Equation: dN/dt = r_max × N

• N = population size
• t = time
• r_max = maximum per capita growth rate

Characteristics:

• J-shaped curve
• Continuous acceleration
• Unsustainable long-term

Examples:

• Bacteria in fresh medium
• Invasive species (initially)
• Populations after disturbance

Logistic Growth (S-curve)

Occurs when:

• Limited resources
• Carrying capacity exists

Equation: dN/dt = r_max × N × (K - N) / K

• K = carrying capacity (maximum sustainable population)

Characteristics:

• S-shaped curve
• Slows as approaches K
• Levels off at K

Phases:

1. Lag: Slow initial growth
2. Exponential: Rapid growth
3. Deceleration: Slowing growth
4. Plateau: Stable at K

Carrying Capacity (K)

Definition: Maximum population size environment can sustain

Determined by:

• Food availability
• Water
• Space
• Shelter
• Waste accumulation

Populations:

• May fluctuate around K
• Can temporarily exceed K (overshoot)
• Resource depletion if exceed K

Limiting Factors

Density-Dependent Factors

Effect increases with population density:

• Competition (food, space, mates)
• Predation
• Disease/parasites
• Accumulation of wastes
• Stress/hormonal changes

Density-Independent Factors

Effect regardless of density:

• Weather (temperature, precipitation)
• Natural disasters (fire, flood, earthquake)
• Seasonal cycles
• Human activities

Reproductive Strategies

r-Selected Species

Maximize growth rate (r):

• Many offspring
• Small body size
• Short lifespan
• Little parental care
• Fast maturation
• Opportunistic
• Examples: Insects, weeds, mice

K-Selected Species

Maximize carrying capacity (K):

• Few offspring
• Large body size
• Long lifespan
• Extensive parental care
• Slow maturation
• Competitive in stable environments
• Examples: Elephants, whales, humans

Survivorship Curves

Type I:

• High survival early/middle life
• Death mainly in old age
• K-selected species
• Example: Humans, elephants

Type II:

• Constant death rate
• Equal probability at any age
• Example: Birds, rodents

Type III:

• High death rate early
• Survivors live long
• r-selected species
• Example: Fish, invertebrates, plants

Human Population Growth

Historical pattern:

• Exponential growth
• Industrial revolution accelerated growth
• Medical advances reduced death rates

Current:

• ~8 billion people
• Growth rate slowing but still increasing
• Approaching carrying capacity?

Demographic transition:

• Stage 1: High birth/death rates
• Stage 2: Death rate drops
• Stage 3: Birth rate drops
• Stage 4: Low birth/death rates (stable)

Factors affecting:

• Economic development
• Education (especially women)
• Access to contraception
• Cultural/religious factors

Key Concepts

1. Exponential growth: J-curve, unlimited resources
2. Logistic growth: S-curve, limited by carrying capacity
3. Carrying capacity (K): Maximum sustainable population
4. Density-dependent factors increase with density
5. r-selected: many offspring, little care, opportunistic
6. K-selected: few offspring, much care, competitive
7. Survivorship curves: Type I (humans), II (constant), III (high early death)