Challenges to Anticipate and Solve

Challenge #1. Finding the right level of complexity in students' models. Students can either go overboard with too much detail or render models that are overly simplistic. The examples provided throughout should model the kinds of detail required. In addition, students sometimes choose to ignore the requirement to write up brief descriptions of the nature of the interactions being depicted, and should be reminded to do so. In general, models should be detailed enough to convey the essential ecological structure, but not too complex so as to lose focus.

Depending on the level of the course, students may benefit from instruction on the types of trophic relationships they are likely to observe in a particular biological community. However, if time is limited in your course, even without knowledge of the specific name for each type of relationship, we have found that students are still able to construct detailed and accurate models.

An important aspect to remember is that generally there is no one perfect model for a given ecosystem. Depending on how components are broken down, multiple models could be constructed for the same ecosystem, all of which provide the same level of detail.

Challenge #2. Redundancy of connections embedded in many students' models. One of the most common problems with students' models is when they inadvertently enter single components more than once. This occurs when a model shows two components as being distinct when, in fact, one component is really a subcomponent of the other. For example, a model may show 'predatory arthropods' as one component and 'dragonflies' as a second, separate component. Since dragonflies are predatory arthropods, only one or the other component should be given in the model. Models showing both components must explicitly indicate that the 'dragonflies' component is part of (along with several other predators) the 'predatory arthropods' component. In this case, links must be drawn from either the 'predatory arthropods' component or from the subcomponents, but not both.

Challenge #3. Novel approaches to linkage symbol use. Another common problem is that some students will misunderstand the specific arrow notation you teach them and use a variant form, where their arrows will mean something slightly different than what you have taught. As long as the "invented" notation is used consistently, very good models can still be constructed. Since this occurs often, we do not penalize the "invented" notation as long as it is consistent. The text that students submit with the models will help you to understand what their notation means. Correcting a student's notation in the pre-field experience model will also help to ensure that the proper notation is grasped and used in the final, post-field experience model.

Challenge #4. Differences between the emphasis students give to subsets of the study ecosystem. Different students will provide greater levels of detail in their models from different parts of the ecosystem. For example, some students will have greater interest in analyzing plants and others may be more interested in chemical/abiotic aspects. This is particularly evident in a non-majors course context. Because we want to keep students interested in the activity, we encourage students to strive for detailed models and give them the freedom to focus on one, or a few parts, of the ecosystem more than other parts, if they choose. In any case, it is generally easy to determine how much thought and effort went into model construction and this effort can be factored into the student’s grade.

Challenge #5. Specifically for Part 2, when considering stability, some rules of thumb to keep in mind when analyzing or building models are:

• At least one diagonal entry ( a11, a22, a33 …) must be negative, or self-regulated, for stability to occur.
• A system with either a row or column of all zeros is unstable.
• Loops of three or more parameters introduce instability. In other words, links that skip a level, such as omnivory, introduce instability. (See May 1973, for a discussion of local vs. global stability. Is it an artifact or does it represent the real thing?)
• The presence of unstable relationships does not mean that the system is unstable overall, but rather that compensations will need to be made in order to stabilize these conditions.

Experiment Description

When planning your unit, consider which combination of activities best suits your needs. We suggest that all faculty begin by using the introduction in Part 1 whether or not they continue with the rest of Part 1 or instead work with POWERPLAY in Part 2 directly afterwards. We believe that Part 1 and Part 2B, 2C, and 2D would make up a full unit for more advanced students.

Introducing the Lab to Your Students

Part 1

We often introduce this exercise during a field trip to the study site. The instructor should first have discussed how ecological models themselves are widely used in ecology. Faculty could introduce different models of ecosystems as portrayed in text books or on-line. Examples of models can be used to illustrate how models provide concise depictions of inter-relationships among factors. Below are some excellent examples of qualitative models available on line.

1. Library of Models from "Teachers in the Woods" web-page:
   Nitrogen cycle (http://cse.pdx.edu/forest/nitrogen_cycle04a.htm)
   Forest succession (http://cse.pdx.edu/forest/succession.htm)
   Phosphorous cycle (http://cse.pdx.edu/forest/phosphorous_cycle.htm)
   Soil food web (http://soils.usda.gov/sqi/concepts/soil_biology/images/B-4.jpg)
2. Qualitative models of stream ecosystem recovery by Salles et al., PDF available at:
   http://monet.aber.ac.uk:8080/monet/summer_school_2003/materials/salles_etal_qrser.pdf

Data Collection and Analysis Methods Used in Part 1

1. Give each student a copy of Student Handout 1: Introduction to Qualitative Modeling (*.doc 48KB) or (*.pdf 61KB), and review if necessary.
2. Take a field trip to your local site to observe biotic and abiotic interactions among the organisms that live there. Based on these interactions, create a qualitative ecosystem model using the symbolic signed digraph notation just presented.
3. Back in class, have students complete materials and methods section B, steps 1-4, "Steps for creating qualitative models." Give them at least 20 minutes to complete a simple model. If necessary, steps 1-4 can be completed as a homework assignment. Make sure they write their names on their initial models for future identification purposes.
4. After students have constructed their own models following steps 1-4, break students into pairs to complete part C.

C. Guided Discussion on Qualitative Ecosystem Modeling

We recommend that students write down specific information about the interactions in their models. Students tend to shy away from doing this. As students create qualitative models, they are engaging in analysis of the phenomena. Students’ ability to analyze an ecosystem can be captured by making sure they take the time to describe the interactions they are modeling, including underlying causal relationships. Otherwise, the models are in themselves meaningless.

It is also important that students consider all possible indirect effects (effects on components two or more steps away from the new component) that may occur, as a perturbation spreads through the components in the system. The ability to easily identify indirect effects of perturbations is one of the main strengths of this type of qualitative model.

D. Refining and Documenting Your Qualitative Ecosystem Model

Chose a few students and ask them to explain their models in front of class or via a class internet-based discussion. Collect the worksheets. Look over students' write-ups for possible misconceptions. See assessment section below for ideas on how to use students' answers.

Optional Extension: Suggest to the students that they could refine their models further based on data they find in the ecology literature (see assessment section below). Provide an example so that students know what you mean and what kinds of additional information could be added.

Optional Extension: With a more advanced group, continue with Part 2 and have students formally revise their models into researchable hypotheses to use at their study sites.

Data Collection and Analysis Methods Used in Part 2

Part D—Provide your students with the name of an appropriate disturbance that they can add on their own to their ecosystem models.

D. Using POWERPLAY to Model Qualitative Stability of an Ecological Community of the Students' Design

Chose a few students and ask them to explain their models in front of class or on a class web-based discussion. Collect the worksheets. Look over students’ write-ups for possible misconceptions.

Questions for Further Thought

Practical Applications

It should be noted that, compared to a more formalized mathematical treatment (such as loop analysis), our informal qualitative analysis may be more likely to err on the ultimate effects of a disturbance on a system of interest. This is important because a complex, interacting system can behave in unexpected ways that are not simply the "sum of its parts." These emergent properties of systems can only be captured with more detailed analyses. Nonetheless, as in any type of analysis, we can still develop hypotheses of direct and indirect effects that could be tested subsequently via scientific experiment. This type of qualitative analysis also serves as an excellent "thought exercise" to encourage students of ecology to begin thinking about chains of indirect effects and complexity.

Comments on Questions from Part 2

Question #2: Models 2 and 3 are different only in the foraging behavior of the New Zealand mud snails. In Model 2 the New Zealand mud snails are seen as a specialist, feeding on only Algae 1. In Model 3 the New Zealand mud snails are seen as a generalist, feeding on both Algae 1 and 2. What can you predict to be the difference between these two systems, if nutrient input to the system is reduced?

Answer: The nutrient reduction is to test the effects of bottom-up forces on species abundance in a community system. Model 2 is very sensitive to the nutrient reduction. All species in the Model 2 system have a negative impact corresponding to the nutrient reduction except for Algae2 which has no effect. On the other hand, the nutrient reduction has no impact on species in the Model 3 system except for New Zealand Mudsnails.

Question #3: Stone (1990) presented a plankton community model to explain Hutchinson’s “The paradox of the phytoplankton”, i.e.: if phytoplankton are competing for exactly the same resources (light, nutrients), why are there some many species (Hutchinson, 1961). Stone analyzed both quantitative and qualitative matrix predictions. In order to explain the paradox, Stone added a positive link from phytoplankton to a source competitor that indicates a commensal contribution of organic carbon to bacteria. Using Stone’s model, discuss why the existence of commensal contribution from phytoplankton to its competitor bacteria can benefit phytoplankton? Compare the two weighted prediction matrices, using the systems with and without the commensal contribution.

Answer: The system with a positive link from phytoplankton to bacteria (commensal distribution) has lower weighted prediction values than the system without a link. Thus, we should exercise caution when using the prediction matrix to analyze system variable responses to the disturbance when the weighted prediction values are low. A similar result can be found in Stone’s paper when we compared the quantitative results with a qualitative analysis of the predication. Some elements of the quantitative prediction matrix did not match the sign or direction in the qualitative prediction matrix.

Question #4: Often we use a qualitative solution so that we can judge what changes of species interactions will affect the system stability. We can use matrix algebra tools to analyze the system’s stability without knowing the precise value of all the parameters. We can continue to use our simple 3-species food-chain model of a self-regulated plant (= 1), its herbivore (= 2) the snowshoe hare, and a specialized predator (= 3) the lynx, to understand the system feedback.

Answer: Students are encouraged to derive the mathematical formula by hand and check the positive and negative loops at each feedback level. For the example of 3-species food-chain model, the community matrix is:

The coefficients of the characteristic equation represent different levels of feedback. As we have mentioned before that system stability requirements are derived from the coefficients of the characteristic equation. The characteristic equation is:

where the coefficients are:

one-cycle feedback loop

two-cycle feedback loops

three-cycle feedback loops

In this 3-species food-chain system, no positive loops are involved at any level, so the system is stable and this result should be consistent in both qualitative and quantitative analyses.

Question #5: In the vegetation, hare, and predator model above, loop analysis showed that the addition of nutrients to the vegetation increased the predator population size, but had no net effect on the numbers of hares (there was more food, and more hare reproduction, but more hares were subsequently eaten, too). Speculate upon the demographic and life history consequences to the hare population of this prediction of higher population turnover from loop analysis. Is loop analysis enough to predict the response of a population to natural selection from simultaneous top-down and bottom-up sources?

Answer: We can use the loop analysis to discuss the relationship between population equilibrium levels and turnover rates in a stable community system. Using the adjoint (prediction) matrix in loop analysis, we can test changes at the equilibrium level for population abundances after an input (positive or negative) is added to a particular species in a community. Sometimes the input could change the population equilibrium level for a particular species, but it might cause a change in its population structure. Using a 3-species system as an example (vegetation, hare, and lynx, see Figure 20), fertilizing vegetation will increase the vegetation abundance and the lynx number, but cause no change in the hare population. Although increased vegetation promotes more hares, the increase will eventually be eaten by the lynx, thereby increasing the lynx population but keeping the hare population the same. Therefore the unchanged population level is actually caused from the balance of higher birth and death rates. However, the interlinked consequences of higher birth and death rates may cause a change in turnover rates and shift the age distribution of the hare population towards the younger age classes because the mature individuals would decline by increased predation, and the average body size of individuals may become smaller.

Assessment of Student Learning Outcomes

The objectives of this activity can be assessed using the techniques described above.

• Have students gained an understanding of the systems interactions in the ecosystem they have been studying, key interrelationships or interactions, and the feedback loops, and have they learned how multiple factors interact in direct and indirect ways? (Measured with Description: Assessment #4)
• Do students demonstrate the ability to develop researchable hypotheses using qualitative models? (Measured with Description: Assessment #3)
• Have students shown an ability to predict, using their models, probable patterns of how their ecological system may change over time? (Measured with Description: Assessments #1 or #2)
• Have students become more explicit about interactions and complexity through analysis of their models? (Measured through the quality of their responses on Student Handout 2: Steps for Creating Qualitative Models [*.doc 29KB] or [*.pdf 20KB], especially if the activity is done again in a series of activities)

There are many other types of assessments that can be devised for measuring student learning. Portfolios can be developed for each student's models generated over the course of the term. Faculty can use these in a series of interviews to gauge how a student has progressed over the course of the term. Students can be asked to compare earlier models with more recent ones and to describe the insights they have gained.

Evaluation of the Lab Activity

Faculty may want find out whether their students think that the qualitative modeling activities are a valuable tool in learning about ecological concepts. This can be done by providing students with a questionnaire, or asking them directly whether they thought particular activities increased their understanding better than others. Students could also be asked how, in their opinion, the activity could be improved. The feedback learned can be very useful in shaping future success in using this approach.

In addition, these qualitative models can be useful in revealing underlying student misconceptions. Faculty will first need to identify what misconceptions are expressed the students' first models, and then develop a strategy for addressing these misconceptions. Did you find evidence that these misconceptions were corrected in later models?

Further discussion of assessment and evaluation is contained in the TIEE site:
Charlene D'Avanzo. July 2000. Evaluation of Course Reforms: A Primer On What It Is and Why You Should Do It. (http://tiee.ecoed.net/teach/essays/evaluation.html)

Translating the Activity to Other Institutional Scales or Locations

Pre-college Settings

Below are suggestions for introducing qualitative models for advanced middle school and high school classes. These suggestions were created by Claire Steiner, a graduate student at Portland State University.

Day 1: Field Trip Activity (20 minutes)

While on a field trip to the students’ field site, each student will individually create a list of the ecological factors (biotic or abiotic) that they see at the field trip site (e.g., water, sediment, trees, invasive species…). The students will then circle or star the top five to ten most important factors they have listed. Remind the students that they need to identify for themselves what an important factor is, and they will need to provide justification for their decision. The students will then individually define a list of the interactions between those circled or stared factors. Students should create as many connections as they believe to exist between the selected factors.

Back in Class Modeling Introduction (20 Minutes)

After the field trip and before the formal introduction to modeling, the ideas of qualitative modeling should be established with the students. Define the term "qualitative" and compare it to the term "quantitative" with the students. Show the students what models are and explain why they are important to science. Explain the terminology of modeling (see the Teachers in the Woods website, http://www.cse.pdx.edu/forest/model_symbols.htm, for an explanation and examples of components, positive, negative, and neutral links). Students should then look at a text that describes a food web and should be asked to explain what they read. They should then look at a model of a food web, and compare the difference. The purpose is to show how helpful models are when studying science.

Day 2: Web of Life Group Version (30 minutes)

This activity will allow the students to create their own models.

Create a stack of cards with images or the names of factors found in the ecosystem of the field trip site. Each card should have only one factor on it. Have students separate into groups of 5 or 6. Give each group a handful of cards. As a group, or individually, the students should pick out the two cards having the two most important factors and begin to create their model using the cards as nodes and the string as links. The group should then add the remaining cards as secondary factors. They could think of this as what they think drives the system.

During or at the end of the activity, students will record what they created with the note cards in model form in their modeling journals. Students will then explain the main components and their interactions demonstrated in the model in an essay, written in their journal. This is the time for the each student to justify why he/she created the links that are in the models. They should finish this essay for homework.

Day 3 and beyond:

The students can continue to work with qualitative models throughout their field project, keeping their different versions in a field notebook. These can be used as a portfolio assessment of their understanding about the interactions at their field site.