Root : shoot ratios, optimization and nitrogen productivity

Abstract

Plants respond to nitrogen availability by changing their root : shoot ratios. One hypothesis used to explain this allocation is that plants optimize their behaviour by maximizing their relative growth rate. The consequences of this hypothesis were investigated by formulating two models for root : shoot allocation, with and without explicit inclusion of maintenance respiration. The models also took into account that relative growth rate is a linear function of plant nitrogen concentration. The model without respiration gave qualitatively reasonable results when predictions were compared with observed results from growth experiments with birch and tomato. The explicit inclusion of maintenance respiration improved considerably the agreement between prediction and observation, and for birch was within the experimental accuracy. Further improvements will require additional details in the description of respiratory processes and the nitrogen uptake function. Plants growing under extreme nutrient stress may also optimize their behaviour with respect to other variables in addition to relative growth rate.

Fig. 1. Assimilation rate (A) and shoot fraction (f_S) as functions of plant nitrogen concentrations (c_N) for different values of nitrogen productivity (P_N)_. Case A: c_A = 0·0534 gN (g d. wt)^–1. For A, c_Nmin = 0·004 gN (g d. wt)^–1 and P_N = 4·3, 5·5 and 7·1 g d. wt (gN)^–1 d^–1 corresponding to quantum fluxes of 5, 14 and 30 mol m^–2 d^–1, respectively, in the experiments with birch by Ingestad et al. (1994b). For f_S, c_Nmin = 0 and 0·004 gN (g d. wt)^–1. Case B: c_B = 0·0511 gN (g d. wt)^–1, P_N = 4·3 and 7·1 g d. wt (gN)^–1 d^–1, and r = 0 and 2. The lower curve for each P_N for A correspond to r = 0. The curves for f_S with r = 0 coincide for the two values of P_N (dotted line).

Fig. 2. Shoot fraction as a function of plant nitrogen concentration. Solid line, c_Nmin > 0, eqn (11A); dotted line, c_Nmin = 0, eqn (12A); broken line: r = 2, eqn (11B). Other parameters as in Table 1. Symbols are data from experiments with birch (Ingestad et al., 1994b) and tomato (Ingestad et al., 1994a). Open symbols represent experiments with low relative addition rates of nitrogen. Solid symbols (circles, squares, triangles, inverted triangles and diamonds) represent faster growing plants at five different light intensities (5, 11, 22, 30 and 39 mol m^–2 d^–1) for birch and (3, 6, 10, 18 and 23 mol m^–2 d^–1) for tomato.

Fig. 3. Simulated and measured assimilation (A) and shoot fraction (f_S). Solid circles, low light; open circles, high light; solid lines, case (A); broken lines, case (B). Data from de Groot et al. (2002).