Optimal Level of Chemical Defense Decreasing with Leaf Age

Abstract

A recent study on a biennial plant demonstrated that pyrrolizidine alkaloids decrease with the age of leaves due to reallocation from old leaves to new leaves. Here we study the optimal age-specific pattern of defense chemical concentration in leaves that achieves the maximum growth rate of the plant. We consider a plant growing exponentially in a constant environment. Assumptions are the following: (1) The loss of leaves due to herbivory decreases with defense chemical concentration (2) The daily net photosynthesis of a leaf decreases with its age. (3) Using photosynthetic products, the plant produces new leaves that may contain defense chemicals. (4) Although there is a cost to producing new defense chemicals, such chemicals can be reallocated without cost. In the optimal schedule calculated using Pontryagin's maximum principle, the chemical defense level decreases with leaf age. The optimal level of chemical defense increases with the cost of leaf production and herbivory intensity but decreases with the cost of defense chemical production, effectiveness of the defense chemical, net productivity, and growth rate of the plant. If both generalist and specialist herbivores attack the same plant, the optimal defense level is dependent only on the generalists' abundance and sensitivity, but is independent of the specialists that are unaffected by the defense chemical.

Optimal Distribution of Defences: Are Plants Smart Investors?

“…We did not test specialist herbivores because they are not affected by PAs. Their presence does not influence optimal A(x) at all and only reduces the relative growth of the plant with a constant (Iwasa et al 1996). Fig.…”

“…Owing to their high PAlevels, the young leaves are avoided by generalist her bivores (van Dam et al 1995b). Moreover, a damage experiment showed that the removal of the youngest three leaves had a greater negative impact on rosette growth than removal of the oldest three leaves (van Dam 1996).…”

“…This idea was elaborated by Iwasa et al (1996) who examined a model which cal culates the particular age-dependent distribution and amount of chemical defence that attains the maximum relative growth rate, r, i.e. the number of leaves pro duced relative to the number of leaves present.…”

“…The third factor quantifies the probability that a leaf will survive to a certain age as a function of its defences. In fact \f(x) -bdA/dx] divided by the cost of producing a new leaf with defences [a + bA(0)], is equal to fertility or the rate of producing new leaves from energy pro duced by a leaf of age x (Iwasa et al 1996). For any age-dependent allocation schedule A(x), we can easily calculate the relative growth of the plants, using the parameters given in the next section.…”

Biotic and abiotic consequences of differences in leaf structure

“…The argument applies primarily in exponential growth, in which reinvestment of photosynthate in the ability to make more photosynthate is a critical determinant of final reproductive biomass and thus of fitness. Indeed, higher investments in defensive alkaloids can be found in younger leaves (Iwasa et al, 1996). However, older leaves can contain more tannins, which cannot be retranslocated to younger leaves (Oleksyn et al, 1997).…”