Population Ecology: Density, Demographics, and Growth

Population Ecology (Ch. 53)

Introduction

Population ecology is a branch of ecology that studies the dynamics of populations of organisms, especially their size, structure, and distribution, and how these change in response to environmental factors. This field is crucial for understanding biodiversity, conservation, and the sustainability of ecosystems.

I. Population Density and Dispersion

1. Population Density

• Population density: The number of individuals per unit area or volume.

• Population size: The total number of individuals in a population.

Examples:

• Rose garden: 50 plants in 500 m2 → Density = $\frac{50}{500} = 0.1$/m2

• Earthworms: 25 in 500 m2 → Density = $\frac{25}{500} = 0.05$/m2

• Dolphins: 10 in 100,000 m3 → Density = $\frac{10}{100,000} = 0.0001$/m3

2. Methods of Estimating Population Size

• Mark-Recapture Method: Used for mobile or elusive species. Involves capturing, marking, and releasing individuals, then recapturing to estimate total population size.

Formula:

• If $M$ individuals are marked in the first sample, $n$ are captured in the second sample, and $m$ of those are marked, then estimated population size $N$ is:

$N = \frac{M \times n}{m}$

Example: 100 dolphins marked, 500 captured later, 50 marked in second sample: $N = \frac{100 \times 500}{50} = 1000$

3. Dispersion Patterns

• Clumped: Individuals aggregate in patches (common in plants, fungi).

• Uniform: Evenly spaced, often due to territoriality (e.g., penguins).

• Random: No predictable pattern, rare in nature.

II. Demographics

1. Demography and Life Tables

• Demography: Study of vital statistics (birth, death rates) and how they change over time.

• Life table: Summarizes survival and reproductive rates of individuals in specific age groups.

Age (years)	Number Alive	Proportion Alive	Death Rate	Avg. Female Offspring
0-1	553	1.000	0.514	0.00
1-2	269	0.486	0.496	1.07
2-3	136	0.246	0.478	1.17
3-4	71	0.128	0.478	2.31
4-5	37	0.067	0.478	2.31
5-6	19	0.034	0.486	2.08
6-7	9	0.016	0.526	1.89
7-8	4	0.007	0.750	1.50
8-9	1	0.002	1.000	1.50
9-10	0	0.000	-	-

2. Survivorship Curves

• Type I: Low death rates early, high late (e.g., humans).

• Type II: Constant death rate (e.g., squirrels).

• Type III: High death rates early, survivors live long (e.g., oysters).

3. Life History Strategies

• Semelparity: Single reproductive event (e.g., agave plant).

• Iteroparity: Multiple reproductive cycles (e.g., oak tree).

• Trade-offs exist between number of offspring, size, and parental care.

Example: Dandelions produce many small seeds; Brazil nut trees produce fewer, larger seeds with more energy reserves.

III. Population Growth

1. Population Growth Rate

• Change in population size:

$\Delta N = (\text{births} + \text{immigrants}) - (\text{deaths} + \text{emigrants})$

• Per capita growth rate:

$r_{\Delta t} = \frac{\Delta N / \Delta t}{N}$

• Instantaneous rate of change:

$\frac{dN}{dt} = rN$

2. Exponential Growth

• Occurs under ideal conditions, resources unlimited.

• Population grows at a constant per capita rate ($r$).

• Produces a J-shaped curve.

Equation:

$\frac{dN}{dt} = rN$

3. Logistic Growth

• Growth slows as population approaches carrying capacity ($K$).

• Produces an S-shaped (sigmoid) curve.

Equation:

$\frac{dN}{dt} = rN \left(1 - \frac{N}{K}\right)$

Population Size (N)	Intrinsic Growth Rate (r)	K-N	(K-N)/K	Population Growth Rate
0	10	1500	1.000	+15
100	10	1400	0.933	+93
250	10	1250	0.833	+208
500	10	1000	0.667	+333
750	10	750	0.500	+375
1000	10	500	0.333	+333
1500	10	0	0.000	0

4. Factors Regulating Population Growth

• Density-independent factors: Affect populations regardless of size (e.g., weather, natural disasters).

• Density-dependent factors: Intensify as population increases (e.g., competition, disease, predation, territoriality, toxic wastes, intrinsic physiological factors).

5. Population Dynamics

• Populations may fluctuate, reach equilibrium, or cycle due to complex interactions of births, deaths, immigration, and emigration.

• Metapopulation: A group of populations linked by immigration and emigration.

6. Human Population Growth

• Human population growth has slowed but continues to increase.

• Demographic transition: Shift from high birth/death rates to low birth/death rates as a country develops.

• Age structure: Distribution of individuals among different ages influences future growth.

• Ecological footprint: Measure of human demand on Earth's ecosystems; varies greatly by country.

Example: Sustainable global footprint is 1.7 global hectares per person; Americans use about 10 global hectares per person.

Summary Table: Key Terms and Concepts

Term	Definition	Example/Application
Population Density	Individuals per unit area/volume	Rose garden: 0.1/m2
Mark-Recapture	Estimating population size by marking and recapturing	Dolphins in a lake
Dispersion	Pattern of spacing among individuals	Clumped, uniform, random
Life Table	Summary of survival and reproduction by age	Ground squirrels
Semelparity	Single reproductive event	Agave plant
Iteroparity	Multiple reproductive cycles	Oak tree
Exponential Growth	Growth at constant rate, unlimited resources	Bacteria in lab culture
Logistic Growth	Growth slows near carrying capacity	Seals on an island
Carrying Capacity (K)	Maximum population size environment can sustain	1,500 in example table
Ecological Footprint	Land/water area needed per person	Americans: 10 gha/person

Additional info: These notes integrate textbook-level explanations, formulas, and examples to provide a comprehensive overview of population ecology, suitable for college-level General Biology students.