FACULTY NOTES

Students should be given background information on the use of matrix modeling and the nature of life cycle figures. For this exercise, students should individually transfer transition values from Figure 2 into the appropriate positions within the matrix found under step 2. You may want to walk through step 1 with them so they understand how values go from a life cycle graph into a matrix. Give students an opportunity to check their number placements with their neighbors. Students should then open the R program and then open the file named 'Lespedeza' (this file can be downloaded from the TIEE site). Have this file in an easily accessible location, such as the desktop, so you can easily direct them to it. Instruct the students to use step 3 and Figure 2 to guide them in using the program to calculate the population growth rate for Lespedeza plants in the control treatment. The λ value they should get is 25.15. This means that the population is increasing 25-fold from one year to the next. They should then proceed to steps 4-6. You may expect them to predict that the bars (population growth rate) will get smaller (lower) as the degree of treatment increases. After steps 4-6 are completed, students are to use step 7 for instructions about how to change in the R program in order to calculate λ for the other clipping treatments. Within R, they are to replace the small to medium transition value they entered from the control treatment with the values given for each of the other treatments on the handout, one at a time, to yield the four other population growth rates for the experiment. They should get the following results for λ: 20%= 25.11; 40%= 24.41; 60%= 24.59; 80%= 24.22. Students should check their answers with their neighbors and problem solve if necessary. Be sure students understand why they are only changing the values for the small to medium transition. You may have to remind them that the researchers had originally found that only this transition (no other transitions or seed set) was found to be affected by herbivory. The students should then individually complete step 8 and compare their findings with the predictions they made in steps 4 and 5. Let them hypothesize answers to question 8b. They will explore this answer next in steps 9 and 10.

After completing step 9, the studentsλ will interpret their results from the elasticity analysis in step 10. The elasticity matrix will show the results for each vital rate - large values of elasticity indicate that small changes in that vital rate would cause large changes in the population growth rate. Management efforts should focus on vital rates with large elasticity values. You may need to remind them that elasticity analyses are used to determine which vital rate λ is most sensitive to. The directions for how to calculate the elasticity matrix are in step 9. The transition with the largest elasticity is the small-small transition; this is reproduction of small plants (i.e., small plants produce seeds that germinate immediately and become small plants in the next year). This might be hard for students to interpret at first. You might need to remind them that all arrows in the life cycle graph represent one-year transitions, and that both reproduction and germination can happen in a single year. Their answers in step 10 should reflect that the λ does not decrease with increasing herbivory because the vital rate that the λ was most sensitive to (seed set of small plants) was unaffected by herbivory (recall only growth and survivorship of small plants was significantly affected by herbivory). Managers interested in decreasing λ should focus on reducing the seed set of small plants. This might be through management of the plants (e.g., herbicide) just prior to fruit maturation, or through a biological control agent that is a seed consumer.

Student Assessment: Essay Quiz

Here, we have shown how demographic matrix modeling can aid in the management of invasive plant species. How would the same modeling techniques be used to plan the management of an endangered species?