Geog310-2010-LimitstoGrowth

# Geog310-2010-LimitstoGrowth - Geography 310 Environment and...

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1 1 Geography 310 – Environment and Resources Limits to Growth vs the Growth of Limits Or, Doomsters vs Boomsters http://www.itulip.com/images/flynnart.gif 2 s system dynamics as a tool for representing interactions within a system s population dynamics and carrying capacity, highlighting the concept of “overshoot” s the concept of “World Modelling” and its role in the limits to growth debate s the counter-arguments to the notion of limits to growth s the impact of human activity on the earth’s ecosystems, particularly as measured by the “ecological footprint” Lecture objectives This lecture will introduce and illustrate the following concepts: 3 0. System dynamics s approach to representing interactions within and behaviour of complex systems s developed by Jay Forrester, MIT professor, in the 1950s 4 System dynamics view of a bank account withdrawals deposits (-) (+) Adapted from Limits to Growth (p. 39)

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2 5 1. Geometric and arithmetic growth s arithmetic growth - A quantity increases by a fixed amount over successive time periods - y t+1 = y t + d s geometric growth - A quantity increases by a fixed fraction over successive time periods - y t+1 = y t + r y t 6 Graphical comparison of geometric and arithmetic growth 0 10 20 30 40 50 0 200 400 600 800 1000 1200 Time (years) y geometric growth (5%/year) arithmetic growth (5/year) 7 2. Lessons from ecology – population dynamics population (–) (+) # births # deaths fertility rate (f) mortality rate (m) net growth rate = r = f – m exponential growth if f > m System dynamics model for fixed fertility and mortality rates (assume predation negligible) 8 population (–) (+) # births # deaths fertility rate (f) mortality rate (m) System dynamics model including mortality rates influenced by competition for resources (+)
3 9 Carrying capacity and population dynamics Carrying capacity (K) s maximum stable population size that a particular environment can support over a relatively long period of time Modified equation for population dynamics s y t+1 = y t + r y t (1 – y t /K) (a simple form of logistic equation) 10 Population Time K Trajectory 1 -- transition from exponential growth to stable population 11 Time Trajectory 2 -- overshoot and recovery K 12 Time Trajectory 3 -- overshoot and recovery after damage to environment K

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Geog310-2010-LimitstoGrowth - Geography 310 Environment and...

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