Population and Natural Resources

Lessons

Senior 6 · Biology

Population and Natural Resources

4 lessons

Lesson 1 of 4

Population characteristics and how to measure them

25 min

Counting a nation, counting a herd

In August 2022, the National Institute of Statistics of Rwanda (NISR) counted every person in the country in the Fifth Population and Housing Census: 13 246 394 people. That is a census of a whole population. Ecologists rarely have that luxury: nobody can count every impala in Akagera or every grasshopper in a field of sorghum. Yet managing a park, a fishery or a pest needs to know how big a population is, whether it is growing, and how it is spread out.

This unit studies populations: what describes them, how they are measured, why they grow or shrink, and what limits them. It ends with the natural resources on which Rwanda's own population depends.

Definition

Population: all the organisms of one species living in one area at the same time, able to interbreed. Example: the impala of Akagera National Park.

Population size ( $N$ ): the number of individuals in the population.

Population density: the number of individuals per unit area (or volume), $\text{density} = \frac{N}{\text{area}}$ . Example: people per $\mathrm{km^2}$ , or plants per $\mathrm{m^2}$ .

Distribution (dispersion): the way individuals are spaced within the area: clumped, random or uniform.

Population structure: the proportions of individuals of each age and sex, shown in an age–sex pyramid.

Size and density

Density lets you compare populations in areas of different sizes. Rwanda's population density rose from 183 people per $\mathrm{km^2}$ in 1978 to 272 in 1991, 321 in 2002, 415 in 2012 and 503 in 2022 (NISR): among the highest in Africa. In ecology, density is often more useful than total size, because many factors that control a population, such as competition for food and the spread of disease, depend on how crowded it is (Lesson 3).

Distribution

Figure 1 shows the three patterns of spacing.

Figure 1: The three patterns of distribution. The same number of individuals (36) is in each square.

Clumped, the most common pattern: resources are patchy (water holes, fruiting trees), or animals live in social groups for protection, like impala herds, or seeds fall close to the parent.
Random: resources are evenly spread and individuals neither attract nor repel one another, for example plants whose seeds are carried by the wind.
Uniform: individuals compete strongly for space and keep apart, like territorial animals, seabirds nesting just beyond pecking distance, or desert shrubs whose roots take all the water nearby. Crops planted in rows are uniform by design.

Age and sex structure

A population pyramid shows the number of males and females in each age group. Its shape tells you how the population has grown in the past and how it is likely to grow. Figure 2 is drawn from NISR's 2022 census data for Rwanda.

Figure 2: Rwanda's population by age and sex, 2022. Data: NISR, Fifth Population and Housing Census, Table 5.

Shape of pyramid	What it shows	Future growth
Broad base, narrow top (expanding)	High birth rate; many young people; fewer survive to old age	Fast growth: many people will soon reach reproductive age
Straight sides (stable)	Birth rate and death rate low and similar	Little or no growth
Narrow base (contracting)	Birth rate below replacement; an ageing population	Decline, unless people migrate in

Worked example 1: analysing Rwanda's 2022 age structure

From the NISR census: 4 956 812 people were aged 0 to 14, 7 737 654 were aged 15 to 64, and 551 928 were aged 65 and over, out of 13 246 394. Calculate (a) the percentage aged under 15, (b) the dependency ratio, and (c) interpret the results.

(a) $\frac{4\,956\,812}{13\,246\,394} \times 100 = 37.4\,\%$ .
(b) The dependency ratio compares the people of dependent ages with those of working age: $\text{dependency ratio} = \frac{N_{0-14} + N_{65+}}{N_{15-64}} \times 100$ $= \frac{4\,956\,812 + 551\,928}{7\,737\,654} \times 100 = 71.2$ so there are about 71 dependants for every 100 people of working age.
(c) Over a third of the population is under 15: the expanding shape of Figure 2. As these young people reach reproductive age, the population will keep growing even if each family has fewer children than before (population momentum). NISR's medium projection is 23.6 million people by 2052.

Measuring population size

Plants and slow-moving animals are sampled with quadrats (Unit 1, Lesson 2): $N = \text{mean density} \times \text{total area}$ .

Mobile animals move between quadrats, so ecologists use capture–mark–release–recapture:

Capture a sample of the population, count it ( $n_{1}$ ) and mark every individual harmlessly: a dab of non-toxic paint on a beetle's shell, a numbered ring on a bird's leg, a clipped fin or tag on a fish.
Release them where they were caught, and give them time to mix back into the population.
Capture a second sample ( $n_{2}$ ) in the same way, and count how many are marked ( $m_{2}$ ).

The fraction of the second sample that is marked estimates the fraction of the whole population that is marked, $\frac{m_2}{n_2} = \frac{n_1}{N}$ . Rearranging gives the Lincoln–Petersen index:

N = \frac{n_1 \times n_2}{m_2}

The estimate is valid only if: marked and unmarked animals mix fully; the marks do not fall off, and do not make animals easier or harder to catch or to be eaten; no births, deaths, immigration or emigration happen between the samples; and both samples are taken in the same way.

Large mammals in open country are often counted from aircraft along transects, and forest animals are increasingly counted with camera traps that recognise individuals by their markings.

Worked example 2: tilapia in a fish pond

A fish farmer's cooperative wants to know how many Nile tilapia are in a pond before harvest (illustrative data). They net 60 fish, clip a small part of a fin on each, and release them. Four days later they net 50 fish, of which 12 have clipped fins. Estimate the population, and state two assumptions.

$n_{1} = 60$ , $n_{2} = 50$ , $m_{2} = 12$ .
$N = \frac{n_1 \times n_2}{m_2} = \frac{60 \times 50}{12} = 250 \text{ fish}$
Check: 12 out of 50, or 24 %, of the second catch were marked, and 60 is 24 % of 250. ✓
Assumptions: the marked fish mixed evenly through the pond in four days; no fish were born, died, added or removed between the two catches; a clipped fin does not change the chance of being netted.

Reliability: if only 2 marked fish had been recaptured, the estimate would be $\frac{60 \times 50}{2} = 1\,500$ , and one fish more or less would change it by hundreds. Large samples and several recaptures give a more reliable estimate.

Warning

Three common mistakes

Swapping the numbers. $m_{2}$ , the marked animals recaptured, goes on the bottom. A small $m_{2}$ means a large population.
Releasing marked animals in one spot. They must be released where caught, or they cannot mix evenly and the estimate will be wrong.
Forgetting welfare. Marks must not harm the animal or make it conspicuous to predators; handle animals briefly and keep them cool and damp.

Miss Estruch Biology: "Mark-Release-Recapture A-level Biology". Watch for the method, the ethics of marking, the calculation and the assumptions, and compare them with Worked example 2.

Tip

Exam technique. For any population-size question, first decide: does the organism move? If not, use quadrats and scale up by area; if it does, use mark–release–recapture. Then always state at least two assumptions; they earn marks in almost every question on this method.

✦

Practice: population characteristics and measurement

Define population density, and explain why density is often more useful than population size.
Name the distribution pattern and suggest a reason for it: (a) mango trees along a river bank, (b) territorial male birds each defending a patch of forest, (c) wind-dispersed weeds in a newly cleared field.
In 2022, Rwanda had 13 246 394 people at a density of 503 people per $\mathrm{km^2}$ . Calculate the area this implies, to 3 significant figures.
Using Figure 2, describe two features of Rwanda's age structure and explain what each suggests about the future.
In a school field, 40 grasshoppers were caught and marked with paint. Next day, 45 were caught, of which 6 were marked. Estimate the population.
Give three assumptions of the mark–release–recapture method, and explain what would happen to the estimate if marked grasshoppers were more easily seen and eaten by birds.
Explain why the estimate in question 5 would be unreliable if the two samples were taken a month apart.

Show answersHide answers

The number of individuals per unit area. It allows comparison of areas of different size, and many factors controlling populations (competition, disease) depend on crowding.
(a) Clumped: water and fertile soil are found only along the river. (b) Uniform: territoriality keeps individuals apart. (c) Random: seeds land by chance and the resources are evenly spread.
$\text{area} = \frac{13\,246\,394}{503} = 26\,335 \approx 26\,300\,\mathrm{km^2}$ (3 s.f.).
A broad base (over a third are under 15), so many people will soon reach reproductive age and the population will keep growing; a narrow top (only about 4 % aged 65 and over), showing lower survival to old age in the past. Also: more females than males at older ages, since women tend to live longer.
$N = \frac{40 \times 45}{6} = 300$ grasshoppers.
Any three: marked and unmarked mix fully; marks do not come off; marking does not affect survival or the chance of recapture; no births, deaths or migration between samples; the samples are taken the same way. If marked grasshoppers were eaten more, fewer would be recaptured, $m_{2}$ would be too small, so $N$ would be overestimated.
In a month, grasshoppers would be born, die and move in or out, and paint marks might wear off, so the proportion marked would no longer represent the original population.

Key points

A population is described by its size, density, distribution (clumped, random, uniform) and age–sex structure.
Rwanda's 2022 pyramid has a broad base: 37.4 % of people were under 15, so the population will keep growing.
Mobile animals are estimated by mark–release–recapture: $N = \frac{n_1 \times n_2}{m_2}$ , valid only if its assumptions hold.

Sources and credits

8.2.2: Population Demography, from Biology 2e by OpenStax (Mary Ann Clark, Matthew Douglas, Jung Choi), via LibreTexts Biology, licensed under CC BY 4.0. Used for population size, density, dispersion patterns, mark and recapture, and age structure. Adapted by Ganzaa.
Population, density and age structure: National Institute of Statistics of Rwanda, Fifth Rwanda Population and Housing Census, 2022: Main Indicators Report, Tables 1, 4 and 5, and the summary of projections. Figures only.
Photo: Impala Rwanda, Wulfstan, CC BY-SA 3.0, via Wikimedia Commons.
Photo: Aphelocoma coerulescens, Florida, USA, leg rings, Lauren from Rockledge, Florida, USA, CC BY 2.0, via Wikimedia Commons.
Video: Mark-Release-Recapture A-level Biology: Estimating population size of animals, Miss Estruch Biology, embedded from YouTube.

Figures 1 and 2, the tables, the worked examples and the practice questions are written by Ganzaa. Figure 2 is drawn from the NISR census data; the data in Worked example 2 are illustrative.

This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.

1Counting a nation, counting a herd

2Size and density

3Distribution

4Age and sex structure

5Measuring population size

Counting a nation, counting a herd

Size and density

Distribution

Age and sex structure

Measuring population size