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This lesson covers population growth curves, carrying capacity, density-dependent and density-independent factors, and predator-prey relationships, as required by the Edexcel A-Level Biology specification (9BI0), Topic 10 -- Ecosystems.
A population is all the organisms of one species living in a particular area at a particular time. The size of a population is determined by the balance between factors that increase it (births, immigration) and factors that decrease it (deaths, emigration).
Population change=(Births+Immigration)−(Deaths+Emigration)
When a population colonises a new, resource-rich environment with no limiting factors, it can grow exponentially -- the rate of increase is proportional to the current population size.
Characteristics:
In reality, resources are limited. The logistic growth curve has four phases:
| Phase | Description | Birth Rate vs Death Rate |
|---|---|---|
| Lag phase | Population is small; individuals are adjusting to the new environment; growth is slow | Birth rate slightly exceeds death rate |
| Log (exponential) phase | Resources are abundant; birth rate exceeds death rate; population grows rapidly | Birth rate >> death rate |
| Deceleration phase | Resources become limiting; growth rate slows as competition increases | Birth rate still exceeds death rate, but the gap narrows |
| Stationary (plateau) phase | Population reaches the carrying capacity (K); birth rate equals death rate; population fluctuates around K | Birth rate ≈ death rate |
graph LR
subgraph "Population Growth Curve"
A["Lag\nphase"] --> B["Log\n(exponential)\nphase"]
B --> C["Deceleration\nphase"]
C --> D["Stationary phase\n(at carrying\ncapacity K)"]
end
The carrying capacity (K) is the maximum population size that an environment can sustain indefinitely given the available resources (food, space, water, shelter, etc.).
| Factor | Effect on K |
|---|---|
| Increased food supply | K increases |
| Habitat destruction | K decreases |
| Introduction of a new predator | K decreases |
| Improved shelter availability | K increases |
| Disease outbreak | K decreases (temporarily or permanently) |
| Climate change (warming in temperate regions) | May increase K for some species and decrease it for others |
These factors have a greater effect as population density increases. They act as negative feedback mechanisms that regulate population size around K.
| Factor | How It Operates | Example |
|---|---|---|
| Intraspecific competition | As density increases, individuals compete more intensely for food, space, mates | Red deer on Rum: higher density leads to lower birth rates and higher calf mortality |
| Predation | More prey in a given area attracts more predators or allows them to catch prey more easily | Lynx-hare cycles in Canada (Hudson Bay Company fur records) |
| Disease | Infectious diseases spread more rapidly in dense populations | Myxomatosis in UK rabbit populations; COVID-19 in dense human populations |
| Parasitism | Parasites spread more easily in dense host populations | Varroa mite in honeybee colonies |
| Accumulation of waste | Toxic waste products build up faster in dense populations | Yeast populations in wine-making (ethanol accumulates) |
These factors affect populations regardless of density. They do not regulate population size around K.
| Factor | Example |
|---|---|
| Natural disasters | Floods, volcanic eruptions, fires |
| Extreme weather | The 2018 UK heatwave reduced water levels in rivers, killing fish regardless of population density |
| Pollution events | Deepwater Horizon oil spill (2010) -- affected marine life irrespective of population density |
| Human activity | Habitat destruction, deforestation |
Exam Tip: Density-dependent factors are the key regulators of population size because they provide negative feedback. As the population grows above K, these factors intensify and bring the population back down. Density-independent factors cause fluctuations but do not regulate the population around K. In exam answers, make sure you explain the feedback mechanism -- not just list the factors.
Predator and prey populations often show linked, oscillating cycles:
Key features of the cycle:
The Hudson Bay Company fur records from the 1840s--1930s show classic predator-prey oscillations with approximately 10-year cycles:
Species can be broadly classified by their reproductive strategies:
| Feature | r-Strategist | K-Strategist |
|---|---|---|
| Reproduction | Many offspring; little parental care | Fewer offspring; high parental care |
| Maturation | Rapid maturation | Slow maturation |
| Lifespan | Short | Long |
| Body size | Small | Large |
| Population growth | Rapid; boom-and-bust cycles | Slow; population close to K |
| Environment | Unpredictable or newly colonised | Stable; competitive |
| Succession stage | Pioneer / early succession | Climax / late succession |
| Examples | Bacteria, insects, dandelions, annual plants | Elephants, whales, oak trees, albatrosses |
Key Link: This connects directly to the ecological succession topic. Pioneer species in early succession tend to be r-strategists (fast reproduction, high dispersal). Climax species tend to be K-strategists (slow reproduction, competitive ability). This explains why community composition changes during succession.
Question: A population of rabbits on an island increases from 50 to 200 over 2 years, then stabilises at approximately 180. Explain the growth pattern.
Answer:
Initially, the rabbit population was in the lag phase (small population adjusting to the environment). As resources were abundant and there were few predators or competitors, the population entered the exponential (log) phase, growing rapidly from 50 to 200.
As the population approached 200, density-dependent factors such as intraspecific competition for food and burrow space intensified. Disease may have spread more easily in the denser population. Birth rate decreased and death rate increased until they were approximately equal.
The population stabilised at approximately 180, which represents the carrying capacity (K) of the island -- the maximum number of rabbits the island can sustainably support given the available food, water, and shelter. The population fluctuates around this value.
Question: A population of 500 organisms has a birth rate of 60 per year and a death rate of 45 per year. There is no immigration or emigration. Calculate (a) the net population growth per year, (b) the per capita growth rate.
Answer:
(a) Net population growth: Growth=Births−Deaths=60−45=15 individuals per year
(b) Per capita growth rate: r=NBirths−Deaths=50015=0.03 per individual per year
This means each individual contributes 0.03 individuals to the population per year (a 3% growth rate).
Question: The graph below shows the population sizes of a prey species and its predator over 20 years. The prey population peaks at years 3, 10, and 17. The predator population peaks at years 5, 12, and 19. Explain the relationship.
Answer:
The predator population peaks approximately 2 years after the prey population, showing a classic predator-prey cycle with a time lag. When prey numbers are high (year 3), there is abundant food for predators, so the predator birth rate increases and the predator population grows, peaking at year 5. The increased predator numbers then reduce the prey population (through predation), causing the prey to decline. With less food available, the predator population then also declines. As predator numbers fall, prey survival improves and the prey population begins to recover, starting the cycle again.
The 2-year time lag reflects the time needed for predators to reproduce and for their young to mature, as well as the time it takes for starvation and reduced reproduction to cause the predator population to decline.
"Carrying capacity is a fixed number." K varies with environmental conditions. A drought, habitat destruction, or arrival of a new competitor can all lower K. An increase in food supply can raise K.
"Populations always reach carrying capacity." Some populations experience boom-and-bust cycles (especially r-strategists) where the population overshoots K and then crashes due to resource depletion, before recovering.
"Predators control prey populations." In reality, prey populations are controlled by a combination of factors, including predation, food availability, disease, and intraspecific competition. Predation alone rarely explains population regulation.
Population dynamics is the quantitative study of how the size and structure of a population change in time and space, and why. The Edexcel 9BI0 treatment turns on four moves: the logistic (sigmoid) growth model with its characteristic phases and asymptote at the carrying capacity K; the contrast between density-dependent regulation (negative feedback that holds populations near K) and density-independent disturbance (non-regulatory perturbation); interspecific dynamics — predator–prey oscillation and competitive exclusion in shared niches; and the estimation of population size from quadrat and mark-release-recapture data. This deep dive deepens each with explicit equations, a worked predator–prey calculation, named UK and global case studies and the mark-scheme literacy needed for Paper 2 Section B.
The Edexcel 9BI0 specification places population dynamics in Topic 5: On the Wild Side — Photosynthesis, Energy and Ecosystems, on Paper 2 (Energy, Exercise and Coordination). This is the quantitative-ecology lesson of Topic 5, treating single-species populations and their pairwise interactions. Statements concern: the definition of a population; the four growth-curve phases (lag, log, deceleration, stationary); carrying capacity K; the contrast between J-curve (exponential) and S-curve (logistic) models; density-dependent factors (intraspecific competition, predation, disease, parasitism, waste accumulation) acting as negative feedback; density-independent factors (drought, fire, frost, flood, pollution incidents) acting irrespective of density; predator–prey oscillations with phase lag; interspecific competition and the competitive exclusion principle; fundamental vs realised niche and resource partitioning; and population estimation by mark-release-recapture and quadrat sampling — refer to the official Pearson Edexcel 9BI0 specification document for exact wording. Synoptic links radiate to lesson 5 — Ecological Succession (r/K-strategist contrast across seres), lesson 7 — Investigating Ecosystems (the empirical methodology of estimation), lesson 1 — Ecosystems and Communities (the niche concept), lesson 8 — Climate Change (range shifts and demographic responses), and Topic 7 — Run for Your Life (the human demographic transition as an applied case).
Question (8 marks):
A population of red deer (Cervus elaphus) was reintroduced to a fenced 50 km² UK upland reserve in 2010. The recorded population sizes (in October each year) are: 2010 — 24; 2012 — 78; 2014 — 240; 2016 — 510; 2018 — 670; 2020 — 695; 2022 — 690; 2024 — 692.
(a) Identify the growth-curve phase that operates between 2010 and 2014, justify your choice with a calculation, and predict the per-capita growth rate r between 2010 and 2012. (3)
(b) Identify the phase between 2018 and 2024 and explain two density-dependent factors that account for this trajectory in red deer. (3)
(c) The reserve manager removes the fencing in 2025 and a wolf reintroduction releases a pack of 6 wolves the same year. Predict, with reasoning, the trajectory of the deer population over the following decade. (2)
Solution with mark scheme:
(a) M1 (AO2.1) — between 2010 and 2014 the population rose from 24 to 240, a 10-fold increase in four years, consistent with the log (exponential) phase in which birth rate greatly exceeds death rate and resources are not yet limiting. M1 (AO2.1) — over the 2010–2012 step the per-capita growth rate is r = \ln(N_t / N_0) / t = \ln(78/24) / 2 = \ln(3.25)/2 ≈ 0.59 per individual per year (accept 0.55–0.62; equivalent to ~80% per year if expressed as λ = N_t/N_0 per year). A1 (AO1.2) — the underlying mechanism is that with abundant food, low predation pressure and few competitors, every reproducing female contributes near-maximal offspring, so each new individual itself reproduces — growth is multiplicative, not additive.
(b) M1 (AO1.1) — the population has reached the stationary phase and is fluctuating around a carrying capacity of K ≈ 690 deer (about 13.8 deer km⁻²), at which birth rate and death rate are approximately equal. M1 (AO1.2) — density-dependent factor 1: intraspecific competition for grazing — at high densities forage per animal falls, body condition deteriorates, calving rates fall and over-winter calf mortality rises (well-documented in the Isle of Rum red-deer study). A1 (AO1.2) — density-dependent factor 2: disease and parasitism — louping-ill virus, lungworm and tick load all transmit more efficiently at high host density, raising adult and juvenile mortality (accept accumulation of nutrient-poor heavily grazed sward, or behavioural stress raising cortisol and reducing fecundity).
(c) M1 (AO2.1) — predict an initial decline over years 1–3 as wolf predation imposes new mortality on a population already at K; deer numbers fall well below the previous K because they were nutrition-stressed and are now also predator-stressed. M1 (AO3.2a) — over years 4–10, expect classic predator–prey oscillation: deer decline → wolves decline (lagged by 1–2 deer-generations) → deer recover → wolves recover, with a new dynamic equilibrium at lower mean deer density and a now-rejuvenated upland flora (the Yellowstone trophic-cascade analogue). Removal of fencing also raises effective carrying capacity by adding lowland habitat, partially offsetting the predation effect.
Total: 8 marks.
Question (6 marks): Explain how density-dependent and density-independent factors together shape the trajectory of a real population, and evaluate why the logistic (sigmoid) model captures regulation more faithfully than the exponential (J-shaped) model.
Mark scheme decomposition by AO:
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