Lesson 10: Populations and Communities

This lesson covers Theme C — populations and communities (SL and HL): how populations grow, what limits them, and how species interactions structure communities. Key IB tools: population growth curves, the Lincoln index for mark–release–recapture, Simpson's diversity index, and chi-square tests for species association.

Population growth: exponential and logistic

With unlimited resources a population grows exponentially — a J-shaped curve, with a constant per-capita growth rate and a characteristic doubling time (e.g. bacteria doubling every 20 minutes reach astronomic numbers within a day, which is precisely why resources never stay unlimited). Real growth is logistic: an S-shaped (sigmoid) curve as density-dependent factors (competition for food and space, predation, disease, accumulation of waste) bite harder as numbers rise, until growth levels off at the carrying capacity (K) — the maximum population the environment can sustain long-term. Density-independent factors (frost, flood, drought) strike regardless of density. Phases of the sigmoid curve to label: exponential (log) phase, transitional phase (growth slowing), plateau phase (birth rate ≈ death rate, population fluctuates around K). Human population growth is the classic discussion case: it has followed an exponential-like trajectory, with debate about whether a logistic plateau (demographic transition) or overshoot follows.

Interactions within communities

Species interactions are classified by their effects (+/−/0): predation (+/−), herbivory (+/−), parasitism (+/−, parasite benefits, host harmed but usually not killed outright), mutualism (+/+, e.g. bees and flowers; mycorrhizal fungi and roots; zooxanthellae and corals), commensalism (+/0), and competition (−/−), which may be intraspecific (within a species — usually the most intense, since niches overlap completely) or interspecific. Two species competing for exactly the same limiting resource cannot coexist indefinitely — competitive exclusion — unless niches differentiate (resource partitioning, as in Darwin's finches or warblers feeding at different tree heights). Predator–prey systems can cycle (lynx–hare data are the textbook case), though examiners reward noting that real hare cycles also involve food supply and stress physiology, not predation alone. Top-down control (predators limit herbivores, which releases plants — keystone predators such as sea otters) contrasts with bottom-up control (nutrient supply limits producers, cascading up).

Sampling populations quantitatively

Sessile or slow organisms are sampled with quadrats: random placement using coordinates removes bias; abundance is recorded as density, percentage cover or frequency. For mobile animals, mark–release–recapture gives the Lincoln index: population size N = (n₁ × n₂) ÷ m, where n₁ = number marked and released, n₂ = number caught in the second sample, m = marked individuals in the second sample. Worked example: 48 woodlice marked and released; second sample catches 60, of which 12 are marked. N = (48 × 60) ÷ 12 = 240. Assumptions — the method stands or falls on them: marked individuals mix randomly with the population; marking does not affect survival or catchability; no significant immigration, emigration, births or deaths between samples; marks are not lost. Diversity is summarised by Simpson's index: D = 1 − Σ n(n−1) / N(N−1), where n is the count per species and N the total; D runs from 0 (no diversity) towards 1 (high diversity). Worked example: counts 20, 12, 8 (N = 40): Σn(n−1) = 380 + 132 + 56 = 568; N(N−1) = 1,560; D = 1 − 0.364 = 0.636. Comparing D between habitats (e.g. grazed vs ungrazed, trampled path edge vs centre) with replicated quadrats is a strong, classic IA.

Testing association between species

To test whether two species are associated (found together more or less often than chance), use quadrat presence/absence data in a 2×2 contingency table and a chi-square test (df = 1): expected frequencies assume independence. Significant positive association may reflect shared habitat preference rather than direct interaction — a distinction examiners probe; association is not causation, and abiotic factors usually explain co-occurrence.

Nature of Science / TOK link

K and carrying capacity look like constants of nature but are model outputs that shift with season, climate and community change. TOK: every index (Lincoln, Simpson) *creates* the quantity it measures by its assumptions; knowing the assumptions is knowing the limits of the knowledge. Field ecology also raises an ethical strand — mark–recapture and sampling should minimise harm to organisms and habitats.

Common mistakes (from examiner reports)

• Applying the Lincoln index with samples where marking made animals more visible to predators — assumption violations must be named in evaluations.
• Computing Simpson's index with percentages instead of counts, or reporting D without interpreting it comparatively.
• Describing mutualism as "both help each other" without specifying the benefit each partner gains.
• Claiming the plateau phase means "no births" — births and deaths balance.

IB Exam Experience

Paper 1 style. 1. In a mark–release–recapture study, 80 fish were marked. A second sample of 50 contained 10 marked fish. The estimated population is… A. 160 B. 250 C. 400 D. 800 2. Which factor is density-dependent? A. A flood B. A late frost C. Disease spread in a crowded population D. A volcanic eruption 3. In mutualism… A. one species benefits, the other is harmed B. both species benefit C. one benefits, the other is unaffected D. both are harmed Answer key. 1 — C (80 × 50 ÷ 10). 2 — C. 3 — B. Paper 2 style. Quadrat sampling of two grassland species gave these counts in 20 quadrats across a field: Species A present in 15, Species B in 12, both present in 11, neither in 4. (a) State whether the observed co-occurrence is greater or less than expected if the species were independent. [2] (b) Suggest two explanations for the pattern that do not involve direct interaction. [2] *Marking notes.* (a) Expected both-present under independence = (15/20) × (12/20) × 20 = 9; observed 11 > 9, so positive association (full chi-square: χ² ≈ 1.9, df 1, not significant at 5% — accept either conclusion if chi-square is correctly computed and compared with 3.84) [2]. (b) Both prefer the same microhabitat (e.g. moister, less trampled areas); shared response to an abiotic gradient such as soil pH or light [2]. IA idea. Compare Simpson's diversity index and species composition between two contrasting microhabitats (e.g. mown vs unmown grass, sunny vs shaded wall base), using random quadrats and a statistical test of difference.

Extended data: succession — how communities assemble

Ecological succession is the directional change in community composition over time: pioneer species colonise (lichens and mosses on bare rock; grasses on sand dunes), modify the environment (soil builds, shade falls, moisture holds), and thereby enable later species, which out-compete the pioneers — until a relatively stable climax community forms, set by climate. On sand dunes the sequence runs: embryo dunes (sand couch grass tolerating burial and salt) → mobile dunes (marram grass, deep roots, traps more sand) → fixed dunes (soil and humus accumulate, grasses and herbs diversify) → dune heath/woodland. Each stage can be sampled with the Lesson 10 toolkit — a transect from the strandline inland is a living time-line (space-for-time substitution), and Simpson's index typically rises along it as niches multiply. Primary succession starts from no soil; secondary succession (after fire, abandonment of farmland) starts from soil and seed banks and is much faster. Disturbance is not an exception but a driver: many ecosystems (savannas, heathlands) are *arrested* successions maintained by fire or grazing — remove the grazers and scrub invades, a conservation-management dilemma that makes excellent discussion material.

Keystone species and trophic cascades — the sea otter case

Robert Paine's removal experiments with the starfish *Pisaster* coined the keystone species concept: a species whose effect on the community is disproportionate to its abundance. The best-documented cascade runs through sea otters, sea urchins and kelp forests off the Aleutian Islands: where otters thrive, they eat urchins, kelp forests flourish, and the forests shelter fish, invertebrates and carbon-storing biomass; where otters were hunted out (and later, where killer whales shifted to eating otters), urchins exploded, kelp was grazed to barrens, and the community restructured. Three lessons for exam answers: define the keystone by *effect relative to abundance*, not by being a top predator per se; trace the cascade level by level with signs (+/− alternation); and note the carbon connection — kelp forests protected by otters store measurably more carbon, an ecosystem-service argument now used in conservation policy. Data questions give otter/urchin/kelp abundances across islands and ask you to *deduce* the interaction web — exactly this pattern.

One more application: biological control — using interactions instead of chemicals

Classical biological control imports a natural enemy of a pest: the vedalia beetle saved California's citrus industry from cottony cushion scale in the 1880s within two years of release, and remains the textbook success. The failures are equally instructive: cane toads, introduced to Australia for cane beetles, ignored the beetles and poisoned native predators instead — a Lesson 11/12 object lesson in why host-specificity testing (does the agent attack non-targets?) is now mandatory before release. For exam purposes, structure any biocontrol evaluation as: mechanism (which interaction from this lesson — predation, parasitism, competition), evidence (population data before/after, ideally Simpson indices and pest counts), specificity and reversibility (chemicals can be stopped; released organisms usually cannot), and the monitoring plan. That structure converts a story into an evaluation.

Examiner's lens: final drills (populations)

• Lincoln index assumptions, compressed: marks persist, marked animals mix and are neither favoured nor avoided by predators/samplers, population is closed during the study, and marking does not harm. Quote the index formula with the symbols defined — unnamed symbols lose the communication mark.
• Simpson's index direction check: this syllabus form, D = 1 − Σn(n−1)/N(N−1), gives values near 1 for *high* diversity. Some texts define the reciprocal or the raw sum instead — state your formula so your interpretation is unambiguous.
• Interaction matrix speed drill (+ benefits, − harmed, 0 unaffected): predation +/−, mutualism +/+, commensalism +/0, competition −/−, parasitism +/− (distinguished from predation by size, duration and lethality).
• Self-test: a population's growth curve flattens while food remains abundant but waste accumulates and disease spreads — which class of limiting factors is operating? (Density-dependent.)