Dynamical transitions in a pollination-herbivory interaction: a conflict between mutualism and antagonism

Abstract

Plant-pollinator associations are often seen as purely mutualistic, while in reality they can be more complex. Indeed they may also display a diverse array of antagonistic interactions, such as competition and victim-exploiter interactions. In some cases mutualistic and antagonistic interactions are carried-out by the same species but at different life-stages. As a consequence, population structure affects the balance of inter-specific associations, a topic that is receiving increased attention. In this paper, we developed a model that captures the basic features of the interaction between a flowering plant and an insect with a larval stage that feeds on the plant's vegetative tissues (e.g. leaves) and an adult pollinator stage. Our model is able to display a rich set of dynamics, the most remarkable of which involves victim-exploiter oscillations that allow plants to attain abundances above their carrying capacities and the periodic alternation between states dominated by mutualism or antagonism. Our study indicates that changes in the insect's life cycle can modify the balance between mutualism and antagonism, causing important qualitative changes in the interaction dynamics. These changes in the life cycle could be caused by a variety of external drivers, such as temperature, plant nutrients, pesticides and changes in the diet of adult pollinators.

Fig 1. Interaction mechanism between plants (P), flowers (F), larva (L), adult insects (A) and associated biomass flows.

Clipart sources: http://etc.usf.edu/clipart/

Fig 2. Outcomes of the PLA model as a function of the larval maturation and herbivory rates for specialist pollinators (ϕ = 0).

The rectangular region in the bottom left is analyzed with more detail in S1 File.

Fig 3. Limit cycles in the PLA model (3).

Plant biomass alternates above and below the carrying capacity (dotted line). Parameters as in Table 1, with γ = 0.01, β = 10. Blue:plant, green:larva, red:adult.

Fig 4. Outcomes of the PLA model as a function of the larval maturation and herbivory rates for generalist pollinators (ϕ = 1).

AeLc: intersection of the Allee effect and Limit cycle zones.

Fig 5. Dynamics of the simplified version of the PLA model.

Plant isoclines in green and larva isoclines in blue. Several trajectories are shown (starting with *). The dotted line at x = 1 is the plant’s carrying capacity. When γσα/ην < 1 the plant’s isocline always decreases, when γσα/ην > 1, it bulges above the carrying capacity and displays a hump. (A) Damped oscillations leading to globally stable coexistence dominated by antagonism (victim–exploiter). (B) The isoclines intersect as a locally stable mutualistic equilibrium and as a saddle point. Insects can coexist with the plant or go extinct depending on the initial conditions. (C) This is similar to case (B), however, a stable mutualism occurs only after damped oscillations or the insect go extinct, depending on the initial conditions. (D) Here the system develops oscillations approaching a limit cycle (thick loop), which creates a periodic alternation between mutualism and antagonism. Common parameters in all panels are β = 10, η = 0.1, μ = 1, ϕ = 0. For the other parameters; in (A): σ = 3, ε = 0.7, α = 3, γ = 0.02, ν = 2; in (B): σ = 2.1, ε = 0.21, α = 2, γ = 0.05, ν = 1.5; in (C): σ = 3.7, ε = 0.2, α = 3, γ = 0.02, ν = 1.5; in (D): σ = 5, ε = 0.3, α = 5, γ = 0.02, ν = 2.