Plants store chemical defenses that act as toxins to herbivores, such as toxic isothiocyanates (ITCs) in Brassica plants, hydrolyzed from the precursor glucosinolates (GLSs). Fitness of herbivorous larvae can be highly affected by these toxins, causing immature deaths. Theoretically, toxins can inordinately reduce larval fitness to death. We model this phenomenon by a set of ordinary differential equations and establish a direct relationship between feeding, toxin exposure and net energy of a larva, where the fitness of an organism is proportional to its net energy according to the optimal foraging theory. Our equations explain that toxin exposure can steeply reduce larval net energy to zero at an instar stage. Since herbivory needs energy, the only choice left for a larva is to stop feeding at the time point. If that time-point is significantly earlier than the end of the last instar stage, the larva dies.

Brassicaceae plants have the glucosinolate-myrosinase defense system, jointly active against herbivory. Glucosinolates (GLS) are hydrolysed by myrosinase to produce isothiocyanates as soon as herbivory begins. Isothiocyanates exert detrimental effects on the feeding insects. However, constitutive GLS defense is observed to occur at levels that do not deter all insects from feeding. That prompts the question of why Brassicaceae plants have not evolved a high constitutive defense. The answer may lie in the contrasting relationship between plant defense and host plant preference of specialist and generalist herbivores. One of the reasons plants are in this dilemma is that they do not know what kind of herbivore will attack them in any given year, and thus have to be prepared for different possibilities. GLS content increases the susceptibility to specialist insects because these are attracted to plants with a high GLS content and are capable of coping with the toxin. In contrast, generalists are deterred by the plant GLS. Although GLS can attract the natural enemies (predators and parasitoids) of these herbivores, enemies can reduce herbivore pressure to some extent only. So, plants can be overrun by specialists if GLS content is too high, whereas generalists can invade the plants if it is too low. Therefore, an optimal constitutive plant defense can minimize the overall herbivore pressure. To explain optimal defense theoretically, we represent the contrasting host selection behavior of insect herbivores and, in addition, the emergence of their natural enemies by a non-autonomous ordinary differential equation model, where the independent variable is the plant GLS concentration. From the model, we quantify the optimal amount of GLS, which minimizes the total herbivore (specialists and generalists) pressure. That quite successfully explains the evolution of constitutive defense in plants from the perspective of optimality theory.

Various herbivorous insects prefer plants of the Brassicaceae family as their hosts, although they are toxic. The two-component chemical defence system of the Brassicaceae against herbivores consists of glucosinolates (GLS) and the activating enzyme myrosinase. GLS hydrolysis by myrosinase leads to isothiocyanate (ITC) products, which are toxic and deterrent to many insect herbivores. Some insects that feed on Brassicaceae, however, have evolved specific adaptations (called counter-defences) against GLS. Two different types of counter-defences can be distinguished: a preemptive counter-defence that prevents the GLS from being hydrolysed to ITC due to metabolic redirection and direct counter-defence, where the ITC is formed, but then metabolized to a non-toxic conjugate. Preemptive counter-defence is believed to be more efficient due to the lower exposure to ITC, but this has not been well demonstrated experimentally. Here, we prove on theoretical grounds that preemptive counter-defence reduces exposure to ITC compared to direct counter-defence by studying the dynamics of GLS defence and counter-defence with two separate ordinary differential equation models. By quantifying the specific ITC concentrations that herbivores are exposed to during feeding with the two types of counter-defences, we show that herbivores with a preemptory detoxification system are less exposed to ITC. In addition, our models explain how the decline in the level of ITC is achieved by both counter-defences, which helps to understand the overall mechanisms and benefits of these techniques.