The resource economics of chemical and structural defenses across nitrogen supply gradients

Abstract

In order to better understand the role of nutrient supplies in determining the prevalence of plant defense types, we investigated the theoretical relationships between ecosystem N supply and the net C gain of shoots that were undefended or defended in one of three ways: (1) by N-free chemical compounds, (2) by N-containing chemical compounds, or (3) by structural defenses. By extending economic models of shoot resource balance to include the relative value of C and N, depreciation, and amortization, we were able to show that the relative net C gain of the three defense types were similar to changes in their generally understood abundance along an N supply gradient. At low N supply, the additional C acquired when investing C in defense is much higher than investing N in defenses. Only at high N supply is it better to invest large quantities of N in defense rather than additional photosynthesis. In a sensitivity analysis, net C gain of shoots was most sensitive to factors that affect the relative value of C and N and the rate of herbivory. Although there is support for the relative value of C and N influencing defense strategies, more research is necessary to understand why tannins are not more prevalent at high N supply and why moderate amounts of N-based defenses are not used at low N supply.

Appendix 1

Formulae used to calculate net C gain of shoots

$$ {{\rm{NetCGain = LeafCGain - CostInitialShoot + Salvage - CostHerbivory}}} $$

(1)

$$ {\text{LeafCGain = Cgainday}} \times {\text{LongevityLeaf}} $$

(2)

$$ {\text{Cgainday = Photo - Resp}} $$

(3)

$$ {\text{Photo = }}k_{{{\text{photo}}}} \times m_{{{\text{photo}}}} \times {\text{\% NLeaf + }}b_{{{\text{photo}}}} $$

(4)

$$ {\text{\% NLeaf = ln(Nsup)}} \times m_{{{\text{Nleaf}}}} {\text{ + }}b_{{{\text{Nleaf}}}} $$

(5)

$$ {\text{Resp = (NBranch + NLeaf)}} \times {\text{RespCoeff}} $$

(6)

$$ {\text{NBranch = \% NBranch}} \times {\text{CBranchStructure}} $$

(7)

$$ {\text{CBranch = CBranchDefense + CBranchStructure}} $$

(8)

$$ {\text{NLeaf = \% NLeaf}} \times {\text{CLeafStructure + NLeafDefense}} $$

(9)

$$ \begin{aligned} {\text{LongevityLeaf = FracShootEaten}} \times {\text{FracLeafEaten}} \times {\text{LeafAgeEaten}} & \\ {\text{ + }}\left[ {} \right.{\text{1 - (FracShootEaten}} \times {\text{FracLeafEaten)}}\left. {} \right] \times {\text{LongevityLeafMax}} & \\ \end{aligned} $$

(10)

$$ {\text{Salvage = (1 - FracShootEaten)(FracLeafEaten)}} \times {\text{CostNLeaf}} \times {\text{Resorption}} $$

(11)

$$ {\text{CostNLeaf = NLeaf}} \times {\text{ValueC/N}} $$

(12)

$$ {\text{ValueC/N = CgainStand/Nsupply}} $$

(13)

$$ {\text{CgainStand = }}m{\text{,Cgain}} \times {\text{ln(Nsupply) + }}b{\text{,Cgain}} $$

(14)

$$ {\text{CostShootInitial = CostLeafInitial + CostBranchInitial}} $$

(15)

$$ {\text{CostLeafInitial = CostCLeaf + CostNLeaf}} $$

(16)

$$ {\text{CostCLeaf = CLeaf}} $$

(17)

$$ {{\rm{CLeaf = CLeafDefense + CLeafStructure + CLeafGrowthResp}}} $$

(18)

$$ {{\rm{CLeafGrowthResp = RespCoeff}} \times {\rm{(CLeafStructure + CLeafDefense)}}} $$

(19)

$$ {\text{CostBranchInitial = CostCBranch + CostNBranch}} $$

(20)

$$ {{\rm{CostCBranch = }}{{{\rm{CBranchDefense}}} \over {{\rm{BranchDefLong}}}}{\rm{ + CBranchStructure + CBranchGrowthResp}}} $$

(21)

$$ {\text{CBranchGrowthResp = RespCoeff}} \times {\text{(CBranchStructure + CBranchDefense)}} $$

(22)

$$ {\text{CostNBranch = NBranch}} \times {\text{ValueC/N}} $$

(23)

$$ {\eqalign{ & {\rm{CostHerbivoryLeaf = FracLeafEaten}} \cr & \times \left\{ {{\rm{(ReplacementLeaf}} \times {\rm{Cgainday)}}} \right. \cr & {\rm{ + }}\left[ {{\left( {{\rm{1 - }}{{{\rm{LeafAgeEaten}}} \over {{\rm{LongevityLeafMax}}}}} \right)}} \right. \cr & \left. { \times {\rm{(CostCLeaf + Resorption}} \times {\rm{CostNLeaf)}}} \right] \cr & {\rm{ + }}\left. {{\left[ {{\rm{(1 - Resorption)}} \times {\rm{CostNLeaf}}} \right]}} \right\} \cr} } $$

(24)