Subject: Ecology & Environmental Biology Unit: Mid 2 Theory Assignment Topic No: 02
Ecology · Theory Assignment
Population
Growth Curve
J-Curve & S-Curve · Phases · Factors · Equations
Format: A3 Single Sheet Level: Undergraduate Year: 2026
① What is Population Growth?

Population growth is the change in the number of individuals in a population over time, determined by the balance of birth rates, death rates, immigration, and emigration.

When resources are unlimited, populations grow exponentially (J-curve). When resources are limited, environmental resistance slows growth until it stabilises at the carrying capacity (K), producing an S-shaped curve.

ΔN/Δt = rN     (Exponential)
ΔN/Δt = rN[(K−N)/K]   (Logistic)

N = population size · r = intrinsic growth rate · K = carrying capacity

② Key Terms
  • Birth Rate (Natality): Number of new individuals added per unit time
  • Death Rate (Mortality): Number of individuals dying per unit time
  • Carrying Capacity (K): Max population an environment can sustain
  • Biotic Potential (r): Maximum possible growth rate under ideal conditions
  • Environmental Resistance: All limiting factors that reduce growth
  • Overshoot: Population temporarily exceeds K, then crashes
③ Phases of the S-Curve (Logistic)
1
Lag Phase Slow initial growth; population is small, individuals adapting to environment. Low reproductive rate.
2
Exponential (Log) Phase Rapid increase; resources are ample. Birth rate >> Death rate. Steepest part of curve.
3
Deceleration Phase Growth slows as resources become scarce. Environmental resistance intensifies.
4
Stationary (Plateau) Phase Population stabilises at K. Birth rate = Death rate. Dynamic equilibrium.
5
Decline Phase If K is exceeded, population may crash due to resource depletion and disease.
④ Phases of J-Curve (Exponential)
  • Slow start: Small initial population, limited reproduction
  • Acceleration: Each generation larger than the last; resources appear unlimited
  • Rapid explosion: Population doubles at constant intervals
  • Crash: Sudden collapse when resources are exhausted (no K regulation)
★ Examples: Bacterial cultures, locust swarms, algal blooms, introduced invasive species
⑤ Factors Affecting Population Growth

Biotic Factors (Density-Dependent)

Food competition Predation Parasitism Disease Intraspecific competition Reproductive rate

Abiotic Factors (Density-Independent)

Temperature Rainfall Natural disasters Drought Floods Pollution

Human Factors

Urbanisation Hunting Habitat destruction Conservation
⑥ Real-World Examples
  • J-Curve: Rabbits introduced to Australia (1859) — no natural predators → explosive growth → ecological damage
  • S-Curve: Sheep population on Tasmania — grew rapidly then stabilised around K ≈ 1.7 million
  • Human Population: Follows J-curve; approaching resource limits; ~8 billion in 2024
  • Yeast in culture: Classic S-curve — exponential, then plateau as alcohol accumulates
📈 Graphical Representation of Population Growth Curves
J-Shaped Curve — Exponential Growth
Population Size (N) Time → 0 Low Mid High Crash! Lag Exponential ↑ Rapid rise No Carrying Capacity → Overshoot & Crash
S-Shaped Curve (Sigmoid) — Logistic Growth
K Carrying Capacity (K) Population Size (N) Time → 0 Low K/2 K Lag Log Phase Decel. Plateau Inflection (K/2) Stabilises at K — Sustainable Growth
⑦ J-Curve vs S-Curve Comparison
Feature J-Curve S-Curve
Shape J-shaped Sigmoid (S)
Growth type Exponential Logistic
Carrying capacity Absent Present (K)
Resources Unlimited Limited
Env. resistance None/Sudden Gradual
Outcome Crash Stabilisation
Example Bacteria, locusts Deer, sheep
Equation dN/dt = rN dN/dt = rN(K-N)/K
⑧ r-selection vs K-selection

Organisms are adapted to either maximise growth rate (r) or stabilise near K:

Trait r-Strategists K-Strategists
Lifespan Short Long
Offspring Many, small Few, large
Parental care None/little Extensive
Maturity Early Late
Population Boom & bust Stable near K
Examples Insects, mice Elephants, whales
⑨ Ecological Significance
  • Helps predict species extinction risk and sustainable population levels
  • Guides wildlife conservation and protected area management
  • Used in fisheries management to set harvest quotas (Maximum Sustainable Yield = K/2)
  • Informs invasive species control — detect J-curve before crash
  • Supports human demographic models for urban planning & resources
✓ Summary

Population growth curves reveal how populations change over time. The J-curve models unchecked exponential growth leading to collapse, while the S-curve models realistic logistic growth regulated by carrying capacity. Understanding these curves is fundamental to ecology, conservation, and sustainable resource management.

POPULATION GROWTH CURVE · ECOLOGY THEORY ASSIGNMENT J-Curve (Exponential) · S-Curve (Logistic) · r & K Selection · Carrying Capacity MID 2 ASSIGNMENT · A3 FORMAT · 2026