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International audience; In this paper, we propose to cluster responses in order to identify groups predicted by specific explanatory components. A response matrix is assumed to depend on a set of explanatory variables, and a set of additional covariates. Explanatory variables are supposed many and redundant, which implies some dimension reduction and regularization. By contrast, additional covariates contain few selected variables which are forced into the regression model, as they demand no regularization. The response matrix is assumed partitioned into several unknown groups of responses. We suppose that the responses in each group are predictable from an appropriate number of specific orthogonal supervised components of explanatory variables. The classification is based on a mixture model of the responses. To estimate the model, we propose a criterion extending that of Supervised Component-based Generalized Linear Regression, a Partial Least Squares-type method, and develop an algorithm combining component-based model and Expectation Maximization estimation. This new methodology is tested on simulated data and then applied to a floristic ecology dataset.

When ordinating plots of tropical rain forests using stand-level structural attributes such as biomass, basal area and the number of trees in different size classes, two patterns often emerge: a gradient from poorly to highly stocked plots and high positive correlations between biomass, basal area and the number of large trees. These patterns are inherited from the demographics (growth, mortality and recruitment) and size allometry of trees and tend to obscure other patterns, such as site differences among plots, that would be more informative for inferring ecological processes. Using data from 133 rain forest plots at nine sites for which site differences are known, we aimed to filter out these patterns in forest structural attributes to unveil a hidden pattern. Using a null model framework, we generated the anticipated pattern inherited from individual allometric patterns. We then evaluated deviations between the data (observations) and predictions of the null model. Ordination of the deviations revealed site differences that were not evident in the ordination of observations. These sites differences could be related to different histories of large-scale forest disturbance. By filtering out patterns inherited from individuals, our model analysis provides more information on ecological processes., Frontiers in Ecology and Evolution, 9, ISSN:2296-701X

How does the genetic architecture of quantitative traits evolve over time? Answering this question is crucial for many applied fields such as human genetics and plant or animal breeding. In the last decades, high-throughput genome techniques have been used to better understand links between genetic information and quantitative traits. Recently, high-throughput phenotyping methods are also being used to provide huge information at a phenotypic scale. In particular, these methods allow traits to be measured over time, and this, for a large number of individuals. Combining both information might provide evidence on how genetic architecture evolves over time. However, such data raise new statistical challenges related to, among others, high dimensionality, time dependencies, time varying effects. In this work, we propose a Bayesian varying coefficient model allowing, in a single step, the identification of genetic markers involved in the variability of phenotypic traits and the estimation of their dynamic effects. We evaluate the use of spike-and-slab priors for the variable selection with either P-spline interpolation or non-functional techniques to model the dynamic effects. Numerical results are shown on simulations and on a functional mapping study performed on an Arabidopsis thaliana (L. Heynh) data which motivated these developments.

Africa is forecasted to experience large and rapid climate change1 and population growth2 during the twenty-first century, which threatens the world’s second largest rainforest. Protecting and sustainably managing these African forests requires an increased understanding of their compositional heterogeneity, the environmental drivers of forest composition and their vulnerability to ongoing changes. Here, using a very large dataset of 6 million trees in more than 180,000 field plots, we jointly model the distribution in abundance of the most dominant tree taxa in central Africa, and produce continuous maps of the floristic and functional composition of central African forests. Our results show that the uncertainty in taxon-specific distributions averages out at the community level, and reveal highly deterministic assemblages. We uncover contrasting floristic and functional compositions across climates, soil types and anthropogenic gradients, with functional convergence among types of forest that are floristically dissimilar. Combining these spatial predictions with scenarios of climatic and anthropogenic global change suggests a high vulnerability of the northern and southern forest margins, the Atlantic forests and most forests in the Democratic Republic of the Congo, where both climate and anthropogenic threats are expected to increase sharply by 2085. These results constitute key quantitative benchmarks for scientists and policymakers to shape transnational conservation and management strategies that aim to provide a sustainable future for central African forests. A large dataset of 6 million trees from 193 taxa is used to map the floristic and functional composition of central African forests and predict their vulnerability to climate change.

This article presents a practical application of experimental transfer path analysis (TPA) for optimizing idle shake vibrations of a front-wheel-drive car with a transversely mounted four-cylinder diesel engine. Performance control of the vehicle engine mounting system must take into account the multiple dynamic interactions between the engine mounting system, subframe modes and the vehicle suspension. Experimental methods can be used in conjunction with simulations to design and optimize the engine mounting system. TPA is a powerful tool for the diagnosis of vibration and noise transmission via multiple solid paths. TPA allows a quick diagnosis of the engine mounting system performances on vehicle comfort. A strong synergy between numerical model and experimental data finally makes it possible to find better design alternatives, not necessarily obvious to the designer. This study is the guideline for an optimization of the engine mount noise vibration and harshness (NVH) performances by using a hybrid approach, combining an analytical approach and measurement data. First, a diagnosis of the transmission of structure-borne vibrations via the engine mounting system to the seat floor is done at constant idle speed. This method is used to rank individual engine mount contributions in the low-frequency vibration level inside the vehicle. Then, an original approach allows the optimization of the vibration level at idle speed by offsetting contributions of the engine mount paths by adding damping in the right engine mount. This approach has led to the design and validation of an original double inertia-track hydroelastic mount prototype which allows a 5-dB reduction on the seat floor vibration level. The future development of a new version is planned to confirm and optimized the obtained results. The length of the second inertia track will be increased to reach the targeted characteristics, and the adjustment system will be removed to respect the overall dimension constraints of the mount.

We address component-based regularization of a multivariate generalized linear model (GLM). A vector of random responses [Formula: see text] is assumed to depend, through a GLM, on a set [Formula: see text] of explanatory variables, as well as on a set [Formula: see text] of additional covariates. [Formula: see text] is partitioned into [Formula: see text] conceptually homogenous variable groups [Formula: see text], viewed as explanatory themes. Variables in each [Formula: see text] are assumed many and redundant. Thus, generalized linear regression demands dimension reduction and regularization with respect to each [Formula: see text]. By contrast, variables in [Formula: see text] are assumed few and selected so as to demand no regularization. Regularization is performed searching each [Formula: see text] for an appropriate number of orthogonal components that both contribute to model [Formula: see text] and capture relevant structural information in [Formula: see text]. To estimate a single-theme model, we first propose an enhanced version of Supervised Component Generalized Linear Regression (SCGLR), based on a flexible measure of structural relevance of components, and able to deal with mixed-type explanatory variables. Then, to estimate the multiple-theme model, we develop an algorithm encapsulating this enhanced SCGLR: THEME-SCGLR. The method is tested on simulated data and then applied to rainforest data in order to model the abundance of tree species.

Tropical forests are major providers of natural resources and ecosystem services but their ecological functions are at threat, due to increasing human pressure linked to economic development. The identification of priority areas for conservation is crucial for land use planning to ensure the protection of biodiversity and ecological function. Intact Forest Landscapes (IFLs), as defined by Greenpeace and World Resources Institute (WRI), are areas of the forest ecosystems not subjected to human activities. They have been identified by mapping human disturbances through remote sensing. Contrary to similar global-scale concepts, IFLs have been integrated into the standards of the certification body Forest Stewardship Council (FSC) and therefore have practical implications for forest management policies. The Motion 65, approved in the general assembly of FSC in 2014, mandates the protection of IFLs located in FSC certified logging concessions. Until the implementation of national standards, forestry operations are banished from 80% of the IFL area within each forest management unit. To trace the history and evaluate the suitability of IFLs in the Central African context, we searched for documents related to the IFL method, and related approaches focusing on the identification of areas devoid of human disturbances. The IFL method is simple and cost-effective and allows for a global assessment of the influence of human infrastructures and industrial exploitation on forests. However, the method does not consider the situation below the canopy and those forest components not visible by satellites. For example, hunting, one of the main threats faced by wildlife in Central African forests today, cannot be detected with satellite imagery. On the other hand, other anthropogenic activities which remote sensing may detect may be compatible with forest ecosystem conservation. To better tailor the IFL approach to Central African forests, we recommend (i) the consideration of wildlife communities in the intactness analysis, (ii) a thorough evaluation of the impacts of human activities on forest ecosystems, and (iii) the integration of local stakeholders and governments in the design of land management strategies to respond to social, economic and environmental needs.

This viewpoint paper presents a reaction to the article by Brandt et al. (2016). It highlights the complexities inherent to the attribution of deforestation impacts to policy interventions when using remote-sensing data. This critique argues that in the context of the Congo a suite of factors (i.e., population density in particular) other than those considered by Brandt et al. (e.g., type of forest, distance from roads and markets) play essential roles in determining the fates of forests. It also contends that care is needed when making decisions regarding which units will be included in the comparison group so that contextual factors and on-the-ground information are properly considered (e.g., when logging operations are inactive or when a concession is used for 'conservation' purposes). Finally, it proposes that a focus on an analysis of deforestation rates for a given level of timber production might be a metric that more accurately represents one aspect of the consequences of forest management, which should also consider the appraisal of trade-offs associated with a larger set of social, financial and ecological objectives.

Forest degradation in the tropics is often associated with roads built for selective logging. The protection of Intact Forest Landscapes (IFL) that are not accessible by roads is high on the biodiversity conservation agenda, a challenge for logging concessions certified by the Forest Stewardship Council (FSC). A frequently advocated conservation objective is to maximise the retention of "roadless space", a concept that is based on distance to the nearest road from any point. We developed a novel use of the empty space function - a general statistical tool based on stochastic geometry and random sets theory - to calculate roadless space in a part of the Congo Basin where there has recently been rapid expansion of road networks. We compared the temporal development of roadless space in certified and non-certified logging concessions inside and outside areas declared as IFL in the year 2000. Between 1999 and 2007, rapid road network expansion led to a marked loss of roadless space in IFL. After 2007, this trajectory levelled out in most areas, due to an equilibrium between newly built roads and abandoned roads that became revegetated. However, concessions within IFL that have been certified by FSC since around 2007 showed continued decreases in roadless space, thus reaching a level comparable to all other concessions. Only national parks remained road-free. We recommend that forest management policies make the preservation of large connected forest areas a top priority by effectively monitoring - and limiting - the occupation of space by roads that are permanently accessible.

Logging roads can trigger tropical forest degradation by reducing the integrity of the ecosystem and providing access for encroachment. Therefore, road management is crucial in reconciling selective logging and biodiversity conservation. Most logging roads are abandoned after timber harvesting; however, little is known about their long-term impacts on forest vegetation and accessibility, especially in Central Africa. In 11 logging concessions in the Congo Basin, we field-sampled a chronosequence of roads that, judging from satellite images, had been abandoned between 1985 and 2015. We assessed recovery of timber resources, tree diversity and above-ground biomass in three zones: the road track, the road edge (where forest had been cleared during road construction) and the adjacent logged forest. The density of commercial timber species

International audience; The present study investigates the thermomechanical behavior of closed-cell TPU foams. The effects of the density and the loading conditions on the softening, the residual strain and the hysteresis have first been characterized. The thermal responses exhibit numerous particularities. First, a threshold effect in terms of the density on the self-heating has been highlighted. Second, entropic effects are strongly weighted by energetic effects (internal energy variations) during the deformation. Typical changes in the thermal response highlight that SIC and crystallite melting occur during the deformation. The characteristic stretches of this phenomenon evolve with the maximum stretch applied. The lower the density, the lower the crystallinity. In the second part of this study, a complete energy balance is carried out during cyclic deformation of compact and foamed crystallizing TPUs. Results show that viscosity is not the only phenomenon involved in the hysteresis loop formation: a significant part of the mechanical energy brought is not dissipated into heat and is stored by the material when the material changes its microstructure, typically when it is crystallizing. Some of this energy is released during unloading, when melting occurs, but with a different rate, which contributes to the hysteresis loop. The part of the mechanical energy stored by the material has been quantified to investigate the effects of the loading rate and the void volume fraction on the energetic response of TPU. These effects cannot be predicted from the mechanical responses and the present study provides therefore information of importance to better understand and model the effects of the density and the loading conditions on the thermomechanical behavior of closed-cell TPU foams.

Understanding how environmental factors could impact population dynamics is of primary importance for species conservation. Matrix population models are widely used to predict population dynamics. However, in species-rich ecosystems with many rare species, the small population sizes hinder a good fit of species-specific models. In addition, classical matrix models do not take into account environmental variability. We propose a mixture of regression models with variable selection allowing the simultaneous clustering of species into groups according to vital rate information (recruitment, growth and mortality) and the identification of group-specific explicative environmental variables. We develop an inference method coupling the R packages flexmix and glmnet. We first highlight the effectiveness of the method on simulated datasets. Next, we apply it to data from a tropical rain forest in the Central African Republic. We demonstrate the accuracy of the inhomogeneous mixture matrix model in successfully reproducing stand dynamics and classifying tree species into well-differentiated groups with clear ecological interpretations. Copyright (c) 2014 John Wiley & Sons, Ltd.

Forest degradation in the tropics is often associated with roads built for selective logging. The protection of intact forest landscapes (IFL) that are not accessible by roads is high on the biodiversity conservation agenda and a challenge for logging concessions certified by the Forest Stewardship Council (FSC). A frequently advocated conservation objective is to maximize the retention of roadless space, a concept that is based on distance to the nearest road from any point. We developed a novel use of the empty-space function - a general statistical tool based on stochastic geometry and random sets theory - to calculate roadless space in a part of the Congo Basin where road networks have been expanding rapidly. We compared the temporal development of roadless space in certified and uncertified logging concessions inside and outside areas declared IFL in 2000. Inside IFLs, road-network expansion led to a decrease in roadless space by more than half from 1999 to 2007. After 2007, loss leveled out in most areas to close to 0 due to an equilibrium between newly built roads and abandoned roads that became revegetated. However, concessions in IFL certified by FSC since around 2007 continuously lost roadless space and reached a level comparable to all other concessions. Only national parks remained mostly roadless. We recommend that forest-management policies make the preservation of large connected forest areas a top priority by effectively monitoring - and limiting - the occupation of space by roads that are permanently accessible.

International audience; Understanding the environmental determinants of forests deciduousness i.e. proportion of deciduous trees in a forest stand, is of great importance when predicting the impact of ongoing global climate change on forests. In this study, we examine (i) how forest deciduousness varies in relation to rainfall and geology, and (ii) whether the influence of geology on deciduousness could be related to differences in soil fertility and water content between geological substrates.The study was conducted in mixed moist semi‐deciduous forests in the northern part of the Congo basin. We modelled the response of forest deciduousness to the severity of the dry season across four contrasting geological substrates (sandstone, alluvium, metamorphic and basic rocks). For this, we combined information on forest composition at genus level based on commercial forest inventories (62 624 0.5 ha plots scattered over 6 million of ha), leaf habit, and rainfall and geological maps. We further examined whether substrates differ in soil fertility and water‐holding capacity using soil data from 37 pits in an area that was, at the time, relatively unexplored.Forest deciduousness increased with the severity of the dry season, and this increase strongly varied with the geological substrate. Geology was found to be three times more important than the rainfall regime in explaining the total variation in deciduousness. The four substrates differed in soil properties, with higher fertility and water‐holding capacity on metamorphic and basic rocks than on sandstone and alluvium. The increase in forest deciduousness was stronger on the substrates that formed resource‐rich clay soils (metamorphic and basic rocks) than on substrates that formed resource‐poor sandy soils (sandstone and alluvium).Synthesis. We found evidence that tropical forest deciduousness is the result of both the competitive advantage of deciduous species in climates with high rainfall seasonality, and the persistence of evergreen species on resource‐poor soils. Our findings offer a clear illustration of well‐known theoretical leaf carbon economy models, explaining the patterns in the dominance of evergreen versus deciduous species. And, this large‐scale assessment of the interaction between climate and geology in determining forest deciduousness may help to improve future predictions of vegetation distribution under climate change scenarios. In central Africa, forest is likely to respond differently to variation in rainfall and/or evapotranspiration depending on the geological substrate.

The biodiversity-productivity relationship (BPR) is foundational to our understanding of the global extinction crisis and its impacts on ecosystem functioning. Understanding BPR is critical for the accurate valuation and effective conservation of biodiversity. Using ground-sourced data from 777,126 permanent plots, spanning 44 countries and most terrestrial biomes, we reveal a globally consistent positive concave-down BPR, showing that continued biodiversity loss would result in an accelerating decline in forest productivity worldwide. The value of biodiversity in maintaining commercial forest productivity alone - US$166 billion to 490 billion per year according to our estimation - is more than twice what it would cost to implement effective global conservation. This highlights the need for a worldwide reassessment of biodiversity values, forest management strategies, and conservation priorities.

Variable selection for mixture of regression models has been the focus of much research in recent years. These models combine the ideas of mixture models, regression models, and variable selection to uncover group structures and key relationships between data sets. The objective is to identify homogeneous groups of objects and determine the cluster-specific subsets of covariates modulating the outcomes. In this chapter we review frequentist and Bayesian methods we have proposed to address in a unified manner the problems of cluster identification and cluster-specific variable selection in the context of mixture of regression models. These methods have a wide range of applications, in particular in the context of high-dimensional data analysis. We illustrate their performance in two diverse areas: one in ecology for modeling species-rich ecosystems and the other in genomics for integrating data from different genomic sources.

We address component-based regularization of a multivariate Generalized Linear Model (GLM). A set of random responses Y is assumed to depend, through a GLM, on a set X of explanatory variables, as well as on a set T of additional covariates. X is partitioned into R conceptually homogeneous blocks X1, …, X R , viewed as explanatory themes. Variables in each X r are assumed many and redundant. Thus, generalized linear regression demands regularization with respect to each X r . By contrast, variables in T are assumed selected so as to demand no regularization. Regularization is performed searching each X r for an appropriate number of orthogonal components that both contribute to model Y and capture relevant structural information in X r . We propose a very general criterion to measure structural relevance (SR) of a component in a block, and show how to take SR into account within a Fisher-scoring-type algorithm in order to estimate the model. We show how to deal with mixed-type explanatory variables. The method, named THEME-SCGLR, is tested on simulated data, and then applied to rainforest data in order to model the abundance of tree-species.

Classifying species into functional groups is a way to understand the functioning of species-rich ecosystems, or to model the dynamics of such ecosystems. Many statistical techniques have been defined to classify species into groups, and a question is whether different techniques bring consistent classifications. In a tropical rain forest in French Guiana, five species classifications have been defined by different authors for the purpose of forest growth modelling but using different data sets and different statistical techniques. The correspondence between the five classifications was measured using four indices that are generalizations of existing indices to compare two classifications. A multiple correspondence analysis was used to identify associations between groups of different classifications. In a second step, two-table multivariate analyses were used to characterize the relationships between species classifications and eight species traits (consisting of seven populational traits and one functional trait). We evidenced a consensus on the potential size of trees: species were similarly clustered by the five classifications along this trait that is correlated to turnover rate. More surprisingly, no consensus was found for growth rate, nor wood density, traits that are correlated with light requirement.

With the growing interest in estimating carbon stocks in forests, available allometric equations have been compiled. These compilations often reveal contrasting models for the same species and site. Rather than choosing a model with the risk of not selecting the best available one, Bayesian model averaging (BMA) offers a way to combine different allometric equations into a single predictive model. In the deterministic version of BMA, existing models with known coefficients are combined. In the statistical version, competing models are at the same time fitted and combined. Using the BMA of deterministic models, we combined three existing multispecies pan-tropical biomass equations for tropical moist forests. The resulting model brought a relatively minor although consistent improvement of the predictions of the aboveground dry biomass of trees. These three models were particular cases of a family of models that were subsequently combined using the BMA of statistical models. Again, the resulting model was able to capture features in the biomass response to diameter that no single model was able to fit. BMA thus is an alternative to model selection that allows integrating the biomass response from different models. (Resume d'auteur)

In the Congo Basin where most timber species are light-demanding, the low logging intensities commonly implemented (1–2 trees harvested ha −1 ) do not provide sufficient canopy gaps to ensure species regeneration. The regeneration of light-demanding timber species may therefore benefit from more intensive logging, or from post-harvest treatments such as thinning by poison girdling that increases light penetration. Little is known of the impact of post-harvest treatments on the floristic composition of tropical moist forests. This study therefore aimed to assess the effects of low and high selective logging (≃2.33 and 4.73 trees harvested ha −1 , and ≃4.96 and 9.16 m 2 ha −1 of basal area removed (logging + damage), respectively) – followed or not by thinning (≃21.14 trees thinned ha −1 , and ≃6.57 m 2 ha −1 of basal area removed) – on the floristic composition of a tropical moist forest in the Central African Republic, from 7 to 23 years after logging. We analyzed abundance data for 110 tree genera recorded every year for 14 years in 25 one-hectare permanent subplots. We used multivariate analysis to detect floristic variations between treatments and we assessed changes in floristic composition throughout the period. We compared floristic composition recovery between thinned and unthinned subplots, using unlogged subplots as a reference characterizing the pre-logging floristic composition. Logging and thinning had little impact on the floristic composition of the subplots as quantified 7 to 23 years later, though they did increase the proportion of pioneer species. Surprisingly, additional thinning at both logging levels failed to further distance floristic composition from that of the unlogged subplots, though it did increase disturbance intensity. Floristic composition recovery appeared to be facilitated when thinning was associated with logging. Thinning seemed to favor the growth and survival of non-pioneer species, to the detriment of pioneer species. These non-pioneer species could either be non-pioneer light demanders or shade-bearers. One explanation for this is that thinning by tree-poison girdling increased light availability without causing major damage to the forest, and thus increased the growth and survival of advance regeneration. The resulting enhanced competition then reduced the survival of pioneer species.

Modelling the local density of tropical saplings can provide insights into the ecological processes that drive species regeneration and thereby help predict population recovery after disturbance. Yet, few studies have addressed the challenging issues in autocorrelation and zero-inflation of local density. This paper presents Hierarchical Bayesian Modelling (HBM) of sapling density that includes these two features. Special attention is devoted to variable selection, model estimation and comparison. We developed a Zero-Inflated Poisson (ZIP) model with a latent correlated spatial structure and compared it with non-spatial ZIP and Poisson models that were either autocorrelated (Spatial Generalized Linear Mixed, SGLM) or not (generalized linear models, GLM). In our spatial models, local density autocorrelation was modeled by a Conditional Auto-Regressive (CAR) process. 13 explicative variables described ecological conditions with respect to topography, disturbance, stand structure and intraspecific processes. Models were applied to six tropical tree species with differing biological attributes: Oxandra asbeckii , Eperua falcata , Eperua grandiflora , Dicorynia guianensis , Qualea rosea , and Tachigali melinonii . We built species-specific models using a simple method of variable selection based on a latent binary indicator. Our spatial models showed a close correlation between observed and estimated densities with site spatial structure being correctly reproduced. By contrast, the non-spatial models showed poor fits. Variable selection highlighted species-specific requirements and susceptibility to local conditions. Model comparison overall showed that the SGLM was the most accurate explanatory and predictive model. Surprisingly, zero-inflated models performed less well. Although the SZIP model was relevant with respect to data distribution, and more flexible with respect to response curves, its model complexity caused marked variability in parameter estimates. In the SGLM, the spatial process alone accounted for zero-inflation in the data. A refinement of the hypotheses employed at the process level could compensate for distribution flaws at the data level. This study emphasized the importance of the HBM framework in improving the modelling of density–environment relationships.

International audience; 1 Considering that the spatial pattern of trees is a footprint of the biological processes that drive their dynamics, increasing work has been undertaken to analyse spatial patterns and fit spatial point processes to them. When diameter is taken into account, the underlying point process is a marked point process. The question then is how to correctly model the dependence between the mark and location, and the different patterns at the different scales, to gain understanding of the underlying biological processes. # 2 The data used comes from the Paracou rain forest in French Guiana (5°15′ N, 52°55′ W). The spatial pattern of trees in this forest exhibits regularity at small distances (c. 6 m) and clustering at larger distances (c. 30 m). The pattern is linked to diameter, with a shift from clustering to regularity as trees grow. # 3 Two models of spatial pattern are used. The first one is pattern-driven in the sense that it breaks down the observed pattern into a mixture of regular, clustered and random contributions. The second one is process-based and uses a simple individual-based space-dependent model of forest dynamics as a simulation algorithm. It is obtained as the limit of this spatio-temporal model when time tends to infinity. # 4 Both models are consistent with the observed pattern, with a better fit provided by the second model. Moreover this second model provides a biological interpretation of the observed pattern in terms of forest dynamics. However the first model's implementation is simpler (both for simulation and for parameter estimation). # 5 Synthesis. Modelling the spatial pattern of plants using spatial point processes gives insights into the biological processes that drive their dynamics. It allows the reconstruction of their dynamics given only a snapshot of plant locations. Very few solutions exist to model complex marked spatial patterns when point location and mark are dependent. We defined and compared two point processes that successfully modelled the spatial pattern of trees in a rain forest with interaction between tree location and tree size. Both models highlight competition (either symmetric or asymmetric) as a driving process towards regularity. The second model further reveals a self-organizing dynamic with a feedback effect of competition

Wood specific gravity is a key element in tropical forest ecology. It integrates many aspects of tree mechanical properties and functioning and is an important predictor of tree biomass. Wood specific gravity varies widely among and within species and also within individual trees. Notably, contrasted patterns of radial variation of wood specific gravity have been demonstrated and related to regeneration guilds (light demanding vs. shade-bearing). However, although being repeatedly invoked as a potential source of error when estimating the biomass of trees, both intraspecific and radial variations remain little studied. In this study we characterized detailed pith-to-bark wood specific gravity profiles among contrasted species prominently contributing to the biomass of the forest, i.e. the dominant species, and we quantified the consequences of such variations on the biomass. Wood specific gravity is a key element in tropical forest ecology. It integrates many aspects of tree mechanical properties and functioning and is an important predictor of tree biomass. Wood specific gravity varies widely among and within species and also within individual trees. Notably, contrasted patterns of radial variation of wood specific gravity have been demonstrated and related to regeneration guilds (light demanding vs. shade-bearing). However, although being repeatedly invoked as a potential source of error when estimating the biomass of trees, both intraspecific and radial variations remain little studied. In this study we characterized detailed pith-to-bark wood specific gravity profiles among contrasted species prominently contributing to the biomass of the forest, i.e. the dominant species, and we quantified the consequences of such variations on the biomass. Results Wood specific gravity profiles from pith-to-bark presented positive, neutral and negative trends. Positive trends mainly characterized light-demanding species, increasing up to 1.8 g.cm-3 per meter for Piptadeniastrum africanum, and negative trends characterized shadebearing species, decreasing up to 1 g.cm-3 per meter for Strombosia pustulata. The linear mixed model showed the greater part of wood specific gravity variance was explained by species only (45%) followed by a redundant part between species and regeneration guilds (36%). Despite substantial variation in wood specific gravity profiles among species and regeneration guilds, we found that values from the outer wood were strongly correlated to values from the whole profile, without any significant bias. In addition, we found that wood specific gravity from the DRYAD global repository may strongly differ depending on the species (up to 40% for Dialium pachyphyllum). Main Conclusion Therefore, when estimating forest biomass in specific sites, we recommend the systematic collection of outer wood samples on dominant species. This should prevent the main errors in biomass estimations resulting from wood specific gravity and allow for the collection of new information to explore the intraspecific variation of mechanical properties of trees., SCOPUS: ar.j, info:eu-repo/semantics/published

Logging roads in the Congo Basin are often associated with forest degradation through fragmentation and access for other land uses. However, in concessions managed for timber production, secondary roads are usually closed after exploitation and are expected to disappear subsequently. Little is known about the effectiveness of this prescription and the factors affecting vegetation recovery rate on abandoned logging roads. In a novel approach we assessed logging roads as temporary elements in the forest landscape that vary in persistence depending on environmental conditions. We analyzed road persistence during the period 1986–2013 in adjacent parts of Cameroon, Central African Republic and Republic of Congo. Three successive phases of road recovery were identified on LANDSAT images: open roads with bare soil, roads in the process of revegetation after abandonment and disappeared roads no longer distinguishable from the surrounding forest. Field based inventories confirmed significant differences between all three categories in density and richness of woody species and cover of dominant herbs. We used dead-end road segments, built for timber exploitation, as sampling units. Only 6% of them were identified as being re-opened. Survival analyses showed median persistence of four years for open roads before changing to the revegetating state and 20 years for revegetating roads before disappearance. Persistence of revegetating roads was 25% longer on geologically poor substrates which might result from slower forest recovery in areas with lower levels of soil nutrient content. We highlight the contrast amongst forests growing on different types of substrate in their potential for ecosystem recovery over time after roads have been abandoned. Forest management plans need to take these constraints into account. Logging activities should be concentrated on the existing road network and sites of low soil resource levels should be spared from business-as-usual exploitation. (Resume d'auteur)

Among the contributions expected from forest sectors in policies of climate mitigation, one consists in increasing forest carbon stocks by changing management practices. This activity, generally referred to as Improved Forest Management (IFM), is of major importance in the Congo Basin forests, where 20 millions of hectares are now managed for timber production. The carbon benefit generated by IFM activities is often obtained by a reduction of harvesting pressures on forest resources. In the case of Extension of Rotation Age/Cutting Cycle (ERA) projects, the reduction of emissions comes from the increase of Minimum Cutting Diameters (MCD) and/or the extension of Felling Cycle Duration (FCD). However, such activities have negative consequences for the profitability of timber companies. Climate instruments such as the mechanism of Reducing emissions from deforestation and forest degradation and the role of conservation, sustainable management of forests and enhancement of forest carbon stocks in developing countries (REDD+) promote a compensatory approach to cover these income losses by the valuation of avoided carbon emissions. To determine the feasibility of such a carbon-based compensation, it is necessary to predict over the long term both the dynamics of forest carbon and the time schedule of timber incomes. The two are closely interrelated. Selective logging can alter the structure, the floristic composition, and thus, the carbon stocks of tropical forests. Modelling these forest-logging relationships is challenging. Selective logging implies to deploy a species level representation of timber harvesting but the high diversity of tropical forests, in pair with the scarcity of data, hinders the correct fitting of species-specific models. We developed a bioeconomic approach coupling a mixture of inhomogeneous matrix models for forest dynamics and an object-oriented model for forest logging companies' operations. For forest dynamics, our methodology addresses the challenge of taking into account the high species richness by simultaneously clustering tree species into groups according to vital rate information and selecting group-specific explicative environmental variables. For the logging operations, the object-oriented approach allows us to precisely describe harvest choices under technical and economic constraints, in a highly configurable manner. In the case of a Central African forest concession managed by a typical sawnwood export-oriented company, we predicted the carbon stock evolution for a wide range of ERA scenarios and for a time scale of 100 years. For several categories of carbon credit, we calculated break-even prices that would enable carbon revenues to compensate logger's loss of timber incomes. Our simulations are based on data from the M'Baïki site, in the Central African Republic (CAR), which has been monitored for 30 years through a collaborative partnership with various French and CAR institutional and research organizations. Economic data are taken from several forest concessionaires in Central Africa. We predicted that without any logging, carbon stock would increase naturally. When logging was simulated, the carbon stock decreased during the first felling cycle and although carbon recovery could be boosted by logging, this decrease was too sharp to catch up with unlogged levels. To ensure low break-even prices of carbon credits, ERA activities had to involve both FCD and MCD. In this case, we found a little dependence of the private discount rate and the alternative MCD and FCD, but a strong dependence of the way how carbon credits are accounted. Thus, from the perspective of the forest concessionaire, depending of the chosen type of credits, carbon revenues could compensate timber revenues for a large number of ERA projects. We focused on IFM projects, but our approach remains appropriate for other strategies of forest sustainability improvement such as Reduced Impact Logging techniques or post-logging silvicultural systems. In the current context of REDD+ deployment, our work is a first step to bring some preliminary answers to the question of carbon-based compensation opportunities for industrial forest concessions in Central Africa, on the basis of an accurate modelling of tropical forestry. (Texte intégral)

International audience; Lignin is a major chemical compound of wood and one of the most abundant organic biopolymers on earth. It accumulates in the secondary cell wall of xylem cells and is a major target for tree breeders because of its foreseen role in the emerging bioeconomy. In this study, we paved the way toward an accelerated domestication of a widely grown tree species, Eucalyptus urophylla, by molecular breeding. To this end, we first described the pattern of nucleotide variation occurring at seven structural and regulatory genes of the lignin biosynthesis pathway and found high levels of average nucleotide and haplotype diversity per gene (pi = 0.0065 and Hd = 0.853). Then, taking advantage of a pre-existing factorial mating design, a candidate-gene-based quantitative trait locus (QTL) detection strategy was used to compare the variation of lignin quality (syringyl by guaiacyl ratio (S/G)) with the nucleotidic variability in these seven genes in 304 genotypes belonging to 33 connected full-sib families. Two genes, encoding cinnamoyl-CoA reductase (CCR) and a Rho-like GTPase (ROP1), were shown to be linked to the variation of S/G through different single and multi-locus single-nucleotide polymorphism (SNP)- and haplotype-based association methods. Providing that relevant candidate genes are selected and their patterns of nucleotide diversity is accurately described, we showed that quantitative trait nucleotides (QTNs) can be detected taking advantage of pre-existing field experiments and trait measurements gathered in the framework of a forest tree breeding program.

The desire to predict the consequences of global environmental change has been the driver towards more realistic models embracing the variability and uncertainties inherent in ecology. Statistical ecology has gelled over the past decade as a discipline that moves away from describing patterns towards modelling the ecological processes that generate these patterns. Following the fourth International Statistical Ecology Conference (1?4 July 2014) in Montpellier, France, we analyse current trends in statistical ecology. Important advances in the analysis of individual movement, and in the modelling of population dynamics and species distributions, are made possible by the increasing use of hierarchical and hidden process models. Exciting research perspectives include the development of methods to interpret citizen science data and of efficient, flexible computational algorithms for model fitting. Statistical ecology has come of age: it now provides a general and mathematically rigorous framework linking ecological theory and empirical data. Fil: Gimenez, Olivier. Universite Montpellier Ii; Francia Fil: Buckland, Stephen T.. University Of St Andrews; Reino Unido Fil: Morgan, Byron J. T.. University Of Kent; Reino Unido Fil: Bez, Nicolas. Centre National de la Recherche Scientifique. Laboratoire Pmmh-umr 7636; Francia Fil: Bertrand, Sophie. Centre National de la Recherche Scientifique. Laboratoire Pmmh-umr 7636; Francia Fil: Choquet, Rémi. Universite Montpellier Ii; Francia Fil: Dray, Stéphane. Universite Lyon 2; Francia Fil: Etienne, Marie Pierre. Centre National de la Recherche Scientifique. Laboratoire Pmmh-umr 7636; Francia Fil: Fewster, Rachel. The University Of Auckland; Nueva Zelanda Fil: Gosselin, Fréderic. Irstea; Francia Fil: Mérigot, Bastien. Universite Montpellier Ii; Francia Fil: Monestiez, Pascal. Institut National de la Recherche Agronomique; Francia Fil: Morales, Juan Manuel. Universidad Nacional del Comahue. Centro Regional Universitario Bariloche. Laboratorio de Ecotono; Argentina. Institut National de la Recherche Agronomique; Francia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Patagonia Norte. Instituto de Investigación en Biodiversidad y Medioambiente; Argentina Fil: Mortier, Frédéric. Universite Montpellier Ii; Francia Fil: Munoz, François. Universite Montpellier Ii; Francia Fil: Ovaskainen, Otso. University Of Helsinki; Finlandia Fil: Pavoine, Sandrine. University Of Oxford; Reino Unido. Muséum National d’Histoire Naturelle; Francia Fil: Pradel, Roger. Universite Montpellier Ii; Francia Fil: Schurr, Frank M.. Universidad de Hohenheim; Alemania Fil: Thomas, Len. University Of St Andrews; Reino Unido Fil: Thuiller, Wilfried. Universite Joseph Fourier; Francia Fil: Trenkel, Verena. Iremer; Francia Fil: de Valpine, Perry. University Of California Berkeley; Estados Unidos Fil: Rexstad, Eric. University Of St Andrews; Reino Unido

Forests of the Congo Basin, the second most important remaining block of tropical moist forest in the world, are facing increasing anthropogenic pressure and climate change. Understanding the biomass and diversity dynamics under these pressures is one major challenge for African nations and international communities. This talk aims to present original methods to model, infer, and predict growth, biomass and diversity of Central African forests, as well as new results on the impacts of global change on those forests, at various scales. With respect to methods, we will present theoretical frameworks allowing (i) to model growth processes in species-rich ecosystems like tropical rain forests, (ii) to take into account uncertainties in biomass estimation. In terms of results, we will highlight at a local scale, how human activities as well as climatic variations would impact (i) the composition and diversity of forests, (ii) the dynamics of biomass and growth processes. At a global scale, we will demonstrate how environmental filtering controls the above ground biomass. The number of studies are currently increasing over the Congo Basin through several research projects led by our team (CoForTips, DynAfFor) and contributing to various international organization's programs (Cifor, FAO, Comifac, Ofac). (Texte intégral)

Large areas of African moist forests are being logged in the context of supposedly sustainable management plans. It remains however controversial whether harvesting a few trees per hectare can be maintained in the long term while preserving other forest services as well. We used a unique 24 year silvicultural experiment, encompassing 10 4 ha plots established in the Central African Republic, to assess the effect of disturbance linked to logging (two to nine trees ha −1 greater than or equal to 80 cm DBH) and thinning (11–41 trees ha −1 greater than or equal to 50 cm DBH) on the structure and dynamics of the forest. Before silvicultural treatments, above-ground biomass (AGB) and timber stock (i.e. the volume of commercial trees greater than or equal to 80 cm DBH) in the plots amounted 374.5 ± 58.2 Mg ha −1 and 79.7 ± 45.9 m 3 ha −1 , respectively. We found that (i) natural control forest was increasing in AGB (2.58 ± 1.73 Mg dry mass ha −1 yr −1 ) and decreasing in timber stock (−0.33 ± 1.57 m 3 ha −1 yr −1 ); (ii) the AGB recovered very quickly after logging and thinning, at a rate proportional to the disturbance intensity (mean recovery after 24 years: 144%). Compared with controls, the gain almost doubled in the logged plots (4.82 ± 1.22 Mg ha −1 yr −1 ) and tripled in the logged + thinned plots (8.03 ± 1.41 Mg ha −1 yr −1 ); (iii) the timber stock recovered slowly (mean recovery after 24 years: 41%), at a rate of 0.75 ± 0.51 m 3 ha −1 yr −1 in the logged plots, and 0.81 ± 0.74 m 3 ha −1 yr −1 in the logged + thinned plots. Although thinning significantly increased the gain in biomass, it had no effect on the gain in timber stock. However, thinning did foster the growth and survival of small- and medium-sized timber trees and should have a positive effect over the next felling cycle.

Matrix population models are widely used to predict population dynamics, but when applied to species-rich ecosystems with many rare species, the small population sample sizes hinder a good fit of species-specific models. This issue can be overcome by assigning species to groups to increase the size of the calibration data sets. However, the species classification is often disconnected from the matrix modelling and from the estimation of matrix parameters, thus bringing species groups that may not be optimal with respect to the predicted community dynamics.We proposed here a method that jointly classified species into groups and fit the matrix models in an integrated way. The model was a special case of mixture with unknown number of components and was cast in a Bayesian framework. An MCMC algorithm was developed to infer the unknown parameters: the number of groups, the group of each species and the dynamics parameters.We applied the method to simulated data and showed that the algorithm efficiently recovered the model parameters.We applied the method to a data set from a tropical rain forest in French Guiana. The mixture matrix model classified tree species into well-differentiated groups with clear ecological interpretations. It also accurately predicted the forest dynamics over the 16-year observation period.Our model and algorithm can straightforwardly be adapted to any type of matrix model, using the life cycle diagram. It can be used as an unsupervised classification technique to group species with similar population dynamics.

1. Understanding how drought affects annual tree growth in tropical forests is of crucial importance to predict their response to climate change. Previous studies, mainly led in the Neotropics and in Southeast Asia, have yielded contradictory results which might be explained by differences in species studied, in the tree development stages considered, or by differences in other environmental factors than water availability. 2. Here, we described the growth responses of functional groups of tree species to drought in a Central African semi-deciduous moist forest. Species groups were automatically defined using a finite mixture model, which grouped species according to their growth model parameters. The growth model considered the variation in species response to drought, and the effect of competition for resources and of tree development stage on growth. Groups were further characterized by species functional traits. Nine species groups were identified. They differed in their ability to acquire, use and conserve resources, as suggested by their differences in maximum growth rate, regeneration guild, maximum dbh, wood density and leaf habit. The species were organized along a light requirement gradient that here closely matched a broader continuum of plant strategies for resource use, from slow-growing shade-tolerant conservative species to fast-growing pioneer acquisitive species. 3. Tree growth decreased with drought intensity, and species drought tolerance was found to be related to resource use strategy: slow-growing species using a conservative strategy were the least sensitive to variations in water availability, while fast-growing species using an acquisitive strategy were the most sensitive. 4. Synthesis. Shade-tolerant species, characterized by a low potential growth rate and thus a conservative strategy of resource use, were found to be the least sensitive to drought. This supports the hypothesis of a single axis summarizing multiple traits that represents a general trade-off between the conservation and rapid acquisition of resources. (Resume d'auteur)

Timber production is an important economic sector in most forested countries of Central Africa, where about 14 million hectares of lowland moist forests are now planned for management. This production is expected to be sustainable, but the actual impact of logging on biodiversity is still questioned. To answer this question, we used a unique long-term controlled experiment implemented more than 20 years ago in an old-growth semi-deciduous moist forest of the Central African Republic (CAR). We tested whether (i) anthropogenic disturbances associated with silvicultural operations had an effect on the composition and diversity of tree communities, and (ii) there is a relationship between diversity and disturbance intensity in those forests. For this, we botanically identified all trees P 10 cm DBH in 28 1-ha plots where no treatment (controls), logging and logging + thinning operations were implemented 24 years ago and created a strong gradient of disturbance. We investigated the relationships between five diversity indices and a disturbance index calculated for each 1-ha plot, for all species and separately for three regeneration guilds. We found a strong positive monotonic relationship between the intensity of disturbance and the percentage of pioneer species in the tree communities, which proved to be equally detrimental, in terms of relative abundance, to the non-pioneer light-demanding and the shade-bearing species. Overall, disturbance appeared to have a weak monotonous negative effect on diversity, irrespective to the index considered. The diversity of shade-bearers slightly decreased along the disturbance gradient without significant decrease in species density; disturbance had no effect on non-pioneer light demanders, but a clear significant negative effect on the diversity of pioneers, with a significant decrease in species density. This negative effect was associated with the massive recruitment of the early-successional, fast-growing Musanga cecropioides R. Br. (Urticaceae), which rapidly preempted space and resources in the most disturbed plots. Despite this effect, disturbance did not significantly affect the local heterogeneity in species distribution. These results suggest that the semi-deciduous moist forests of CAR are locally resilient to small-scale disturbances associated with silvicultural operations. This may be a consequence of the past anthropogenic and/or climatic disturbances, which have been stronger and more long-lasting than elsewhere within the tropical forest biome, and would have removed the most vulnerable species. Because logging intensity in these forests is usually low, we do not expect any direct major impact on tree species diversity, at least after the first felling cycle.

In the current estimation of a GLM model, the correlation structure of regressors is not used as the basis on which to lean strong predictive dimensions. Looking for linear combinations of regressors that merely maximize the likelihood of the GLM has two major consequences: (1) collinearity of regressors is a factor of estimation instability, and (2) as predictive dimensions may lean on noise, both predictive and explanatory powers of the model are jeopardized. For a single dependent variable, attempts have been made to adapt PLS regression, which solves this problem in the classical Linear Model, to GLM estimation. In this paper, we first discuss the methods thus developed, and then propose a technique, Supervised Component Generalized Linear Regression (SCGLR), that combines PLS regression with GLM estimation in the multivariate context. SCGLR is tested on both simulated and real data.

Determining how tropical tree populations subject to selective felling (logging) pressure may be conserved is a crucial issue for forest management and studying this issue requires a comprehensive understanding of the relationships between population demography and gene flow. We used a simulation model, SELVA, to study (1) the relative impact of demographic factors (juvenile mortality, felling regime) and genetic factors (selfing, number and location of fathers, mating success) on long-term genetic diversity; and (2) the impact of different felling regimes on population size versus genetic diversity. Impact was measured by means of model sensitivity analyses. Juvenile mortality had the highest impact on the number of alleles and genotypes, and on the genetic distance between the original and final populations. Selfing had the greatest impact on observed heterozygote frequency and fixation index. Other factors and interactions had only minor effects. Overall, felling had a greater impact on population size than on genetic diversity. Interestingly, populations under relatively low felling pressure even had a somewhat lower fixation index than undisturbed populations (no felling). We conclude that demographic processes such as juvenile mortality should be modelled thoroughly to obtain reliable long-term predictions of genetic diversity. Mortality in selfed and outcrossed progenies should be modelled explicitly by taking inbreeding depression into account. The modelling of selfing based on population rate appeared to be oversimplifying and should account for inter-tree variation. Forest management should pay particular attention to the regeneration capacities of felled species.

The forests in overseas territories are highly varied and shelter huge and often unique biological riches due to high rates of endemicity. Four of the five biodiversity hot spots in France are located in overseas territories, making for the country’s global responsibilities in this area. Over time, their surface area has decreased and their conservation status has changed in some places. They are under various forms of pressure: urbanisation, agricultural development, gold digging, etc. The value of these overseas forests is now better recognized and many measures have been undertaken in these territories: creation of protected areas, control of invasive species, enhanced productivity through forest-based industry uses and ecotourism. Nonetheless, they are still seriously threatened and secure land tenure system appears to be a pre-requisite for conducting public policies of conservation. Better knowledge of how the ecosystems function, which is still very fragmentary, is essential to enhance efficiency of the management and conservation measures undertaken. Finally, it is crucial for the future that the efforts of public players be pooled and coordinated within the framework of an overall, network-based approach to conservation.

International audience; As most georeferenced data sets are multivariate and concern variables of different types, spatial mapping methods must be able to deal with such data. The main difficulties are the prediction of non-Gaussian variables and the modeling of the dependence between processes. The aim of this article is to present a new hierarchical Bayesian approach that permits simultaneous modeling of dependent Gaussian, count, and ordinal spatial fields. This approach is based on spatial generalized linear mixed models. We use a moving average approach to model the spatial dependence between the processes. The method is first validated through a simulation study. We show that the multivariate model has better predictive abilities than the univariate one. Then the multivariate spatial hierarchical model is applied to a real data set collected in French Guiana to predict topsoil patterns.

As most georeferenced data sets are multivariate and concern variables of different kinds, spatial mapping methods must be able to deal with such data. The main difficulties are the prediction of non Gaussian variables and the modelling of the dependence between processes. The aim of this paper is to propose a new approach that permits simultaneous modelling of Gaussian, count and ordinal spatial processes. We consider a hierarchical model implemented within a Bayesian framework. The method used for Gaussian and count variables is based on the generalized linear mixed models. Ordinal variable is taken into account through a generalization of the ordinal probit model. We use a moving average approach to model the spatial dependence between the processes. The proposed model is applied to pedological data collected in French Guiana.

The high species diversity of some ecosystems like tropical rainforests goes in pair with the scarcity of data for most species. This hinders the development of models that require enough data for fitting. The solution commonly adopted by modellers consists in grouping species to form more sizeable data sets. Classical methods for grouping species such as hierarchical cluster analysis do not take account of the variability of the species characteristics used for clustering. In this study a clustering method based on aggregation theory is presented. It takes account of the variability of species characteristics by searching for the grouping that minimizes the quadratic error (square bias plus variance) of some model’s prediction. This method allows one to check whether the gain in variance brought by data pooling compensate for the bias that it introduces. This method was applied to a data set on 94 tree species in a tropical rainforest in French Guiana, using a Usher matrix model to predict species dynamics. An optimal trade-off between bias and variance was found when grouping species. Grouping species appeared to decrease the quadratic error, except when the number of groups was very small. This clustering method yielded species groups similar to those of the hierarchical cluster analysis using Ward’s method when variance was small, that is when the number of groups was small.

International audience; The spatial pattern of trees in forests often combines different types of structure (regularity, clustering, or randomness) at different scales. Taking species or size into account leads to marked patterns. The question addressed is to model such multi-scale marked patterns using a single process. Within the category of Markov processes, the area-interaction process has the advantage of being locally stable, whether it is attractive or repulsive. This process was originally defined as a one-scale non-marked process. We propose an extension as a multi-scale marked process. Three examples are presented to show the adequacy of this process to model tree patterns: 1. A pine pattern showing anisotropic regularity and clustering at different scales. 2. A bivariate (adult / juvenile) kimboto pattern in French Guiana, showing regularity for one type, clustering for the other, and repulsion between the two. 3. A marked pattern in Gabon where the mark is tree diameter.

When predicting population dynamics, the value of the prediction is not enough and should be accompanied by a confidence interval that integrates the whole chain of errors, from observations to predictions via the estimates of the parameters of the model. Matrix models are often used to predict the dynamics of age- or size-structured populations. Their parameters are vital rates. This study aims (1) at assessing the impact of the variability of observations on vital rates, and then on model’s predictions, and (2) at comparing three methods for computing confidence intervals for values predicted from the models. The first method is the bootstrap. The second method is analytic and approximates the standard error of predictions by their asymptotic variance as the sample size tends to infinity. The third method combines use of the bootstrap to estimate the standard errors of vital rates with the analytical method to then estimate the errors of predictions from the model. Computations are done for an Usher matrix models that predicts the asymptotic (as time goes to infinity) stock recovery rate for three timber species in French Guiana. Little difference is found between the hybrid and the analytic method. Their estimates of bias and standard error converge towards the bootstrap estimates when the error on vital rates becomes small enough, which corresponds in the present case to a number of observations greater than 5000 trees.

Summary Designing permanent sample plots is a key issue in forestry where long-term data are required to assess the sustainability of forest logging. The data that are collected in permanent sample plots are used to set parameters in a population dynamics matrix model which in turn is used to predict stock recovery rates for each species. The sampling plan for permanent plots can be designed to estimate stock recovery rates with a required accuracy at a given confidence level, while minimizing installation costs. This can be formulated as a constrained optimization problem (one constraint for each species). The question then is to quantify sampling variability, i.e. the variability of model predictions that are generated by the distribution of parameter estimators. In this study, we address the question of sampling variability for a size-classified population matrix model in a hierarchical context where sample size is itself random and driven by a multivariate spatial point process. An approximate expression is given for the accuracy of the stock recovery rate estimator. This expression is the limit of the accuracy as the expectation of sample size tends to ∞. We extend this expression to the multispecies case. To a first approximation, interactions between species do not affect the accuracy of the stock recovery rate for each species. A sampling plan is designed using the data for three species in a tropical rainforest in French Guiana. The optimal sampling plan appears to be determined by the most constrained species.

The stock recovery rate, the ratio of the wood stock at the end of a felling cycle over the wood stock just before logging, is a key parameter for the management of tropical rainforests. It is thus essential to predict it with a reliable precision. It can be predicted using the stock recovery formula or Usher matrix models, that are projection matrix models for size-structured populations. Both depend on estimates of vital rates, that are mortality rates, recruitment rates and upgrowth rates. The precision of estimation of the stock recovery rate is related to the amount of data available for the estimation of vital rates and to the type of estimator used. As data on tropical tree species are scarce, the choice of an appropriate estimator for vital rates is crucial. Classical estimators include the proportion estimator and estimators based on the conditional expectation of diameter increments. We show that the later are biased and define a correction that partially corrects this bias. In all, 14 estimators of the vital rates were compared in this study, to predict the stock recovery rate of Dicorynia guianensis, a major timber species in French Guiana. These estimators were compared on the basis of the prediction error, of the sensitivity of the stock recovery rate to diameter intervals, and of the bias and variance of the stock recovery rate estimator. The predicted stock recovery rate varied greatly depending on the estimator used for vital rates, with even contradictory conclusions as whether the stock depletes or increases. However some the estimators were strongly biased and gave unreliable estimates. Which estimator was the most statistically efficient depended on sample size. The proportion estimators had a small bias and a large variance and were efficient for large samples, whereas the estimators based on the conditional expectation of diameter increments had a large bias and a small variance and were efficient for small samples. The former were more sensitive to the diameter breakpoints than the latter.

Individual or stand-level biomass is not easy to measure. The current methods employed, based on cutting down a representative sample of plantations, make it possible to assess the biomasses for various compartments (bark, dead branches, leaves, . . .). However, this felling makes individual longitudinal follow-up impossible. In this context, we propose a method to evaluate individual biomasses by compartments when these biomasses are taken as ordinals. Biomass is measured visually and observations are therefore not destructive. The technique is based on a probit model redefined in terms of latent variables. A generalization of the univariate case to the multivariate case is then natural and takes into account the dependency between compartment biomasses. These models are then extended to the longitudinal case by developing a Dynamic Multivariate Ordinal Probit Model. The performance of the MCMC algorithm used for the estimation is illustrated by means of simulations built from known biomass models. The quality of the estimates and the impact of certain parameters, are then discussed.

The objective of this paper is first to predict generalized Euclidean distances in the context of discrete and quantitative variables and then to derive their statistical properties. We first consider the simultaneous modelling of discrete and continuous random variables with covariates and obtain the likelihood. We derive an important property useful for its practical maximization. We then study the prediction of any Euclidean distances and its statistical proprieties, especially for the Mahalanobis distance. The quality of distance estimation is analyzed through simulations. This results are applied to our motivating example: the official distinction procedure of rapeseed varieties. © 2005 Elsevier Inc. All rights reserved.