1. 1 Population Models (History) Carrying Capacity Scott Matthews 12-712 / 19-622 Lecture 5

2. Administrative Issues  How was Monday? Brundtland joke  HW 1 Graded. Average XX  HW 2 Due Today  HW 3 Due Next Wed 2

3. Recap of Last Time  Efforts over time have had similar findings and goals (CoR, WECD, BCSD)  Yet we’ve made little progress  The government level and business-level efforts show their interests  “..30 years of recommendations, and we’re still asking ‘paper vs plastic’  Models to assess impacts of trends limited 3

4. Recap: Club of Rome  Point wasn’t predicting, but really looking at effects of exponential growth  “A major purpose in constructing the world model has been to determine which, if any, of these behavior modes will be most characteristic of the world system as it reaches the limits to growth.”  In the end, it is “just a model” (revisited a few times since then) Lecture 1:4

5. Time to Depletion  In general, the formula for calculating the amount of time left for a resource with constant consumption growth is :  where:  y = years left  g = 1.026 (2.6% annual cons. growth)  R = reserve  C = consumption (annually)  ~95 years of chromium left

6. Results  Static index from initial equation  Exponential from slide above  5x comes assuming our reserve #s too low Source: Wikipedia, “exponential reserves index”6

7. Today  The effects of population growth  WECD definition was “meeting needs of present without sacrificing needs of future”  What are our needs and what are they functions of?  Food and water (shelter to a lesser extent - land)  Similar to IPAT, we know population has an effect (but is not the only/strongest effect) 7

8. Models of Population  Birth and death rates as drivers for balance (or lack of balance)  Analogous to measuring rate of sediment buildup/etc in environment  Define variables: N (pop), Q, k, r, t (year) 8

9. Recall: Separation of Variables If we assume N(0)=N 0 …  “Initial value problem” – separate variables 9 Why? Calc review N 0 is pop at t=0 Usually write as: =>

10. World Population (1750-1999) 10 Source: http://www.un.org/esa/population/publications/sixbillion/sixbilpart1.pdf

11. Creator: Malthus (pre-1800)  Was worried about food production keeping up with population (200 yrs ago)  Food production increase arithmetically, population geometrically – cant keep up  Counterarguments that nothing stays at exponential growth (verhulst, others)  Pop density and other factors  What are we seeing with birth and death rates? What is effect on r? 11

12. Carrying capacity  Recall: The supportale population, given the food, habitat, etc, available within an environment  “Maximum persistently sustainable load”  Can revise basic Malthus equation to:  Where K is the carrying capacity (the right hand side adds a “correction factor” to original model to limit growth by capacity 12

13. Food  Now that we have models to estimate population, we can use them to estimate impacts on other factors of interest  Define land Area A needed for food  Alpha = A/N  Scenarios: alpha constant as pop. Rises  What is wrong with this assumption? (run out of land as we need to find places to live) 13

14. Water  At a high level, how do population and food trends affect water availability?  More consumption  Less arable land (runoff/etc issues) 14