Modeling has become an important tool in ecology. There are many reasons why an ecological system or process cannot be directly manipulated in a field test and therefore why a mathematical approach becomes necessary. For example, realistic funding restrictions prevent ecologists to carry on large-scaled and long-term trimming experiments for testing community responses to an environmental disturbance. Models can help explore ideas in regards to one’s thinking, define questions more precisely, assist in testing hypotheses, and identify data needs.

More and more ecology students consider modeling as an essential component of their education. However, some students may be mislead to think that ecological models (particularly those dealing with ecosystems and communities) are extremely complex and detailed, and filled with intractable mathematical equations. In reality, an ecological model can be as simple as a visual representation in which two species are connected by an arrow to represent some relationship, such as predator and prey. A complex system can thus be represented by and analyzed from a relatively simple visual representation. This modeling approach is called qualitative modeling, or loop analysis. It is more practical than quantitative modeling, because qualitative models require fewer resources and less modeling experience. Mostly importantly, qualitative models are critical in defining research questions.

As used in mathematical ecology, qualitative modeling is simply a rigorous analytical approach of complexity. It applies well established mathematical concepts, some dating back over a century. It emerged in its present conception in the 1960’s following the efforts of economists, whose work strongly influenced the theory of community ecology in the following decades, led mostly by Robert May and Richard Levins. The availability of symbolic processors for PCs and novel mathematical advances have led to a renew interest in the approach.

Qualitative models are typically drawn as diagrams, called signed digraphs, with circles and lines that represent the ecological variables and flows of materials, energy, or causation between two variables, respectively. If there is a direct positive effect of one variable upon another, the line will be ended in a pointed arrow. A line with a solid circle at the end of it represents a negative interaction. An absence of line means no direct interaction between two variables. Thus, the interactions between populations of different species in a community can be classified according to combinations of the three symbols {–,0,+}. In general, there are 5 types of interactions: predator-prey (+/-), interference (-/0), mutualism (+/+), commensalism (0/+), and amensalism (0/-). Since it is difficult, or often impossible, to fully understand the quantitative relationship between two variables, a qualitative specification of an ecological system is often the best that ecologists can do. Simply knowing the sign of their interactions can provide important insights to the dynamic behavior of complex systems. Thus one can “draw” an ecological community system just based upon his knowledge of species interaction. The signed digraph is then converted to a community matrix with only three numbers {-1,0,1}. Several matrix algebra functions are used to test the system and predict the behavior of system response to a disturbance. Because of its simplicity, qualitative modeling is now becoming accepted as a standard approach in biology.

The two analyses that have become standard are of stability and of predictability. In evaluating stability, a system is assessed for conditions under which stability is possible. Novel criteria allow provide greater insight and subtlety in evaluations of stability (Dambacher, Luh, Li and Rossignol 2003). The response of the density of variables of the system to a sustained perturbation can then be assessed, or ‘predicted’ based on a probabilistic scale (Dambacher, Li and Rossignol 2002). A novel algorithm now provides predictions of changes in life expectancy as well (Dambacher, Levins and Rossignol 2004).