How Plant Toxins Cause Early Larval Mortality in Herbivorous Insects: An Explanation by Modeling the Net Energy Curve

Abstract

Plants store chemical defenses that act as toxins against herbivores, such as toxic isothiocyanates (ITCs) in Brassica plants, hydrolyzed from glucosinolate (GLS) precursors. The fitness of herbivorous larvae can be strongly affected by these toxins, causing immature death. We modeled this phenomenon using a set of ordinary differential equations and established a direct relationship between feeding, toxin exposure, and the net energy of a larva, where the fitness of an organism is proportional to its net energy according to optimal foraging theory. Optimal foraging theory is widely used in ecology to model the feeding and searching behavior of organisms. Although feeding provides energy gain, plant toxins and foraging cause energy loss for the larvae. Our equations explain that toxin exposure and foraging can sharply reduce larval net energy to zero at an instar. Since herbivory needs energy, the only choice left for a larva is to stop feeding at that time point. If that is significantly earlier than the end of the last instar stage, the larva dies without food. Thus, we show that plant toxins can cause immature death in larvae from the perspective of optimal foraging theory.

Keywords: glucosinolates (GLSs); herbivory; isothiocyanates (ITCs); larval death; metabolic cost; net-energy; non-autonomous differential equations; optimal foraging theory.

Figure 1

Scheme for the net energy of a larva, obtained through herbivory.

Figure 2

(A) Herbivory (H) and GLS ingestion (G) by a larva, as calculated using Equations (2) and (4), respectively. Parameters: $\theta =0.3$, $\alpha =0.4$. (B) ITC (I) exposure of a larva, as calculated using Equation (7). Parameters: $\beta =0.2$, $\gamma =0.8$.

Figure 3

Net energy ($E_N$) of a larva becomes 0 at some time point, initial value $E_{N_0}=0.2$; parameters $\kappa =0.3$, $\mu =0.1$, $\delta =0.03$, $\beta$, $\gamma$ are the same as in Figure 2.

Figure 4

Net energy ($E_N$) of a larva can be zero early or later, depending upon the parameters of benefits ($\kappa$) and costs ($\mu$ and $\delta$).

Figure 5

Plot of data points from Table 1.