Wiki site of the practical exercise of the VI Southern-Summer School on Mathematical Biology.

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Plants evolved a huge and diverse weaponery against herbivory, like toxic chemicals and mechanical defenses.

Although such defenses do hinder herbivory, top-down control by predators is also very important to keep the population of many herbivores in check. Oddly enough, it is well documented that plant defenses can attenuate the predation pressure on herbivorous insects.

Ian Kaplan and Jennifer Thaler (2010) made a nice case on the multiple (and not mutually exclusive) explanations for that:

• Predation decreases in well-protect plants because herbivores can accumulate on their own tissues the toxic compounds of plants, making the preys less edible for predators.
• Predators are attracted by volatiles that the plant elicits when injured by herbivores. Herbivores make less injuries (e.g. less leaf chewing) in protected plants, making preys harder to be spotted by the predators.
• Non-consumptive predator effects¹⁾ may be attenuated because the prey can perceive that the risk of attack is lower in protected plants.
• Non-consumptive predator effects can also be attenuated because prey tend to be malnourished in protected plants and thus are less prone to pay the costs of defensive strategies, like anti-predator behaviors.

Propose a simple but realistic mathematical model to describe the coupled dynamics of populations of protected and unprotected plants, herbivores and predators. Your model should take into account at least two of the explanations presented above for the decreasing of predation in more protected plants. You are welcome to build on the case study of Kaplan & Lather (2010) or choose any other one with similar features.

Here are some questions you may explore, but further well-grounded insights are also welcome.

• Are the tri-trophic systems ²⁾ based on protected and unprotected plants viable under realistic values of the parameters of your model?
• Under which conditions protected and unprotected plants can coexist?
• What is a more effective way to control crop pests: to plant protected varieties or to increase predator densities?

• Kaplan, I. and Thaler, J.S., 2010. Plant resistance attenuates the consumptive and non‐consumptive impacts of predators on prey. Oikos, 119(7), pp.1105-1113.
• Thaler's Lab Website
• Kaplan's Lab Website

• Group presentation