Predicting tree distributions in an East African biodiversity hotspot : model selection, data bias and envelope uncertainty

The Eastern Arc Mountains (EAMs) of Tanzania and Kenya support some of the most ancient tropical rainforest on Earth. The forests are a global priority for biodiversity conservation and provide vital resources to the Tanzanian population. Here, we make a first attempt to predict the spatial distribution of 40 EAM tree species, using generalised additive models, plot data and environmental predictor maps at sub 1 km resolution. The results of three modelling experiments are presented, investigating predictions obtained by (1) two different procedures for the stepwise selection of predictors, (2) down-weighting absence data, and (3) incorporating an autocovariate term to describe fine-scale spatial aggregation. In response to recent concerns regarding the extrapolation of model predictions beyond the restricted environmental range of training data, we also demonstrate a novel graphical tool for quantifying envelope uncertainty in restricted range niche-based models (envelope uncertainty maps). We find that even for species with very few documented occurrences useful estimates of distribution can be achieved. Initiating selection with a null model is found to be useful for explanatory purposes, while beginning with a full predictor set can over-fit the data. We show that a simple multimodel average of these two best-model predictions yields a superior compromise between generality and precision (parsimony). Down-weighting absences shifts the balance of errors in favour of higher sensitivity, reducing the number of serious mistakes (i.e., falsely predicted absences); however, response functions are more complex, exacerbating uncertainty in larger models. Spatial autocovariates help describe fine-scale patterns of occurrence and significantly improve explained deviance, though if important environmental constraints are omitted then model stability and explanatory power can be compromised. We conclude that the best modelling practice is contingent both on the intentions of the analyst (explanation or prediction) and on the quality of distribution data; generalised additive models have potential to provide valuable information for conservation in the EAMs, but methods must be carefully considered, particularly if occurrence data are scarce. Full results and details of all species models are supplied in an online Appendix. (C) 2008 Elsevier B.V. All rights reserved

How to make R, PostGIS and QGis cooperate for statistical modelling duties: a case study on hedonic regressions

International audienceWe describe in this communication how we managed to make R, PostGIS and QGis work together to assist us in our econometric modelling of housing prices. We have evaluated different combinations of these three pieces of software that we have used extensively during the course of this research, to finally converge to the system that we are currently using. We were concerned mainly with performance (as large amounts of data are involved), spatial query capabilities, easiness to compute new spatial indicators and to take them into account in the statistical modelling, and finally spatial visualisation of statistical results and map production. As it is often the case with open source software, several possibilities exist to connect the pieces of software two by two. We tried some of them and give an insight on the results of our experiments

Query processing of geometric objects with free form boundarie sin spatial databases

The increasing demand for the use of database systems as an integrating factor in CAD/CAM applications has necessitated the development of database systems with appropriate modelling and retrieval capabilities. One essential problem is the treatment of geometric data which has led to the development of spatial databases. Unfortunately, most proposals only deal with simple geometric objects like multidimensional points and rectangles. On the other hand, there has been a rapid development in the field of representing geometric objects with free form curves or surfaces, initiated by engineering applications such as mechanical engineering, aviation or astronautics. Therefore, we propose a concept for the realization of spatial retrieval operations on geometric objects with free form boundaries, such as B-spline or Bezier curves, which can easily be integrated in a database management system. The key concept is the encapsulation of geometric operations in a so-called query processor. First, this enables the definition of an interface allowing the integration into the data model and the definition of the query language of a database system for complex objects. Second, the approach allows the use of an arbitrary representation of the geometric objects. After a short description of the query processor, we propose some representations for free form objects determined by B-spline or Bezier curves. The goal of efficient query processing in a database environment is achieved using a combination of decomposition techniques and spatial access methods. Finally, we present some experimental results indicating that the performance of decomposition techniques is clearly superior to traditional query processing strategies for geometric objects with free form boundaries

Regeneration ecology of anemochorous tree species Qualea grandiflora (Mart.) and Aspidosperma tomentosum (Mart.) of the cerrado Aguara Ñu located in the Mbaracayú Nature Forest Reserve (MNFR), Paraguay

Understanding of the diverse aspects affecting the regeneration ecology of species is crucial to make decisions regarding management and conservation strategies, especially in highly fragile and threatened ecosystem as the Neotropical savanna (cerrado) formations. Available knowledge of regeneration ecology of cerrado species is too limited to attain optimal or suitable management actions. The objectives of the present study were: i) analysis of the characteristic parameters of the anemochorous seed dispersal of study species Q. grandiflora, (ii) determine the spatial distribution of tree species Q. grandiflora for growth stages (seedlings to juveniles) and interrelations between the stages, and (iii) determining variables of the spatial distribution of recruitment of tree species A. tomentosum. The present study was conducted in the cerrado Aguara Ñu of the Mbaracayú Nature Forest Reserve located in the northeast of Paraguay. The cerrado Aguara Ñu is part of the Mbaracayú Biosphere Reserve and represents one of the most important ecoregions in the world, the cerrado ecosystem. The cerrado biome encompasses areas from northeastern to southwestern Brazil, eastern Bolivia, and northern Paraguay. It is characterized by the presence of high plant and animal biodiversity and also high endemism (Myers et al., 2000). Tree species Q. grandiflora and A. tomentosum are typical species of the cerrado formation. Based on the selected investigated regeneration cycle stages of study tree species Q. grandiflora and A. tomentosum, the present thesis describes the spatial analysis of recruitment of both study species and the anemochorous diaspore dispersal of tree species Q. grandiflora. The purpose of the present investigation is to address regeneration aspects not attained so far as certain seed dispersal aspects, such as seed densities and distances from conspecific adult trees and spatial arrangements of seedlings of species A. tomentosum. Results of the present study aim to contribute to existing information and at the same time provide new knowledge on ecological aspects so far not investigated. Research results on seed dispersal of tree species Q. grandiflora revealed that dispersal can be modeled by inverse modelling considering isotropy and lognormal density function presenting mean dispersal distances of 10.69 to 62.48 m. Estimations of the fruit production of a seed tree yielded a total 50671 to 70632 (DBH = 70 cm). Results of spatial arrangement of seedlings and juveniles revealed a significant distance effect to conspecific adult trees. Moreover, results also showed: (i) highest densities or intensities (m2) of seedlings (heights <50 cm) close to the conspecific adult trees and (ii) a shift of intensity of seedlings with increase of growth stage or size for tree species Q. grandiflora. Additionally, seedlings (up to 200 cm height) of study species Q. grandiflora indicated gradual decreasing clumping patterns and juveniles (200 – 500 cm height) presented clumping patterns. Modelling results of spatial patterns of seedlings (heights ≤ 200 cm) of study tree species A. tomentosum revealed aggregation patterns. Moreover, shade effect resulted to be a statistical significant factor for the establishment of seedlings of tree species A. tomentosum (p-value = 0.0266), whereas distance effect to seed tree resulted not significant (p-value= 0.4936). Considering the findings of seed dispersal and spatial patterns analysis of tree species Q. grandiflora and A. tomentosum some management aspects to be attained for conservation purposes are avoiding fragmentation of the ecosystem, management of the spatial and time fire frequency and maintain minimum amount of seed trees per unit area in order to guarantee successful recruitment.:1. Introduction 1 References 8 2. Materials and Methods 13 2.1 Characterization of the cerrado biome 13 2.2 Description of the study area and study sites 15 2.3 Characterization of the study tree species 23 2.3.1 Qualea grandiflora (Mart.) 23 2.3.2 Aspidosperma tomentosum (Mart.) 24 2.4 Principles and selection criteria 25 2.5 Data collection 26 2.5.1 Seed dispersal 26 2.5.2 Spatial patterns of plants 27 2.6 Data analysis 28 2.6.1 Statistical analysis of data 28 2.6.2 General statistical procedures of data analysis 30 2.6.3 Spatial point process analysis – Inverse modelling and spatial point patterns 31 2.6.4 Spatial point patterns analysis procedure 33 2.6.4.1 Descriptive statistics in spatial point patterns 36 2.6.4.1.1 Distance effect of seedlings from seed trees (rhohat function) 36 2.6.4.1.2 Pair correlation function (pcf) 36 2.6.4.2 Point process modelling 38 References 43 3. Seed dispersal of Qualea grandiflora (Mart.) 49 3.1 Introduction 49 3.2 Methodology 51 3.2.1 Data collection and seed trap design 51 3.2.1 Data analysis – inverse modelling 53 3.3 Results 58 3.3.1 Seed density 58 3.3.2 Inverse modelling results – seed production, dispersal and distances 60 3.3.2.1 Isotropic modelling 61 3.3.2.2 Anisotropic modelling 63 3.3.2.3 Statistical comparison isotropy vs. anisotropy 66 3.4 Discussion 67 3.4.1 Applied methodology for seed dispersal – trap design and inverse modelling 67 3.4.2 Seed dispersal modelling 69 3.5 Conclusion 74 References 75 4. Spatial analysis of Qualea grandiflora (Mart.) 80 4.1 Introduction 80 4.2 Methodology 82 4.2.1 Data collection – Field sampling 82 4.2.2 Data analysis 85 4.2.2.1 Spatial point pattern – Explorative analysis 85 4.2.2.2 Point process modelling (Poisson and Gibbs models) 87 4.2.3 Results 89 4.2.3.1 Spatial distribution of individuals of study species 89 4.2.3.2 Modelling distance effect of recruitment to adult trees 95 4.2.4 Discussion 102 4.2.4.1 Applied methodology for spatial analysis of study species 102 4.2.4.2 Spatial arrangement of study species 103 4.2.5 Conclusion 109 References 109 5. Spatial analysis of Aspidosperma tomentosum (Mart.)115 5.1 Introduction 115 5.2 Methodology 117 5.2.1 Data collection – Field sampling 117 5.2.2 Data analysis 120 5.2.2.1 Spatial point pattern – Explorative analysis 120 5.2.2.2 Point process modelling – Replicated point patterns 120 5.3 Results 123 5.3.1 Spatial distribution of natural regeneration of study species 123 5.3.2 Modelling shade and distance to seed tree effect on natural regeneration of study species 130 5.4 Discussion 133 5.4.1 Applied methodology for data collection and analysis 133 5.4.2 Spatial distribution of natural regeneration of study species 134 5.5 Conclusion 139 References 140 5. Concluding discussion and summary 146 6.1 Regeneration ecology of Qualea grandiflora and Aspidosperma tomentosum 146 6.1.1 Inferences on relation of seed dispersal and spatial distribution of recruitment of Qualea grandiflora 146 6.1.2 Inferences on spatial patterns of recruitment of Aspidoserma tomentosum 149 6.2 Management implications for Qualea grandiflora Aspidosperma tomentosum 150 6.3 Future research 153 6.4 Concluding summary 154 References 15

A Bayesian spatial random effects model characterisation of tumour heterogeneity implemented using Markov chain Monte Carlo (MCMC) simulation

The focus of this study is the development of a statistical modelling procedure for characterising intra-tumour heterogeneity, motivated by recent clinical literature indicating that a variety of tumours exhibit a considerable degree of genetic spatial variability. A formal spatial statistical model has been developed and used to characterise the structural heterogeneity of a number of supratentorial primitive neuroecto-dermal tumours (PNETs), based on diffusionweighted magnetic resonance imaging. Particular attention is paid to the spatial dependence of diffusion close to the tumour boundary, in order to determine whether the data provide statistical evidence to support the proposition that water diffusivity in the boundary region of some tumours exhibits a deterministic dependence on distance from the boundary, in excess of an underlying random 2D spatial heterogeneity in diffusion. Tumour spatial heterogeneity measures were derived from the diffusion parameter estimates obtained using a Bayesian spatial random effects model. The analyses were implemented using Markov chain Monte Carlo (MCMC) simulation. Posterior predictive simulation was used to assess the adequacy of the statistical model. The main observations are that the previously reported relationship between diffusion and boundary proximity remains observable and achieves statistical significance after adjusting for an underlying random 2D spatial heterogeneity in the diffusion model parameters. A comparison of the magnitude of the boundary-distance effect with the underlying random 2D boundary heterogeneity suggests that both are important sources of variation in the vicinity of the boundary. No consistent pattern emerges from a comparison of the boundary and core spatial heterogeneity, with no indication of a consistently greater level of heterogeneity in one region compared with the other. The results raise the possibility that DWI might provide a surrogate marker of intra-tumour genetic regional heterogeneity, which would provide a powerful tool with applications in both patient management and in cancer research

Evolutionary and demographic correlates of Pleistocene coastline changes in the Sicilian wall lizard Podarcis wagleriana

Aim Emergence of coastal lowlands during Pleistocene ice ages might have provided conditions for glacial expansions (demographic and spatial), rather than contraction, of coastal populations of temperate species. Here, we tested these predictions in the insular endemic Sicilian wall lizard Podarcis wagleriana. Location Sicily and neighbouring islands. Methods We sampled 179 individuals from 45 localities across the whole range of P. wagleriana. We investigated demographic and spatial variations through time using Bayesian coalescent models (Bayesian phylogeographic reconstruction, Extended Bayesian Skyline plots, Isolation‐with‐migration models) based on multilocus DNA sequence data. We used species distribution modelling to reconstruct present and past habitat suitability. Results We found two main lineages distributed in the east and west portions of the current species range and a third lineage restricted to a small area in the north of Sicily. Multiple lines of evidence from palaeogeographic (shorelines), palaeoclimatic (species distribution models), and multilocus genetic data (demographic and spatial Bayesian reconstructions) indicate that these lineages originated in distinct refugia, located in the north‐western and south‐eastern coastal lowlands, during Middle Pleistocene interglacial phases, and came into secondary contact following demographic and spatial expansions during the last glacial phase. Main conclusions This scenario of interglacial contraction and glacial expansion is in sharp contrast with patterns commonly observed in temperate species on the continent but parallels recent findings on other Mediterranean island endemics. Such a reverse expansion–contraction (EC) dynamic has been likely associated with glacial increases of climatically suitable coastal lowlands, suggesting this might be a general pattern in Mediterranean island species and also in other coastal regions strongly affected by glacial marine regressions during glacial episodes. This study provides explicit predictions and some methodological recommendations for testing the reverse EC model in other region and taxa

Is more data always better? A simulation study of benefits and limitations of integrated distribution models

Species distribution models are popular and widely applied ecological tools. Recent increases in data availability have led to opportunities and challenges for species distribution modelling. Each data source has different qualities, determined by how it was collected. As several data sources can inform on a single species, ecologists have often analysed just one of the data sources, but this loses information, as some data sources are discarded. Integrated distribution models (IDMs) were developed to enable inclusion of multiple datasets in a single model, whilst accounting for different data collection protocols. This is advantageous because it allows efficient use of all data available, can improve estimation and account for biases in data collection. What is not yet known is when integrating different data sources does not bring advantages. Here, for the first time, we explore the potential limits of IDMs using a simulation study integrating a spatially biased, opportunistic, presence‐only dataset with a structured, presence–absence dataset. We explore four scenarios based on real ecological problems; small sample sizes, low levels of detection probability, correlations between covariates and a lack of knowledge of the drivers of bias in data collection. For each scenario we ask; do we see improvements in parameter estimation or the accuracy of spatial pattern prediction in the IDM versus modelling either data source alone? We found integration alone was unable to correct for spatial bias in presence‐only data. Including a covariate to explain bias or adding a flexible spatial term improved IDM performance beyond single dataset models, with the models including a flexible spatial term producing the most accurate and robust estimates. Increasing the sample size of presence–absence data and having no correlated covariates also improved estimation. These results demonstrate under which conditions integrated models provide benefits over modelling single data sources

Long term nitrogen budget modelling in a small agricultural watershed: hydrological control assessment of nitrogen losses with semi-distributed (SWAT) and distributed (TNT2) models

Nitrogen exports in catchments are known to be greatly variable because nitrogen cycle in watershed is controlled by different factors such as landuse, farm management practices, climate, soil type and hydrological setting. Our aim is to study the relative importance of the processes controlling nitrogen losses at catchment scale in the long term using a modelling approach constrained by a long term record of observations. The study area is a catchment of 330 ha with 95 % of intensive agriculture in a hilly shallow soil context, in the south west of France. Historical field rotation and nitrogen river load data have been collected for a 20 year period. Two process-based and spatially distributed models have been chosen to simulate nitrogen transfer and transformation in the whole catchment. The first one is the fully distributed TNT2 model, developed and validated in a different context (farming systems in north-western France). The second one is the widely used, semi-distributed SWAT model, used and recognizedto be realistic in many studies on nitrogen transfer in river. This comparative modelling approach was used to evaluate the effect of different modelling approaches on the identification of controlling factors, and the ability of both models to simulate alternative scenarios. The discharge, especially during storm flow, is well simulated by the curve number approach and the semi-distributed hydrological parameter description used SWAT, while the Topmodel-derived approach used in TNT2 tends to underestimate some peak discharges. Nitrogen dynamic simulations are considered to be acceptable for both models for a long time period but the use of both models allows to exhibit their respective capacity and limits. TNT2 has higher potentiality to test the impact of complex agricultural scenarios because the description of management practices and the simulation of crops to management options is more detailed. It permits the assessment of spatial interactions and focussed spatial management, like the set up of grass or tree strips. SWAT can then be used to scale up change scenarios from TNT2 small catchment results to large catchments

On the spatial modelling of mixed and constrained geospatial data

Spatial uncertainty modelling and prediction of a set of regionalized dependent variables from various sample spaces (e.g. continuous and categorical) is a common challenge for geoscience modellers and many geoscience applications such as evaluation of mineral resources, characterization of oil reservoirs or hydrology of groundwater. To consider the complex statistical and spatial relationships, categorical data such as rock types, soil types, alteration units, and continental crustal blocks should be modelled jointly with other continuous attributes (e.g. porosity, permeability, seismic velocity, mineral and geochemical compositions or pollutant concentration). These multivariate geospatial data normally have complex statistical and spatial relationships which should be honoured in the predicted models. Continuous variables in the form of percentages, proportions, frequencies, and concentrations are compositional which means they are non-negative values representing some parts of a whole. Such data carry just relative information and the constant sum constraint forces at least one covariance to be negative and induces spurious statistical and spatial correlations. As a result, classical (geo)statistical techniques should not be implemented on the original compositional data. Several geostatistical techniques have been developed recently for the spatial modelling of compositional data. However, few of these consider the joint statistical and/or spatial relationships of regionalized compositional data with the other dependent categorical information. This PhD thesis explores and introduces approaches to spatial modelling of regionalized compositional and categorical data. The first proposed approach is in the multiple-point geostatistics framework, where the direct sampling algorithm is developed for joint simulation of compositional and categorical data. The second proposed method is based on two-point geostatistics and is useful for the situation where a large and representative training image is not available or difficult to build. Approaches to geostatistical simulation of regionalized compositions consisting of several populations are explored and investigated. The multi-population characteristic is usually related to a dependent categorical variable (e.g. rock type, soil type, and land use). Finally, a hybrid predictive model based on the advanced geostatistical simulation techniques for compositional data and machine learning is introduced. Such a hybrid model has the ability to rank and select features internally, which is useful for geoscience process discovery analysis. The proposed techniques were evaluated via several case studies and results supported their usefulness and applicability