Population Ecology

5.1 Populations and Population Change (Expanded)

Definition: A population is a group of individuals of the same species living in the same geographic area at a specific time, who have the potential to interbreed.

Core Equation for Population Change:
$N_{t} = N_{0} + (B - D) + (I - E)$
Where:

$N_{t}$ = Population size at time t
$N_{0}$ = Initial population size
B = Births (natality)
D = Deaths (mortality)
I = Immigration (individuals entering)
E = Emigration (individuals leaving)

Key Rates:

Crude Birth Rate: Number of births per 1,000 individuals per year.
Crude Death Rate: Number of deaths per 1,000 individuals per year.
Per Capita Growth Rate (r): The average contribution of each individual to population growth ( $r = (B - D) / N$ ).

Real-World Data Examples:

Human Population Growth: As of 2024, global human population is ~8.1 billion. Annual growth rate is ~0.9% (down from 2.2% in 1962).
Seasonal Insect Populations: Mosquito populations can double in size every 7–10 days during warm, wet seasons due to high birth rates and low death rates.

Additional Factors:

Sex Ratio: A population with more females often grows faster (more births).
Age Structure: A population with many pre-reproductive individuals is poised for rapid growth (demographic momentum).

5.2 Dispersal of Organisms (Expanded)

Definition: Dispersal is the movement of individuals from their birth site (natal dispersal) or breeding site (breeding dispersal) to another location.

Detailed Types:

Type	Description	Examples	Advantages
Active	Organism uses its own energy to move.	Flying (birds, bats), walking (wolves), swimming (salmon), crawling (larvae).	Can choose direction; avoid obstacles.
Passive	Relies on external forces.	Wind (dandelion seeds, spiderlings), water (coconuts), animal fur (burdock seeds).	Requires less energy; can cover large distances.

Ecological Importance (Expanded):

Reduces Inbreeding: Mixes genes between populations (gene flow).
Avoids Competition: Reduces sibling competition for food and space.
Colonizes New Habitats: Allows species to expand range after disturbances (e.g., fire, volcanic eruption).
Disease Dynamics: Dispersal of infected individuals can spread pathogens; dispersal of healthy individuals can escape outbreaks.

Barriers to Dispersal:

Physical: Oceans (for land animals), mountains, deserts, roads.
Biotic: Predators, competitors, lack of food.

Example Data: A single dandelion produces ~200 seeds, and 99% of them land within 10 meters of the parent, but wind can carry the remaining 1% >1 km.

5.3 Patterns in Population Dynamics (Expanded)

Definition: Population dynamics studies the causes and consequences of fluctuations in population size over time.

Four Major Patterns (with more data):

Pattern	Description	Graph Shape	Real Example & Data
Stable	Fluctuates narrowly around carrying capacity (K).	Flat line with small wobbles	Tropical rainforest insects (constant temp/humidity)
Irruptive	Dramatic, rapid increase followed by sudden crash (boom-bust).	Sharp peaks	Locust swarms: Can increase 100,000x in 6 months; crash when food exhausted.
Cyclic	Regular, predictable oscillations (3–10 year periods).	Regular sine wave	Lynx & Hare (Hudson Bay) : Hare peak every 10 years; Lynx follows 1-2 years later.
Chaotic	Apparently random, unpredictable fluctuations.	No repeating pattern	Some phytoplankton populations in variable ocean currents.

Driving Factors (Detailed):

Food Availability (Bottom-up control): More food = higher birth rates.
Predation (Top-down control): Fewer predators = more prey.
Disease: Epizootics (animal epidemics) can kill 50–90% of a population.
Climate: El Niño events cause population crashes in marine iguanas (food algae dies).
Social Behavior: Stress from overcrowding (e.g., in lemmings) can lower birth rates.

5.4 Presentation of Demographic Data (Expanded)

Demography: The statistical study of human (or any) populations, focusing on size, structure, and change.

Advanced Tools:

Life Table: A cohort (group born at same time) followed from birth to death. Columns include:
- $x$ = Age interval
- $l_{x}$ = Proportion surviving to start of age x
- $m_{x}$ = Average number of female offspring produced per female of age x
- Net Reproductive Rate ( $R_{0}$ ) = $\sum l_{x} m_{x}$ . If >1, population growing; if <1, shrinking.
Survivorship Curves (Three Types with % data):
- Type I (Convex): High survival early; most deaths in old age. Example: Humans (80% survive to age 60 in developed countries).
- Type II (Diagonal): Constant death rate at all ages. Example: Songbirds (~50% die each year, regardless of age).
- Type III (Concave): Very high mortality in early stages; survivors live long. Example: Oak trees (99.9% of acorns die; one grown tree lives 200+ years).
Population Pyramids (Expanded Shapes):
- Expanding (Triangle): High birth rates, broad base. Example: Nigeria (age 0-14 = 42% of population).
- Stable (Bell-shaped): Birth rates ≈ death rates. Example: USA (age 0-14 = 18%).
- Contracting (Urn-shaped): Low birth rates, narrow base. Example: Japan (age 0-14 = 12%; >65 = 29%).
- Dependency Ratio: (Number of people <15 + >65) / (Number age 15-64). High ratio = economic pressure.

Importance: Used for urban planning (schools, hospitals), economic forecasting (workforce size), and environmental impact assessment.

5.5 Evolutionary Strategies: r vs K (Expanded)

This is a continuum, not a binary. Most organisms fall between pure r and pure K.

Feature	r-Strategists (Opportunists)	K-Strategists (Competitors)
Environment	Unstable, unpredictable, short-lived habitats	Stable, predictable, long-lived habitats
Population size	Highly variable; often below carrying capacity	Stable; close to carrying capacity
Body size	Small	Large
Lifespan	Short (hours to months)	Long (years to decades)
Reproduction	Early maturity; one-time (semelparity)	Late maturity; repeated (iteroparity)
Offspring #	Very many (thousands to millions)	Few (1 to ~100)
Parental care	None	Extensive (feeding, protection)
Mortality	High, often density-independent	Low, often density-dependent
Examples	Bacteria, weeds, cockroaches, mice	Whales, elephants, humans, sequoia trees
$r_{m a x}$ (max growth rate)	Very high (E. coli doubles every 20 min)	Very low (Elephant doubles every 20 years)

Real-World Continuum: A mouse is not pure r (has some care); a human is not pure K (high reproduction in some settings). Disturbance favors r; competition favors K.

5.6 Population Growth (Expanded with Calculus)

1. Exponential Growth (J-curve)

Assumptions: Unlimited resources, no predation/disease, constant birth/death rates.
Differential Equation:
$\frac{d N}{d t} = r N$
where $r$ = intrinsic rate of increase (births - deaths per individual).
Integrated Form:
$N_{t} = N_{0} e^{r t}$
where $e$ = Euler's number (~2.718).
Doubling Time ( $T_{d}$ ): $T_{d} = \frac{\ln (2)}{r} \approx \frac{0.693}{r}$
Example: If $r = 0.05$ (5% per year), doubling time = 0.693/0.05 = 13.86 years.

2. Logistic Growth (S-curve)

Assumptions: Limited resources; growth slows as population approaches Carrying Capacity (K) .
Differential Equation:
$\frac{d N}{d t} = r N (1 - \frac{N}{K})$
The term $(1 - N / K)$ = "remaining room" or environmental resistance. When N is small, term ≈1 (exponential). When N approaches K, term →0 (growth stops).
Inflection Point: Maximum growth rate occurs at $N = K / 2$ .

Comparison Table:

Feature	Exponential	Logistic
Resources	Unlimited	Limited
Environment	Constant, ideal	Variable, realistic
Growth rate	Constant per capita	Declines as N increases
Upper limit	None	Carrying capacity (K)
Graph shape	J-curve	S-curve
Real-world duration	Short-term (bacteria in flask)	Long-term (deer on a fenced island)

Example: A deer population on an island with $K = 1000$ , $r = 0.3$ , starting at $N = 100$ . At $N = 100$ , growth is fast. At $N = 900$ , $(1 - 900 / 1000) = 0.1$ , so growth is 10% of maximum.

5.7 Factors Regulating Population Size (Expanded)

Density-Dependent Factors (Effect intensifies as population grows)

Competition: For food, water, mates, nesting sites. Mechanism: Less food → lower birth rates, higher death rates.
Predation: Predators catch more prey when prey is abundant. Example: Wolves kill 5% of moose when moose density is low; 15% when high.
Disease: Transmission rate increases with density. Example: TB in badgers: below 1/km², disease dies out; above 5/km², epidemic occurs.
Accumulation of Wastes: Alcohol in yeast cultures kills cells; ammonia in fish tanks.

Density-Independent Factors (Effect same regardless of density)

Climate: Drought, flood, hurricane, heat wave, deep freeze.
Natural Disasters: Volcanic eruption, earthquake, wildfire, tsunami.
Human Activities: Oil spills, deforestation, pesticide spraying.
Example: A flood kills 50% of a mouse population whether there were 100 or 1000 mice.

Carrying Capacity (K) Detailed:

Definition: Maximum number of individuals an environment can support indefinitely without degrading the environment.
Not constant: K changes with seasons, climate, technology (for humans).
Overshoot & Die-off: When N exceeds K temporarily (due to stored resources), followed by crash. Example: Reindeer on St. Matthew Island: introduced 29 (1944) → peaked at 6,000 (1963) → crashed to 42 (1966) due to overgrazing.

Human Impact on Population Regulation:

Overpopulation: Humans have raised their own K by technology (agriculture, medicine), causing other species' K to shrink.
Habitat Destruction: Fragmentation reduces K for native species.
Pollution: Eutrophication causes algal blooms (irruptive growth) then dead zones.
Climate Change: Shifts K geographically (species must migrate or die).

📊 Quick Revision Table (Expanded)

Topic	Key Points	Key Formula/Data	Real Example
Population Change	B, D, I, E	$N_{t} = N_{0} + (B - D) + (I - E)$	India: +1% per year
Dispersal	Active vs Passive	Gene flow = mutation + migration	Monarch butterfly: 4,000 km migration
Dynamics	Stable, Irruptive, Cyclic, Chaotic	Period = time between peaks	Snowshoe hare: 10-year cycles
Demography	Life tables, pyramids	$R_{0} = \sum l_{x} m_{x}$	Japan: contracting pyramid
r vs K	Continuum, not binary	$r_{m a x}$ = intrinsic rate	E. coli (r) vs Elephant (K)
Exponential Growth	Unlimited resources	$N_{t} = N_{0} e^{r t}$	COVID-19 early spread
Logistic Growth	Carrying capacity (K)	$\frac{d N}{d t} = r N (1 - \frac{N}{K})$	Yeast in a flask
Regulation	Density-dependent/independent	K = carrying capacity	Forest fire (indep); disease (dep)

Summary / Key Takeaways (Expanded)

Populations change through births, deaths, emigration, and immigration. The balance determines growth.
Dispersal is critical for gene flow, colonization, and reducing competition. It can be active or passive.
Population dynamics show four patterns (stable, irruptive, cyclic, chaotic) driven by food, predators, disease, and climate.
Demographic tools (life tables, pyramids, $R_{0}$ ) allow prediction of future population trends and resource needs.
Evolutionary strategies range from r-selected (many offspring, little care) to K-selected (few offspring, high care). Most organisms are in between.
Exponential growth occurs briefly under ideal conditions; logistic growth with a carrying capacity is more realistic long-term.
Regulation involves density-dependent factors (competition, disease) that increase with density, and density-independent factors (disasters, climate) that affect all equally.
Human activities (habitat destruction, pollution, climate change) are now the dominant regulators of most other species' populations.