L'atelier qu'il a organisé en décembre 2007 pour l'analyse des données de l'Inventaire forestier national (IFN) des Alpes et du Jura, en compagnie de Cécile Albert, Sébastien Lavergne, Wilfried Thuiler (LECA, Grenoble), David Coomes (Université de Cambridge, Cambridge) , Benoît Courbaud et Nicklaus E. Je les remercie de m'avoir transmis leurs connaissances et de m'avoir encouragé dans la voie scientifique.
Gestion difficile des peuplements mélangés en zone de mon- tagne
La complémentarité de niche résulte d'une différence entre espèces dans l'utilisation des ressources, dans le temps ou dans l'espace, et d'interactions positives entre espèces (Loreau et Mouquet, 1999 ; Tilman, 1999 ; Mittelbach et al., 2001). Ce qui signifie que la relation entre diversité et productivité peut changer en fonction des mécanismes de coexistence considérés (Cardinale et al., 2000).
Les forêts mélangées de Sapin et d’Epicéa en zone de mon- tagne
Les traitements actuellement préconisés pour l'aménagement des peuplements mixtes sont associés à une sylviculture proche de la nature (Bruciamacchie et de Turckeim, 2005). Dans les Alpes, les peuplements mixtes d'épicéas et de sapins se trouvent principalement dans les massifs intérieurs.
Autécologie du Sapin et de l’Epicéa
- Habitats du Sapin et de l’Epicéa
- Croissance
- Mortalité
- Dispersion et recrutement
- Dynamique naturelle supposée du Sapin et de l’Epicéa
Seynave et al., 2004) ont étudié les facteurs climatiques et pédologiques influençant la productivité de l'épicéa (mesurée par un indice de fertilité égal à la hauteur dominante à un âge de référence). Les facteurs qui limitent la croissance des épicéas et des sapins contribuent à augmenter le risque de décès.
Variabilité et incertitude dans les modèles en éco- logie
- Intérêt de la modélisation
- Variabilité spatio-temporelle des processus écologiques
- Sources de variabilité et d’incertitude
- Incertitude et modèles non-paramétriques
- Statistiques bayésiennes hiérarchiques
- Formule de Bayes et réseau Bayésien
- Statistiques Bayésiennes hiérarchiques et modèles mixtes
- Prédictions probabilistes et principe de précaution
L'incertitude des paramètres doit être reflétée dans les simulations pour fournir des informations sur l'incertitude de la prédiction (Pacala et al., 1996 ; Deutschman et al., 1999 ; Clark, 2003a). En plus de l'incertitude des paramètres, la variabilité individuelle et temporelle entraîne une incertitude dans la prédiction en raison du tirage aléatoire de paramètres individuels ou temporels lors de la simulation (Vieilledent et al., en revuec).
Mécanismes de coexistence des espèces
Le modèle de niche de Hutchinson
La probabilité de présence d'une espèce selon l'altitude est par exemple différente sur un versant nord et sur un versant sud. Pour des conditions environnementales totalement identiques, les individus d'une même espèce, différents par leurs caractéristiques génétiques et leur histoire, ont une probabilité de présence différente de la moyenne de l'espèce.
Déclinaisons du modèle de niche de Hutchinson : notion de trade-off
Ainsi, une absence apparente d'interaction entre deux espèces lorsqu'on se concentre uniquement sur deux axes de la niche peut s'avérer erronée si l'on raisonne en prenant en compte un troisième axe (Fig. 2.20). La variance d'abondance entre les différents sites reste stable tout au long de l'Holocène, tandis qu'un modèle neutre prédit une augmentation de la variance au fil du temps.
Prise en compte des trade-offs multidimensionnels et des différences entre individus
- Cas particulier du modèle neutre
- Modèles de niche stochastiques
- Modèles de niches à variabilité structurée
La variabilité des processus démographiques à l'échelle individuelle et annuelle a des conséquences sur la coexistence des espèces (2007) présente donc des résultats de simulation où la dynamique du mélange « peuplier tulipe » et « érable rouge ». opposé. Pour une valeur fixe de variabilité individuelle pour la compétition, Courbaud et al. à l’étude) ont étudié l’effet d’un compromis colonisation-compétition sur la dynamique d’une communauté à deux espèces.
Objectifs du travail de thèse
Obtenir un modèle de dynamique basé sur des données de terrain
Utiliser et développer des méthodes d’estimation statis- tiques adaptées
Plan de la thèse et hypothèses de test
Compte tenu de la petite taille des graines d’épinette par rapport à celles du sapin, nous supposons que l’épinette disperse ses graines sur une plus grande distance que le sapin. En raison de la tolérance relative à l'ombre du sapin par rapport à l'épicéa, on émet l'hypothèse que le sapin a une probabilité de recrutement plus élevée que l'épicéa sous un éclairage faible et vice versa sous un éclairage plus intense.
Introduction
The light interception model was then used to test the effect of individual canopy size variability on the species' light interception and regeneration strategies. We used calibrated allometric measurements to implement an explicit radiative transfer model (Courbaud et al., 2003) to analyze the effect of individual allometric variability on light interception and penetration in a real forest stand.
Materials and methods
- Field measures
- Model comparison for allometric equations
- Structure of the best model
- Computing light interception by the tree and ground cell
The model probability included both the uncertainty in the data (observation error) and the variability of the process (process error). These two quantities were studied to see how individual variability in allometries could change light source allocation in a forest stand.
Results
- Species and site effects
- Competition effects and crown plasticity
- Individual allometric variability
- Impact of individual allometric variability on light alloca- tion
- Impact on light intercepted by species
- Impact on light arriving on ground cells
At each site, individual variation in crown size completely blurred species differences in terms of light interception (Fig. 3.4). Individual allometric variation allowed some trees to have a much larger or smaller crown than their population average, so they intercepted a much higher or lower amount of light.
Discussion
Phenotypic plasticity and individual variability in crown shape
In contrast to the model's error term, individual effects describe the variation associated with individuals over time, leading to different individual trajectories (Henry and Aarssen, 1999). Individual effects on allometries can initiate differentiation among trees and, in combination with competition, create a hierarchy of sizes among trees and heterogeneous spatial structure (Oliver and Larson, 1996).
Individual variability obscures species differences in crown size
Intraspecific variability in crown size and successional dy- namics
Acknowledgements
Tables
The model with the lowest DIC was selected if the difference in DIC was greater than 25. When the difference in DIC was less than 25, the model with the lowest deviation was selected.
Figures
A light interception model was used for Abies alba and Picea abies stands (Courbaud et al., 2003) and was applied to the Queige (a) and Teppas (b) sites, mixedA. On the vertical axis the mean (black dot) and 95% quantiles (gray vertical lines) for intercepted light for each cell over the 500 simulations, including individual variability.
Appendices
- Appendix S1 : General characteristics of the nine plots composing the data-set
- Appendix S2 : Measurement errors
- Measurement error protocol
- Appendix S3 : Selection of the best mathematical functions for allometries
- Function selection protocol
- Function selection results
- Function selection comments
- Appendix S4 : Comparison of priors and posteriors for pa- rameters
- Appendix S5 : Full mathematical model for allometric re- lations
- Appendix S6 : Competition index in allometric relations
- Appendix S7 : Means and standard deviations of the esti- mated parameters
- Tables
- Figures
We also checked the graphical superposition between the selected function and a non-parametric curve representing the mean of the response for covariate classes. The DIC is the sum of the mean deviation (which represents the goodness of fit of the model: Deviation =−2 log(Likelihood)) and of the effective number of parameters pD (with pD as the posterior mean of the deviation minus the deviation of the posterior middle).
Introduction
Materials and methods
- Field data
- Parametric models to compute mortality rate as a function of DBH
- Semi-parametric model to compute mortality rate as a function of DBH
- Modified Ayer’s algorithm to determine minimum mortality and DBH bins
- Bayesian model to infer mortality rate considering DBH
- Deviance comparison between approaches
- Fitting models on simulated unbalanced and balanced data- sets
After identifying the minimum mortality rate DBH0 and the bin values for each DBH class, we estimated the mortality rate of each DBH class using a Bayesian approach. We expressed 1−µ0Dij in function of the annual mortality rate µDj associated with diameter class j and Yi.
Results
Different estimates of mortality rates with parametric ap- proaches
Unbalanced data-set affects the parametric model shapes
Improved goodness of fit for the semi-parametric model
Discussion
Bias in the estimation of a mortality-diameter function with parametric models
The semi-parametric approach we developed allowed us to make the most of the existing data by combining several datasets regardless of variable time intervals for dead counts and avoiding biases associated with unbalanced datasets. The semi-parametric model provided maximum flexibility to fit patterns to the data with minimal assumptions.
Advantages of the semi-parametric method for forest dy- namics study
We believe that the potential bias of parametric methods in estimating mortality at extreme diameter has been largely overlooked in previous studies. We show that this bias can have important consequences for the assessment of tree species' life traits, such as shade tolerance and longevity.
Tables
The models are L-Poly2 for logistic function with degree two polynomials, L-Poly3 for logistic function with degree three polynomials, Log-N for log-normal function and SP for semi-parametric model. The models are L-Poly2 for logistic function with degree two polynomials, L-Poly3 for logistic function with degree three polynomials, Log-N for log-normal function and SP for semi-parametric model.
Figures
Bar widths represent bin values obtained from modified Ayer's algorithm for semi-parametric model and bar heights represent maximum likelihood estimates obtained within Ayer's algorithm. Bar widths represent bin values obtained from modified Ayer's algorithm for semi-parametric model and bar height represents annual mortality rate for A. alba used to simulate mortality data.
Introduction
Tree mortality process
Taking into account both size- and growth-dependent mor- tality in a flexible model
Nevertheless, since competition, age, and abiotic factors all influence growth, growth is a more integrative measure of whole-plant carbon balance, which determines tree vitality (Kobe et al., 1995). Second, their estimates are highly dependent on the distribution of data points, which are often unbalanced in diameter due to far fewer observations for large trees (Lavine, 1991; Vieilledent et al., in reviewb; Wyckoff and Clark, 2000) .
Objectives and hypothesis
Tree growth can be estimated from tree-ring arrays, which provide high-resolution records of tree growth, or from sequential standing plot censuses, which provide coarse resolution of growth with measures of DBH increment (Wunder et al., 2007). Such experimental devices are not always available (but see Wunder et al. 2007) and Monserud (1976)), so some authors have proposed statistical methods to obtain mortality growth models from a reduced sample of dead and living trees from a unique census (Kobe et al ., 1995; Wyckoff and Clark, 2000).
Materials and methods
- Field data for mortality-diameter model
- Mortality-diameter model
- Modified Ayer’s algorithm to determine DBH bins
- Hierarchical Bayes model to infer on the annual mortality rate given DBH
- Field data including growth and diameter for dead and living trees
- Mortality rate integrating both DBH and past radial growth for each species
- Use of the Bayes formula to compute the combined mortality rate For smaller trees (with DBH < 45 cm), we obtained the combined mortality rate
- Two-dimensional Ayer’s algorithm to determine diameter and growth bins
- Mortality-growth model
DBH of all living and dead trees is divided into bins j = 1,2,. mD and a corresponding annual mortality rate for each binµDj were estimated using the maximum likelihood approach. Taken together, these two probabilities can be used to calculate the annual mortality rate given diameter class j and growth class k: p(death|Dj, Gk) (see next part for details).
Results
Mortality-diameter relationship
Mortality-growth relationship
Size- and growth-dependent mortality model
The low number of data for large trees (DBH≥45 cm) (Fig. 5.1) did not allow separating growth-related mortality from size-related mortality. For large trees (DBH≥ 45 cm), size-related mortality referred to both irregular and senescence mortality (Fig. 5.2 and Fig. 5.5).
Discussion
A model combining size-dependent and growth-dependent mortality
A flexible model making the most of available data
Such traits determine the trade-off between competition and colonization (Tilman, 1994) and the successional niche (Pacala and Rees, 1998; Rees et al., 2001), which hypothesize species coexistence. Our results suggest that this advantage may be offset by a higher low-light mortality rate for P.
Tables
Figures
Nevertheless, there is still a process-level variation missing in the RITES approach: intra-individual variability. Combined with RITES, intra-individual variability tends to equalize fitness between species and individuals.
Introduction
Scientific background
An important input aimed at improving the niche model, including both theoretical aspects and data, was the work of Clark et al. 2007) on forest community dynamics, based on the recognized high-dimensional differences between species (Hutchinson, 1961). The approach of Clark et al. 2007) advocates structuring variability at different hierarchical levels in space and time more than including purely stochastic processes where sources of stochasticity and underlying mechanisms are difficult to identify (Adler et al., 2007; Clark et al., 2007; Tilman, 2004 ).
Knowledge gap
Objectives and hypothesis
To do this, we compared growth simulations obtained from classical niche and neutral processes with a growth process structured in space and time. Finally, based on our trophic niche study, we discussed the potential advantages and limits of a spatially and temporally structured niche model for understanding and predicting community dynamics.
Materials and methods
Collecting data
- Field data
- Plot reconstitution in three dimensions
- Light computation
Cutting registers from the National Forest Office showed that forestry operations ceased before 1977 on the site, apart from felling of dead trees for sanitary reasons. In the plot, we found ten scattered and recent stumps in terms of their state of decomposition, which can be attributed to sanitary cutting of dead trees during this period.
Comparing growth-light models with different spatio-temporal structures
- The RITES model
- RITES-Autoregressive model
- Model comparison
The RITES model (for which parameters were indicated with a superior index (1)) allowed trees to have different growth capabilities from one individual to another due to individual variability, represented by the individual's variance Vb(1). random effectsb(1)i that deviated the log growth potential from the species mean A(1). The DIC is the sum of the mean deviation (representing the goodness of fit of the model: deviation = −2 log(likelihood)) and of the effective number of parameters pD (where pD is the posterior mean of the deviation minus the deviation of the posterior means) (Spiegelhalter et al., 2002).
Growth simulations and equalizing forces
- The niche model
- The neutral model
- The stochastic niche model
- Comparing simulations
N(git|lit, V(4)) (6.9) We used non-informative conjugate priors for the only parameter of the model. For each of the 8 models, we calculated the number of incidents for which the growth of aP.
Results
A high dimensional trophic niche
- A trophic niche differenciation between species
- A large individual variability of the species trophic niche
- A large intra-individual variability with a significant growth memory process
The predicted values for the RITES+AR model were much closer to the observations than for the RITES model (Fig. 6.2). The RITES+AR model led to low residual variance compared to the RITES model (Tab. 6.1) suggesting that we managed to structure a large part of the existing variability in the growth-light process.
Process-level variations as equalizing forces
The RITES+AR model appeared to be significantly better than the RITES model for both species, as the DIC differences were significantly better than 15 (Table 6.2). The RITES+AR model implied a memory process for growth, as growth per year+1 was more likely to be close to growth per year.
Discussion
Intra-individual variability as a process-level variation
Process-level variation and equalizing mechanisms
RITES represent high-dimensional variations resulting from many measurable and unmeasured factors (Clark et al., 2003b). Interactions between a reduced number of ecological processes can lead to a variety of stabilizing trade-offs in development (Pacala et al., 1996).
Aknowledgments
Tables
The growth RITES+AR model was significantly better than the RITES model, as the DIC difference was strongly superior to 15. The RITES+AR model led to an almost complete decomposition of the variability due to interannual, individual and intra- individual variability.
Figures
On the left, we plotted the data against the RITES model growth predictions, including the estimated interannual effect λt and the individual effect λt (see comparisons in Materials and Methods). For a fixed low light level (first quantile = 8.657 GJ.an−1), we simulated the growth of ten trees for each species on 25 dates using 8 models, including process variability in different ways.
Appendices
Effects of light and dispersal on recruitment limitation of Abies alba and Picea abies in the Western Alps. We have shown that in the old-growth forests comprising our dataset, the recruitment limitation of A.
Introduction
To test these three hypotheses, we counted the number of recruits of the two species that passed 1.30 m in height during the last 10 years using growth segments. The relative light on each cell was obtained using a light transmission model (Courbaud et al., 2003).
Materials and methods
Field data
- Recruit count
- Adult trees
- Light measurement
To calculate the relative light (% full light) arriving at each soil cell of each plot, we used an updated version of the light transmission model developed by Courbaud et al. Due to the slow growth of the trees, we assumed that we can ignore the variations of the light regime on an individual cell over a period of 10 years.
Recruitment model
- Zero-Inflated Poisson model
- Dispersal model
- Habitat suitability
- Hierarchical Bayes to estimate parameters
Light rays come from all directions in the sky and arrive at the center of each terrestrial cell (Courbaud et al., 2003). Following Lian et al. (2008), we assumed that the mean Poisson process λijt was determined by the seed shadow Sij and by a potential recruit production potential ρjt which depended on plot and year.
Results
Potential of viable recruits and inter-annual variability
Discussion
Recruitment limitation and coexistence of A. alba and P
- Median dispersal distance and recruitment limitation
- Micro-site suitability and recruitment limitation
- Potential of viable recruits and recruitment limitation
In old forest, the soil can more easily become saturated with seeds due to the proximity of the seed trees (Rees et al., 2001; Sagnard et al., 2007). Differences in potential for viable recruits can be attributed to differences in seed production, seed bank mortality, predation, germination, and seedling growth and survival (Clark et al., 1999).
Ackowledgements
Tables
Figures
We calculated the average number of recruits per year (see equation 7.2) from a mature tree of 30 cm DBH for a relative light availability of 20%. We represented the average number of recruits per year (see equation 7.2) from a mature tree of 30 cm DBH, for a relative light availability of 20%.
Appendices
In the central zone, which is limited by a distance of 10 m from the edge of each plot, we mapped all saplings (crosses) of P. The shape of the samaras allows the wind to carry the seeds away from the mother tree.
Bilan des résultats : différences entre espèces et variabilité
Allométries du Sapin et de l’Epicéa
- Allométries et tolérance à l’ombre
- Plasticité dans la forme des houppiers
Le mécanisme principalement utilisé pour expliquer la variabilité intraspécifique de la forme de la couronne est la plasticité des espèces par rapport à la lumière et à l'espace disponible. La plasticité phénotypique en fonction de la lumière et de l'espace disponible est une vision déterministe de la variabilité intraspécifique de la forme de la couronne.
Mortalité du Sapin et de l’Epicéa
- Bien estimer la mortalité
- Différences entre espèces
Dans un tel contexte, il est sans doute préférable d’avoir une vision stochastique de la variabilité individuelle. On observe également une forte diminution de la mortalité des deux espèces avec la croissance (Fig. 5.4).
Croissance du Sapin et de l’Epicéa