Table 1.

Full description of the assumptions regarding allocation made in the models for the simulations in this paper

Model	Representation of allocation	Timestep
Fixed coefficients
CABLE	Allocation coefficients are fixed, but fractions differ between three phenological phases:  (1) maximal leaf growth phase: 80% of available C allocated to foliage; 10% each to wood and roots  (2) steady growth phase: plant functional type (PFT)- specific allocation coefficients used  (3) final phase: no leaf growth; available C allocated to wood and roots in ratio 55%: 45%	Daily
CLM4	For this study, allocation fractions were set as fixed empirical constants based on site observations, which did not vary through the year. Note: The standard version of the model allocates C to the stem and foliage as a dynamic function of NPP.	Daily
EALCO	For this study, allocation coefficients were determined to maintain a prescribed relationship among plant tissues, namely: foliage: sap wood: fine root = 1: 0.75: 0.5 for conifers and = 1: 3: 2 for deciduous trees The start of plant growth is determined by a temperature sum. During the early growing season, all available C is allocated to foliage because leaf biomass is small relative to sapwood and fine roots. Leaves stop growing when LAI reaches a maximum LAI that is prescribed for each year and treatment based on the site data. After LAI reaches its maximum, available C is allocated to sapwood and fine root only to maintain their prescribed relationship mentioned above (i.e. 60% vs 40%). The growth of coarse roots and heartwood occurs during the senescence of fine root and sapwood, respectively On an annual basis, the outcome of this set of assumptions is that root vs sapwood allocation relationship is fixed, and foliage allocation yields the observed maximum LAI when enough C is fixed by the plants Note: in other work the model EALCO often uses a ‘transport resistance scheme’ where flows of C and N depend on concentration gradients (Thornley, 1972; Wang et al., 2002)	Daily
GDAY	Allocation fractions are empirical constants set from site observations. Theses coefficients were varied between ambient and eCO2 treatments at ORNL to reflect empirical site measurements	Annual
Functional relationships
ED2	Allocation is determined such that the biomass components follow allometric relationships given by Medvigy et al. (2009): 2 3 4 (Ba, active biomass pool; Bleaf, Broot and Bwood, biomass pools of foliage, sapwood and roots, respectively). Leaf phenology is described by a phenology parameter (e(t)) [0–1]). Sapwood biomass and peak leaf biomass are maintained in the proportion qsw h (h, tree height; qsw, fixed leaf : sapwood area ratio). Root biomass and peak leaf biomass are maintained in the ratio q, which increases with increasing water or nitrogen limitation. After allocating to leaves and roots on a daily basis, ED2 uses a 70 : 30 split of available ‘reserve’ C between woody growth and reproduction Note: in the standard ED2 model, allocation fractions do not vary with N limitation	Daily
LPJ-GUESS	A new version of the model incorporating N limitation was used (Smith et al., 2014). The allocation model follows Sitch et al. (2003), with the addition of N dependence of the leaf: root biomass ratio First, 10% of NPP is allocated to reproduction. The remaining NPP is allocated to the foliage, wood and roots on an annual time step based on allometric relationships among biomass components The ratio of LAI to sapwood area (SA) is constant 5 (kla:sa, a PFT-dependent constant). Additionally, upward tree growth requires an increase in supporting stem diameter 6 (H, tree height; D, stem diameter; kallom2 and kallom3, PFT dependent allometric constants). These two relationships define the wood biomass to leaf biomass ratio The root biomass to leaf biomass ratio depends on a PFT-specific maximum leaf-to-root mass ratio lrmax and N and water availability factors (N and W, ranging 0–1): 7 (Cr, root biomass pool; Cf, foliage biomass pool)	Annual
O-CN	Implements the same scheme as LPJ-GUESS, with the key changes being that: (1) allocation takes place on a daily time step, (2) the leaf-to-root mass ratio and leaf-to-sapwood ratios do not vary with PFT, and (3) partitioning of NPP to reproduction also occurs on a daily basis and depends on the amount of remaining NPP after allocation to foliage, wood and fine roots has taken place. A fast turnover labile pool buffers NPP against short-term variations in GPP; and a nonrespiring reserve pool buffers interannual variability and facilitates bud burst in deciduous trees	Daily
Resource limitations
DAYCENT	Carbon is allocated according to priorities. Fine roots have first priority, then foliage and finally wood. Demand by the fine roots varies between 5% and 18% of total NPP depending on the maximum of two limitations (soil water and nutrient availability). The remaining carbon available for allocation is then distributed to the foliage pool until the maximum LAI is reached. The maximum LAI is set for each PFT depending on an allometric relationship with wood biomass. Allocation to woody tissue only takes place once the maximum LAI has been attained	Daily
ISAM	Allocation formulation after Arora & Boer (2005), with a dependence on light and water availability (but not explicitly nutrient limitation). Under high LAI, light limitation occurs, and allocation to wood increases to compete for light. When water limitation occurs, allocation to roots increases. Allocation to foliage is calculated as the residual. The allocation fractions are calculated as follows: 8 9 10 (W, soil water availability factor [0–1]; L, light availability factor; ω ɛw,ɛr, PFT-dependent allocation parameters). L is given by L = exp(–k LAI), (k, light extinction coefficient; LAI, leaf area index, which is input from observations). For broadleaf PFTs, this scheme is modified using three phenological growth phases:  (1) Leaf onset phase: allocation is completely to leaves, with zero allocation to wood or roots  (2) Steady growth phase: resource limitation model used  (3) Leaf senescence phase: allocation to foliage is set to zero, and aw and ar are increased to sum to one The phases are determined by the ratio of LAI to a maximum LAI value for the biome. Phase (2) starts once the LAI reaches half the maximum LAI, and ends once LAI falls below 95% of the maximum LAI value	Daily
TECO	The total amount of carbon available for allocation on a given day is given by the tissue growth rate (G), which is a function of temperature and water availability. The model prioritises allocation to foliage and roots. The demand for carbon by foliage is given by the amount of carbon needed to reach the maximum LAI. Growth is allocated to foliage to meet this demand, but at any time step the allocation cannot exceed 40% of the total available carbon to be exported. Demand for carbon by the roots increases with decreasing water availability, but cannot exceed 30% of the total available carbon to be exported. The remaining available carbon is then allocated to the stem. The allocation coefficients are thus calculated as follows: 11 12 13 (G, total carbon to be allocated; LAImax, PFT-specific maximum leaf area index; SLA, specific leaf area; W, soil water availability factor [0–1]; bmL and bmR, parameters defining the ratio of fine roots to foliage). LAImax depends on canopy height, but height was assumed constant in these simulations for both PFTs. The maximum LAI thus did not vary in TECO, unlike the other models	Daily
Optimisation
SDGVM	SDGVM optimises canopy LAI such that net canopy C uptake is maximised. The annual carbon balance of the lowest canopy layer is calculated. Allocation to foliage in the current year is determined such that the lowest layer of the canopy had a positive carbon balance in the previous year. Allocation of remaining labile carbon between roots and woody tissue are given by constant PFT-specific fractions	Daily

Note that in several instances, alternative allocation sub-models are available for the models used here, so other applications of these models may not use the allocation routines described here.