The number of people in the world is the balance between reproduction and mortality. Reproduction per person is affected by the product of economic assets per person and the number of people, where economic assets are evaluated in emergy units which include environmental as well as urban assets. Mortality increases by diseases and decreases by economic assets used for health care. PEOPLE is a model which combines these factors (Odum and Scott, 1983). As countries develop economically the emergy per person gradually declines as do birth rates. In other words this model has built into it the hypothesis that population reproduction in one way or another is diminished as people become crowded relative to their resources.

Explanation of the diagram and program

On the left of the diagram production of economic assets is generated by interaction of the flow of renewable resources remaining unused R nonrenewable resource reserves F feedback inputs from economic assets A and feedback input from population N. The renewable resources available are the remainder R of the inflow J not yet in use (See Model II-2-Renew) for more explanation of the limitations of constant renewable sources. One production flow, K3*R*F*N*A, operates only when there are still nonrenewable fuels available: another K4*R*A becomes important only when they are gone. The quantity of economic assets A is a balance between the productive flows and the outflows. The outflows include depreciation K5*A, the economic assets used to develop populations K6*(A/N)*N, the economic assets used for regular health and medicine L0*(1-K9*A) and those used for epidemic disease L0*N*N*(1-K9*A).

The population N is the balance between births and deaths. The birth rate L1*(A/N)*N is directly proportional to assets. Two pathways of mortality are included regular deaths and deaths from epidemic disease. Regular mortality K7*N*(1-K9*A) is in proportion to the population N, but diminished in proportion to the economic assets used in health care (1-K9*A). Epidemic mortality is increased in proportion to the square of the population but diminished in proportion to those assets used in health care and medicine (1-K9*A). A square of population N*N, is appropriate because epidemics spread when people are crowded in proportion to population interactions which is mathematically the square of the number.

The program was calibrated with values for 1980. In Table IV-19a is the data used to calibrate the coefficients. When the program is run it generates the graph shown in Figure IV-19b. As the nonrenewable fuels are used up economic assets pass through a maximum and start to decrease. Not many years later the population crests and decreases rapidly a result of declining birth rates and higher mortalities.

The population simulation shows that the assets per person during growth are higher than those during the decline period. However later with lower populations the assets per person are reasonably good. In one sense this model is an optimistic one implying that a reasonable standard of living is possible in lower energy times providing population levels are adjusted to be in proportion to resources available for use.

"What If" Experimental

1. If the fossil fuel tank F is set to zero the model depicts a human population growing on renewable energies alone. How will the graph differ from the original? Why?
   


2. What would you change to demonstrate the results of increased medical care (increase K9)? How does this change the long-range population?
   


3. How would the graph change if after about 250 years the birth rate were cut 90% - what would be the changes in the immediate and long-range futures? (Add statement 515 If T = 250 THEN L1 = 0.0001) Explain also the difference in the graph of the fuels.
   


4. If an epidemic of a disease like AIDS gets worse how would this change the population prediction? Increase K8 ten times and run the simulation. Then to make things worse also cut the medical care K9 to zero.

COMPUTER MINIMODELS AND SIMULATION EXERCISES FOR SCIENCE AND SOCIAL STUDIES

Howard T. Odum* and Elisabeth C. Odum+
* Dept. of Environmental Engineering Sciences, UF
+ Santa Fe Community College, Gainesville

Center for Environmental Policy, 424 Black Hall
University of Florida, Gainesville, FL, 32611
Copyright 1994

Autorização concedida gentilmente pelos autores para publicação na Internet
Laboratório de Engenharia Ecológica e Informática Aplicada - LEIA - Unicamp
Enrique Ortega
Mileine Furlanetti de Lima Zanghetin
Campinas, SP, 20 de julho de 2007