객관식
An island has a population of 10,000 rabbits at the beginning of the year. During the year, there were 400 births and 150 deaths. Calculate the population growth rate and the per capita population growth rate.
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50. Population Ecology
Introduction to Population Growth Models
Multiple Choice
Which equation represents the logistic growth rate of a population?
A
\(\frac{dN}{dt} = rN\)
B
\(\frac{dN}{dt} = rK \left(1 - \frac{N}{r}\right)\)
C
\(\frac{dN}{dt} = rN \left(1 - \frac{N}{K}\right)\)
D
\(\frac{dN}{dt} = K - N\)
검증된 단계별 안내1
Step 1: Understand the concept of logistic growth. Logistic growth describes how a population grows when resources are limited. Unlike exponential growth, which assumes unlimited resources, logistic growth incorporates a carrying capacity (K), which is the maximum population size that the environment can sustain.
Step 2: Analyze the components of the logistic growth equation. The equation \( rac{dN}{dt} = rN ig(1 - rac{N}{K}ig)\) includes: (1) 'r', the intrinsic growth rate of the population, (2) 'N', the current population size, and (3) 'K', the carrying capacity. The term \(ig(1 - rac{N}{K}ig)\) represents the fraction of resources still available as the population approaches the carrying capacity.
Step 3: Compare the given equations. The first equation, \( rac{dN}{dt} = rN\), represents exponential growth, which does not account for resource limitations. The second equation, \( rac{dN}{dt} = rK ig(1 - rac{N}{r}ig)\), incorrectly mixes variables and does not align with the logistic growth model. The third equation, \( rac{dN}{dt} = rN ig(1 - rac{N}{K}ig)\), correctly represents logistic growth. The fourth equation, \( rac{dN}{dt} = K - N\), does not describe population growth dynamics.
Step 4: Focus on the correct equation, \( rac{dN}{dt} = rN ig(1 - rac{N}{K}ig)\). This equation shows that as the population size (N) approaches the carrying capacity (K), the growth rate slows down due to limited resources. When N is much smaller than K, the term \(ig(1 - rac{N}{K}ig)\) is close to 1, and the population grows nearly exponentially. As N gets closer to K, the term \(ig(1 - rac{N}{K}ig)\) approaches 0, slowing growth.
Step 5: Apply this understanding to real-world scenarios. Logistic growth is commonly observed in populations where resources such as food, space, or water are limited. It is a foundational concept in ecology and helps explain population dynamics in various environments.
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