APES 3.3-3.4: Population Growth and Resource Availability

Population growth

The increase in the number of individuals in a population or dispersed group over time. For human populations, growth depends on births, deaths, immigration, and emigration.

What factors determine the change in a human population?

Population change is determined by births plus immigration minus deaths minus emigration. A population can grow even with low fertility if immigration exceeds losses.

Population growth rate

The change in population per unit time relative to the population at the beginning of the interval: $\frac{P(t_2)-P(t_1)}{P(t_1)(t_2-t_1)}$. It is often reported as a percentage by multiplying the result by $100\%$.

How should positive, negative, and zero population growth rates be interpreted?

A positive rate means the population increased, a negative rate means it decreased, and a zero rate means the beginning and ending populations were equal. Zero net growth can still involve substantial births, deaths, migration, or changes in age distribution.

Absolute population increase versus population growth rate

Absolute increase is the number of additional individuals, whereas growth rate expresses that increase relative to the starting population and time interval. A large population can add many individuals even when its percentage growth rate is relatively small.

Net reproduction rate

The average number of daughters produced by a female during her lifetime who survive to reproductive age. A net reproduction rate greater than $1$ indicates that the female population is increasing; a value below $1$ indicates sub-replacement and eventual decline in the absence of offsetting migration.

Exponential population growth

Growth in which the population increases at a rate proportional to its current size, producing a continuously accelerating curve when resources are unlimited. A simple model is $\frac{dP}{dt}=rP$, where $r$ is the relative growth-rate coefficient.

Logistic population growth

A model in which growth slows as population size approaches the environment's carrying capacity. It accounts for density-dependent limitations such as restricted food, space, or other resources.

Logistic growth equation

The logistic model is $\frac{dP}{dt}=rP\left(1-\frac{P}{K}\right)$, where $P$ is population size, $r$ is the relative growth coefficient, and $K$ is the carrying capacity.

Carrying capacity ($K$)

The maximum population size that a particular environment can sustain under specified conditions. It can change when resource availability, technology, disease, or environmental conditions change.

Why does the logistic growth rate become zero at carrying capacity?

When $P=K$, the limiting factor becomes $1-P/K=0$, so $dP/dt=0$. The population is modeled as stable because resource limitations balance reproduction and losses.

How does the logistic model behave when $P$ is much smaller than $K$?

The factor $1-P/K$ is close to $1$, so $dP/dt\approx rP$ and growth is approximately exponential. As $P$ approaches $K$, the growth rate decreases.

At what population size is the absolute growth rate greatest in the logistic model?

The growth rate $dP/dt$ is greatest at approximately $P=K/2$. At this point, the population has enough individuals to reproduce rapidly but remains sufficiently below carrying capacity that resource limitation is moderate.

What are limiting factors?

Limiting factors are biotic or abiotic environmental conditions that restrict population growth, abundance, or distribution. Examples include food, water, space, disease, predation, competition, temperature, and natural disasters.

Density-dependent versus density-independent limiting factors

Density-dependent factors have stronger effects as population density increases, such as competition, predation, parasitism, and disease. Density-independent factors affect populations regardless of density, such as droughts, floods, fires, freezes, and hurricanes.

Environmental resistance

The combined effect of limiting factors that prevents a population from growing indefinitely. Environmental resistance causes logistic growth to slow as population size approaches carrying capacity.

Demographic transition

The process by which populations shift from high birth and death rates to low birth and death rates as living standards, education, urbanization, and economic development increase. Growth often slows substantially during later stages of this transition.

Why did global human population growth accelerate after industrialization?

Agricultural improvements increased food production, while sanitation, medicine, and improved living conditions reduced mortality, especially among children. When death rates fell before birth rates, population growth increased rapidly.

What role did the Haber process play in human population growth?

The Haber process produces ammonia from nitrogen and hydrogen, enabling large-scale manufacture of nitrogen fertilizers. Greater fertilizer availability increased agricultural productivity and helped support a much larger human population.

How can improved nutrition and sanitation affect population growth?

They generally reduce mortality, particularly childhood and infant mortality. If fertility remains high while mortality falls, the population's growth rate increases.

What is population momentum?

Population momentum is continued population growth after fertility declines because a large proportion of the population is still young and entering reproductive age. Growth eventually slows as lower fertility is reflected across the age structure.

Why can a country have a declining population even if its birth rate is not zero?

Population declines when deaths and emigration exceed births and immigration. Low fertility, an older age distribution, high mortality, or net emigration can each contribute to negative growth.

How are population growth and environmental impacts related?

Population growth combined with increased per-person consumption can increase extraction of food, water, energy, and raw materials. These pressures can contribute to climate change, biodiversity loss, pollution, and ecological overshoot.

Malthusian pressure

A condition in which population growth outpaces local resource or food production, causing shortages or reduced living standards. Technological innovation can temporarily or persistently weaken this pressure by increasing resource productivity.

How can technological progress alter future population projections?

Technology can increase agricultural productivity and improve health, changing both carrying capacity and mortality. It can also increase the demand for education and make child-rearing more expensive, which may reduce fertility.

Why do population projections differ among models?

Projections use different assumptions about future fertility, mortality, migration, economic development, urbanization, and technological change. Small differences in long-term assumptions can produce large differences in projected population size.

What is an age structure diagram?

A graph showing the distribution of males and females among different age groups in a population. Its shape helps predict population growth trends and the population's need for resources and services.

What does a pyramid-shaped age structure diagram indicate?

A broad base indicates a large proportion of prereproductive individuals and high birth rates. This structure generally indicates rapid potential population growth and a youthful population.

What does a constrictive age structure diagram indicate?

A narrow base compared with the reproductive-age groups indicates declining birth rates and a smaller young population. The population is likely to grow slowly or eventually decline.

What does a stationary age structure diagram indicate?

A relatively even distribution across age groups indicates that birth and death rates are approximately balanced. The population is generally stable or growing very slowly.

How can age structure diagrams be used to predict population growth?

A large prereproductive group signals population momentum and likely future growth, even if fertility declines. A small prereproductive group and a large older population suggest slow growth, zero growth, or decline.