Population Dynamics

Exponential Population Growth:

Definition: Population growth at a constant rate, producing a J-shaped curve. Growth rate increases over time as population size increases.

EQUATION: dN/dt = rN

Where: • dN/dt = change in population size over time (growth rate) • r = per capita rate of increase (intrinsic growth rate) • N = population size

Alternatively: Nₜ = N₀e^(rt)

Where: • Nₜ = population size at time t • N₀ = initial population size • e = base of natural logarithm (≈2.718) • r = per capita growth rate • t = time

Characteristics:

1. CONSTANT r • Birth rate - death rate stays constant • r does not change with population size • Per capita growth rate fixed

2. J-SHAPED CURVE • Slow start (small N) • Increasingly rapid growth • Curve gets steeper over time • No upper limit

3. ACCELERATING GROWTH • More individuals → more reproduction • Positive feedback loop • Doubling time constant • Growth rate (dN/dt) increases continuously

Graph: Population ↑ │ ╱ │ ╱ │ ╱ │ ╱ │ ╱ │ ╱ │╱ └──────────→ Time (J-shaped curve)

Conditions for Exponential Growth:

1. UNLIMITED RESOURCES • Food always available • No resource competition • Water abundant • Space unlimited

2. NO PREDATORS/DISEASE • No mortality from predation • No disease transmission • No parasites

3. NO EMIGRATION • All offspring stay in population • No dispersal losses

4. IDEAL ENVIRONMENT • Optimal temperature • No environmental stress • No toxic waste accumulation

5. NO DENSITY-DEPENDENT FACTORS • No competition • No social stress • Unlimited breeding sites

When Does Exponential Growth Occur?

1. Small population in large habitat • Resources seem unlimited • Example: Invasive species first introduced

2. Recovery after disturbance • Population below carrying capacity • Example: Recolonization after fire

3. Laboratory conditions • Bacteria in fresh culture medium • Controlled ideal conditions

4. Temporary situations • Brief periods only • Cannot last long

Examples:

1. Bacteria in culture • Fresh medium, nutrients abundant • Double every 20 minutes • 1 → 2 → 4 → 8 → 16... • Exponential until nutrients depleted

2. Invasive species • Zebra mussels in Great Lakes (1980s-90s) • No predators, abundant food • Population explosion • Eventually slowed as resources depleted

3. Human population (historical) • After agricultural revolution • After industrial revolution • Medical advances reduced death rate • Currently ~7.8 billion and still growing

4. Algal blooms • Nutrient pollution → exponential algae growth • Brief exponential phase • Crashes when nutrients exhausted

Why Exponential Growth CANNOT Continue Indefinitely:

1. RESOURCE LIMITATION • All environments have finite resources • Food, water, space eventually run out • Competition increases • "No such thing as a free lunch"

2. WASTE ACCUMULATION • Metabolic waste products build up • Toxic at high concentrations • Inhibits growth • Example: Bacteria poisoned by own waste

3. ENVIRONMENTAL RESISTANCE • Density-dependent factors kick in • Disease spreads • Predators attracted • Social stress increases

4. PHYSICAL LIMITS • Finite space on Earth • Cannot exceed carrying capacity long-term • Mathematical impossibility

5. EVOLUTIONARY CONSTRAINTS • No organism has evolved for infinite growth • r-selection has limits • Trade-offs with other traits

Consequences of Unlimited Growth:

Calculation Example: • Start with 2 bacteria • Double every 20 minutes • After 24 hours (72 doublings): N = 2 × 2^72 = ~9.4 × 10^21 bacteria! • Mass would exceed Earth's mass • Clearly impossible

Reality Check - Humans: • Current: ~8 billion • Growth rate: ~1.05% per year • If continued at this rate:

• 2100: ~11 billion
• 2200: ~29 billion
• 2500: ~500 billion! • Earth cannot support unlimited growth • Resources finite

What Happens Instead:

• Exponential growth transitions to LOGISTIC growth • Population approaches carrying capacity (K) • Growth rate slows as N approaches K • S-shaped (sigmoid) curve instead of J-shaped • Density-dependent factors regulate population

Transition: Exponential (early) → Logistic (later) J-shaped → S-shaped Unlimited → Limited by K

Key Principle: Exponential growth represents the POTENTIAL for rapid population increase under ideal conditions, but environmental limits always eventually constrain growth. It's a temporary phase, not a sustainable long-term pattern!

Logistic Population Growth:

Definition: Population growth that slows as population size approaches carrying capacity, producing an S-shaped (sigmoid) curve.

CARRYING CAPACITY (K): Maximum population size that an environment can sustain indefinitely given available resources.

Determined by: • Food availability • Water supply • Space/habitat • Nesting/breeding sites • Shelter • Other limiting resources

LOGISTIC GROWTH EQUATION: dN/dt = rN(K - N)/K

OR simplified: dN/dt = rN(1 - N/K)

Where: • dN/dt = population growth rate • r = intrinsic (maximum) per capita growth rate • N = current population size • K = carrying capacity

Key Component: (K - N)/K or (1 - N/K) • This is the "braking term" • Reduces growth rate as N approaches K • When N is small: term ≈ 1 (like exponential) • When N = K: term = 0 (no growth) • When N > K: term < 0 (negative growth)

S-SHAPED CURVE Phases:

Phase 1: LAG PHASE (Early) • Population small (N << K) • Slow initial growth • Establishing population • Growth accelerating

Phase 2: EXPONENTIAL PHASE (Middle) • Rapid growth • N still well below K • Resources abundant • Steepest part of curve • Maximum growth rate when N = K/2

Phase 3: DECELERATION PHASE (Late) • Growth slows • N approaching K • Resources becoming limited • Competition increases • Curve flattens

Phase 4: EQUILIBRIUM (Plateau) • Population at or near K • Zero net growth (births ≈ deaths) • Fluctuates around K • Stable population size

Graph: Population ↑ │ ───────K (carrying capacity) │ ╱ │ ╱ │ ╱ │╱ └──────────→ Time (S-shaped curve)

Analysis at Different N values:

When N is very small (N ≈ 0): • (K - N)/K ≈ 1 • dN/dt ≈ rN (exponential-like) • Resources unlimited relative to population

When N = K/2 (midpoint): • (K - N)/K = 0.5 • dN/dt = 0.5rN • MAXIMUM growth rate (most individuals added per time) • Inflection point of curve

When N = K: • (K - N)/K = 0 • dN/dt = 0 • No net growth (equilibrium) • Births = deaths

When N > K (overshoot): • (K - N)/K < 0 • dN/dt < 0 • Negative growth (population declining) • Die-off occurs

COMPARISON: Exponential vs. Logistic

Feature | Exponential | Logistic -----------------|-----------------|------------------ Equation | dN/dt = rN | dN/dt = rN(K-N)/K Curve shape | J-shaped | S-shaped Growth rate | Constant r | Variable (slows) Carrying cap? | No limit | Limited by K Realistic? | Short-term only | Long-term Density factors? | Ignored | Included Plateau? | No | Yes (at K)

Mechanisms Causing Logistic Growth:

Density-dependent factors:

1. Competition for resources
2. Disease transmission
3. Predation
4. Waste accumulation
5. Social stress
6. Territoriality

All increase in intensity as N → K

Real-World Examples:

1. Yeast in Culture • Start with few cells in sugar solution • Exponential growth initially • Levels off as sugar depleted • Classic S-curve • K determined by nutrient availability

2. Paramecium in Lab • Grown in culture medium • Clear S-shaped growth • K ~200-500 individuals depending on conditions • Well-studied example

3. Reindeer on St. Paul Island • 1911: 25 reindeer introduced • 1938: ~2,000 (near K) • Stabilized around K • Limited by lichen food supply

4. Sheep in Tasmania • Introduced 1800s • Rapid initial growth • Leveled at K ~1.6 million • Determined by grazing land

5. Human Populations (Some) • Developed countries approaching K • Growth rates slowing • Example: Japan, many European countries

K is NOT Fixed:

K can change due to:

1. Environmental change • Climate change • Drought reduces K • Good rainfall increases K

2. Human activities • Habitat destruction decreases K • Conservation increases K • Supplemental feeding increases K

3. Technological change (humans) • Agriculture increased K • Medicine increased K • Sanitation increased K

4. Species interactions • Predator arrival decreases prey K • Competitor removal increases K • Mutualist arrival increases K

Overshoots and Crashes:

Sometimes N exceeds K: • Population inertia (time lag) • Reproducing before resources depleted • Then crash below K • Example: Reindeer on St. Matthew Island

• 1944: 29 reindeer
• 1963: 6,000 (overshoot)
• 1966: 42 (crash after overgrazing)

Fluctuations Around K: • Real populations rarely stable at K • Oscillate above and below • Predator-prey cycles • Environmental variation

Limitations of Logistic Model:

1. Assumes K is constant • Actually varies with conditions

2. Assumes smooth approach to K • Real populations may overshoot

3. Ignores age structure • All individuals contribute equally

4. Ignores time lags • Reproduction has delays

5. Ignores stochasticity • Random events matter

Despite limitations: • Useful approximation • Better than exponential for most situations • Captures key biological reality (limits exist)

Human Population: • Currently ~8 billion • Still growing (but rate slowing) • What is Earth's K for humans?

• Estimates: 8-15 billion
• Depends on:
  • Technology
  • Lifestyle (consumption)
  • Resource management
  • Climate change • May be approaching or exceeding K • Controversial topic!

Key Insight: Logistic growth incorporates biological reality - no population can grow without limits. Carrying capacity represents the fundamental constraint imposed by finite resources. The logistic equation elegantly captures how growth slows as populations approach environmental limits.

Logistic Growth Problem:

Given: • N₀ = 100 rabbits (initial population) • r = 0.5 per year (intrinsic growth rate) • K = 1,000 rabbits (carrying capacity) • t = 1 year

Find:

1. Current growth rate (dN/dt)
2. Population after 1 year (N₁)

SOLUTION:

Part 1: Calculate dN/dt

Logistic equation: dN/dt = rN(K - N)/K

Substitute values: dN/dt = 0.5 × 100 × (1000 - 100)/1000 dN/dt = 0.5 × 100 × 900/1000 dN/dt = 0.5 × 100 × 0.9 dN/dt = 50 × 0.9 dN/dt = 45 rabbits per year

Interpretation: • Population currently growing at 45 rabbits/year • This is the instantaneous growth rate at N = 100

Part 2: Estimate Population After 1 Year

Simple approximation (assuming constant rate): N₁ ≈ N₀ + dN/dt × t N₁ ≈ 100 + 45 × 1 N₁ ≈ 145 rabbits

More accurate (using logistic integral, approximation): For small time steps, iterative approach:

Year 1 calculation: • Start: N = 100 • Growth rate: 45 rabbits/year • End of year: N ≈ 145

Actual N₁ ≈ 145 rabbits

CHECKING OUR WORK:

Verify the calculation makes sense:

1. Is growth positive? YES • N < K, so population should grow • ✓

2. Is growth less than exponential? YES • Exponential would be: dN/dt = rN = 0.5 × 100 = 50 • Logistic: dN/dt = 45 • Logistic is less (0.9 factor from (K-N)/K) • ✓

3. Does braking term make sense? YES • (K - N)/K = (1000 - 100)/1000 = 0.9 • Population is 10% of K • So growth is 90% of maximum • ✓

COMPARISON: Exponential vs. Logistic

If growth were EXPONENTIAL: dN/dt = rN = 0.5 × 100 = 50 rabbits/year N₁ = N₀e^(rt) = 100 × e^(0.5×1) = 100 × 1.649 = 165 rabbits

With LOGISTIC growth: N₁ ≈ 145 rabbits

Difference: 165 - 145 = 20 fewer rabbits with logistic

Why? • Carrying capacity constrains growth • Even at low N, some limitation present • Difference will become more pronounced as N increases

PROJECTING FURTHER:

Let's see what happens in subsequent years:

Year 2 (N ≈ 145): dN/dt = 0.5 × 145 × (1000-145)/1000 dN/dt = 72.5 × 0.855 dN/dt ≈ 62 rabbits/year N₂ ≈ 145 + 62 = 207 rabbits

Year 3 (N ≈ 207): dN/dt = 0.5 × 207 × (1000-207)/1000 dN/dt = 103.5 × 0.793 dN/dt ≈ 82 rabbits/year N₃ ≈ 207 + 82 = 289 rabbits

Year 5 (N ≈ 500): dN/dt = 0.5 × 500 × (1000-500)/1000 dN/dt = 250 × 0.5 dN/dt = 125 rabbits/year (MAXIMUM growth rate!)

Year 10 (approaching K): N ≈ 900+ dN/dt much slower Approaching equilibrium

Eventually: N → 1,000 (carrying capacity) dN/dt → 0 (equilibrium)

KEY OBSERVATIONS:

1. Growth rate INCREASES initially • From 45 → 62 → 82 → 125 • Even though per capita rate decreasing • More individuals reproducing

2. Maximum growth at N = K/2 • N = 500 gives dN/dt = 125 (maximum) • Inflection point of S-curve • Most individuals added per time unit

3. Growth rate depends on N • Not constant like exponential • Changes as population grows • Slows as approaches K

4. Approaches K asymptotically • Gets closer and closer to 1,000 • Never quite reaches it (mathematically) • In reality, fluctuates around K

BIOLOGICAL INTERPRETATION:

At N = 100 (10% of K): • Resources still abundant • 90% of K available • Little competition • Growth nearly exponential

At N = 500 (50% of K): • Moderate resource availability • Noticeable competition • Maximum population growth rate • Half of resources used

At N = 900 (90% of K): • Resources scarce • Strong competition • Growth rate very slow • Nearly at equilibrium

FACTORS AFFECTING K for Rabbits:

• Food (vegetation) • Predators (foxes, hawks, coyotes) • Disease • Shelter/burrows • Territory size • Water availability • Winter survival

If these change, K changes!

MANAGEMENT IMPLICATIONS:

For sustainable harvest: • Remove individuals at rate = growth rate • Maximum sustainable yield at N = K/2 • Can harvest ~125 rabbits/year sustainably at N = 500 • More at higher/lower N → population declines

FINAL ANSWER:

1. Current growth rate: dN/dt = 45 rabbits per year
2. Population after 1 year: N₁ ≈ 145 rabbits

Predator-Prey Population Cycles:

Classic Example: Lynx and Snowshoe Hare

Data Source: • Hudson's Bay Company fur trading records (1845-1935) • ~90 years of data • Canadian boreal forest • Well-documented oscillations

OBSERVED PATTERN:

Cycle characteristics: • Period: ~10 years (8-11 years typical) • Both populations oscillate • Oscillations linked (not independent) • Predictable, regular pattern • Repeats for decades

Population Graph: Number ↑ │ ∩ ∩ ∩ HARES (prey) │ / \ / \ /
│ / \ / \ /
│/ \ / \ /
│ ∩ / ∩ / │ / V / V LYNX (predator) │ / / └─────────────────────────→ Time 10 yr 20 yr

Key Observation: • Predator peaks LAG behind prey peaks • Time lag: ~1-2 years • Hare peaks → then lynx peaks • Hare crashes → then lynx crashes

THE CYCLE - Four Phases:

PHASE 1: High Hare Population • Hares abundant • Food (vegetation) still adequate • Lynx population still relatively low • Hares increasing or near peak

PHASE 2: Hare Decline, Lynx Increase • Lynx population increases (abundant food) • More lynx → more predation on hares • Hares also overgraze vegetation • Hare population starts declining • Lynx still increasing (time lag)

PHASE 3: Low Hare Population • Hares scarce • Lynx population peaks (but food now scarce) • Heavy predation on remaining hares • Vegetation recovers • Hares at minimum

PHASE 4: Lynx Decline, Hare Recovery • Lynx starve, die, emigrate (no food) • Lynx population crashes • Reduced predation allows hare recovery • Vegetation recovered • Hares start increasing • Return to Phase 1

MECHANISM Explained:

Step-by-step causation:

1. HARES INCREASE Why: Low lynx numbers, vegetation abundant Result: Hare population grows

2. LYNX INCREASE (delayed) Why: Abundant hares = good food supply Lynx effects: • Higher survival • Better reproduction • More kits survive Result: Lynx population grows Time lag: Reproduction takes time

3. HARES DECREASE Why: Two factors: a) Heavy predation by abundant lynx b) Overgrazing of vegetation (food limited) Result: Hare population crashes

4. LYNX DECREASE (delayed) Why: Hares scarce = starvation Lynx effects: • Low survival • Poor reproduction • Kits starve • Adults emigrate Result: Lynx population crashes Time lag: Takes time to starve/die

5. Cycle repeats

LOTKA-VOLTERRA MODEL:

Mathematical model of predator-prey dynamics:

Prey equation: dH/dt = rH - aHL

Where: • H = hare population • r = hare growth rate • a = predation rate coefficient • L = lynx population • rH = hare reproduction (exponential) • aHL = hare deaths from predation

Predator equation: dL/dt = baHL - mL

Where: • L = lynx population • b = efficiency (prey → predator conversion) • a = attack rate • H = hare population • m = lynx mortality rate • baHL = lynx reproduction (depends on prey) • mL = lynx deaths

Predictions: • Populations oscillate • Predator lags behind prey • Cycle period depends on r, a, b, m • Neutral stability (cycles continue indefinitely)

PHASE RELATIONSHIP:

Predator vs. Prey timing:

• Prey peaks FIRST • Predator peaks LATER (lag 1-2 years) • Prey troughs FIRST
• Predator troughs LATER (lag 1-2 years)

Why the lag?

1. Reproduction takes time • Lynx gestation ~2 months • Kits take time to mature • Cannot instantly respond to prey increase

2. Starvation not instant • Lynx don't immediately die when hares decline • Can survive period without food • Gradual decline

3. Behavioral responses • Lynx may switch to other prey • May emigrate • Delayed numerical response

AMPLITUDE of Oscillations:

Hares: • Peak: 150,000+ per 100 km² • Trough: 5,000 per 100 km² • ~30-fold variation!

Lynx: • Peak: 20-30 per 100 km² • Trough: 1-2 per 100 km² • ~10-20 fold variation

Prey oscillations larger amplitude than predator

ADDITIONAL FACTORS (Beyond Simple Model):

1. Vegetation Recovery • Hares overgraze during peaks • Plants need recovery time • Affects hare nutrition and reproduction • Not just predation causing hare decline

2. Hare Quality • Stressed hares (high density) have fewer offspring • Poorer body condition • Maternal stress effects

3. Other Predators • Lynx not only predator • Hawks, owls, foxes also eat hares • Cumulative predation

4. Winter Severity • Harsh winters increase mortality • Food harder to find • Can synchronize cycles

5. Lynx Alternative Prey • Can eat squirrels, birds, small mammals • Buffers lynx decline slightly

EXPERIMENTAL EVIDENCE:

1. Predator exclusion experiments • Fence areas to exclude lynx • Hare populations still cycle (but less amplitude) • Shows predation not only factor • Food also important

2. Food supplementation • Add food for hares • Reduces amplitude of decline • Shows food limitation important

3. Combined effects • Predation + food both affect cycle • Interaction between factors

OTHER EXAMPLES of Predator-Prey Cycles:

1. Arctic foxes and lemmings • ~4 year cycle • Shorter period

2. Wolves and moose (Isle Royale) • Less regular cycles • ~20-40 year observations

3. Phytoplankton and zooplankton • Short cycles (weeks) • Aquatic systems

4. Laboratory systems • Paramecium and Didinium • Can demonstrate cycles in controlled conditions

ECOLOGICAL SIGNIFICANCE:

• Demonstrates population regulation • Shows species interactions drive dynamics • No equilibrium - continuous change • Natural fluctuations normal • Both species persist despite crashes

CONSERVATION IMPLICATIONS:

• Populations naturally fluctuate • Low numbers don't necessarily mean extinction • Need long-term data to see patterns • Manage for cycle, not fixed number • Preserve both predator and prey • Ecosystem-level approach

Key Insight: Predator-prey cycles demonstrate that populations don't exist in isolation - species interactions create complex dynamics. The time lag between predator and prey is critical for sustaining oscillations. This is a natural, stable pattern, not a sign of ecosystem dysfunction!

Metapopulation Dynamics:

Definition: A "population of populations" - a group of spatially separated populations of the same species that interact through dispersal and migration.

Structure: • Multiple LOCAL POPULATIONS • Occupy separate HABITAT PATCHES • Connected by DISPERSAL • Each patch can support a population • Patches embedded in unsuitable habitat matrix

KEY FEATURES:

1. PATCH OCCUPANCY • Some patches occupied • Some patches empty (temporarily) • Occupancy changes over time • Dynamic pattern

2. LOCAL EXTINCTIONS • Individual patches can go extinct • Small populations vulnerable • Stochastic events • Demographic stochasticity • Environmental variation • Genetic drift

3. RECOLONIZATION • Dispersers from occupied patches • Find and colonize empty patches • Re-establish extinct populations • Gene flow between patches

4. REGIONAL PERSISTENCE • Metapopulation persists • Even though local populations blink in/out • Balance: extinction vs. colonization • "Shifting mosaic" of occupancy

CORE-SATELLITE Model:

Two types of patches:

1. CORE (Source) Populations • Large patches • High-quality habitat • Large populations • Rarely go extinct • Produce emigrants • Rescue other populations

2. SATELLITE (Sink) Populations • Small patches • Lower quality habitat • Small populations • Frequently go extinct • Maintained by immigration • Dependent on core populations

METAPOPULATION DYNAMICS:

Rate of change in patch occupancy: dp/dt = cp(1 - p) - ep

Where: • p = proportion of patches occupied • c = colonization rate • e = extinction rate • cp(1-p) = colonization (occupied patches colonize empty) • ep = extinction (occupied patches go extinct)

Equilibrium: When colonization = extinction p* = 1 - (e/c)

Conditions: • If c > e: metapopulation persists (p* > 0) • If c < e: metapopulation goes extinct (p* = 0) • Colonization must exceed extinction!

FACTORS AFFECTING PERSISTENCE:

1. PATCH SIZE Larger patches: • Support larger populations • Lower extinction risk • More stable • Better sources

2. PATCH ISOLATION Less isolated patches: • Easier to reach for dispersers • Higher colonization rate • Receive immigrants • Demographic rescue

3. PATCH QUALITY Higher quality: • Better survival and reproduction • Larger populations • More emigrants • Lower extinction

4. NUMBER OF PATCHES More patches: • Higher overall occupancy • More sources for colonization • Insurance against extinction • Greater regional population

5. DISPERSAL ABILITY Better dispersers: • Connect distant patches • Higher colonization • Gene flow • Maintain metapopulation

CLASSIC EXAMPLE: Pika (Small Mammal)

American pika (Ochotona princeps):

Habitat: • Mountain talus slopes (rock piles) • Cool, rocky areas • Surrounded by forest/meadows (unsuitable) • Patches of habitat naturally fragmented

Metapopulation structure: • Each talus slope = separate population • Populations 10-100 individuals • Limited dispersal between slopes • Small populations → extinction risk

Dynamics: • Some talus patches occupied • Some empty (recent extinction) • Colonization from nearby occupied patches • Turnover: patches go extinct and recolonize • Overall persistence depends on balance

Observations: • Small, isolated patches: frequent extinction • Large, connected patches: rarely extinct • Recolonization within 5-10 years typical • Climate warming: threatening (need cool habitat)

THREATS to Metapopulations:

1. HABITAT LOSS • Reduces number of patches • Lowers p (occupancy) • Fewer sources for colonization • If too many patches lost → extinction

2. HABITAT FRAGMENTATION • Increases isolation • Reduces dispersal • Lower colonization rate • Breaks connectivity • Rescue effect lost

3. CLIMATE CHANGE • Alters habitat quality • Some patches become unsuitable • Shifts spatial distribution • May isolate populations

4. EDGE EFFECTS • Smaller effective patch size • Quality degradation • Increased extinction risk

OTHER EXAMPLES:

1. BUTTERFLIES on Habitat Patches • Bay checkerspot butterfly (California) • Serpentine grassland patches • Host plants in patches • Turnover documented over decades • Some patches empty, then recolonized

2. AMPHIBIANS in Ponds • Pond-breeding salamanders • Each pond = population • Ponds can dry up (extinction) • Recolonization from nearby ponds • Network of ponds maintains species

3. PLANTS in Meadows • Alpine wildflowers • Meadow patches in forest • Seeds disperse between meadows • Local extinction from succession • Recolonization maintains presence

4. SMALL MAMMALS on Islands • Mice on coastal islands • Island populations small • Some go extinct (storms, predators) • Recolonization from mainland or other islands

5. REEF FISH among Coral Patches • Coral heads = patches • Larval dispersal connects patches • Recruitment varies • Some patches empty, then recolonize

RESCUE EFFECT:

Definition: • Immigration prevents local extinction • Dispersers boost small populations • Reduces extinction risk • Demographic rescue • Genetic rescue (reduce inbreeding)

Mechanism: • Population declining • Immigrants arrive from other patches • Add individuals • Bolster population size • Prevent extinction that would otherwise occur

Importance: • Stabilizes small populations • Maintains genetic diversity • Critical for persistence • Depends on connectivity

CONSERVATION APPLICATIONS:

1. CORRIDOR DESIGN • Connect habitat patches • Facilitate dispersal • Increase colonization • Enable rescue effect • Example: Wildlife corridors, green bridges

2. HABITAT PROTECTION • Preserve multiple patches • Protect both core and satellite • Maintain network • Don't just protect largest patch

3. RESTORATION • Create new patches • Increase patch size • Improve connectivity • Enhance quality

4. TRANSLOCATION • Artificial recolonization • Move individuals to empty patches • Supplement small populations • Genetic rescue

5. STEPPING STONES • Small patches between large ones • Aid dispersal • Increase connectivity • Don't need to support permanent populations

MODERN RELEVANCE:

• Habitat increasingly fragmented (human development) • Many species now exist as metapopulations • Understanding dynamics critical for conservation • Manage at landscape level, not just local • Consider connectivity, not just area

DIFFERENCE from Simple Population:

• Single population: one location, one fate • Metapopulation: multiple locations, asynchronous dynamics • Insurance against total extinction • Spatial structure matters • Regional vs. local perspective

Key Insight: Metapopulation dynamics show that local extinction doesn't mean species extinction! As long as colonization rate exceeds extinction rate across the landscape, the metapopulation persists through a dynamic balance of local extinctions and recolonizations. This has profound implications for conservation - we must maintain networks of habitat patches with sufficient connectivity, not just protect individual sites in isolation.