# AHL: Population dynamics

> IB Biology HL · Theme C: Interaction and Interdependence
> Source: https://www.owlsprep.com/study/ib-biology-hl-u3-ahl-population-dynamics/

This AHL subtopic covers how populations change over time, including growth models, survivorship patterns, and regulation mechanisms. You will learn to analyze real-world population data and explain factors limiting population size in ecosystems.

**Prerequisites:** [IB Biology HL: Species and communities](https://www.owlsprep.com/study/ib-biology-hl-species-and-communities/); [Ecosystem energy flow](https://www.owlsprep.com/study/ib-biology-hl-ecosystem-energy-flow/)

## Learning objectives

- Explain factors that affect population growth and carrying capacity
- Analyze survivorship curves to interpret life history strategies
- Calculate population growth rates using exponential and logistic models
- Distinguish between top-down and bottom-up population regulation
- Evaluate how limiting factors shape population size over time

## Population Growth Models

**Population Growth Rate** — The per capita change in the number of individuals in a population over a set time period

*Notation:* $r = \text{per capita growth rate}, N = \text{current population size}, t = \text{time}$

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

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

**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.

> **tip**
>
> Exponential growth is only seen in natural populations for short periods (e.g. invasive species colonizing a new habitat). Always use logistic growth if a carrying capacity is given.

## Carrying Capacity & Limiting Factors

**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.

## Survivorship Curves & Life History Strategies

**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.

## Population Regulation

**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.

**Exam command terms**

Common command terms for this topic have specific exam expectations:

- **Distinguish** — State clear differences between two concepts, not just separate definitions *(Distinguish between density-dependent and density-independent factors requires a direct comparison to get full marks)*

- **Calculate** — Show all working (formula, substitution) even if you get the final answer right *(Calculating growth rate requires writing the formula to earn full marks)*

## Common pitfalls

- **Wrong:** Using the exponential growth model when carrying capacity is given
  - Why it fails: Exponential growth only applies to unlimited resource conditions; the logistic model accounts for limiting resources
  - Correct: Always use logistic growth if carrying capacity (K) is provided in the question
- **Wrong:** Confusing density-dependent and density-independent limiting factors
  - Why it fails: Students often misclassify natural disasters as density-dependent
  - Correct: Remember: impact that changes with population size = density-dependent; same impact regardless of size = density-independent
- **Wrong:** Claiming carrying capacity is a fixed, unchanging value
  - Why it fails: Carrying capacity shifts when environmental conditions change (e.g. drought, habitat loss)
  - Correct: Treat K as an estimate that can change over time with changing resource availability
- **Wrong:** Mixing up top-down and bottom-up regulation
  - Why it fails: Students often reverse the direction of control
  - Correct: Use the mnemonic: Top-down = top predator controls down; Bottom-up = bottom resource controls up
- **Wrong:** Assigning modern humans to Type II survivorship
  - Why it fails: Humans have low mortality early in life and high mortality late in life with access to healthcare
  - Correct: Modern humans are always classified as Type I survivorship

## Cheatsheet

| Concept | Key Exam Details |
| --- | --- |
| Exponential growth | $dN/dt = rN$, unlimited resources, J-shaped curve |
| Logistic growth | $dN/dt = rN(1-N/K)$, 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 |

## 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.

- [AHL: Conservation biology](https://www.owlsprep.com/study/ib-biology-hl-u3-ahl-conservation-biology/)
- [AHL: Climate change impacts](https://www.owlsprep.com/study/ib-biology-hl-u3-ahl-climate-change-impacts/)
- [AHL: Ecosystem management](https://www.owlsprep.com/study/ib-biology-hl-u3-ahl-ecosystem-management/)

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