# Stochastic modelling of tree annual shoot dynamics

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## Abstract

### • Context

Modelling annual shoot development processes is a key step towards functional–structural modelling of trees. Various patterns of meristem activity can be distinguished in tree shoots, with active periods of phytomer production followed by rest periods. This approach has seldom been integrated in functional–structural tree models.

### • Aims

This paper presents theoretical research work on modelling and computation of the dynamics of tree annual shoots using stochastic processes with various development patterns: continuous or rhythmic, monocyclic or polycyclic, “seasonal” or “a-seasonal”, with preformation or neoformation produced from meristem functioning.

### • Methods

The renewal theory is used to compute stochastic aspects of phytomer production, resulting from meristem extension or rest periods and meristem mortality.

### • Results

Continuous development can be modelled with a Bernoulli process, while rhythmic development is modelled by alternation between extension and rest periods, the duration of each period following specific distributions.

### • Conclusion

The application of such stochastic modelling is the estimation of organ production during tree development as a component of the demand in functional–architectural tree models, used for computing biomass production and partitioning.

### Keywords

Renewal theory Architectural tree model Meristem functioning Polycyclism Monocyclism GreenLab## Notes

### Acknowledgments

This work was undertaken as a collaborative work within the LIAMA (the Sino-French laboratory for computer science, automation and applied mathematics) with funding from the Natural Science Foundation of China (grant numbers 31170670), Zhejiang Tengtou Landscape Co. LTD., CIRAD, and INRA.

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