Table 1.

Model variables and parameters. For those parameters calibrated in the present work the calibrated 99% confidence intervals are reported in brackets. Cal, calibrated in the present work; Fix, fixed in the present work; see electronic supplementary material.

variable		dim.	description
S		g	shoot structural dry mass
R		g	root structural dry mass
CS		g	shoot carbon substrate
CR		g	root carbon substrate
NS		g	shoot nitrogen substrate
NR		g	root nitrogen substrate
D		DU	plant-induced defences
A		ind.	aphid population
parameter	value	dim.	description	source
C and N assimilation
${\sigma }_{\mathrm{C}}$	0.1	d−1	assimilation rate of C	[33]
${\sigma }_{\mathrm{N}}$	6.70–17.08 10−3 [1.76–19.54] [4.56–43.04] 10−3 a	d−1	assimilation rate of N	Cal
ν	1000	g	shoot (root) mass halving substrate assimilation due to self-shading (competition)	[33]
${\iota }_{\mathrm{C}}$	0.1	/	semi-saturation C concentration	[33]
${\iota }_{\mathrm{N}}$	0.01	/	semi-saturation N concentration	[33]
C and N substrate allocation to plant growth
${\phi }_{\mathrm{C}}$	0.50	/	unit of substrate C per unit of structural dry mass	[33]
${\phi }_{\mathrm{N}}$	2.50 10−2	/	unit of substrate N per unit of structural dry mass	[33]
κ	142–223 [56–601] [48–876]b	d−1	maximum rate of substrate utilization	Cal
η	73	/	switch-off function of plant growth: steepness	Fix
λ	169	d	switch-off function of plant growth: date of equal partitioning between growth and reserves	Fix
transport
q	0.86 [0.84–0.89]	/	plant architecture scaling parameter	Cal
defences development
α	0.02 [0.01–0.03]	g d−1 ind−1	allocation of substrates to defences per unit of aphid	Cal
${\epsilon }_{\mathrm{C}}$	5 10−2	DU g−1	conversion efficiency of C substrate in defences	[50]
${\epsilon }_{\mathrm{N}}$	1	DU g−1	conversion efficiency of N substrate in defences	[50]
aphid
θ	1.12 10−3	g d−1 ind−1	maximum food intake per aphid	[51]
ξ	171	ind g−1	maximum conversion efficiency of ingested food into descendants	[52]
μ	0.04	d−1	aphid natural mortality rate	[53]
π1	8.52 10−3 [3.70–23.12] 10−3	DU g−1	swich-on function of defences protected phloem fraction: concentration of defences at which the defence effect is half-saturated	Cal
δ1	0.65 [0.55–0.73]	/	swich-on function of defences protected phloem fraction: steepness	Cal
${\pi }_2$	0.05 [0.03–0.08]	DU g−1	swich-on function of defences induced mortality/repulsion rate: concentration of defences at which the defence effect is half-saturated	Cal
${\delta }_2$	118 [27–251]	/	swich-on function of defences induced mortality/repulsion rate: steepness	Cal
β1	1	/	swich-on function of defences protected phloem fraction: asymptotic value	Fix
${\beta }_2$	28 [13–76]	/	swich-on function of defences induced mortality/repulsion rate: asymptotic value	Cal

^aValues refer to different fertilization treatments. ^bValues refer to different irrigation treatments.