Vivien Rossi

Convolution particle filtering for parameter estimation in general state-space models

The state-space modeling of partially observed dynamic systems generally requires estimates of unknown parameters. From a practical point of view, it is relevant in such filtering contexts to simultaneously estimate the unknown states and parameters. Efficient simulation-based methods using convolution particle filters are proposed. The regularization properties of these filters is well suited, given the context of parameter estimation. Firstly the usual non Bayesian statistical estimates are considered: the conditional least squares estimate (CLSE) and the maximum likelihood estimate (MLE). Secondly, in a Bayesian context, a Monte Carlo type method is presented. Finally we present a simulated case studyThe state-space modeling of partially observed dynamical systems generally requires estimates of unknown parameters. The dynamic state vector together with the static parameter vector can be considered as an augmented state vector. Classical filtering methods, such as the extended Kalman filter (EKF) and the bootstrap particle filter (PF), fail to estimate the augmented state vector. For these classical filters to handle the augmented state vector, a dynamic noise term should be artificially added to the parameter components or to the deterministic component of the dynamical system. However, this approach degrades the estimation performance of the filters. We propose a variant of the PF based on convolution kernel approximation techniques. This approach is tested on a simulated case study.

Water availability is the main climate driver of neotropical tree growth.

• Climate models for the coming century predict rainfall reduction in the Amazonian region, including change in water availability for tropical rainforests. Here, we test the extent to which climate variables related to water regime, temperature and irradiance shape the growth trajectories of neotropical trees. • We developed a diameter growth model explicitly designed to work with asynchronous climate and growth data. Growth trajectories of 205 individual trees from 54 neotropical species censused every 2 months over a 4-year period were used to rank 9 climate variables and find the best predictive model. • About 9% of the individual variation in tree growth was imputable to the seasonal variation of climate. Relative extractable water was the main predictor and alone explained more than 60% of the climate effect on tree growth, i.e. 5.4% of the individual variation in tree growth. Furthermore, the global annual tree growth was more dependent on the diameter increment at the onset of the rain season than on the duration of dry season. • The best predictive model included 3 climate variables: relative extractable water, minimum temperature and irradiance. The root mean squared error of prediction (0.035 mm.d –1) was slightly above the mean value of the growth (0.026 mm.d –1). • Amongst climate variables, we highlight the predominant role of water availability in determining seasonal variation in tree growth of neotropical forest trees and the need to include these relationships in forest simulators to test, in silico, the impact of different climate scenarios on the future dynamics of the rainforest.

Depth of soil water uptake by tropical rainforest trees during dry periods: Does tree dimension matter?

Though the root biomass of tropical rainforest trees is concentrated in the upper soil layers, soil water uptake by deep roots has been shown to contribute to tree transpiration. A precise evaluation of the relationship between tree dimensions and depth of water uptake would be useful in tree-based modelling approaches designed to anticipate the response of tropical rainforest ecosystems to future changes in environmental conditions. We used an innovative dual-isotope labelling approach (deuterium in surface soil and oxygen at 120-cm depth) coupled with a modelling approach to investigate the role of tree dimensions in soil water uptake in a tropical rainforest exposed to seasonal drought. We studied 65 trees of varying diameter and height and with a wide range of predawn leaf water potential (Ψpd) values. We confirmed that about half of the studied trees relied on soil water below 100-cm depth during dry periods. Ψpd was negatively correlated with depth of water extraction and can be taken as a rough proxy of this depth. Some trees showed considerable plasticity in their depth of water uptake, exhibiting an efficient adaptive strategy for water and nutrient resource acquisition. We did not find a strong relationship between tree dimensions and depth of water uptake. While tall trees preferentially extract water from layers below 100-cm depth, shorter trees show broad variations in mean depth of water uptake. This precludes the use of tree dimensions to parameterize functional models.

Generalization of the Partitioning of Shannon Diversity

Traditional measures of diversity, namely the number of species as well as Simpsons and Shannons indices, are particular cases of Tsallis entropy. Entropy decomposition, i.e. decomposing gamma entropy into alpha and beta components, has been previously derived in the literature. We propose a generalization of the additive decomposition of Shannon entropy applied to Tsallis entropy. We obtain a self-contained definition of beta entropy as the information gain brought by the knowledge of each community composition. We propose a correction of the estimation bias allowing to estimate alpha, beta and gamma entropy from the data and eventually convert them into true diversity. We advocate additive decomposition in complement of multiplicative partitioning to allow robust estimation of biodiversity.

Pan-Tropical Analysis of Climate Effects on Seasonal Tree Growth

Climate models predict a range of changes in tropical forest regions, including increased average temperatures, decreased total precipitation, reduced soil moisture and alterations in seasonal climate variations. These changes are directly related to the increase in anthropogenic greenhouse gas concentrations, primarily CO2. Assessing seasonal forest growth responses to climate is of utmost importance because woody tissues, produced by photosynthesis from atmospheric CO2, water and light, constitute the main component of carbon sequestration in the forest ecosystem. In this paper, we combine intra-annual tree growth measurements from published tree growth data and the corresponding monthly climate data for 25 pan-tropical forest sites. This meta-analysis is designed to find the shared climate drivers of tree growth and their relative importance across pan-tropical forests in order to improve carbon uptake models in a global change context. Tree growth reveals significant intra-annual seasonality at seasonally dry sites or in wet tropical forests. Of the overall variation in tree growth, 28.7% was explained by the site effect, i.e. the tree growth average per site. The best predictive model included four climate variables: precipitation, solar radiation (estimated with extrasolar radiation reaching the atmosphere), temperature amplitude and relative soil water content. This model explained more than 50% of the tree growth variations across tropical forests. Precipitation and solar radiation are the main seasonal drivers of tree growth, causing 19.8% and 16.3% of the tree growth variations. Both have a significant positive association with tree growth. These findings suggest that forest productivity due to tropical tree growth will be reduced in the future if climate extremes, such as droughts, become more frequent.

Toward trait-based mortality models for tropical forests

Tree mortality in tropical forests is a complex ecological process for which modelling approaches need to be improved to better understand, and then predict, the evolution of tree mortality in response to global change. The mortality model introduced here computes an individual probability of dying for each tree in a community. The mortality model uses the ontogenetic stage of the tree because youngest and oldest trees are more likely to die. Functional traits are integrated as proxies of the ecological strategies of the trees to permit generalization among all species in the community. Data used to parametrize the model were collected at Paracou study site, a tropical rain forest in French Guiana, where 20,408 trees have been censused for 18 years. A Bayesian framework was used to select useful covariates and to estimate the model parameters. This framework was developed to deal with sources of uncertainty, including the complexity of the mortality process itself and the field data, especially historical data for which taxonomic determinations were uncertain. Uncertainty about the functional traits was also considered, to maximize the information they contain. Four functional traits were strong predictors of tree mortality: wood density, maximum height, laminar toughness and stem and branch orientation, which together distinguished the light-demanding, fast-growing trees from slow-growing trees with lower mortality rates. Our modelling approach formalizes a complex ecological problem and offers a relevant mathematical framework for tropical ecologists to process similar uncertain data at the community level.

Relationships between demography and gene flow and their importance for the conservation of tree populations in tropical forests under selective felling regimes

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.

Parallel and interacting Markov chain Monte Carlo algorithm

In many situations it is important to be able to propose N independent realizations of a given distribution law. We propose a strategy for making N parallel Monte Carlo Markov chains (MCMC) interact in order to get an approximation of an independent N-sample of a given target law. In this method each individual chain proposes candidates for all other chains. We prove that the set of interacting chains is itself a MCMC method for the product of N target measures. Compared to independent parallel chains this method is more time consuming, but we show through examples that it possesses many advantages. This approach is applied to a biomass evolution model.

Climate drivers of the Amazon forest greening

Our limited understanding of the climate controls on tropical forest seasonality is one of the biggest sources of uncertainty in modeling climate change impacts on terrestrial ecosystems. Combining leaf production, litterfall and climate observations from satellite and ground data in the Amazon forest, we show that seasonal variation in leaf production is largely triggered by climate signals, specifically, insolation increase (70.4% of the total area) and precipitation increase (29.6%). Increase of insolation drives leaf growth in the absence of water limitation. For these non-water-limited forests, the simultaneous leaf flush occurs in a sufficient proportion of the trees to be observed from space. While tropical cycles are generally defined in terms of dry or wet season, we show that for a large part of Amazonia the increase in insolation triggers the visible progress of leaf growth, just like during spring in temperate forests. The dependence of leaf growth initiation on climate seasonality may result in a higher sensitivity of these ecosystems to changes in climate than previously thought.

Predation success by a plant-ant indirectly favours the growth and fitness of its host myrmecophyte

Mutualisms, or interactions between species that lead to net fitness benefits for each species involved, are stable and ubiquitous in nature mostly due to “byproduct benefits” stemming from the intrinsic traits of one partner that generate an indirect and positive outcome for the other. Here we verify if myrmecotrophy (where plants obtain nutrients from the refuse of their associated ants) can explain the stability of the tripartite association between the myrmecophyte Hirtella physophora, the ant Allomerus decemarticulatus and an Ascomycota fungus. The plant shelters and provides the ants with extrafloral nectar. The ants protect the plant from herbivores and integrate the fungus into the construction of a trap that they use to capture prey; they also provide the fungus and their host plant with nutrients. During a 9-month field study, we over-provisioned experimental ant colonies with insects, enhancing colony fitness (i.e., more winged females were produced). The rate of partial castration of the host plant, previously demonstrated, was not influenced by the experiment. Experimental plants showed higher δ15N values (confirming myrmecotrophy), plus enhanced vegetative growth (e.g., more leaves produced increased the possibility of lodging ants in leaf pouches) and fitness (i.e., more fruits produced and more flowers that matured into fruit). This study highlights the importance of myrmecotrophy on host plant fitness and the stability of ant-myrmecophyte mutualisms.