HON 301Welcome to the Anthropocene

IV. Carrying Capacity

F. WalterSeptember 2021

Carrying Capacity

• In equilibrium, the birth rate = the death rate• The human population is not in equilibrium• The human population growth is > 1%/yr

• This growth rate is unsustainable

Survival of Species?

The typical species survives about 106 years• Species go extinct, or evolve

Species that survive longer tend to be• Adaptable• Not too specialized• MotileHumans satisfy these requirements

Invasive Species

• Transported to new ecosystem• Out of equilibrium with the ecosystem– Some fail to thrive– Some thrive in absence of natural prey

• If the invasion is small, the ecosystem can rebalance

• If not, a new balance is struck

Examples of Invasive Species• Rabbits and foxes in (Australia)• Kudzu (southeastern US)• Knotweed (everywhere)• Pythons (Florida)• Zebra Mussels (Great Lakes)• Brown tree snake (Guam)• Common Carp (freshwater lakes)• Rats (almost everywhere)• Dutch Elm Disease (US)• Gypsy Moth (NE US)• Fire Ants (Texas)

Humans as an Invasive Species

• Homo Heidelbergensis ~ 1.8 Mya• Homo Sapiens “Out of Africa” ~ 75,000 yaTechnology permitted adaptation to wide range of climates• Humans populated – entire Old World by ~30,000 ya– entire New World by ~15,000 ya– Polynesia by 900 CE

• Inhabit all continents except Antarctica; elevations to 16,000 ft

Humans as a Facilitator

Carried useful and not-so-useful species• Beasts of burden• Cattle• Edible plants

• Rats• Human parasites

Humans as an Invasive Species

Two effects:• Direct impact on the environment• Indirect impact on the environment

Example of Direct Impact:Extinction of Large Mammals

• Large animals have few natural enemies• Most large animals have a reproduction

strategy of few young infrequently• Hunting, combined with environmental

stresses, can explain extinction of large mammals ~ 10,000 years ago

Did not occur in Africa

Indirect Impact:Removal of geographic barriers

Increase in invasive species from:• Rapid intercontinental travel • Trade in exotic species

Extinction leads to drops in bio-diversity

Carrying Capacity

What is the maximum number of human beings the planet can support?

We need resources, including:• Fresh water• Food• Energy• Raw materials for manufacturing

Food Resources

• Wild• Domesticated– Plants– Animals

Sustainability depends on • Population pressure• Climate change

Energy Resources• Renewable– Biotic

• Animals (e.g., beasts of burden)• Combustion of plant materials• Animal oils

– Abiotic• Solar• Hydro• Wind

• Non-renewable– Petroleum (oil/gas)

• Peak oil– Nuclear

Peak Oil

Raw Materials

• Renewable (biotic)– Plant products (e.g., wood) – Animal products (e.g., bone, sinew)

• Non-renewable– ores

Anaconda mine, Butte MT

Fresh Water

• Renewable– Precipitation runoff

• Non-renewable– Aquifers

• Desalinization of seawater

Ogallala Aquifer

Contains ~3.3x109 acre-feetTypically 112 feet deep6000 years to rechargeOver 11% depleted by 2009; current rate ~ 2%/yr

Ogallala Aquifer

Ground Water Depletion

Long Island Aquifers

Long Island Aquifers

Volume of fresh water• 10-20 trillion gallons• Inflow: ~1500 Mgal/day• Use: ~400 Mgal/day

Saltwater intrusion is a concern

Multipliers

Three hundred trout are needed to support one man for a year. The trout, in turn, must consume 90,000 frogs, that must consume 27 million grasshoppers that live off of 1,000 tons of grass.

G. Tyler Miller, Jr., American Chemist (1971)

Net Primary Production (NPP) is production in units of its least common denominator - grass

Net Primary Production

Net Primary Product (grass)Source: https://na.unep.net/geas/archive/pdfs/GEAS_Jun_12_Carrying_Capacity.pdf

Some Numbers• Surface area of Earth: 5.10 x 1014 m2

• Land Area: 1.49 x 1014 m2 = 1.49 x 1010 ha– ha=104 m2 ~ 2.5 acres

• Current number of humans: 7.90 x109

• Area/person: 1.88 ha (was 1.99 in 2018)

• Arable land: ~ 4.2 x 109 ha• Arable land (in use)/person: ~0.25 ha

=> ~ half of potentially arable land is in use

It takes about 1 acre (0.45 ha) to feed an American (http://www.farmlandlp.com)

Overpopulation

Earth has a finite carrying capacity• We need sufficient– Fresh water– Food

• We need space for plants and animals

Carrying Capacity is unknown • Estimates range 4 - 16 billion

Human Population Growth

Why the Population is Growing

http://www.eoearth.org/view/article/153596/

How Long Until the Earth is Full?

Exponential Growth• Y=tX, X>1

The Meaning of Exponential Growth• A constant percentage increase per time– e.g, a 2% population growth is exponential.

• The doubling time t½ :– 70 ÷ the percentage growth• Let a(t)=a0eRt

• When a(t)=2a0, eRt=2• Rt½ =ln(2)=0.693• t½ =0.693/R = 69.3/pct, where pct=100*R

The Meaning of Exponential GrowthConsider a test tube with one bacterium.

• The size of a bacterium is ~1 μm (10-4 cm)• Volume of the bacterium ~ 10-12 cm3

• The bacterium divides every 30 minutes.• The volume of the test tube is 40 cm3.• 4x1013 bacteria fit in the test tube

How long until the test tube is full?

The Meaning of Exponential Growth• Doubling time is 30 minutes• % growth = 70/30 =2.3% per minute• 40/10-12 = 4 x 1013 bacteria fit in the test tube.• When is the test tube full of bacteria?

The Meaning of Exponential Growth• Doubling time is 30 minutes• % growth = 70/30 =2.3% per minute• 40/10-12 = 4 x 1013 bacteria fit in the test tube.• When is the test tube full of bacteria?• After ln(3 x 1013)/ln(2) doubling times• After 44 doubling times, there are 2x1013 bacteria

• In another 30 minutes the test tube is full.

• That’s 22.5 hours!

The Meaning of Exponential Growth• There are now 7.9 billion people on Earth• Population growth is about 1.03% per year

• The surface area of Earth is about 5x1014 m2

• About 29% of the Earth is land.• Each person has, in principle, about 20,000 sq m

When is Earth Full?• Define the Earth as full when each person has 1 sq m. • That requires 20,000 times the present population, or

about 1014 people on Earth.• Current doubling time is 70/1.03 = 68 years• At the current rate, that will take 13.6 doubling times,

or 924 years!

• in 2020:– the growth rate was 1.05 – the time to fill the planet was 910 years

When will Humans Fill the Galaxy?Suppose we cap Earth at its current population, andstart colonizing extrasolar planets.• Assume one Earth-like planet per star• We fill the galaxy (4x1011 stars) in 38 doubling times.

That’s only 2600 years!

In the space of one hundred and seventy-six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over one mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the Old Silurian Period, just a million years ago next November, the Lower Mississippi River was upwards of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing rod. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three quarters long, and Cairo and New Orleans will have joined their streets together, and be plodding comfortably along under a single mayor and a mutual board of aldermen. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.

Life on the Mississippi, by Mark Twain

Malthusian Theory

Famine seems to be the last, the most dreadful resource of nature. The power of population is so superior to the power of the earth to produce subsistence for man, that premature death must in some shape or other visit the human race.

Malthus, T.R. 1798. An essay on the principle of population. Chapter VII, p61

Malthusian Theory. I.

• Population increases exponentially• Food production does not

• At some point, we’ll have too little food, and something will have to give.

• This applies to fresh water and other limited resources too

Malthusian Theory. II.

So far:• Population growth rate

has decreased• The “Green Revolution”

has kept pace with population growth

Necessity is the Mother of Invention

Long Term Survival of a Civilization

Based in part on Collapse, by Jared Diamond

Influences on Survival

1. Self-inflicted ecological damage2. Climate change3. Hostile neighbors4. Friendly neighbors (trade)5. Response to problems

Examples

• Rome• Easter Island (Rapa Nui)• Mesopotamia• Anasazi• Maya• Greenland/Iceland• Tikopia

Rapa Nui (Easter Island)

• 16,000 ha• Settled ~ 700-1100 CE• Temperate climate; poor soil

• See “The growth and decline in Rapa Nui's population is a lesson for our future” https://phys.org/news/2020-09-growth-decline-rapa-nui-population.html Phys Org, 9/3/20

Rapa Nui

• 16,000 ha• Settled ~ 700-1100 CE• Temperate climate; poor soil• Originally forested, including largest known

palm trees• Population peaked @~15,000 ~1500 CE

Rapa Nui

• 16,000 ha• Settled ~ 700-1100 CE• Temperate climate; poor soil• Originally forested, including largest known palm

trees• Population peaked @~15,000 ~1500 CE

• By 1770, population 1,000-2,000• Today: no trees; mainly grassland

Rapa Nui

The Story: All was well for ~500 years. But…• Too distant for regular human contact• Humans introduced rats to Rapa Nui• Trees lost to– Harvesting by humans – and/or –– Predation by rats

• No trees -> no boats; no fishing

• Recent work suggests this is too simplistic

Reality• No idyllic equilibrium• No rapid collapse• Variable climate– Cold ESNO phases -> decreased rainfall

• Population growth – Adapted by developing a simpler society

• 1450-1550 CE crisis coincides with Little Ice Age (?) (late 14th – early 19th century)

• 19th century crises due to introduced diseases

Rapa Nui

Causes of the collapse?

1. Self-inflicted ecological damage YES2. Climate change YES3. Hostile neighbors NO4. Friendly neighbors (trade) NO5. Response to problems maybe

Lessons from Rap Nui

Life is tough on• A small island with limited resources• In isolation• Facing climate change

Tikopia

• 500 ha• Settled ~ 1000 BCE

Tikopia

• 500 ha – good soil• Settled ~ 1000 BCE• Population stable at ~1200 through population

control• ~1600 CE: all pigs slaughtered; diet changed• ~1900 CE: Christian missionaries outlaw birth

control/abortion; population increased 50%• Now: emigration keeps population stable• 3000 years of stability

Tikopia

Reasons for avoiding the collapse?

1. Self-inflicted ecological damage YES2. Climate change unknown3. Hostile neighbors NO4. Friendly neighbors (trade) (yes)5. Response to problems YES

Pressure relieved by population control

Responses to Crises

• Ignorance• Reasoning by False Analogy• Creeping Normalcy• Local Amnesia• Rational Behavior• Tragedy of the Commons• Irrational Behavior

Relevance to Earth

Earth is a closed environment with finite resources.

1. Self-inflicted ecological damage? YES2. Climate change it happens3. Hostile neighbors NO4. Friendly neighbors (trade) NO5. Response to problems TBD

Steffen, W. et al. 2015 Science 13 February 2015: Vol. 347 no. 6223

Earth SystemPlanetary Boundaries