IB Biology · Theme C · C4.1

Numbers,
in nature.

Populations grow, crash, compete, cooperate. The maths of ecology starts here.

18Sub-topics
0Key terms
SL+HLLevel
EcosystemsLevel of organisation
C4.1
Why this topic

What this topic answers.

Every sub-topic below feeds at least one of these questions.

Topic focus

Populations and Communities.

C4.1.1 – C4.1.18 · Standard & Higher Level

18 things to lock in.

The required syllabus content for C4.1, in order. Each card is one lesson-sized checkpoint.

C4.1.1

Define population; explain reproductive isolation

All individuals of the same species living in a defined area at the same time.

C4.1.2

Distinguish population, community, ecosystem

Distinguish population, community, ecosystem

C4.1.3

Use quadrats for random sampling (NOS)

IB Biology DP | C4.1 Populations and Communities | SL & HL

C4.1.4

Apply Lincoln index (mark-release-recapture)

IB Biology DP | C4.1 Populations and Communities | SL & HL

C4.1.5

Explain carrying capacity (K)

Carrying Capacity (K) — C4.1.5

C4.1.6

Density-dependent factors & negative feedback

Density-dependent factors & negative feedback

C4.1.7

Sigmoid growth curve — phases & K

Sigmoid (S-shaped) Growth — Logistic

C4.1.8

Compare sigmoid vs exponential growth

Compare sigmoid vs exponential growth

C4.1.9

Intraspecific vs interspecific relationships

IB Biology DP | C4.1 Populations and Communities | SL & HL

C4.1.10

Mutualism: root nodules (Fabaceae/Rhizobium) ★HL

Species 1: Legumes (Fabaceae): peas, beans, clover, soy

C4.1.11

Mutualism: mycorrhizae (Orchidaceae) ★HL

Species 1: Orchids (Orchidaceae) — tiny seeds with no endosperm

C4.1.12

Mutualism: zooxanthellae (hard corals) ★HL

Species 1: Hard corals (reef-building) — Scleractinia

C4.1.13

Evaluate invasive species impacts

IB Biology DP | C4.1 Populations and Communities | SL & HL

C4.1.14

Chi-squared test for association (NOS)

IB Biology DP | C4.1 Populations and Communities | SL & HL

C4.1.15

Predator-prey cycles (lynx–snowshoe hare)

IB Biology DP | C4.1 Populations and Communities | SL & HL

C4.1.16

Top-down & bottom-up control

IB Biology DP | C4.1 Populations and Communities | SL & HL

C4.1.17

Allelopathy — black walnut/juglone

The release of chemical compounds by a plant that inhibit the germination or growth of neighbouring plants.

C4.1.18

Antibiotics — Penicillium/penicillin

Antibiotics — Penicillium/penicillin

C4.1.1 / C4.1.2 · Levels of ecology

From individual to ecosystem.

The nested hierarchy of ecology: population → community → ecosystem.

Population

One species

All individuals of the same species in one place at one time. Members can interbreed to produce fertile offspring. Reproductive isolation between populations of the same species can lead to speciation.

Community

Many species

All populations of different species living and interacting in the same area. Includes interactions: competition, predation, mutualism, parasitism.

Ecosystem

+ abiotic

A community plus the non-living environment with which it interacts — soil, water, climate, nutrients.

C4.1.3 / C4.1.4 · Estimating populations

Two methods: quadrats and mark-recapture.

Quadrats for stationary organisms; Lincoln index for mobile ones.

Quadrat sampling

  1. Define the area to be surveyed.
  2. Set up a grid with measuring tapes along two sides.
  3. Generate random coordinates using random number tables.
  4. Place quadrat at each coordinate; count individuals or estimate % cover.
  5. Calculate mean per quadrat; extrapolate to the total area.

Lincoln index (mark-release-recapture)

For mobile species:

⚠️

Five assumptions

  1. Marked individuals mix randomly back into the population.
  2. No significant births, deaths, immigration or emigration.
  3. Mark doesn't affect survival or behaviour.
  4. All individuals are equally likely to be captured.
  5. Marks aren't lost and can be reliably identified.
C4.1.5 / C4.1.6 · Carrying capacity & density dependence

The ceiling, and what enforces it.

No population grows forever. Density-dependent factors create negative feedback that stabilises populations around carrying capacity (K).

As population grows toward K, the per-capita availability of resources falls. Disease spreads more easily. Predators concentrate where prey are dense. Intraspecific competition intensifies. Births fall, deaths rise — bringing the population back down. K is not fixed: if resources change, K changes.

C4.1.7 / C4.1.8 · Sigmoid vs exponential growth

S-shaped or J-shaped.

Two ways populations grow — one bounded by K, one not. In nature, exponential growth is short-lived.

Sigmoid (logistic)

Four phases

Lag — small population; slow growth as organisms acclimatise.
Exponential — abundant resources; rapid growth; births >> deaths.
Deceleration — resources become limiting; growth slows.
Plateau — at K; births ≈ deaths.

Exponential (J)

Unbounded

Each individual contributes the same offspring. Population doubles repeatedly. Only sustained while resources unlimited — early colonisation, invasive introductions, bacterial culture, population recovery from a crash.

C4.1.9 · Interspecies relationships

Five named interactions.

Categorised by who benefits and who's harmed.

RelationshipABExample
Intraspecific competitionMale deer fighting for mates
Interspecific competitionGrey vs red squirrels in UK
Predation+Lynx and snowshoe hare
Mutualism++Clownfish & sea anemone
Commensalism+0Epiphyte on tree
Parasitism+Tapeworm in a mammal
C4.1.10 – C4.1.12 · Three named mutualisms

Plants partnered with bacteria, fungi, and algae.

Three IB-named cases of obligate mutualism, each crucial to an entire ecosystem.

Root nodules

Fabaceae × Rhizobium

Legumes (peas, beans, clover, soy) host Rhizobium bacteria in root nodules. Bacteria fix N₂ → NH₄⁺ using the nitrogenase enzyme — providing nitrogen the plant needs for amino acids. Plant provides carbohydrates and a protected, oxygen-free environment for nitrogenase.

Mycorrhizae

Orchidaceae × fungi

Orchid seeds have no endosperm — they cannot germinate without fungal partners. Fungi provide water, minerals, organic carbon during germination. Once mature, the plant returns carbohydrates from photosynthesis.

Zooxanthellae

Hard corals × Symbiodinium

Reef-building corals host photosynthetic dinoflagellate algae in their tissues. Algae supply up to 90% of coral energy; coral provides shelter, CO₂, and nutrients. Coral bleaching = expulsion of zooxanthellae under heat stress; without them, coral starves.

C4.1.13 · Invasive species

When a species arrives without its enemies.

Non-native species introduced to a new ecosystem often lack natural predators and competitors. They can spread rapidly and devastate native communities.

Grey squirrel

UK

Introduced from North America. Outcompetes the native red squirrel for food and habitat. Carries squirrelpox virus (lethal to red squirrels, not grey). Red squirrel populations now restricted to isolated refugia.

Zebra mussel

North America

From Europe/Asia via ballast water. Filters phytoplankton at huge rates, depleting food for native zooplankton and fish larvae. Outcompetes native mussels for space; colonises water pipes and infrastructure. Ecosystem-wide impact.

C4.1.14 · Chi-squared test

Testing for association.

Are two species found together more (or less) often than expected by chance? The chi-squared test answers this with a single number.

Method:

  1. State H₀: "no association between the two species".
  2. Record data in a 2×2 contingency table (presence/absence).
  3. Calculate expected values: E = (row total × column total) ÷ grand total.
  4. Calculate χ² = Σ [ (O − E)² ÷ E ].
  5. Find degrees of freedom: (rows − 1) × (cols − 1) = 1 for a 2×2 table.
  6. Compare χ² to critical value at p = 0.05 (df=1: critical = 3.841).
  7. χ² > 3.841 → reject H₀; association is statistically significant.

A significant result tells you the species are associated — but not why. They might compete (negative association), or co-require the same conditions (positive association).

C4.1.15 · Predator-prey cycles

Lynx and snowshoe hare.

Hudson Bay Company fur records from the 1800s revealed a striking ~10-year cycle of paired population oscillations.

  1. Abundant vegetation → hare population grows.
  2. More hares → more food for lynx → lynx population grows (after ~1–2 year lag).
  3. Intense predation + vegetation overgrazing → hare population crashes.
  4. Prey scarcity → lynx starves, reproduction falls → lynx population crashes.
  5. Vegetation recovers; hare recovers; cycle repeats every ~10 years.

Lynx peaks always follow hare peaks. Neither population goes extinct — they oscillate around each other indefinitely. Modern analysis shows it's not purely top-down — vegetation availability (bottom-up) also matters.

C4.1.16 · Top-down & bottom-up control

Wolves change rivers.

Populations are controlled by both resource availability (bottom-up) and predators (top-down). The Yellowstone wolf reintroduction is a famous trophic cascade.

Bottom-up

Resources drive

Primary productivity → herbivores → predators. Adding resources at the base ripples up the food web.

Top-down

Predators regulate

Predators limit prey populations, which limit vegetation. Remove apex predators → prey explode → vegetation collapses.

🐺

Yellowstone wolves

Wolves reintroduced in 1995 after 70-year absence. Elk had been overpopulated and overgrazed riparian zones. With wolves back, elk changed behaviour ("landscape of fear") — avoided riverbanks. Willows and aspens recovered → beavers returned → beaver dams stabilised rivers → erosion fell → river meanders reduced. Wolves changed the geomorphology of the park.

C4.1.17 / C4.1.18 · Chemical competition

Allelopathy and antibiotics.

Some organisms compete by releasing chemicals that harm rivals. Two named examples — one botanical, one microbial.

Allelopathy

Black walnut

Juglans nigra produces juglone in roots, hulls and leaves. Juglone inhibits cellular respiration in many sensitive plants — tomatoes, apples, blueberries can't grow underneath. The tree reduces its own competition.

Antibiotics

Penicillium & penicillin

Penicillium mould produces penicillin — kills competing bacteria by blocking peptidoglycan synthesis. Fleming discovered this in 1928 from clear zones around mould colonies on bacterial culture plates. The first antibiotic, and a form of interspecific chemical competition exploited for medicine.

Vocabulary

0 terms to own.

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