Deciphering the developmental plasticity of walnut saplings in relation to climatic factors and light environment.

Developmental plasticity, the acclimation of plants to their local environment, is known to be crucial for the fitness of perennial organisms such as trees. However, deciphering the many possible developmental and environmental influences involved in such plasticity in natural conditions requires dedicated statistical models integrating developmental phases, environmental factors, and interindividual heterogeneity. These models should be able to analyse retrospective data (number of leaves or length of annual shoots along the main stem in the present case). In this study Markov switching linear mixed models were applied to the analysis of the developmental plasticity of walnut saplings during the establishment phase in a mixed Mediterranean forest. In the Markov switching linear mixed models estimated from walnut data sets, the underlying Markov chain represents both the succession and lengths of growth phases, while the linear mixed models represent both the influence of climatic factors and interindividual heterogeneity within each growth phase. On the basis of these integrative statistical models, it is shown that walnut saplings have an opportunistic mode of development that is primarily driven by the changing light environment. In particular, light availability explains the ability of a tree to reach a phase of strong growth where the first branches can appear. It is also shown that growth fluctuation amplitudes in response to climatic factors increased while interindividual heterogeneity decreased during tree development.

Markov and semi-Markov switching linear mixed models used to identify forest tree growth components.

Tree growth is assumed to be mainly the result of three components: (i) an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous among individuals, (ii) a time-varying environmental component assumed to take the form of synchronous fluctuations among individuals, and (iii) an individual component corresponding mainly to the local environment of each tree. To identify and characterize these three components, we propose to use semi-Markov switching linear mixed models, i.e., models that combine linear mixed models in a semi-Markovian manner. The underlying semi-Markov chain represents the succession of growth phases and their lengths (endogenous component) whereas the linear mixed models attached to each state of the underlying semi-Markov chain represent-in the corresponding growth phase-both the influence of time-varying climatic covariates (environmental component) as fixed effects, and interindividual heterogeneity (individual component) as random effects. In this article, we address the estimation of Markov and semi-Markov switching linear mixed models in a general framework. We propose a Monte Carlo expectation-maximization like algorithm whose iterations decompose into three steps: (i) sampling of state sequences given random effects, (ii) prediction of random effects given state sequences, and (iii) maximization. The proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along Corsican pine trunks influenced by climatic covariates.

Identifying ontogenetic, environmental and individual components of forest tree growth.

BACKGROUND AND AIMS: This study aimed to identify and characterize the ontogenetic, environmental and individual components of forest tree growth. In the proposed approach, the tree growth data typically correspond to the retrospective measurement of annual shoot characteristics (e.g. length) along the trunk. METHODS: Dedicated statistical models (semi-Markov switching linear mixed models) were applied to data sets of Corsican pine and sessile oak. In the semi-Markov switching linear mixed models estimated from these data sets, the underlying semi-Markov chain represents both the succession of growth phases and their lengths, while the linear mixed models represent both the influence of climatic factors and the inter-individual heterogeneity within each growth phase. KEY RESULTS: On the basis of these integrative statistical models, it is shown that growth phases are not only defined by average growth level but also by growth fluctuation amplitudes in response to climatic factors and inter-individual heterogeneity and that the individual tree status within the population may change between phases. Species plasticity affected the response to climatic factors while tree origin, sampling strategy and silvicultural interventions impacted inter-individual heterogeneity. CONCLUSIONS: The transposition of the proposed integrative statistical modelling approach to cambial growth in relation to climatic factors and the study of the relationship between apical growth and cambial growth constitute the next steps in this research.