Towards modelling the flexible timing of shoot development: simulation of maize organogenesis based on coordination within and between phytomers

Abstract

Background and aims: Experimental evidence challenges the approximation, central in crop models, that developmental events follow a fixed thermal time schedule, and indicates that leaf emergence events play a role in the timing of development. The objective of this study was to build a structural development model of maize (Zea mays) based on a set of coordination rules at organ level that regulate duration of elongation, and to show how the distribution of leaf sizes emerges from this.

Methods: A model of maize development was constructed based on three coordination rules between leaf emergence events and the dynamics of organ extension. The model was parameterized with data from maize grown at a low plant population density and tested using data from maize grown at high population density.

Key results: The model gave a good account of the timing and duration of organ extension. By using initial conditions associated with high population density, the model reproduced well the increase in blade elongation duration and the delay in sheath extension in high-density populations compared with low-density populations. Predictions of the sizes of sheaths at high density were accurate, whereas predictions of the dynamics of blade length were accurate up to rank 9; moderate overestimation of blade length occurred at higher ranks.

Conclusions: A set of simple rules for coordinated growth of organs is sufficient to simulate the development of maize plant structure without taking into account any regulation by assimilates. In this model, whole-plant architecture is shaped through initial conditions that feed a cascade of coordination events.

Fig. 1.

Schematic diagram of two successive phytomers, showing the relationships among the time of collar emergence, the lengths of the sheaths (S_n and S_n–1) and the length (I_n) of internode n. Adapted from Fournier and Andrieu (2000a).

Fig. 2.

Conceptual model of lengths (A) and elongation rates (B) of blade, sheath and internode (see key) of a phytomer n with leaf tip emergence before tassel initiation, plotted against thermal time. Vertical dotted lines separate four phases of growth of the phytomer. Phase I: from blade initiation until tip emergence. Phase II: from tip emergence until collar emergence of the preceding leaf. Phase III: from collar emergence of the preceding leaf until collar emergence of the leaf itself. Phase IV: from collar emergence until completion of growth. The short horizontal line segments in (A) represent the length of the sheath that has the highest ligule on the plant at tip emergence (left line) and collar emergence (right line). The succession of leaf emergence events that linked with coordination rules comprised tip emergence, collar emergence of the preceding leaf and collar emergence of the leaf itself. Further explanation is given in the text. Adapted from Zhu et al. (2014).

Fig. 3.

Dynamics of sheath length of ranks 5–10, as indicated in the key, at (A) normal density and (B) high density. The vertical solid line indicates the time of tassel initiation. Vertical dotted lines indicate collar emergence times of ranks 4–9. Symbols are measurements on maize ‘Déa’ in 2000 and lines are fitted curves. Filled symbols and rank 8 in panel B represent the sheaths that initiated after tassel initiation. No line is shown for rank 5 at normal density since fitting was not successful due to lack of data points between 200 and 250 °Cd.

Fig. 4.

Model verification (A, B) and model validation (C, D) of the dynamics of blade length, sheath length and internode length (see key) of phytomers 7 and 11. Symbols are measurements on maize ‘Déa’ in 2000 and lines are simulations. RMSE values for blade, sheath and internode of phytomer 7 in (A) were 3·7, 1·8 and 2·5 cm respectively, and those for phytomer 11 in (B) were 2·8, 1·5 and 2·4 cm, respectively. RMSE values for blade, sheath and internode of phytomer 7 in (C) were 3·8, 1·8 and 1·3 cm, respectively, and those for phytomer 11 in (D) were 11·2, 2·5 and 4·8 cm, respectively.

Fig. 5.

Model verification (A, B) and model validation (C, D) of tip emergence and collar emergence (see key in A), and final lengths of blade, sheath and internode (see key in B) versus phytomer rank. Symbols are measurements from maize ‘Déa’ in 2000 and lines are simulations. RMSE values of model verification were 8·6 °Cd for tip emergence, 12·4 °Cd for collar emergence, 12·3 cm for final blade length, 1·2 cm for sheath length and 2·4 cm for internode length. RMSE values of model validation were 17·9 °Cd for tip emergence, 16·7 °Cd for collar emergence, 21·8 cm for final blade length, 2·6 cm for sheath length and 1·7 cm for internode length.

Fig. 6.

Analysis of the sensitivity of the time of leaf tip emergence to changes in r_B,n at normal density.

Fig. 7.

Simulated effects of changes in final sheath length of ranks 1–3 on the dynamics of blade and sheath extension of phytomers 5 and 7. The final sheath lengths of ranks 1–3 were changed jointly by –30 % (solid lines), –20 % (dashed lines), –10 % (dotted lines), no change (bold solid lines), +10 % (dot-dashed lines), +20 % (long-dashed lines) and +30 % (two dashed lines).