1. Ecology & Environmental Problems Dr. Ron Chesser Lecture #4 No new reading assignment. POPULATION GROWTH

2. Models of population growth Exponential growth: N t = N t-1 + rN t-1 +rN t-2 +rN t-3 +… = N 0 e r 0 t t=generation r=intrinsic increase rate N t = population size at time t. N t-1 =population size in prior generation N 0 =initial population size e=exponential r 0 =ln(1+r) t N

3. Example of Exponential growth Fold 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 2 n Thickness (in km) = 2 n x.1 x 10 -6 100 folds yields 1.2677 x 10 22 km This is about 12 billion light years This is about the radius of the known universe

4. Bacterial Division start with 1…after 100 divisions? After 100 cell divisions there would be 1.27 x 10 30 bacteria 127,000,000,000,000,000,000,000,000,000,000 Why aren’t we knee-deep in bacteria?

5. Carrying 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.

6. LOG SCALE SHOWS EXPONENTIAL GROWTH OF ENERGY CONSUMPTION

7. 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 CO 2 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

8. POPULATION AND AVAILABILITY OF RENEWABLE RESOURCES 19902010 Total Change (%) Per Capita Change (%) Population (millions) 5,2907,03033 Fish Catch (million tons)8510220-10 Irrigated Land (million hectares) 23727717-12 Cropland (million hectares)1,4441,5165-21 Rangeland and Pasture (million hectares) 3,4023,5404-22 Forests (million hectares)3,4133,165-7-30

9. Models of population growth Logistic Population growth: N t = K/(1+[[K-N 0 ]/N 0 ]e -rt ) t=generation r=intrinsic increase rate N t = population size at time t. K=carrying capacity N 0 =initial population size e=exponential t NK

10. 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 Growth Was Thomas Malthus correct?

11. r=0.001 and r=0.018 With highest Growth rate r=0.018 Rwanda With slowest Growth rate r=0.001 Latvia

12. r = 0.001 (as in Latvia)

13. 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 Growth Was Thomas Malthus correct?

14. With highest Growth rate r=0.018 Rwanda With slowest Growth rate r=0.001 Latvia

15. 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.