Unit 2 Population size
Key unit competence: Analyse factors that affect population size and evaluate the effects of human population growth.
Key ideas
- A population is a group of organisms of the same species living in the same area at the same time and able to interbreed. Population size is the number of individuals; population density is the number per unit area (e.g. per km²).
- Population size changes by births and immigration (increase) and deaths and emigration (decrease). Growth rate = (births + immigration) − (deaths + emigration).
- A population growth curve (sigmoid, S-shaped) has phases: lag phase (slow growth, organisms adjusting, few breeders), exponential (log) phase (rapid growth, plenty of resources), stationary phase (births = deaths, population levels off at the carrying capacity), and sometimes a death (decline) phase when resources run out or wastes build up.
- Carrying capacity is the maximum population an environment can support for a long time with the resources available.
- Limiting factors stop a population growing for ever. Density-dependent factors act more strongly as the population becomes crowded: competition for food and space, predation, disease and parasites, accumulation of wastes. Density-independent factors affect populations whatever their size: floods, drought, fire, frost, volcanic eruptions.
- Measuring population size: direct counting (large animals, aerial counts), quadrats for plants and slow animals (count in sample squares, then multiply up), and capture-mark-release-recapture for moving animals: estimated population = (number first marked × number in second catch) ÷ number marked in second catch.
- The human population has grown very quickly (exponential growth) because of better food production, medicine, vaccination, clean water and sanitation, which lowered death rates while birth rates stayed high.
- Effects of rapid human population growth: land shortage, deforestation, soil erosion and overcultivation, pollution, pressure on water, schools, health services and jobs, overcrowding and spread of disease, loss of biodiversity. Rwanda is one of the most densely populated countries in Africa.
- Managing population growth: family planning, education (especially of girls), better health care, land-use planning, urban planning, sustainable farming and job creation.
Common misconceptions
- "A population includes all the animals in an area." No: a population is one species only; all species together form a community.
- "Populations can grow forever if they have food." No: other limiting factors (space, disease, wastes, predators) set a carrying capacity.
- "Floods affect crowded populations more than sparse ones." No: floods are density-independent; they kill a similar proportion whatever the density.
- "Medicine has made human birth rates rise." No: medicine mainly lowered death rates, causing faster growth.
Worked examples
Example 1. In a capture-recapture study, 40 fish were caught, marked and released. Later 50 were caught, of which 10 were marked. Estimate the population.
Solution
Population = (40 × 50) ÷ 10 = 2000 ÷ 10 = 200 fish. This assumes marked fish mixed evenly, marks were not lost and no births, deaths or migration occurred between samples.
Example 2. Yeast grown in a flask of sugar solution shows slow growth, then rapid growth, then a level phase, then a fall. Explain each phase.
Solution
Lag: yeast adjusts and makes enzymes; few cells divide. Exponential: plenty of sugar and space, cells divide rapidly. Stationary: sugar becomes limited and alcohol builds up; births equal deaths. Decline: sugar runs out and alcohol (waste) poisons the cells, so deaths exceed births.
Practice questions
Define: (a) population; (b) population density; (c) carrying capacity.
Show answer
(a) All individuals of one species living in an area at one time. (b) Number of individuals per unit area. (c) The maximum population size an environment can support for a long time.
Common mistake: Defining population as many species.
Sketch and label the phases of a sigmoid growth curve.
Show answer
Lag phase (slow start), exponential phase (rapid growth), stationary phase (levels off at carrying capacity), and possibly decline phase.
Common mistake: Leaving out the axis labels (number vs time).
Distinguish between density-dependent and density-independent factors, with two examples of each.
Show answer
Density-dependent: effect increases with crowding (competition, disease, predation, wastes). Density-independent: effect is the same whatever the density (flood, drought, fire, frost).
Common mistake: Calling disease density-independent.
Describe how to estimate the number of grasshoppers in a field.
Show answer
Catch a sample with a sweep net, mark them harmlessly, release; after some time catch a second sample, count marked and total; estimate = (first marked × second total) ÷ marked recaptured.
Common mistake: Using quadrats for fast-moving animals.
Give four effects of rapid population growth in Rwanda.
Show answer
Land shortage and small farms; deforestation and soil erosion; pollution; pressure on schools, hospitals and jobs; overcrowding and disease; loss of biodiversity.
Common mistake: Listing only positive effects.
State three ways of controlling human population growth.
Show answer
Family planning; education especially of girls; delaying marriage; reproductive health services; economic development.
Common mistake: Suggesting harmful methods.
State two assumptions of the capture-recapture method.
Show answer
Marked animals mix evenly with the population; marks are not lost and do not affect survival; no births, deaths or migration between samples.
Common mistake: Assuming all animals are caught.
Explain why the human population grew fast in the last century.
Show answer
Better medicine, vaccines, clean water, sanitation and food production lowered death rates, especially of infants, while birth rates stayed high.
Common mistake: Saying birth rates increased because of medicine.
Matching and drag-and-drop
Matching
Match each item in column A with the correct answer in column B. Write the letter next to each number.
Column A Column B 1. Which is a density-dependent factor? a. exponential (log) phase 2. A square frame used to sample plants is a: b. Disease 3. The phase of rapid population growth is the: c. Drought 4. Which is a density-independent factor? d. quadrat Show answer
1 → b (Disease) · 2 → d (quadrat) · 3 → a (exponential (log) phase) · 4 → c (Drought)
- Disease spreads faster in crowded populations.
- Numbers in quadrats are scaled up.
- Resources are plentiful.
- It affects the population whatever its size.
Drag and drop
Choose the correct word or phrase from the box for each gap. One word in the box is not needed.
higher soil fertility · soil erosion and loss of habitats · capture-mark-release-recapture · few organisms are breeding yet- The lag phase of a growth curve is slow because .
- The method used to estimate populations of moving animals is .
- Deforestation linked to population pressure leads to .
Show answer
1: few organisms are breeding yet · 2: capture-mark-release-recapture · 3: soil erosion and loss of habitats
- Growth speeds up later.
- Marked animals mix with unmarked ones.
- Tree roots hold soil.
Matching
Match each item in column A with the correct answer in column B. Write the letter next to each number.
Column A Column B 1. Movement of individuals out of a population is: a. slow population growth 2. Movement of individuals into a population is: b. immigration 3. Family planning helps to: c. emigration 4. Accumulation of toxic wastes in a crowded population is a: d. density-dependent limiting factor Show answer
1 → c (emigration) · 2 → b (immigration) · 3 → a (slow population growth) · 4 → d (density-dependent limiting factor)
- It decreases the population.
- It increases the population.
- Couples choose the number of children.
- Its effect grows with density.
Drag and drop
Choose the correct word or phrase from the box for each gap. One word in the box is not needed.
density-dependent · births, deaths, immigration and emigration · 200 · 1200- A disease kills a higher proportion of a goat herd when the goats are crowded. This disease is .
- Population growth rate depends on .
- 30 rats were marked and released. Later 40 were trapped, 6 of them marked. The estimated population is .
Show answer
1: density-dependent · 2: births, deaths, immigration and emigration · 3: 200
- Crowding helps the pathogen spread.
- All four change population size.
- (30 × 40) ÷ 6 = 200.