sd causal loop diagram

introduction

CLD or causal loop diagram is used to conceptually model dynamic systems in a holistic manner ( Marketlinks, 2019 ), since

• it is a snapshot of all relations that matter,
• it is a visual representation of key variables (i.e. factors, issues, processes) and how they are interconnected,
• it shows the direction of causality, the nature of relationships (i.e. proportional or inverse), and whether there is any delay in an expected effects’ occurence.

In CLD variables are represented as texts and causal relationships between them are represented as arrows.

example

• One of the common causal loop diagram is that represents relation between population, birth rate and dead rate ( Singh & Frostell, 2016 ), which can be modified and drawn as follow

• Population element should be in the same shape, but it is drawn separately as in above due to limitation of Mermaid ( Baketarić & Vinod, 2023 ), in order to stress the two loops, balancing and reinforcing loops.

• Common symbol for time delay is || which is used as |+| and |-| here.

• The symbol >> or << is for no time delay.

equation

Some variables and equations related to previous diagram are as follow ( NRHS Teacher, 2016 ).

• Population size is symbolized with $N$.
• Population growth is $$\tag{1} \frac{dN}{dt} = B - D, $$ where $B$ and $D$ stand for birth and death rates, respectively.
• Exponential growth is $$\tag{2} \frac{dN}{dt} = r_{\max} N, $$ where $r_{\max}$ is maximum per capita growth rate of population.
• Logistic growth is $$\tag{3} \frac{dN}{dt} = r_{\max} N \left( \frac{K - N}{K} \right), $$ where $K$ is carrying capacity.