# Stock and Flow Analysis - Community Population

Updated on May 10, 2020

Ryan is currently studying for his master's degree in systems engineering at Drexel University, participating in several discussions weekly.

## Introduction

For those new to the Systems Engineering field, a common concept to get used to is the Stock and Flow Diagram. They represent the quantitative factors of a system (the stock) and the paths they take throughout said system (the flow). A simplified example is the population of a community. The stocks highlighted in the diagram are the total population of the city/community, regardless of age, and the number of adults and children. The flow, shown by the arrows, represents the path an individual may or may not take while being part of the system, as they can affect it in a number of ways.

## Inputs

To start, the first and possibly most prominent "cloud", called the sink or source, represents the children that will be born into the community. Once born, the person counts as a child, and the population increases by one, and with multiples, the population increases by one per child born (as populations usually go). An additional input is the bottom cloud, representing the people who do not live in the selected community. There is an input coming from them, as some members may move into the selected system from outside, adding to the total population. If the individuals moving in are adults, they can still have children and contribute to the first input. If those moving in are children, they are still part of the system and can contribute as such. As the children grow, they become adults. Children and adults were counted as two separate stocks in the diagram based on how they can affect the population. As adults, couples sometimes decide to start a larger family, and have children. This loops back to the “births” input, and more children are born, and the cycle repeats, all while adding to the “total population” stock. This is a reinforcing feedback loop, as it contributes to increasing the population, which in return has more births. In “Thinking in Systems”, the author, Donella H. Meadows, calls Reinforcing Feedback Loops “a vicious or virtuous circle that can cause healthy growth or runaway destruction”, and is all the more prominent in this case. Increasing the population through births can lead to a population boom, which if left alone, can have devastating consequences, and if controlled, can lead to prosperity. For example, if the input gets to be too high and the community isn’t prepared, living conditions may decrease in quality and space. It will be harder to find jobs, and the quality of care in education and medical facilities will decline. If the input is monitored properly, the mayor (or an official) can plan for this and work to prepare for the sudden increase in population. Factors such as these are important to take into consideration, even if they don’t show up directly on the diagram.

A city population can be observed as a closed system if it's closed off from immigration and emigration.

## Outputs

Two outputs are considered for the stock to follow. The first flow is death, with the cloud representing anyone who has lived and died in the city. This is not flowing out of the children or adult stocks, as no matter who dies, it affects the population in the same way, and it decreases. The other output is the opposite of the cloud across from it, and represents those moving out of the community to pursue their life elsewhere. This decreases the population, and can be either children or adults leaving.

## Setting Boundaries

Theoretically, a city population can be observed as a closed system if it’s closed off from immigration and emigration. In “Diagnosing and Engaging with Complex Environmental Problems”, John Reuter explains that the first step in observing information from a system is by setting boundaries (Reuter 94). In a closed system, the boundaries disregard all external sources and instead only focus on the flow between stocks. In this diagram, it’s possible to track the flow of an individual from a child to adult, possibly reinforcing their original stock by having more children, and eventually dying, all without leaving the population of the city. With this in mind, a city could thrive with no immigrants/emigrants, assuming the birth-death ratio is balanced and properly observed. Whether that is a realistic or suggested route to take is highly debatable, but in terms of the stock and flow diagram, it is possible.

## Defining Factors

While each stock and flow is simplified, there are a large number of factors that can increase or decrease the flow rate of inputs or outputs. For example, terrible living conditions, poor healthcare, and insignificant education can contribute to increasing the rate at which the population decreases. Death of a loved one can lead to depression and suicide, and the population will decrease further. On the other hand, and a brighter note, an excellent economy, large job market, and a clean community can entice people to move to this community from other areas. Good school and healthcare systems are appealing for those looking to start families. This contributes to the input, even if they aren’t specific stocks themselves.

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