Population Ecology: Principles, Models, and Human Impact

Population Ecology

Definition and Scope

Population ecology is a branch of ecology that studies populations of organisms, especially in relation to their environment. It focuses on how environmental factors influence population density, distribution, age structure, and overall population size.

• Population ecology examines the interactions between populations and their abiotic and biotic surroundings.

• Population: A group of individuals of the same species living in a defined geographic area.

• Key factors studied include birth rates, death rates, immigration, emigration, and resource availability.

• Example: A population of sea turtles hatching and migrating on a beach.

Survivorship Curves

Patterns of Survivorship

Survivorship curves graphically represent the proportion of individuals in a cohort that survive at each age. These curves help ecologists understand mortality patterns within populations.

• Survivorship curve: A plot showing the number or proportion of individuals surviving at each age for a given population.

• Used to compare survival strategies among species.

• Example: Belding’s ground squirrels exhibit a relatively constant rate of death, as shown by a straight-line survivorship curve.

Types of Survivorship Curves

Survivorship curves are classified into three general types, each reflecting different life history strategies.

• Type I: Low death rates during early and middle life, with increased mortality in older age groups. Common in species that produce few offspring but provide substantial parental care (e.g., humans, large mammals).

• Type II: Constant death rate throughout the organism’s life span. Typical of some birds, rodents, and reptiles.

• Type III: High death rates for young individuals, with lower death rates for survivors. Found in species that produce many offspring but provide little or no parental care (e.g., oysters, many fish, plants).

• Trade-offs: Type I species invest more in fewer offspring, increasing survival; Type III species produce many offspring with low survival rates.

Population Growth Models

Exponential Growth Model

The exponential growth model describes population increase under ideal, unlimited environmental conditions. It is useful for understanding the potential for rapid population expansion.

• All species have the potential for rapid growth when resources are abundant.

• In nature, unlimited growth is unsustainable due to resource depletion.

• Exponential growth is observed in populations introduced to new environments or recovering from catastrophic events.

Mathematical Representation

• Change in population size over a time interval: $\Delta N = B - D$ where $\Delta N$ is the change in population size, $B$ is the number of births, and $D$ is the number of deaths.

• Per capita birth and death rates: $B = bN$ $D = mN$ where $b$ is the per capita birth rate, $m$ is the per capita death rate, and $N$ is population size.

• Population growth rate: $\frac{\Delta N}{\Delta t} = bN - mN$ Per capita rate of increase: $r = b - m$

• Exponential growth equation: $\frac{dN}{dt} = rN$ where $r$ is the per capita rate of increase and $N$ is population size.

Logistic Growth Model

The logistic growth model incorporates environmental limits by introducing the concept of carrying capacity. It describes how population growth slows as resources become limited.

• Carrying capacity (K): The maximum population size that an environment can sustain.

• As population size ($N$) approaches $K$, growth rate decreases.

Mathematical Representation

• Logistic growth equation: $\frac{dN}{dt} = rN \left( \frac{K-N}{K} \right)$ where $r$ is the intrinsic rate of increase, $N$ is population size, and $K$ is carrying capacity.

• When $N$ is much less than $K$, growth is nearly exponential; as $N$ approaches $K$, growth slows and eventually stops.

Example Table: Logistic Growth of a Hypothetical Population (K=1,500)

Population Size (N)	Intrinsic Rate of Increase (r)	(K-N)/K	Per Capita Growth Rate	Population Growth Rate
25	10	0.983	0.983	+25
100	10	0.933	0.933	+93
250	10	0.833	0.833	+208
500	10	0.667	0.667	+333
750	10	0.500	0.500	+375
1,000	10	0.333	0.333	+333
1,500	10	0.000	0.000	0

Real-World Application of Logistic Model

Laboratory populations, such as Paramecium, often follow logistic growth, forming an S-shaped curve. Some populations may overshoot carrying capacity before stabilizing.

• Logistic growth is more realistic for natural populations than exponential growth.

• Population density stabilizes near carrying capacity in a constant environment.

Life History Traits

Evolutionary Outcomes and Trade-Offs

Life history traits are characteristics that affect an organism’s schedule of reproduction and survival. These traits are shaped by natural selection and include:

• Age at first reproduction (maturity)

• Frequency of reproduction

• Number of offspring per reproductive episode

• Trade-offs between number and size of offspring

Species with low juvenile survival often produce many small offspring (e.g., dandelions), while species with higher parental investment produce fewer, larger offspring (e.g., Brazil nut trees).

Human Population Growth

Global Trends and Demographic Transition

The human population has grown rapidly over the past centuries, with the doubling time decreasing significantly. However, the rate of growth has begun to slow in recent decades.

• Annual rate of increase peaked at 2.2% in 1962, declining to 1.1% in 2018.

• Demographic transition: Shift from high birth and death rates to low birth and death rates, often associated with improved healthcare and education.

• Replacement fertility rate is about 2.1 children per female in industrialized nations.

Age Structure and Population Growth

Age structure diagrams (population pyramids) illustrate the distribution of individuals among age groups, helping predict future growth trends.

• Countries with a large proportion of young individuals (e.g., Zambia) may experience rapid population growth.

• Stable or declining populations have more balanced age structures (e.g., Italy).

Example Table: Age Structure Comparison

Country	Growth Pattern	Age Structure
Zambia	Rapid growth	Broad base, many young
United States	Slow growth	More uniform distribution
Italy	No growth	Narrow base, more older individuals

Carrying Capacity and Ecological Footprint

Limits to Human Population Growth

Ecologists estimate the Earth’s carrying capacity for humans by considering resource requirements such as food, water, fuel, and materials.

• Ecological footprint: The total land and water area required to support an individual, city, or nation’s resource use.

• Global average sustainable footprint is about 1.7 global hectares (gha) per person; the U.S. average is 8 gha.

• Overshooting the sustainable footprint leads to resource depletion and environmental degradation.

Example Table: Ecological Footprint Comparison

Region	Average Ecological Footprint (gha/person)
United States	8
Global Average	2.7

Additional info: The ecological footprint concept is used to assess sustainability and guide policy decisions regarding resource use and conservation.