Table of contents

1. Introduction to Biology2h 42m
2. Chemistry3h 37m
3. Water1h 26m
4. Biomolecules2h 23m
5. Cell Components2h 26m
6. The Membrane2h 31m
7. Energy and Metabolism2h 0m
8. Respiration2h 40m
9. Photosynthesis2h 49m
10. Cell Signaling59m
11. Cell Division2h 47m
12. Meiosis2h 0m
13. Mendelian Genetics4h 44m
14. DNA Synthesis2h 27m
15. Gene Expression3h 6m
16. Regulation of Expression3h 31m
17. Viruses37m
- Viruses
  37m
18. Biotechnology2h 58m
19. Genomics17m
- Genomes
  17m
20. Development1h 5m
21. Evolution3h 1m
22. Evolution of Populations3h 53m
23. Speciation1h 37m
24. History of Life on Earth2h 6m
25. Phylogeny2h 31m
26. Prokaryotes4h 59m
27. Protists1h 12m
28. Plants1h 22m
29. Fungi36m
- Fungi
  19m
- Fungi Reproduction
  17m
30. Overview of Animals34m
- Overview of Animals
  34m
31. Invertebrates1h 2m
32. Vertebrates50m
33. Plant Anatomy1h 3m
34. Vascular Plant Transport1h 2m
- Water Potential
  1h 2m
35. Soil37m
- Soil and Nutrients
  20m
- Nitrogen Fixation
  16m
36. Plant Reproduction47m
- Flowers
  33m
- Seeds
  14m
37. Plant Sensation and Response1h 9m
38. Animal Form and Function1h 19m
39. Digestive System1h 10m
- Digestion
  1h 3m
- Blood Sugar Homeostasis
  7m
40. Circulatory System1h 49m
41. Immune System1h 12m
42. Osmoregulation and Excretion50m
- Osmoregulation and Excretion
  50m
43. Endocrine System1h 4m
- Endocrine System
  1h 4m
44. Animal Reproduction1h 2m
- Animal Reproduction
  1h 2m
45. Nervous System1h 55m
- Neurons and Action Potentials
  1h 8m
- Central and Peripheral Nervous System
  46m
46. Sensory Systems46m
- Sensory System
  46m
47. Muscle Systems23m
- Musculoskeletal System
  23m
48. Ecology3h 11m
49. Animal Behavior28m
- Animal Behavior
  28m
50. Population Ecology3h 41m
51. Community Ecology2h 46m
52. Ecosystems2h 36m
53. Conservation Biology24m
- Conservation Biology
  24m

50. Population Ecology

Introduction to Population Ecology

General Biology

50. Population Ecology

Introduction to Population Ecology

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2:50 minutes

Problem 7

Textbook Question

According to the logistic growth equation

$\frac{d N}{d t} = r N \frac{(K - N)}{K}$

a. The number of individuals added per unit time is greatest when N is close to zero.
b. The per capita population growth rate increases as N approaches K.
c. Population growth is zero when N equals K.
d. The population grows exponentially when K is small.

Verified step by step guidance

Understand the logistic growth equation: $ \frac{dN}{dt} = rN \frac{(K-N)}{K} $, where $ N $ is the population size, $ r $ is the intrinsic rate of increase, and $ K $ is the carrying capacity.

Identify the condition for zero population growth: Set $ \frac{dN}{dt} = 0 $. This occurs when $ N = K $, meaning the population size equals the carrying capacity.

Analyze the per capita growth rate: The per capita growth rate is $ r \frac{(K-N)}{K} $. As $ N $ approaches $ K $, $ \frac{(K-N)}{K} $ approaches zero, thus the per capita growth rate decreases.

Consider when the number of individuals added per unit time is greatest: This occurs when $ N $ is at half the carrying capacity, $ N = \frac{K}{2} $, not when $ N $ is close to zero.

Evaluate the condition for exponential growth: Exponential growth occurs when $ K $ is very large or effectively infinite, not when $ K $ is small. In the logistic model, exponential growth is not dependent on the size of $ K $.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Logistic Growth Equation

The logistic growth equation models population growth by incorporating the carrying capacity (K), which limits growth as the population size (N) approaches K. It is expressed as dN/dt = rN(K−N)/K, where r is the intrinsic growth rate. This equation reflects how growth slows as resources become limited, contrasting with exponential growth where resources are unlimited.

Carrying Capacity (K)

Carrying capacity (K) is the maximum population size that an environment can sustain indefinitely without degrading the habitat. It is determined by available resources such as food, habitat, water, and other necessities. In the logistic growth model, as N approaches K, the growth rate decreases, eventually reaching zero when N equals K, indicating a stable population.

Per Capita Growth Rate

Per capita growth rate refers to the average individual contribution to population growth. In the logistic model, this rate decreases as the population size (N) nears the carrying capacity (K) due to increased competition for limited resources. Initially, when N is small, the per capita growth rate is higher, but it diminishes as the population grows and resources become scarce.

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Related Practice

Textbook Question

With regard to its rate of growth, a population that is growing logistically

a. Grows fastest when density is lowest

b. Has a high intrinsic rate of increase

c. Grows fastest at an intermediate population density

d. Grows fastest as it approaches carrying capacity

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Textbook Question

Pose a hypothesis to explain why the human population has undergone especially rapid growth over the past 200 years. Describe two examples of density-dependent factors that limit human population growth. Is it possible that humans have surpassed Earth's carrying capacity?

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Textbook Question

All of the following are density-dependent factors that can influence population size except

a. Weather

b. Food supply

c. Waste concentration in the environment

d. Infectious disease

e. Supply of suitable habitat for survival

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Textbook Question

In contrast to nonhuman populations, human population growth rates have begun to decline due to

a. Voluntarily increasing death rates

b. Voluntarily decreasing birth rates

c. Involuntary increases in death rates

d. Involuntary decreases in birth rates

e. Density-dependent factors

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Textbook Question

Which of the following represents a demographic transition?

a. A population switches from exponential to logistic growth

b. A population reaches a fertility rate of zero

c. There are equal numbers of individuals in all age groups

d. A population switches from high birth and death rates to low birth and death rates

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Textbook Question

Explain why biologists want to maintain (a) 'habitat corridors' that connect populations in a metapopulation, and (b) unoccupied habitat that is appropriate for the species in question.

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Textbook Question

Populations that rely on stored resources are likely to overshoot the carrying capacity of the environment and consequently experience a(n).

a. Demographic momentum

b. Cultural carrying capacity

c. Decrease in death rates

d. Population crash

e. Exponential growth

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Textbook Question