Optimizing Crop Rotations and Pest Management Strategies in Agriculture

Student: Madeleine Ferguson
Major: Mathematics
Minors: Environmental Studies, French
Advisor: Dr. John Ramsay
The goal of this project is to investigate how operations research techniques, specifically dynamic programming, can be applied to crop rotation decisions in agriculture. One major concern that farmers face is pests. This project seeks to respond to this by solving optimization models that represent scenarios in which pests are present and pose a threat to potential yield. The final model discussed in this paper optimizes field crop rotations for five years in an ecosystem in which soybean cyst nematodes and soybean aphids are present. When aphids infest in the first and fourth years of our five year system, the optimal crop rotation is as follows: corn, susceptible soybean, corn, corn, susceptible soybean. A sensitivity analysis is then performed to help explain why this rotation is chosen.

Description

My independent study focused on field crops rotations in agriculture, specifically with the presence of pests. Agricultural pests are a major concern to farmers and in bad years can cause major profit loss. After replicating relevant previously published models, I created my own model for soybean cyst nematodes and soybean aphids. Soybean cyst nematodes are microscopic organisms which create the cysts their name implies on the roots of soybeans. In contrast, aphids impact the leaves of soybean crops. Both are economically important pests for soybean crops in the Midwest. Recently published research suggests that an aphid infestation can increase the number of nematodes that survive in a season. This means that the yield loss if both pests are present is greater than the individual yield losses combined! The nematode population will increase throughout the growing season, but as they do not reproduce in the winter, the population will stay the same from the end of one season to the beginning of the next. In the construction of this model we assume an infestation every three years. In this model we consider five different planting options. The yield of each option will be impacted differently by the nematodes and will in turn impact nematode population growth differently. Therefore, crop rotation decisions will impact the yield of one year and the starting nematode population of the next. If there is an aphid infestation in one year, there will be yield loss due to both aphid and nematode damage, and the following year there will be more nematodes than there would have been had there not been an aphid infestation. A dynamic programming model was used. Dynamic programming models work backwards from the last season to the first to find the most optimal solution, in this case the rotation that will yield the largest profit. This is faster than a “brute force” method of calculating every option. The optimal crop rotation is given in Table 1 where infestations occur in years 2014 and 2017. Note that corn was chosen in years of aphid infestation and the only soybean crop chosen is susceptible soybean with nematicide. This can be explained by the graph in Fig. 6. The yield for the nematicide is so much higher under any nematode level than other options that it will always be chosen. There are many options for future work of this project, including adding a corn pest.
Madeleine will be online to field comments on May 8:
10am-noon EDT (Asia: late evening, PST 6am-8am, Africa/Europe: late afternoon)

Posted in I.S. Symposium, Independent Study on April 30, 2020.