Guide to Qualitative Symbols and Interaction Representations

A complex ecological system can be simply yet formally described using a qualitative approach with a set of 'boxes and arrows.' Qualitative models are typically drawn as familiar and intuitive diagrams consisting of ecological ‘components', such as a species (in
circles) and interactions shown as positive , negative or neutral 'links' (arrows).

 

Systems: The term ‘system' refers to any combination of two or more components having interactions between them. Models are hypotheses or proposed representations of how a system is structured. No model is a ‘perfect' representation of the system. Ecologists use qualitative modeling in loop analysis.  It is convention to use triangles around components that are abiotic components and circles around components that are biotic.

 

Basic interactions: Five basic types of interactions can be depicted.

  1. Commensalism (0/+)

    Component 1 has a positive effect on component 2 without any effect on itself. For example, if the sun is component 1 and plants are component 2, plant growth and reproduction are enhanced with increased exposure to solar radiation, but this has no effect on the sun. This relationship is not a feedback loop because there is no return signal (input) to component 1.

  2. Ammensalism (0/-)

    a- Component 1 is abiotic and has a negative effect on component 2 without any effect on itself.

    b- Component 1 is biotic and has a negative effect on component 2 without any effect on itself. This relationship does not constitute a feedback loop because there is no return signal (input) to component 1.

  3. Mutualism (+/+)

    Two components positively affect each other. If each component is biological, this relationship is referred to as a ‘mutualism'. If component 1 represents flowering plants and component 2 bees, flowers provide food while the bees help the plants to reproduce. This relationship is a positive feedback loop since the signs of the input and output are the same (here they are both positive).

     

  4. Predator/Prey (+/-)

    Component 1 has a positive effect on component 2, but component 2 has a negative effect on component 1. This relationship between a predator and its prey could be represented by this digraph. As the predators (component 2) increase in numbers, they deplete the prey (component 1), which in turn has a decreasing effect back to the predators. Likewise, as the predators decrease in numbers, the prey benefit from reduced predation, and this has an increasing effect on the predators as a result of increased food resources. This is a negative feedback loop because, for either component, the input is opposite in sign to the output.

  5. Competition (-/-)

    Two components negatively affect each other. Two species in competition for the same resource can lead to this type of interference. Note that, in effect, this relationship constitutes a net positive feedback loop because the signs of the input and output are the same (they are both negative). The net effect is positive feedback since, as explored by May 1973, this interaction will result in instability - unless it is mediated by regulatory processes stemming from self-regulation or from interactions with other components.

Complex interactions: Below, three more complex types of interactions are shown

  1. A three-species community system with of plant, herbivore, and predator

    The plant has a "self regulation" negative loop shown.

  2. Feedback. A feedback loop occurs when a signal leaves one component and returns to the original component after passing through one or more other components in the system. If the signs of the output and input signals are the same (either both positive or both negative), then it is a positive feedback loop. If the signs of the output and input signals are opposite, then it is a negative feedback loop.

  3. Indirect effects. Effects that occur as a result of a change in a component that is not immediately connected to the original component (two or more links separate the two components) are called indirect effects. According to the model below, if root-feeding click beetle populations increase the amount of root mass should decrease. This is a direct effect, because there is a single link separating these two components. As a result of this decrease in root biomass, the amount of its mycorrhiza, the root-symbiotic fungus, present in the soil may also decrease. The decline in root-symbiotic fungi occurring as a result of adding click beetles to the system is an indirect effect, because the fungi and beetle component are separated by more than one link.