Industrialization/Food Consumption Impact

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This segments adds the impact of a limited food supply on the population growth for the "Modeling Industrialization for a Simple Agrarian Society" as presented by Hannon & Ruth^[1]. This segment only presents the additions from the Agrarian Society segment.

Model Development

This segment adds the dimension of deaths which is dependent on population and death rate as well as the implications of food consumption on the population. These are depicted in Fig. 1.

Element Definitions

• deaths - the number of people that die every year thus reducing the population
  • Flow Rate = [death rate] * [population]
  • Units = Individuals per Year
• food - the cache of food available to sustain the individuals on the island
  • Initial Value = 1000
  • Show Value Slider = Yes
  • Slider Max = 5000
  • Slider Min = 100
  • Units = Kilograms
• food per capita - the amount of food available per person
  • Value/Equation = [food] / [population]
  • Units = Kilograms per Individual
• eat per head - a Converter indicating the percentage of food an individual will consume per year dependent on how much is available, i.e. food per capita
  • Interpolation = Linear
  • Input Source = food per capita
  • Inputs = 0,1,2,3,4,5,6,7,8,9,10
  • Outputs = 0,.04,.155,.27,.385,.52,.63,.72,.82,.92,.995
  • Units = Kilograms per Individual per Year
• death rate - a Converter indicating the death rate as a function of eat per year.
  • Interpolation = Linear
  • Input Source = eat per head
  • Inputs = 0,.1,.2,.3,.4,.5,.6,.7,.8,.9,1
  • Outputs = .197,.19,.184,.173,.163,.147,.121,.095,.061,.028,.013
  • Units = Individuals per Individuals per Year
• eat - the rate at which the population consumes their food supply
  • Flow Rate = [eat per head] * [population]
  • Units = Kilograms per Year

Running this model produces a number of insights as depicted in the following graphs.

Fig. 2 shows that the group consumes the majority of their food in the first 40 years, which one would expect to have a marked impact on the population.

Fig. 3 shows that the population grows very readily during the first 25 years while there is ample food supply and then declines readily.

Fig. 4 shows the rapid rise of births as the population rises followed by a rapid increase in deaths as the food supply is consumed.

Summary

It's quite evident that with a fixed food supply individuals on the island will sooner or later exhaust their food supply and eventually starve to death. You might alter some of the food consumption scenarios to get a sense of the extendability of life on the island, though the end with a fixed food supply is inevitable.

In the next segment food production will be added to the model to investigate the impact on the population over time.

Prev: Agrarian Society * Next: Adding Agriculture

References

1. ↑ Hannon, Bruce & Ruth, Matthias (1994) Dynamic Modeling. Springer-Verlag

• Modeling & Simulation with Insight Maker

Additional Resources Systems Thinking World Discussions Systems Thinking World Q&A * Gene Bellinger