SIAM News Blog

Volatile Plant Defenses Against Insect Herbivores

By Karen Cumings, Peter R. Kramer, and Brad Lister

Freshly-cut grass is a signature fragrance of summer, but it is also a distress signal [4]. When damaged by insects (or lawnmowers), plants emit airborne volatile chemicals, which induce defenses that reduce the impact of herbivore attacks [8], signal neighboring plants to prepare their own defenses (priming) [10], and attract predators of the herbivores [11]. However, herbivores also use these volatiles to locate suitable host plants [17]. Because measuring volatiles under field conditions is quite complex, our knowledge of plant volatiles stems primarily from greenhouse experiments. Previous mathematical models have focused on volatile-mediated attraction of predatory insects to reduce herbivore populations [1, 9, 12]. Our study takes a novel approach by modeling volatile concentrations within a simulated field, as well as the direct effects of these volatiles on insect behavior and plant losses to herbivores.

We developed a mathematical model of the interactions between goldenrod (Solidago altissima) and the goldenrod leaf beetle (Trirhabda virgata) to study how volatile defenses influence mean plant fitness (reproductive success) in a simulated field. Goldenrod is native to North America and is fed upon by over 100 insect species [14]. T. virgata is one of the most abundant herbivore species that specializes on goldenrod and can defoliate entire fields in outbreak years [6, 13]. Because it specializes on goldenrod for both food and shelter, T. virgata is a strong selective agent on goldenrod defensive strategies.

We were unable to find data about T. virgata’s attraction to volatiles, so we modeled insect attraction using data for other specialist insects [16]. Based on this data, we assumed that low to moderate volatile concentrations signal the presence of a food source and attract insects, while high volatile concentrations signal the presence of highly defended plants and are repulsive. We model insect movement via continuous time Markov chains, with transition rates dependent upon insect movement strategy. When moving toward more suitable host plants, upwind gradient sensing insects increase or decrease their rates of movement in the upwind direction in response to the gradient in the attractiveness of the volatile concentration between their current locations and one row upwind. Local concentration sensing insects increase their rates of movement in all directions when the local volatile concentration is repellent and decrease their rates of movement when the local volatile concentration is attractive; this maximizes time spent in nutrient-rich environments.

Figure 1. Plant defenses change depending on the presence or absence of herbivores. The production and emission of volatile chemicals increases with the duration of herbivore attacks and decreases after the insect herbivores depart. Primed plants increase their production of volatiles much more quickly when attacked compared to unprimed plants.
We utilized plant and field characteristics from empirical studies [5] and sampled wind speed measurements from a goldenrod field in upstate New York (this data is available online). Our model classifies plants as unattacked, primed, attacked, or recovering, based on recent insect encounters and local volatile concentrations (see Figure 1). We assume that plants release volatiles at a minimum baseline release rate both initially [7] and when fully recovered from attacks. They increase the level of volatile release to a maximum rate while attacked and decrease it when all insects have departed. High volatile concentrations prime unattacked plants, which then rapidly mobilize defenses when attacked. We assume that each plant’s leaves emit volatiles at the same rate and disperse according to a Gaussian plume model [18]. Plant volatiles also induce the production of proteinase inhibitors within plant leaves to reduce insect consumption rates. We explored the ways in which plant fitness depends on maximum volatile release rates, plant priming threshold, time required for plants to fully induce defenses, and time required for them to recover from attacks; this was based on studies of goldenrod volatile defenses and the metabolic costs of defense [2, 15].

Our results indicate that over a full growing season (May-September), high ratios of maximum to baseline volatile release rates—combined with high insect responsiveness to local volatile concentrations—cause the largest reductions in plant losses to herbivore attacks when compared with undefended plants. As expected, we found that low maximum volatile release rates increased plant losses to local concentration sensing insects, while high maximum volatile release rates reduced losses to these insects (see Figure 2a). However, increasing the maximum volatile release rate produced no significant changes in the gradient of attraction to volatiles from one row to the next. As a consequence, varying maximum volatile release rate generated very little variation in mean plant fitness in response to up- wind gradient sensing insects. The volatile-induced production of proteinase inhibitors was primarily responsible for the reduction in losses against these insects (see Figure 2b).

Figure 2. We compare plant fitness using the mean sugars not produced due to the removal of leaf area by herbivores (averaged over all plants within the simulated field). Results are separated by insect movement type. Within each figure, we plot results for four values of a nondimensional parameter proportional to the volatile concentration of maximal insect attraction. The horizontal dashed lines correspond to plants that exhibit no defenses. Standard errors are shown for each combination of parameters. 2a. When local concentration sensing insects attack plants, mean plant losses decrease as maximum volatile release rate increases to a factor of 50 above the baseline volatile release rate. This improves plant fitness. 2b. When upwind gradient sensing insects attack plants, mean plant fitness does not depend substantially on the ratio of the maximum to baseline volatile release rate.

Additionally, our model suggests that volatile concentrations are only high enough to prime plants along the downwind edge of the simulated field. However, insects in our current model enter from the downwind edge of the simulated field, so plants spend most of their time attacked or recovering and do not benefit from priming in response to volatiles. This directly contradicts empirical work that demonstrates that primed plants induce defenses more quickly and lose less leaf area to herbivores than their unprimed counterparts [15]. It also contradicts the idea that plants can form “memories” of previous attacks that allow them to amplify their defenses when attacked a second time [3].

Is plant priming only beneficial under special conditions, or could it be widespread in nature? Further work is required to explore the relationship between simulated field size, spatial separation between plants, and priming effectiveness, both in response to local volatile concentration and recent attacks. Future studies should also include the population dynamics of plants and insects over multiple seasons to determine how variations in insect attack rates influence mean goldenrod fitness.

Karen Cumings presented this work during a minisymposium presentation at the 2017 SIAM Conference on Applications of Dynamical Systems, which took place in Snowbird, Utah. 

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Karen Cumings is an adjunct professor at Great Bay Community College and Southern New Hampshire University.
Peter R. Kramer is a professor of mathematical sciences at Rensselaer Polytechnic Institute. He studies biology via stochastic modeling.
Brad Lister is a tropical ecologist who works on the effects of climate warming in the Luquillo rainforest in Puerto Rico and the Chamela-Cuixmala Biosphere Reserve in western Mexico.  
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