Ecology & Environmental Problems

• Dr. Ron Chesser• Lecture #4• No new reading assignment.

POPULATION GROWTH

Models of population growth

Exponential growth: Nt = Nt-1 + rNt-1+rNt-2+rNt-3+… = N0er0t

t=generationr=intrinsic increase rateNt = population size at time t.Nt-1=population size in prior generationN0=initial population sizee=exponentialr0=ln(1+r)

t

N

Example of Exponential growthFold a piece of paper in half 100 times…How thick would it be?

• Piece of paper is .1 x 10-6 km thick• Number of thicknesses after “n” folds is

equal to 2n

• Thickness (in km) = 2n x .1 x 10-6

• 100 folds yields 1.2677 x 1022 km• This is about 12 billion light years• This is about the radius of the known

universe

Bacterial Divisionstart with 1…after 100 divisions?

• After 100 cell divisions there would be 1.27 x 1030 bacteria

• 127,000,000,000,000,000,000,000,000,000,000• Why aren’t we knee-deep in bacteria?

Carrying CapacityCarrying Capacity

The theoretical number of individuals that can be supported by the resources within an ecosystem. The theoretical number of individuals that can be supported by the resources within an ecosystem.

LOG SCALE SHOWS EXPONENTIAL GROWTH OF ENERGY CONSUMPTION

Earth’s Resources• we have already transformed or degraded 39-50% of the Earth's

land surface (agriculture, urban). • we use 8% of the primary productivity of the oceans. • we have increased atmospheric CO2 concentration by 30% • we use more than half of the accessible surface fresh water • over 50% of terrestrial nitrogen fixation is caused by human

activity (use of nitrogen fertilizer, planting of nitrogen-fixing crops, release of reactive nitrogen from fossil fuels into the atmosphere)

• on many islands, more than half of plant species have been introduced by man; on continental areas the fraction is 20% or more

• about 20% of bird species have become extinct in the past 200 years, almost all of them because of human activity

• 22% of marine fisheries are overexploited or depleted, 44% more are at the limit of exploitation

POPULATION AND AVAILABILITY OFRENEWABLE RESOURCES

1990 2010Total

Change (%)

Per CapitaChange

(%)Population (millions)  5,290 7,030 33

Fish Catch (million tons) 85 102 20 -10

Irrigated Land (million hectares)

237 277 17 -12

Cropland (million hectares)

1,444 1,516 5 -21

Rangeland and Pasture (million hectares)

3,402 3,540 4 -22

Forests (million hectares)

3,413 3,165 -7 -30

Models of population growth

Logistic Population growth:

Nt = K/(1+[[K-N0]/N0]e-rt)t=generationr=intrinsic increase rateNt = population size at time t.K=carrying capacity N0=initial population sizee=exponential

t

N K

A. At the beginning of 2000, the human population had reached a size of 6,000,000,000. Assuming that r=0.001 (the intrinsic rate of growth of Latvia) and an exponential growth model, what will the size of the human population be in 2025?

B. Now, assuming the same information in A, but with r=0.018 (the intrinsic rate of growth of Rwanda), use the exponential growth model to estimate the size of the human population in 2025?

A. At the beginning of 2000, the human population had reached a size of 6,000,000,000. Assuming that r=0.001 (the intrinsic rate of growth of Latvia) and an exponential growth model, what will the size of the human population be in 2025?

B. Now, assuming the same information in A, but with r=0.018 (the intrinsic rate of growth of Rwanda), use the exponential growth model to estimate the size of the human population in 2025?

Human Population GrowthWas Thomas Malthus correct?

Human Population Growth

6,000,000,000

7,000,000,000

8,000,000,000

9,000,000,000

10,000,000,000

11,000,000,000

12,000,000,000

0 10 20 30 40 50 60

Years

Po

pu

lati

on

Siz

er=0.001 and r=0.018

With highestGrowth rater=0.018 Rwanda

With slowestGrowth rater=0.001 Latvia

Human Population Growth

5,950,000,000.00

6,000,000,000.00

6,050,000,000.00

6,100,000,000.00

6,150,000,000.00

6,200,000,000.00

6,250,000,000.00

6,300,000,000.00

6,350,000,000.00

0 10 20 30 40 50

Years

Po

pu

lati

on

Siz

er = 0.001 (as in Latvia)

A. At the beginning of 2000, the human population had reached a size of 6,000,000,000. Assuming that r=0.001 (the intrinsic rate of growth of Latvia) and an exponential growth model, what will the size of the human population be in 2025?

B. Now, assuming the same information in A, but with r=0.018 (the intrinsic rate of growth of Rwanda), use the exponential growth model to estimate the size of the human population in 2025?

C. Using the information in Problem A, plus a hypothetical carrying capacity, K=15,000,000,000 for the earth, estimate the size of the human population in 2025, using the logistic growth model?

D. Repeat C, except assume that r=0.018.

A. At the beginning of 2000, the human population had reached a size of 6,000,000,000. Assuming that r=0.001 (the intrinsic rate of growth of Latvia) and an exponential growth model, what will the size of the human population be in 2025?

B. Now, assuming the same information in A, but with r=0.018 (the intrinsic rate of growth of Rwanda), use the exponential growth model to estimate the size of the human population in 2025?

C. Using the information in Problem A, plus a hypothetical carrying capacity, K=15,000,000,000 for the earth, estimate the size of the human population in 2025, using the logistic growth model?

D. Repeat C, except assume that r=0.018.

Human Population GrowthWas Thomas Malthus correct?

Carrying Capacity = 15 Bil

6 000 000 000

7 000 000 000

8 000 000 000

9 000 000 000

10 000 000 000

11 000 000 000

12 000 000 000

13 000 000 000

14 000 000 000

0 20 40 60 80 100 120 140 160 180 200

Years

Po

pu

lati

on

Siz

e

With highestGrowth rater=0.018 Rwanda

With slowestGrowth rater=0.001 Latvia

Rising Death Rates• In 1999 the Worldwatch Inst. reported that rising death rates are

slowing world population growth for the first time since famine killed 30 million people in China in 1959-61.  Partly because of these rising death rates, the U.N. revised its estimate for world population in 2025 from 9.4 to 8.9 billion.  Three factors are pushing the death rates up, especially in sub-Saharan Africa and the Indian sub-continent:

• the HIV epidemic - between a fifth and a quarter of adults are already infected in Zimbabwe, Botswana, Namibia, Zambia and Swaziland. In India, four million adults are now HIV positive, more than in any other country.

• the depletion of aquifers - another serious problem in India, where water tables are falling annually by 1- 3 meters over much of the country.

• shrinking cropland area per person. More than half of the children in India are already malnourished and underweight.  Dwindling cropland also threatens food security in Nigeria, Ethiopia and Pakistan.