follows the logistic model: \( \frac{dN}{dt} = rN \left( 1 - \frac{N}{K} \right) \). If the carrying capacity \( K \) is \( 2,000 \) individuals and the intrinsic growth rate \( r \) is \( 0.4 \text{ year}^{-1} \), at what population size \( N \) will the absolute number of individuals added to the population per year be at its maximum?

A demographic analysis of Country Z reveals a Total Fertility Rate (TFR) of \( 1.8 \) and a high dependency ratio due to an aging population. Despite the TFR being below replacement level, the population continues to grow for several decades. This phenomenon is best explained by:

Given the following demographic data for a hypothetical country:
- Crude Birth Rate (CBR): 24 per 1,000
- Crude Death Rate (CDR): 8 per 1,000
- Net Migration Rate: +2 per 1,000
Calculate the doubling time for this population in years.

In a population of 2,000 individuals, the Crude Birth Rate (CBR) is \( 35 \) per 1,000 and the Crude Death Rate (CDR) is \( 15 \) per 1,000. If the population also experiences a net migration of \( +5 \) individuals per 1,000, calculate the annual growth rate (r) and the time required for the population to triple in size.

A population of a K-selected species is experiencing a sharp decline. Scientists observe that the current population density is well below the carrying capacity \( (K) \), yet the growth rate \( (r) \) remains negative. Which of the following is the most likely explanation for this phenomenon?

In a population of 500 individuals, the crude birth rate is 25 per 1,000 and the crude death rate is 10 per 1,000. Calculate the intrinsic rate of increase (r) and determine the time required for the population to double.

A developing nation is transitioning from Stage 2 to Stage 3 of the Demographic Transition Model. Explain why the Crude Birth Rate (CBR) begins to decline during this phase, referencing specific socio-economic changes, and describe the resulting effect on the total population growth rate.

Unit 3: Populations
A population of an endangered species of herbivore is introduced into a new wildlife reserve. The population size over a period of 50 years follows a logistic growth model. The carrying capacity \( (K) \) of the reserve is determined to be \( 1,500 \) individuals, and the intrinsic rate of increase \( (r) \) is \( 0.2 \text{ year}^{-1} \).
(a) Using the formula for logistic growth \( \frac{dN}{dt} = rN \left( 1 - \frac{N}{K} \right) \), calculate the population growth rate when the population size \( (N) \) is \( 750 \) individuals.
(b) Explain the biological significance of the term \( \left( 1 - \frac{N}{K} \right) \) in the context of density-dependent limiting factors.
(c) Discuss two specific environmental factors that could cause the carrying capacity \( (K) \) to decrease suddenly.
(d) Describe the difference between r-selected and K-selected species in terms of their survivorship curves. <\/p>