AHL: Population dynamics

IB Biology HL· 6 min read

1. Population Growth Models★★★☆☆⏱ 20 min

📘 Definition

Population Growth Rate

$r = per capita growth rate, N = current population size, t = time$

The per capita change in the number of individuals in a population over a set time period

Two core models describe population growth, depending on resource availability:

Exponential growth: Occurs when resources are unlimited, produces a J-shaped curve: $d N / d t = r N$
Logistic growth: Occurs when resources are limited, growth slows as population approaches carrying capacity, produces an S-shaped curve: $d N / d t = r N (1 - N / K)$

📐 Worked Example

A population of 200 deer has a per capita growth rate of 0.2 per year. The carrying capacity of the habitat is 1000 deer. Calculate the annual population growth rate.

1
Identify all variables from the question:
2
$N = 200, r = 0.2, K = 1000$
3
Use the logistic growth equation, as carrying capacity is given and resources are limited:
4
$dN/dt = rN (1 - \frac{N}{K})$
5
Substitute values and simplify:
6
$dN/dt = (0.2)(200) (1 - \frac{200}{1000}) = 40 (0.8) = 32$
7
Final answer: The population will increase by 32 deer this year.

2. Carrying Capacity & Limiting Factors★★☆☆☆⏱ 15 min

📘 Definition

Carrying Capacity (K)

The maximum sustainable population size of a species that can be supported by a given environment

Example:

A 100km² forest can support a maximum of 12 wolf packs due to limited prey availability

Limiting factors that regulate population size are split into two categories:

Density-dependent: Impact increases as population size grows (e.g. competition for food, disease transmission, predation)
Density-independent: Impact is the same regardless of population size (e.g. wildfires, hurricanes, drought, sudden habitat destruction)

📐 Worked Example

A drought reduces plant growth in a grassland, and reduces the rabbit population by 50% regardless of the original rabbit population size. Classify this limiting factor and explain its effect on carrying capacity.

1
Check if the impact depends on population density: The 50% reduction is the same no matter how many rabbits were present before the drought.
2
Classify the factor: This is a density-independent limiting factor.
3
Explain the effect on carrying capacity: Reduced plant growth means less food available for rabbits long-term, so the carrying capacity of the grassland for rabbits decreases. The population will stabilize at a lower size after the drought.

3. Survivorship Curves & Life History Strategies★★★☆☆⏱ 20 min

📘 Definition

Survivorship Curve

A graph that plots the proportion of individuals from a founding cohort that are still alive at each age, used to classify life history strategies

Survivorship Type	Key Characteristics	Example
Type I	Low mortality early in life, high mortality late in life; few offspring, high parental care	Humans, large mammals (elephants, bears)
Type II	Constant mortality rate across all age groups	Many songbirds, small rodents
Type III	Very high mortality early in life, low mortality for surviving adults; many offspring, little parental care	Sea turtles, fish, insects, most plants

📐 Worked Example

A researcher tracks 1000 newly hatched sea turtles. Only 80 survive past the first year, and most of the remaining individuals live to 60 years old. What type of survivorship curve does this represent? Justify your answer.

1
Identify the mortality pattern: Most mortality occurs early in life, with very low mortality for individuals that reach adulthood.
2
Match to the survivorship type: This matches a Type III survivorship curve.
3
Justify: Sea turtles produce hundreds of eggs but provide no parental care. Most hatchlings are eaten before reaching the ocean, which matches the defining characteristic of Type III survivorship.

4. Population Regulation★★★★☆HL only⏱ 25 min

📘 Definition

Population Regulation

The process that maintains population size within a stable range, controlled by biotic or abiotic factors

There are two main mechanisms of population regulation in food webs:

Top-down regulation: Population size is controlled by consumers at higher trophic levels. For example, reintroduction of wolves (top predators) controls the size of elk populations in Yellowstone National Park.
Bottom-up regulation: Population size is controlled by the availability of resources at lower trophic levels. For example, the amount of grass (producer) limits the size of elk populations.

📐 Worked Example

Fertilizer runoff into a lake increases nutrient levels, which increases algae biomass, which increases zooplankton abundance, which increases small fish population size. What form of population regulation does this represent?

1
Identify the direction of change: The change originates from increased resources at the lowest trophic level, and propagates up the food chain.
2
Classify: This is bottom-up regulation, because population sizes at higher trophic levels are limited by resource availability from lower trophic levels.
3
Contrast: If overfishing removed all top predator fish, leading to an increase in small fish, this would be top-down regulation.

5. Common Pitfalls

Wrong move:

Using the exponential growth model when carrying capacity is given

Why:

Exponential growth only applies to unlimited resource conditions; the logistic model accounts for limiting resources

Correct move:

Always use logistic growth if carrying capacity (K) is provided in the question

Wrong move:

Confusing density-dependent and density-independent limiting factors

Why:

Students often misclassify natural disasters as density-dependent

Correct move:

Remember: impact that changes with population size = density-dependent; same impact regardless of size = density-independent

Wrong move:

Claiming carrying capacity is a fixed, unchanging value

Why:

Carrying capacity shifts when environmental conditions change (e.g. drought, habitat loss)

Correct move:

Treat K as an estimate that can change over time with changing resource availability

Wrong move:

Mixing up top-down and bottom-up regulation

Why:

Students often reverse the direction of control

Correct move:

Use the mnemonic: Top-down = top predator controls down; Bottom-up = bottom resource controls up

Wrong move:

Assigning modern humans to Type II survivorship

Why:

Humans have low mortality early in life and high mortality late in life with access to healthcare

Correct move:

Modern humans are always classified as Type I survivorship

6. Quick Reference Cheatsheet

Concept	Key Exam Details
Exponential growth	$d N / d t = r N$ , unlimited resources, J-shaped curve
Logistic growth	$d N / d t = r N (1 - N / K)$ , limited resources, S-shaped curve, $K$ = carrying capacity
Density-dependent factors	Competition, disease, predation; effect increases with population size
Density-independent factors	Natural disasters, climate extremes; effect independent of population size
Type I survivorship	Low early mortality, high late mortality, few offspring, high parental care
Type II survivorship	Constant mortality across all ages
Type III survivorship	High early mortality, low late mortality, many offspring, low care
Top-down regulation	Population size controlled by top trophic level predators
Bottom-up regulation	Population size controlled by lower trophic level resource availability

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2022 · 2
Analyze logistic growth of invasive mussels
2021 · 1
Compare Type I/III survivorship curves
2023 · 2
Explain top-down vs bottom-up control

Going deeper

syllabusOfficial IB Biology HL Theme CFull AHL syllabus reference

What's Next

Population dynamics is the foundation for understanding all larger ecological concepts, from community interactions to conservation biology. The models and patterns you learned here are used to predict how native populations will respond to climate change, habitat destruction, and invasive species, which are common topics in IB Biology HL extended response questions. Understanding carrying capacity also helps explain human population growth trends and the global impact of human activity on the biosphere. This knowledge will prepare you for deeper study of conservation and global ecological change.