Population Model

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JerzyW
Junior Member
Posts: 8
Joined: Sun Aug 15, 2021 9:41 pm
Vensim version: PLE+

Population Model

Post by JerzyW »

Year 2022 marks the 50th anniversary of the introduction of the Population Model, the most popular model in system dynamics. The model was first published in a very popular book at that time, “The Limits to Growth” (1972) by Meadows. Book was a success but nobody noticed that the Population Model was incorrect.

The intuitive approach to system dynamics taken by the authors led them to believe that positive (reinforcing) feedback always creates growth and decline is the results of negative (balancing) feedback. At first glance this approach may look logical but this is not how reinforcing and balancing feedback work and how to distinguish one from the other. The key differentiating criteria between them is not an odd or even number of negative signs (because development of any model is wide open to interpretations) but the convergence (or lack of it) to specific goal. The reinforcing feedback loops have no specific goals to reach so they drift from plus to minus infinity (or zero). The balancing feedback loops however always have specific goals (objective) to achieve and maintain.

The authors of the book overlooked the fact that deaths are also a phenomena with reinforcing (positive) feedback. Births could increase population to infinity and deaths could decline population to zero (superposition helps to see that). The claimed “balancing effect” of the two feedback loops of opposite polarity is actually a result of two reinforcing feedback loops counterbalancing each other (working against each other). This is not a stable system.

Note: This observation by no means undermines the usefulness of Vensim program, which has permanent place in my toolbox.
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Population_Model_220123.png
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LAUJJL
Senior Member
Posts: 1421
Joined: Fri May 23, 2003 10:09 am
Vensim version: DSS

Re: Population Model

Post by LAUJJL »

Hi
Can you post a vensim model that can be run, to illustrate your ideas with concrete runs. Regards. JJ
LAUJJL
Senior Member
Posts: 1421
Joined: Fri May 23, 2003 10:09 am
Vensim version: DSS

Re: Population Model

Post by LAUJJL »

Hi
The deaths loop is a balancing loop and the births one is a reinforcing loop. Balancing loops do not necessarily need a goal. If the population is increasing the births are increasing as the deaths do, but births are added and deaths are subtracted to the population and this makes the difference between the reinforcing and the balancing loop. JJ
LAUJJL
Senior Member
Posts: 1421
Joined: Fri May 23, 2003 10:09 am
Vensim version: DSS

Re: Population Model

Post by LAUJJL »

joined a simplistic population model. You can vary with the sysnthesim the average lifetime and the average fertility or the initial population and see what happens. JJ
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population.mdl
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JerzyW
Junior Member
Posts: 8
Joined: Sun Aug 15, 2021 9:41 pm
Vensim version: PLE+

Re: Population Model

Post by JerzyW »

I have no interest in building realistic Population Models but if I would have to build one then I would include government as the controlling entity. Governments develop long term demographic forecasts and they use them to control population size through social policies (e.g. from ‘draconian rule of one child per family’ to ‘generous incentive plans for young families’, and immigration if those policies fail to deliver the required outcome). In system dynamics terms, my Population Model would be a large BALANCING loop with many smaller feedback loops inside (some of them reinforcing). Population model for animal kingdom would be substantially different from the human population model because it would be based on REINFORCING loop.
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Population_Model_220130.png
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LAUJJL
Senior Member
Posts: 1421
Joined: Fri May 23, 2003 10:09 am
Vensim version: DSS

Re: Population Model

Post by LAUJJL »

HI
In Vensim, the deaths arrow is going outward and not inward and the loop is still balancing like in your CD.
Last edited by LAUJJL on Sun Jan 30, 2022 7:15 pm, edited 1 time in total.
LAUJJL
Senior Member
Posts: 1421
Joined: Fri May 23, 2003 10:09 am
Vensim version: DSS

Re: Population Model

Post by LAUJJL »

the population model is very approximative and does not resist to extreme conditions tests. For example, if the births are set to constant 0 with the synthesim starting at year 1900 and the final time set to 2200. 8 % of the initial population is still in life 200 years later.
It comes from the fact that the average age of the population is assumed constant in the model. if the births are set to 0, the population is getting older and the mortality is increasing. To correct this one must allow the mortality to take into account the average age of the population that will influence the fertility and the mortality.
Joined a model that takes into account the eventual ageing of the population.
It illustrates the difficulty of SD. It took me several hours to arrive at a reasonable model, that behaves apparently well. And I am not sure that it has no bug conception in it. I leave to the reader the opportunity to verify it.
To force the births to 0, one has just to set the standard fertility to 0. One can make a lot of scenarios already with this simple model, modifying the parameters, forcing steps, imagining epidemics, etc…
It works with the Vensim PLE.
Best.
JJ
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population_ageing_2.mdl
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