Density Dependence

From Exponential Growth to Density Dependence

Start from:

dN/dt = rN

This implies:

• Constant per capita growth rate rr

• No feedback from population density

Why This Fails in Reality

Biological systems are constrained by:

• Finite energy flow (primary productivity limits food webs)

• Space limitation (territories, nesting sites)

• Waste accumulation (toxic by-products in microbes)

Mechanistic Basis of Density Dependence

Density dependence is not a single process—it is the emergent result of multiple interacting mechanisms:

(A) Resource Competition

• Exploitative (indirect) competition

• Interference (direct) competition

(B) Disease Transmission

• Higher density → higher contact rate

• Classic epidemiological scaling

(C) Behavioural Stress

• Aggression

• Hormonal suppression of reproduction

(D) Predation (functional + numerical responses)

• Predators concentrate where prey density is high

Density dependence integrates ecological, behavioural, and physiological processes across levels of organisation.

At low density

• Birth rate > death rate → population grows

At high density:

• Death rate > birth rate → population declines

At equilibrium:

• Birth rate = death rate → carrying capacity (K)

Carrying Capacity (K) – Not a Fixed Number

Mechanistic Interpretation

Your slide shows:

• Birth rate declines with density

• Death rate increases with density

Intersection = K

Why K is Dynamic

K varies with:

• Climate (e.g. drought reduces K)

• Resource pulses (e.g. mast years increase K)

• Species interactions

Carrying capacity is better viewed as a moving equilibrium, not a fixed ceiling

Case Study Link: Red deer on Isle of Rum

Study: Tim Clutton-Brock

Findings:

• Population does not stabilise at a single value

• Fluctuates around K depending on winter severity

Key mechanism:

• Harsh winters reduce food → lower survival → temporary drop in K

Logistic Growth – Beyond the Curve

dN​/dt = rN((K−N​)/K)

Mechanistic Breakdown

• rN → exponential growth component

• (K−N)/K → strength of density dependence

Important Interpretation

• When N≪K : growth ≈ exponential

• When N≈K : growth slows sharply

Experimental evidence Case Study: Paramecium aurelia

Experiment: Georgy Gause (1934)

Experimental Design

• Cultured in controlled lab conditions

• Varied:

  • Food (bacteria)

  • Light

Results

• Populations followed logistic growth

• Plateau differed by treatment

Mechanism

• Food limitation → reduced reproduction

• Waste accumulation → increased mortality

Evaluation

Strength:

• Controlled conditions isolate density effects

Limitation:

• Oversimplifies natural ecosystems

Experimental evidence Case Study: Tribolium confusum

Experiment: Georgy Gause (1931)

Findings

• Population grows → plateaus

• Higher flour → higher K

Mechanisms

• Larval competition for food

• Cannibalism (eggs and larvae eaten)

Density dependence can operate through unexpected mechanisms (e.g. cannibalism).

Density-Dependent Dispersal Case study: Africanized honey bee

Background

• Introduced in Brazil (1956)

• Hybridised with European bees

Key Data

• Spread rate: 300–500 km/year

• Reached most of South and Central America by 2000

Mechanism

• High density → increased swarming frequency

• Colony fission creates new populations

Ecological Impact

• Displacement of native bees

• Altered pollination networks

Density-Dependent Dispersal Case study: Eurasian collared dove

Expansion Timeline

• Origin: Turkey

• 1930s → Eastern Europe

• 1980s → Entire Europe

Mechanism

• Density-dependent dispersal

• High reproductive rate

Dispersal allows populations to avoid local density limits by expanding spatially.

Density-Dependent Dispersal Case study: Blackfly

• Dispersal increases logarithmically with larval density

Interpretation: Individuals respond nonlinearly to crowding, suggesting threshold effects.

Density-Dependent Morphology (Phenotypic Plasticity)

Concept: Phase Polyphenism

Same species → different forms depending on density

Case study: Desert locust

Mechanism

• Physical contact triggers serotonin release

• Leads to:

  • Colour change

  • Behavioural shift

  • Swarm formation

Ecological Consequence

• Swarms travel hundreds of km

• Massive agricultural damage

Density-Dependent Morphology (Phenotypic Plasticity)

Concept: Phase Polyphenism

Same species → different forms depending on density

Case study: Pea aphid

Mechanism

• Crowding → hormonal signal → wing development

Adaptive Value

• Enables escape from overcrowded host plants

Insight: Density dependence can operate via developmental plasticity, altering life-history trajectories

Density-Dependent Growth (Individual Level → Population Level) case study: Indian bullfrog

Findings

• High density → reduced growth rate

• Smaller adult size

Mechanism

• Reduced per capita food availability

Density-Dependent Growth (Individual Level → Population Level) case study: Seed beetle

Findings

• Increased larval density per seed → reduced adult mass

• Females remain larger (sexual dimorphism)

Mechanism

• Competition within a fixed resource unit (seed)

Insight: Growth limitation feeds forward into reproductive output, amplifying density dependence.

Density-Dependent Fertility case study: harp seal

Findings

• Increased population size → delayed reproduction

Mechanism

• Reduced body condition due to competition

Density-Dependent Fertility case study: American bison

Findings

• Fertility declines nonlinearly with density

Mechanism

• Nutritional stress

• Social hierarchy effects

Density-Dependent Fertility case study: Red deer

Findings

• Proportion of breeding females declines linearly with density

Mechanism

• Food limitation → reduced ovulation rates

Fertility is highly sensitive to density because reproduction is energetically expensive.

Density-Dependent Mortality case study: Soay sheep

Long-Term Study (St Kilda)

Findings

• Mortality increases with population size

• Lamb mortality highest

Mechanisms

1. Starvation (limited vegetation)

2. Parasites (strongyles)

3. Weather interactions

Key Detail

• Parasite load increases with density

• Females often more affected

Insight: Mortality often shows threshold responses, leading to sudden population crashes.

Full Density-Dependent Feedback System

At high density:

Trait	Direction
Dispersal	↑
Growth	↓
Fertility	↓
Mortality	↑

Combined effect: Population growth slows → stabilises → fluctuates around K

Real-World Logistic Growth: COVID-19

Study: Evgeny Pelinovsky et al. (2020)

Observed Pattern

• Initial exponential growth

• Slowing phase

• Plateau

Mechanisms

• Behavioural changes

• Immunity

• Public health interventions

Insight: Density dependence applies to disease systems, not just ecological populations.

r vs K Selection

r-selected Example:

• Pacific oyster

  • ~500 million eggs/year

  • High juvenile mortality

K-selected Example:

• Chimpanzee

  • One offspring every ~5 years

  • High parental investment

Mechanistic Difference

Trait	r-selected	K-selected
Environment	Unstable	Stable
Density	Low	High
Strategy	Rapid reproduction	Competitive survival

Life-history strategies reflect adaptation to density-dependent selection pressures.

Invasive Species and Density Dependence Case Study: Atlantic blue crab

Findings

• Rapid spread across Mediterranean

• Became dominant predator

Key Insight: Early invasion = weak density dependence → rapid growth

Invasive Species and Density Dependence Case Study: Red lionfish

Study: Caroline Benkwitt (2013)

Findings

• Growth rate declines with density

• Recruitment not density-dependent

Critical Insight: Different life-history stages respond differently to density.

r-selected species

• High reproduction

• Low parental care

• Short lifespan

k-selected species

• Low reproduction

• High parental care

• Long lifespan