Optimizing Crop Rotations and Pest Management Strategies in Agriculture

April 30, 2020   /  

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.


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)

31 thoughts on “Optimizing Crop Rotations and Pest Management Strategies in Agriculture”

  1. How might differential input costs and crop prices for corn and soybeans affect your model output?

    1. My model assumed that soybean was the more profitable crop. If the profitability of the two crops changed enough, then the overall crop rotation would certainly change. For example, if corn became more profitable, it is certainly possible that corn would be chosen over soybean in certain cases. Especially if there is a population of nematodes present.

  2. How much greater was the optimal profit than that of other suboptimal planting decisions, e.g. just alternating soybeans and corn?

    1. Although I don’t have an exact number to share, a sub-optimal decision like the one you describe would be much less profitable. For example, if soybean were planted in a year of an aphid infestation, my model predicts a very small profit(<$50), and if there is also a high level of nematodes, there might even be a loss for the season.

  3. Having connections to farm families in my home state, I have heard about nematode-related crop destruction for a long time. This is an interesting tool in agricultural pest management. Well done!

    1. Knowing absolutely nothing about soybeans, corn, and just a little about nematodes, this IS was very interesting. Are nematacides very expensive? Are you interested in the food industry or farming? Though no model predicts a pandemic where the meat industry (a major market for soybeans and corn) is devastated, is there a possible outcome in your model where leaving the fields idle for a year would be the most profitable?

      1. Thanks! My model shows that nematodes can be expensive in that it is profitable to plant soybean only under low levels of nematodes.
        I’m interested in sustainable food systems- so a little of both!
        That is an interesting question! I did not include an option to leave fields empty, but I believe that it would depend on prices of corn and soybean. If there is a predicted aphid infestation, high nematode levels, and the cost of production of corn is higher than expected profit, then leaving field empty for a year would be most profitable. Of course, this does not take into account other factors, such as weed control.

    1. It would be best to re-evaluate based on new aphid predictions and prices of corn and soybean.

  4. You assume an infestation occurs every three years according to your write up. I assume that means infestations were deterministic then? Can you assume a more complex cycle of infestations in your model? For example, could the infestations be drawn from known probability distributions? Also, does the probability of infestation depend on production choices? (Excellent research question by the way!)

    1. That’s a great question! Yes, in order to keep this model manageable for myself I kept aphid infestations deterministic, but introducing probability would be a great extension of this project. Research suggests that aphid infestations occurred once every two years, but with farmers taking precautionary measures such as removing buckthorn bushes (where aphids over-winter) as well as resistant soybean, infestations have reduced to once every three years.

  5. Do you have any opinions on crop diversification overall? For example, corn is used for many purposes. Are pests more likely to succeed as the number of acres of a particular crop increase?

    1. This may depend on the pest but seems a reasonable conclusion. For example nematode populations only succeed or fail in the field they occupy, but trends for aphids may be impacted by planting by farmers overall.

  6. Mady – Congratulations! This looks wonderful. I am so glad that you found this topic! -J. Bowen

  7. Hi Mady! You are my first visit so I’m learning how this works. I assume you are online now.
    I love your poster. You have laid out your work so nicely.

  8. Very interesting to see that the yield of the SCN resistant/aphid susceptible is similar to the SCN susceptible line. Why do you think the yields are similar- could it be due to aphid disease pressure or do you think there are other factors at play here?

    1. That could be a possibility, but I believe there are other factors at play. I think the susceptible and resistant yields are so similar due to the fact that the pesticide yield is different. The researchers of the original yield equations noted that the pesticide yields may have been higher because the pesticide removed possible damage from other pests as well. This is an important note that my since my model largely depends on these equations, it is important that they are accurate!

  9. This is super interesting! I wish we could talk about it in person. Are you planning on continuing doing agricultural research after Wooster?

    1. Thanks Maya I enjoyed reading about your I.S. too! I’m hoping to go into data analysis/data science and use that to research sustainable food systems!

  10. Hi Madelaine, this is great stuff. I didn’t know you were working on a crop rotation I.S.! You mention previous models early in your research description. Where did these come from, i.e. were they produced by agronomists, or crop consultants, or mathematicians, etc? And how would you say your model improves or builds upon them?

    1. The first paper I looked at is by researchers Lazarus and Swanson and is entitled: Insecticide Use and Crop Rotation Under Risk: Rootworm Control in Corn. This model only looks at one year, so my model builds on this by extending the idea of optimizing yields to several.
      The next paper I looked at is by researches Zacharias, Liebman, and Noel and is called: Management Strategies for Controlling Soybean Cyst Nematode: An Application of stochastic Dynamic Programming. This model looked at nematodes over several years. Therefore my model is an extension of their work with aphids (and their relation to nematodes) added.

      Although both have quite a lot of math jargon, I would encourage you to check them out if you are interested!

  11. Congratulations Mady! I love how you combined the environmental studies topic with analysis using math. We miss you!

  12. I’ve been wanting to know more about your I.S. project! You really weave a lot of interesting strands together in your compelling research. Toutes mes félicitations!

  13. Madeleine,
    Have you ever spoken to practicing farmers? My family has acreage in Northwestern Ohio, farmed locally by a native Ohioan. He and his father before him have avoided the impact of these pests through better rotation and pesticide selection and application than your synopsis suggests.
    Also, you did not address the impact of processing opportunities and shipping costs on crop choices for rotation. When I was a teenager and visiting the farms with my father, the choices were determinate field tomatoes, sugar beets, wheat, corn, and soybeans. The first two went away as the processing plants disappeared. Now it is the usual three. Thank the agricultural schools in the universities for hybrids, for example rust resistant wheat.
    I suspect that your project is off to a good start but it is far more complicated than your paper synopsis suggests.
    I trust you will persevere in further development taking more influences into consideration. It is not just the bugs but the economic, financial, and political pressures as well.
    William (Jeff) ’68

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