# Population dynamics

> IB Biology SL · Theme C: Interactions and Interdependencies, Unit 3
> Source: https://www.owlsprep.com/study/ib-biology-sl-u3-population-dynamics/

This sub-topic explores how populations change in size over time, the biotic and abiotic factors that limit growth, and core patterns observed in wild populations, forming the foundation for understanding ecological interactions.

**Prerequisites:** [Basic ecosystem structure and ecology concepts](https://www.owlsprep.com/study/ib-biology-sl-u2-ecosystem-structure/)

## Learning objectives

- Distinguish between exponential and logistic population growth
- Define carrying capacity and categorize limiting factors
- Interpret population growth curves for exam questions
- Explain how environmental change impacts population dynamics

## Core Definitions and Limiting Factors

**Population** — A group of individuals of the same species that occupy the same geographic area at the same time

*Example:* A population of sea turtles nesting on a single Caribbean island

Population dynamics studies changes in population size over time, driven by birth rates, death rates, immigration, and emigration. All populations are constrained by limiting factors, which are categorized by whether their impact depends on population density.

- **Density-dependent factors**: Impact increases as population density rises, e.g. competition for food, disease spread, predation
- **Density-independent factors**: Impact is unrelated to population density, e.g. hurricanes, wildfires, sudden drought

**Worked example:** Classify each limiting factor as density-dependent or density-independent: (a) Spread of avian influenza in a wild duck population, (b) A volcanic eruption wiping out 80% of a population

1. Recall: density-dependent factors have stronger effects at higher population density
2. For (a): Avian influenza spreads more easily when ducks are crowded at high density, so this is:
3. Density-dependent limiting factor
4. For (b): A volcanic eruption kills individuals regardless of how dense the population is, so this is:
5. Density-independent limiting factor

> **Exam tip:** Always link the type of limiting factor to population density in your answer to earn full marks

## Population Growth Patterns

Populations follow two primary growth patterns depending on resource availability. When resources are unlimited, populations grow exponentially. When resources become limited, growth follows a logistic pattern that stabilizes at carrying capacity.

**Exponential Growth** — Growth where per capita growth rate is constant, leading to increasingly rapid population increase

*Notation:* J-curve

*Example:* Invasive species colonizing a new habitat with no predators

$$\frac{dN}{dt} = rN$$

**Logistic Growth** — Growth that slows as population size approaches carrying capacity, stabilizing at a constant size

*Notation:* S-curve

*Example:* Most wild populations with limited resources

$$\frac{dN}{dt} = rN \frac{(K-N)}{K}, \quad K = \text{carrying capacity}$$

**Worked example:** Identify the growth pattern for: (1) Zebra mussels newly introduced to the Great Lakes, (2) A deer population on a small island with fixed vegetation area

1. Recall: Exponential growth = unlimited resources, logistic growth = limited resources and carrying capacity
2. 1. Zebra mussels are new to the habitat, with abundant resources and few predators, so growth is:
3. Exponential (J-curve) growth
4. 2. The island has a fixed amount of vegetation for food, so resources are limited, growth will stabilize, so this is:
5. Logistic (S-curve) growth

**Check your understanding**

Test your understanding

1. What is the net population growth rate when a population is at carrying capacity?

   - Maximum
   - Zero
   - Negative
   - Constant exponential

   *Why:* Correct! At carrying capacity, birth rates equal death rates, so net growth is zero.

## Carrying Capacity and Real-World Dynamics

**Carrying Capacity (K)** — The maximum number of individuals of a species that an environment can support indefinitely, given available resources

> **info**
>
> Carrying capacity is not fixed: it increases or decreases when the environment changes. Drought, deforestation, or pollution often reduce carrying capacity for wild species, while resource input can increase it.

In real ecosystems, populations rarely stay perfectly stable at carrying capacity. Small fluctuations around K are normal, driven by seasonal changes, predator-prey cycles, and random environmental disturbances.

**Worked example:** A drought reduces grass growth by 50% in a savanna ecosystem. How does this affect the carrying capacity for wildebeest?

1. 1. Carrying capacity depends on the availability of limiting resources, which for wildebeest is grass (food)
2. 2. The drought reduced the total amount of grass available to support the wildebeest population
3. 3. Therefore, the carrying capacity (K) for wildebeest will decrease, and the new stable population size will be lower than before the drought

> **Exam tip:** Always link changes in carrying capacity to changes in resource availability in exam answers

## Common pitfalls

- **Wrong:** Confusing a population with a community
  - Why it fails: A community includes multiple species, while a population only includes individuals of the same species
  - Correct: Remember: population = one species, community = all species in the same area
- **Wrong:** Claiming carrying capacity is a fixed constant that never changes
  - Why it fails: Carrying capacity depends on environmental conditions, which change over time due to disturbance or climate change
  - Correct: Always evaluate if environmental change has altered resource availability when discussing carrying capacity
- **Wrong:** Assuming all density-independent factors are abiotic and all density-dependent are biotic
  - Why it fails: This is a common generalization, not a rule. Some abiotic factors can be density-dependent
  - Correct: Classify limiting factors by whether their impact depends on population density, not by whether they are biotic or abiotic
- **Wrong:** Thinking exponential growth only occurs in lab settings
  - Why it fails: Exponential growth is common in natural populations during colonization or recovery from disturbance
  - Correct: Recognize exponential growth occurs in wild populations whenever resources are temporarily unlimited

## Cheatsheet

| Term | Key Feature | Curve Shape |
| --- | --- | --- |
| Exponential growth | Unlimited resources, constant growth rate | J-curve |
| Logistic growth | Growth limited by carrying capacity | S-curve |
| Carrying capacity (K) | Maximum sustainable population size | N/A |
| Density-dependent factor | Impact increases with population density | N/A |
| Density-independent factor | Impact unrelated to population density | N/A |

## What's next

Population dynamics forms the foundation for understanding all higher-level ecological interactions, from community structure to ecosystem function. Mastering this sub-topic will help you answer questions about conservation, human impacts on ecosystems, and species interactions that appear frequently on IB Biology SL exams. It connects directly to core themes of interdependence in IB Biology.

- [Nitrogen and nutrient cycling](https://www.owlsprep.com/study/ib-biology-sl-u3-nitrogen-and-nutrient-cycling/)
- [Theme D: Continuity and Change](https://www.owlsprep.com/study/ib-biology-sl-u4-overview/)
- [DNA replication and transcription](https://www.owlsprep.com/study/ib-biology-sl-u4-dna-replication-and-transcription/)

---

From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/ib-biology-sl-u3-population-dynamics/