Population Basics
The Census File📋 What Is a Population?
A population is a group of individuals of the same species living in the same area at the same time, who can interbreed. Population ecology studies how and why population sizes change over time. It is fundamental to conservation, fisheries management, disease control, and understanding evolution.
Four processes control population size: births add individuals, deaths remove individuals, immigration adds individuals from elsewhere, and emigration removes individuals to elsewhere. The balance between these four determines whether a population grows, shrinks, or stays stable.
📊 Population Density
- Number of individuals per unit area (or volume)
- Formula: Density = Population size ÷ Area
- High density → more competition, more disease transmission
- Low density → mate-finding difficulty (Allee effect)
- Can be measured by: direct count, quadrats, mark-recapture
📍 Population Distribution
- Clumped — individuals cluster in groups (most common); herds, schools, social groups; resources are patchy
- Uniform — evenly spaced; strong competition or territorial behaviour; e.g. nesting seabirds
- Random — no pattern; each individual settles independently; rare in nature; e.g. dandelion seeds
📦 Quadrat Method
- Used for non-moving organisms (plants, barnacles, slow invertebrates)
- Place random sampling frames (quadrats) in the habitat
- Count individuals in each quadrat
- Calculate average per quadrat
- Multiply average by total habitat area to estimate population
- More quadrats = more accurate estimate
🔖 Mark-Recapture (Lincoln-Petersen)
- Used for mobile animals (fish, birds, mammals)
- Step 1: Capture a sample, mark them, release
- Step 2: Later, capture a second sample
- Step 3: Count how many in second sample are marked
- Formula: N = (M × C) ÷ R
- N = population estimate; M = first catch marked; C = second catch total; R = recaptured marked individuals
Population Growth Curves
J-curve vs S-curve📈 Two Models, Two Very Different Futures
Populations grow in predictable patterns. In theory, with unlimited resources, a population grows exponentially — the J-curve. In reality, resources are always limited, and growth eventually slows and levels off at the carrying capacity — the S-curve (logistic growth). Understanding both curves, and what drives the transition between them, is the core of population ecology.
📈 J-Curve: Exponential Growth
⚙️ What Causes J-Curve Growth?
- Unlimited resources — food, space, water
- No predators or disease pressure
- Occurs in: newly colonised habitats, introduced species, early phases of population growth
- Each individual reproduces at maximum rate (biotic potential)
- Cannot continue indefinitely in nature
📐 The Maths
- Rate of increase is proportional to current population size
- The more individuals, the faster the growth
- Doubling time stays constant
- Even slow-reproducing species can reach enormous numbers given enough time and space
- Real-world examples: bacteria in new nutrient broth; rabbits introduced to Australia
📊 S-Curve: Logistic Growth
📋 Three Phases
- Lag phase — slow initial growth; small population, few individuals reproducing
- Exponential phase — rapid growth; resources still available; fastest growth rate occurs at K/2
- Plateau (stationary) phase — growth rate slows and stabilises at carrying capacity (K); births ≈ deaths
🎯 Carrying Capacity (K)
- Maximum population size an environment can sustainably support
- Set by availability of: food, water, shelter, space, light
- Not fixed — changes with environmental conditions
- When N = K: birth rate = death rate, net growth = 0
- Fastest population growth occurs at N = K/2
Limiting Factors
What Keeps Populations in Check⚖️ Why Populations Cannot Grow Forever
In reality, no population grows without limit. Environmental resistance — the combined effect of all factors that reduce population growth — eventually counteracts biotic potential (the maximum reproductive rate). Limiting factors fall into two categories: density-dependent (their effect gets stronger as population density increases) and density-independent (their effect is the same regardless of population size).
| Feature | Density-Dependent Factors | Density-Independent Factors |
|---|---|---|
| Effect changes with density? | Yes — stronger effect at higher densities | No — same effect regardless of population size |
| Type of regulation | Negative feedback — acts as natural regulator | Not regulatory — random events |
| Examples | Food competition, predation, disease, parasitism, territorial behaviour | Fire, flood, drought, frost, volcanic eruption, storms |
| Effect on population | More intense as population grows — self-regulating | Can wipe out any percentage regardless of density |
| Responsible for | S-curve shape — logistic growth | Sudden population crashes — boom-bust patterns |
🦁 Intraspecific Competition
- Competition between individuals of the SAME species
- Most intense — same ecological niche, same resource needs
- As population grows: more competition per individual → reduced reproduction, increased mortality
- Self-regulating: high density → more competition → population growth slows → density falls → less competition
- Example: deer competing for grazing in winter; trees competing for light in forest
🐆 Interspecific Competition
- Competition between individuals of DIFFERENT species for the same resource
- Less intense than intraspecific (different niches overlap only partially)
- Competitive exclusion principle: two species with identical niches cannot coexist — one will outcompete the other
- Resource partitioning: species avoid direct competition by using different parts of the resource
- Example: lions and hyenas competing for carcasses
🦠 Disease & Parasitism
Pathogens and parasites spread more easily in dense populations — more contact between individuals. Death rates from disease rise as density increases. Classic example: myxomatosis virus in high-density rabbit populations in Australia.
🐍 Predation
When prey population is high, predators have more food → predator numbers increase → predation pressure increases → prey population falls → predators decline. Classic oscillating predator-prey cycles: lynx and snowshoe hare in Canada.
🌡️ Examples & Effects
- Drought — reduces food/water for entire population simultaneously
- Fire — destroys habitat indiscriminately
- Frost/freeze — kills a percentage of population regardless of density
- Volcanic eruption — can eliminate entire local populations instantly
- Floods — habitat destruction affects all individuals present
📉 Effect on Population Growth Curve
- Causes sudden, unpredictable drops in population size
- Does not produce the smooth S-curve of logistic growth
- Populations may crash well below K very suddenly
- After the event, if habitat recovers, exponential regrowth often follows (J-phase)
- Responsible for much of the irregularity seen in real population data
Calculations
The Data Analyst Toolkit🔢 Population Mathematics — What You Need to Know
IEB and CAPS both require you to perform calculations involving population size, growth rate, birth rate, death rate, and mark-recapture estimates. These are not difficult — but you must know your formulas, show your working clearly, and include units. Here are all the formulas you need.
Example 1 — Mark-Recapture
A researcher catches 60 fish, marks them, and releases them. Two weeks later, she catches 80 fish and finds 12 are marked. Estimate the population size.
N = (M × C) ÷ R
N = (60 × 80) ÷ 12
N = 4800 ÷ 12
N = 400 fish
Example 2 — Birth Rate Calculation
A town has a population of 25 000. In one year, 375 births were recorded. Calculate the crude birth rate.
Birth rate = (Births ÷ N) × 1000
Birth rate = (375 ÷ 25 000) × 1000
Birth rate = 0.015 × 1000
Birth rate = 15 per 1000 per year
Example 3 — Rate of Natural Increase
A population has a birth rate of 22 per 1000 and a death rate of 9 per 1000. Calculate the rate of natural increase and interpret your answer.
r = b − d
r = 22 − 9
r = 13 per 1000 per year (or 1.3%)
Interpretation: The population is growing at 13 per 1000 (1.3%) per year. Since r is positive, the population is increasing.
Human Population
The Special Case🌍 Humans — A Population That Broke the Rules
For most of human history, the global population grew slowly and was kept in check by disease, famine, and high infant mortality. Then the industrial revolution, agricultural advances, and modern medicine drastically reduced death rates without a corresponding immediate reduction in birth rates. The result: the most dramatic population explosion in the history of any large mammal. Understanding the demographic transition model explains how and why this happened — and what comes next.
| Stage | Birth Rate | Death Rate | Population Change | Typical Context |
|---|---|---|---|---|
| Stage 1 — Pre-industrial | High | High | Stable / very slow growth | Pre-industrial societies; high infant mortality; no modern medicine |
| Stage 2 — Early industrial | High | Falling rapidly | Rapid growth (J-curve) | Improved sanitation, medicine, food security; birth rate stays high |
| Stage 3 — Late industrial | Falling | Low | Slowing growth | Urbanisation; education; women in workforce; contraception available |
| Stage 4 — Post-industrial | Low | Low | Stable / very slow growth | Developed nations; small families; high cost of living |
🔺 Wide Base (Expanding)
- Large proportion of young people — high birth rate
- Narrow top — high death rate, short life expectancy
- Population is growing rapidly
- Typical of developing nations (Stage 2-3 DTM)
- Future implication: population will continue to grow rapidly
🔷 Uniform/Narrow (Stable or Declining)
- Roughly equal proportions at each age group
- Wide top — long life expectancy, ageing population
- Birth rate ≈ death rate — stable population
- Typical of developed nations (Stage 4 DTM)
- Future implication: population stable or declining; ageing workforce
🌿 Factors Increasing Population
- Improved medical care and vaccines — reduced disease mortality
- Improved sanitation and clean water — reduced infectious disease
- Improved agricultural productivity — reduced famine
- Reduced infant and child mortality
- Increased life expectancy
- Cultural/religious values favouring large families
🏙️ Factors Decreasing Growth Rate
- Urbanisation — children are a financial cost, not an asset
- Education of women — later marriage and fewer children
- Availability of contraception
- Higher cost of living in developed countries
- Women's participation in the workforce
- Government policies (e.g. China's one-child policy)
🎯 Census Assessment
Eight questions on population ecology.