Population Ecology: Principles, Models, and Human Impacts

Population Ecology

Definition and Scope

Population ecology is the branch of biology 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: A group of individuals of the same species living in a specific geographic area, capable of interbreeding.

• Population ecologists analyze how populations change over time and space, and what factors regulate these changes.

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

Survivorship Curves

Patterns of Survivorship

A survivorship curve is a graphical representation showing the number or proportion of individuals surviving at each age for a given cohort (group of individuals born at the same time) within a population.

• Survivorship curves help ecologists understand mortality patterns and life history strategies.

• Example: Belding's ground squirrels exhibit a nearly straight-line survivorship curve, indicating a relatively constant rate of death throughout life.

Types of Survivorship Curves

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

• Type II: Constant death rate throughout the lifespan. Common in some birds, rodents, and some reptiles.

• Type III: High mortality rates for the young, with survivors experiencing much lower death rates. Typical of species producing many offspring with little or no parental care (e.g., oysters, many fish, most plants).

Trade-offs: Type I species invest more in fewer offspring, increasing survival chances, while Type III species produce many offspring with low individual survival probability.

Population Growth Models

Exponential Growth Model

The exponential growth model describes population increase under ideal, unlimited environmental conditions. All species have the potential for rapid population growth when resources are abundant, but such growth is unsustainable in nature due to resource limitations.

• Population growth rate is determined by the difference between birth and death rates, ignoring immigration and emigration.

• Mathematical expression for 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 rates:

$B = bN$ $D = mN$

• $b$ = per capita birth rate, $m$ = per capita death rate, $N$ = population size.

• Population growth rate:

$\frac{\Delta N}{\Delta t} = bN - mN$

• Per capita rate of increase: $r = b - m$

• Zero population growth (ZPG) occurs when $r = 0$ (birth rate equals death rate).

• Instantaneous rate of change:

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

• Exponential growth produces a J-shaped curve; the rate of increase is constant, but the number of individuals added per unit time increases as the population grows.

• Examples: Populations introduced to new environments or recovering from catastrophic events (e.g., elephants in Kruger National Park after hunting bans).

Logistic Growth Model

The logistic growth model incorporates environmental limits by introducing the concept of carrying capacity ($K$), the maximum population size an environment can sustain.

• As population size ($N$) approaches $K$, the growth rate slows and eventually stops.

• Logistic growth equation:

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

• When $N$ is much less than $K$, growth is nearly exponential.

• When $N$ is close to $K$, growth slows dramatically.

• When $N = K$, population growth ceases.

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

Population Size (N)	Intrinsic Rate of Increase (r)	K-N	(K-N)/K	Population Growth Rate (rN[(K-N)/K])
25	10	1,475	0.983	+25
100	10	1,400	0.933	+93
250	10	1,250	0.833	+208
500	10	1,000	0.667	+333
750	10	750	0.500	+375
1,000	10	500	0.333	+333
1,500	10	0	0.000	0

Example: Laboratory populations of Paramecium grown in constant environments often follow logistic growth, forming an S-shaped curve. Some populations may overshoot $K$ before stabilizing.

Life History Traits and Natural Selection

Life History Strategies

An organism's life history consists of traits that affect its schedule of reproduction and survival. These traits are shaped by natural selection and include:

• Age at first reproduction (maturity)

• How often reproduction occurs

• Number of offspring per reproductive episode

Trade-offs: Species with low offspring 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

The human population has grown rapidly over the past four centuries, with the doubling time decreasing dramatically. However, the rate of growth has slowed since the 1960s.

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

• Population growth is now fastest in less industrialized countries.

Demographic Transition

Demographic transition is the shift from high birth and death rates to low birth and death rates, typically associated with improved healthcare and education.

• Zero population growth can occur with either high or low birth and death rates.

• Most industrialized nations are near or below the replacement fertility rate (2.1 children per female).

Age Structure

Age structure refers to the relative number of individuals in each age group within a population. Age structure diagrams (population pyramids) can predict future growth trends.

• Populations with a large proportion of young individuals (e.g., Zambia) are likely to experience rapid growth.

• Populations with more even age distribution (e.g., United States) grow slowly, while those with a higher proportion of older individuals (e.g., Italy) may not grow at all.

Carrying Capacity and Ecological Footprint

Carrying capacity for humans depends on resource availability and consumption patterns. The ecological footprint measures the total land and water area required to sustain an individual, city, or nation.

• Global average sustainable footprint: 1.7 global hectares (gha) per person.

• Average U.S. footprint: 8 gha; global average: 2.7 gha.

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

Example: If the global population reaches 9 billion by 2050, resource management and reduction of ecological footprints will be critical for sustainability.