Population Ecology: r and K Species, Survivorship and Human Populations

r-selected and K-selected species

Every living thing has limited energy. It can spend it on many young or on a few well-cared-for young.

• r-selected species: many small offspring, early breeding, short life, little or no parental care. Numbers can shoot up fast when conditions are good and crash when they are bad. Examples: insects, mice, most fish, frogs, weeds, bacteria.
• K-selected species: few large offspring, late breeding, long life, lots of parental care. Numbers stay near the carrying capacity (K), the largest population the habitat can support. Examples: elephants, whales, great apes, humans, coconut trees.

The letters come from the growth equation: r is the growth rate, K is the carrying capacity. Most species are somewhere between the two. Populations also vary inside: individuals differ in size, speed or resistance to disease, and that variation helps a population survive change.

Survivorship curves

A survivorship curve starts with a group born at the same time (say 1000) and plots how many are alive at each age. The y-axis is usually on a log scale, so a steady death rate looks like a straight line.

• Type I: flat at first, then drops in old age. Most young survive because parents care for them. Humans in rich countries, elephants. (K-selected.)
• Type II: a straight diagonal line. The chance of dying is the same at every age. Many birds, lizards, squirrels.
• Type III: drops very steeply at the start, then flattens. Most die as eggs, seeds or larvae; the few survivors live long. Fish, oysters, frogs, trees. (r-selected.)

Generalist and specialist species

A species' niche is its role: what it eats, where it lives, when it is active.

• Generalists have a broad niche: many foods, many habitats. Crows, rats, cockroaches, raccoons, house sparrows. They cope well when habitats change and often become invasive.
• Specialists have a narrow niche: one food or one habitat. Giant panda (bamboo), koala (eucalyptus leaves), monarch caterpillars (milkweed). They compete well in a stable habitat but are in danger when that one resource disappears.

Age structure diagrams

An age structure diagram (population pyramid) has a bar for each age group, males on one side and females on the other, youngest at the bottom.

• Expanding (wide base, like a triangle): many children and young adults → fast future growth. Example: many countries in sub-Saharan Africa.
• Stable (straight sides, like a column): births roughly equal deaths → little growth. Example: the USA, France.
• Shrinking (narrow base, bulge higher up): fewer children than adults → the population will fall and age. Example: Japan, Italy, South Korea.

The bulge of young people in a wide pyramid causes population momentum: even if each family has fewer children, the population keeps growing for decades because so many people are entering parent age. India today is between expanding and stable.

Total fertility rate and human population dynamics

The total fertility rate (TFR) is the average number of children a woman would have in her lifetime. Replacement-level fertility is about 2.1: two children replace the parents, and the extra 0.1 covers children who die young. In countries with high child death, replacement is higher (about 2.5).

Human population change: growth rate (%) = (birth rate − death rate) ÷ 10 + net migration, where birth and death rates are per 1000 people per year. The rule of 70 gives the doubling time: doubling time ≈ 70 ÷ growth rate (%).

Factors that lower TFR: education of girls, jobs for women, access to family planning, lower child death, city life and pensions. Factors that keep it high: child labour on farms, children as old-age support, high child death and cultural or religious traditions. The world's population passed 8 billion in 2022 and is growing more slowly each year.

The demographic transition

The demographic transition model describes how countries change as they develop:

1. Stage 1 (pre-industrial): high birth rate, high death rate → small, steady population.
2. Stage 2 (transitional): food, clean water, vaccines and medicine cut the death rate; the birth rate stays high → very fast growth.
3. Stage 3 (industrial): schooling, cities, jobs for women and family planning cut the birth rate → growth slows.
4. Stage 4 (post-industrial): low birth and death rates → large, steady population. Some countries go into a Stage 5 where births fall below deaths and the population shrinks.

The gap between the birth and death lines in stages 2 and 3 is where the population grows. The model fits Europe's history well, but each country moves at its own speed.

Try it: build a mini survivorship curve

Take 64 dried beans (or paper squares) as a newborn group. Each 'year', remove half for a Type III-like early loss in the first two years, then remove only 2 per year. In another group remove 8 per year (Type II). Write the number left each year and plot both on graph paper. Then, in the 3D above, slide the TFR to 1.5 and 3.0 and predict the third-generation size before you look.

Key formulas and definitions

• Growth rate (%) = (birth rate − death rate) ÷ 10 [rates per 1000 per year]
• Growth rate (%) with migration = (b − d + immigration − emigration) ÷ 10
• Doubling time (years) ≈ 70 ÷ growth rate (%)
• Replacement-level fertility ≈ 2.1 children per woman
• Population change = (births + immigration) − (deaths + emigration)
• r-selected: many, small, no care, Type III; K-selected: few, large, care, Type I

Worked examples

Common mistakes

• Thinking r-selected species are 'worse'. They are just as successful; they suit changing, unpredictable places.
• Reading a survivorship curve on a normal scale. On a log scale, a straight line (Type II) means the same chance of dying each year.
• Saying replacement fertility is exactly 2. It is about 2.1 because some children die before having their own children.
• Forgetting that in Stage 2 of the demographic transition the death rate falls first while the birth rate is still high; that is why growth is fastest there.