Table 2.

Partials required to expand and solve equation (9) for either an above- or below-ground herbivore. Setting u_h = 0, gives the solution for the growth strategy of an attacked plant.

Derivative with respect to	Carbon	Nitrogen
Roots	$\frac{\partial {\pi }_C}{\partial u_r}=-c_{cr}$	$\frac{\partial {\pi }_N}{\partial u_r}=V_{N}N(e^{-V_N{u}_r})-c_{nr}-\beta (1-e^{-a{u}_h})$
Shoots	$\frac{\partial {\pi }_C}{\partial u_s}=V_{C}C(e^{-V_c{u}_s})-c_{cs}-\alpha (1-e^{-a{u}_h})$	$\frac{\partial {\pi }_N}{\partial u_s}=-c_{ns}$