Advanced geostatistical and machine-learning models for spatial data analysis of radioactively contaminated regions

Radioactive soil-contamination mapping and risk assessment is a vital issue for decision makers. Traditional approaches for mapping the spatial concentration of radionuclides employ various regression-based models, which usually provide a single-value prediction realization accompanied (in some cases) by estimation error. Such approaches do not provide the capability for rigorous uncertainty quantification or probabilistic mapping. Machine learning is a recent and fast-developing approach based on learning patterns and information from data. Artificial neural networks for prediction mapping have been especially powerful in combination with spatial statistics. A data-driven approach provides the opportunity to integrate additional relevant information about spatial phenomena into a prediction model for more accurate spatial estimates and associated uncertainty. Machine-learning algorithms can also be used for a wider spectrum of problems than before: classification, probability density estimation, and so forth. Stochastic simulations are used to model spatial variability and uncertainty. Unlike regression models, they provide multiple realizations of a particular spatial pattern that allow uncertainty and risk quantification. This paper reviews the most recent methods of spatial data analysis, prediction, and risk mapping, based on machine learning and stochastic simulations in comparison with more traditional regression models. The radioactive fallout from the Chernobyl Nuclear Power Plant accident is used to illustrate the application of the models for prediction and classification problems. This fallout is a unique case study that provides the challenging task of analyzing huge amounts of data ('hard' direct measurements, as well as supplementary information and expert estimates) and solving particular decision-oriented problems.

Very high-resolution environmental predictors in species distribution models: moving beyond topography?

Recent advances in remote sensing technologies have facilitated the generation of very high resolution (VHR) environmental data. Exploratory studies suggested that, if used in species distribution models (SDMs), these data should enable modelling species' micro-habitats and allow improving predictions for fine-scale biodiversity management. In the present study, we tested the influence, in SDMs, of predictors derived from a VHR digital elevation model (DEM) by comparing the predictive power of models for 239 plant species and their assemblages fitted at six different resolutions in the Swiss Alps. We also tested whether changes of the model quality for a species is related to its functional and ecological characteristics. Refining the resolution only contributed to slight improvement of the models for more than half of the examined species, with the best results obtained at 5 m, but no significant improvement was observed, on average, across all species. Contrary to our expectations, we could not consistently correlate the changes in model performance with species characteristics such as vegetation height. Temperature, the most important variable in the SDMs across the different resolutions, did not contribute any substantial improvement. Our results suggest that improving resolution of topographic data only is not sufficient to improve SDM predictions - and therefore local management - compared to previously used resolutions (here 25 and 100 m). More effort should be dedicated now to conduct finer-scale in-situ environmental measurements (e.g. for temperature, moisture, snow) to obtain improved environmental measurements for fine-scale species mapping and management.

Response to comment on "Climatic niche shifts are rare among terrestrial plant invaders"

Webber et al. take a critical view of our findings that niche expansions are rare in plant invaders, arguing mainly that we did not include nonanalog climates in our analyses. Yet, their concerns include misunderstandings and go beyond the scope of our study, which was purposely restricted to analog climates. We further explain why our results remain robust to other factors of niche dynamics in the native range. We conclude that the implications of our findings remain valid for projections of niche models in analog climates and that projections in nonanalog climates should be undertaken with care.

Characterizing variation in mycorrhiza effect among diverse plant varieties.

Exploitation of arbuscular mycorrhizal fungi may be an important approach for development of reduced-input agriculture. We discuss the use of linear models to analyze variation in mycorrhiza response among diverse plant varieties in order to assess the value of mycorrhizas. Our approach allows elimination of variation linked to differences in plant performance in the absence of mycorrhizas and the selection of plant lines that might harbor genetic variation of use to improve the mycorrhizal symbiosis in agriculture. We illustrate our approach by applying it to previously published and to novel data. We suggest that in dealing with a relative trait such as mycorrhiza effect, the choice of measure used to quantify the trait greatly affects interpretation. In the plant populations under consideration, we find evidence for a greater potential to increase mycorrhiza benefit than previously suggested.

Predicting current and future spatial community patterns of plant functional traits

Community-level patterns of functional traits relate to community assembly and ecosystem functioning. By modelling the changes of different indices describing such patterns - trait means, extremes and diversity in communities - as a function of abiotic gradients, we could understand their drivers and build projections of the impact of global change on the functional components of biodiversity. We used five plant functional traits (vegetative height, specific leaf area, leaf dry matter content, leaf nitrogen content and seed mass) and non-woody vegetation plots to model several indices depicting community-level patterns of functional traits from a set of abiotic environmental variables (topographic, climatic and edaphic) over contrasting environmental conditions in a mountainous landscape. We performed a variation partitioning analysis to assess the relative importance of these variables for predicting patterns of functional traits in communities, and projected the best models under several climate change scenarios to examine future potential changes in vegetation functional properties. Not all indices of trait patterns within communities could be modelled with the same level of accuracy: the models for mean and extreme values of functional traits provided substantially better predictive accuracy than the models calibrated for diversity indices. Topographic and climatic factors were more important predictors of functional trait patterns within communities than edaphic predictors. Overall, model projections forecast an increase in mean vegetation height and in mean specific leaf area following climate warming. This trend was important at mid elevation particularly between 1000 and 2000 m asl. With this study we showed that topographic, climatic and edaphic variables can successfully model descriptors of community-level patterns of plant functional traits such as mean and extreme trait values. However, which factors determine the diversity of functional traits in plant communities remains unclear and requires more investigations.

Effects of alternative sets of climatic predictors on species distribution models and associated estimates of extinction risk: a test with plants in an arid environment

Aim To evaluate the effects of using distinct alternative sets of climatic predictor variables on the performance, spatial predictions and future projections of species distribution models (SDMs) for rare plants in an arid environment. . Location Atacama and Peruvian Deserts, South America (18º30'S - 31º30'S, 0 - 3 000 m) Methods We modelled the present and future potential distributions of 13 species of Heliotropium sect. Cochranea, a plant group with a centre of diversity in the Atacama Desert. We developed and applied a sequential procedure, starting from climate monthly variables, to derive six alternative sets of climatic predictor variables. We used them to fit models with eight modelling techniques within an ensemble forecasting framework, and derived climate change projections for each of them. We evaluated the effects of using these alternative sets of predictor variables on performance, spatial predictions and projections of SDMs using Generalised Linear Mixed Models (GLMM). Results The use of distinct sets of climatic predictor variables did not have a significant effect on overall metrics of model performance, but had significant effects on present and future spatial predictions. Main conclusion Using different sets of climatic predictors can yield the same model fits but different spatial predictions of current and future species distributions. This represents a new form of uncertainty in model-based estimates of extinction risk that may need to be better acknowledged and quantified in future SDM studies.

Using niche-based models to improve the sampling of rare species

Because data on rare species usually are sparse, it is important to have efficient ways to sample additional data. Traditional sampling approaches are of limited value for rare species because a very large proportion of randomly chosen sampling sites are unlikely to shelter the species. For these species, spatial predictions from niche-based distribution models can be used to stratify the sampling and increase sampling efficiency. New data sampled are then used to improve the initial model. Applying this approach repeatedly is an adaptive process that may allow increasing the number of new occurrences found. We illustrate the approach with a case study of a rare and endangered plant species in Switzerland and a simulation experiment. Our field survey confirmed that the method helps in the discovery of new populations of the target species in remote areas where the predicted habitat suitability is high. In our simulations the model-based approach provided a significant improvement (by a factor of 1.8 to 4 times, depending on the measure) over simple random sampling. In terms of cost this approach may save up to 70% of the time spent in the field.

Are niche-based species distribution models transferable in space?

Aim To assess the geographical transferability of niche-based species distribution models fitted with two modelling techniques. Location Two distinct geographical study areas in Switzerland and Austria, in the subalpine and alpine belts. Methods Generalized linear and generalized additive models (GLM and GAM) with a binomial probability distribution and a logit link were fitted for 54 plant species, based on topoclimatic predictor variables. These models were then evaluated quantitatively and used for spatially explicit predictions within (internal evaluation and prediction) and between (external evaluation and prediction) the two regions. Comparisons of evaluations and spatial predictions between regions and models were conducted in order to test if species and methods meet the criteria of full transferability. By full transferability, we mean that: (1) the internal evaluation of models fitted in region A and B must be similar; (2) a model fitted in region A must at least retain a comparable external evaluation when projected into region B, and vice-versa; and (3) internal and external spatial predictions have to match within both regions. Results The measures of model fit are, on average, 24% higher for GAMs than for GLMs in both regions. However, the differences between internal and external evaluations (AUC coefficient) are also higher for GAMs than for GLMs (a difference of 30% for models fitted in Switzerland and 54% for models fitted in Austria). Transferability, as measured with the AUC evaluation, fails for 68% of the species in Switzerland and 55% in Austria for GLMs (respectively for 67% and 53% of the species for GAMs). For both GAMs and GLMs, the agreement between internal and external predictions is rather weak on average (Kulczynski's coefficient in the range 0.3-0.4), but varies widely among individual species. The dominant pattern is an asymmetrical transferability between the two study regions (a mean decrease of 20% for the AUC coefficient when the models are transferred from Switzerland and 13% when they are transferred from Austria). Main conclusions The large inter-specific variability observed among the 54 study species underlines the need to consider more than a few species to test properly the transferability of species distribution models. The pronounced asymmetry in transferability between the two study regions may be due to peculiarities of these regions, such as differences in the ranges of environmental predictors or the varied impact of land-use history, or to species-specific reasons like differential phenotypic plasticity, existence of ecotypes or varied dependence on biotic interactions that are not properly incorporated into niche-based models. The lower variation between internal and external evaluation of GLMs compared to GAMs further suggests that overfitting may reduce transferability. Overall, a limited geographical transferability calls for caution when projecting niche-based models for assessing the fate of species in future environments.

Hormone signalling crosstalk in plant growth regulation.

The remarkable plasticity of plant ontogeny is shaped by hormone pathways, which not only orchestrate intrinsic developmental programs, but also convey environmental inputs. Several classes of plant hormones exist, and among them auxin, brassinosteroid and gibberellin are central for the regulation of growth in general and of cell elongation in particular. Various growth phenomena can be modulated by each of the three hormones, in a sometimes synergistic fashion, suggesting physiological redundancy and/or crosstalk between the different pathways. Whether this means that they target a common and unique transcriptome module, or rather separate growth-promoting transcriptome modules, remains unclear, however. Nevertheless, while surprisingly few molecular mediators of direct crosstalk in the proper sense have been isolated, evidence is accumulating for complex cross-regulatory relations between hormone pathways at the level of transcription, as exemplified in root meristem growth. The growing number of available genome sequences from the green lineage offers first glimpses at the evolution of hormone pathways, which can aid in understanding the multiple relationships observed between these pathways in angiosperms. The available analyses suggest that auxin, gibberellin and brassinosteroid signalling arose during land plant evolution in this order, correlating with increased morphological complexity and possibly conferring increased developmental flexibility.

Providing more informative projections of climate change impact on plant distribution in a mountain environment

Summary Due to their conic shape and the reduction of area with increasing elevation, mountain ecosystems were early identified as potentially very sensitive to global warming. Moreover, mountain systems may experience unprecedented rates of warming during the next century, two or three times higher than that records of the 20th century. In this context, species distribution models (SDM) have become important tools for rapid assessment of the impact of accelerated land use and climate change on the distribution plant species. In my study, I developed and tested new predictor variables for species distribution models (SDM), specific to current and future geographic projections of plant species in a mountain system, using the Western Swiss Alps as model region. Since meso- and micro-topography are relevant to explain geographic patterns of plant species in mountain environments, I assessed the effect of scale on predictor variables and geographic projections of SDM. I also developed a methodological framework of space-for-time evaluation to test the robustness of SDM when projected in a future changing climate. Finally, I used a cellular automaton to run dynamic simulations of plant migration under climate change in a mountain landscape, including realistic distance of seed dispersal. Results of future projections for the 21st century were also discussed in perspective of vegetation changes monitored during the 20th century. Overall, I showed in this study that, based on the most severe A1 climate change scenario and realistic dispersal simulations of plant dispersal, species extinctions in the Western Swiss Alps could affect nearly one third (28.5%) of the 284 species modeled by 2100. With the less severe 61 scenario, only 4.6% of species are predicted to become extinct. However, even with B1, 54% (153 species) may still loose more than 80% of their initial surface. Results of monitoring of past vegetation changes suggested that plant species can react quickly to the warmer conditions as far as competition is low However, in subalpine grasslands, competition of already present species is probably important and limit establishment of newly arrived species. Results from future simulations also showed that heavy extinctions of alpine plants may start already in 2040, but the latest in 2080. My study also highlighted the importance of fine scale and regional. assessments of climate change impact on mountain vegetation, using more direct predictor variables. Indeed, predictions at the continental scale may fail to predict local refugees or local extinctions, as well as loss of connectivity between local populations. On the other hand, migrations of low-elevation species to higher altitude may be difficult to predict at the local scale. Résumé La forme conique des montagnes ainsi que la diminution de surface dans les hautes altitudes sont reconnues pour exposer plus sensiblement les écosystèmes de montagne au réchauffement global. En outre, les systèmes de montagne seront sans doute soumis durant le 21ème siècle à un réchauffement deux à trois fois plus rapide que celui mesuré durant le 20ème siècle. Dans ce contexte, les modèles prédictifs de distribution géographique de la végétation se sont imposés comme des outils puissants pour de rapides évaluations de l'impact des changements climatiques et de la transformation du paysage par l'homme sur la végétation. Dans mon étude, j'ai développé de nouvelles variables prédictives pour les modèles de distribution, spécifiques à la projection géographique présente et future des plantes dans un système de montagne, en utilisant les Préalpes vaudoises comme zone d'échantillonnage. La méso- et la microtopographie étant particulièrement adaptées pour expliquer les patrons de distribution géographique des plantes dans un environnement montagneux, j'ai testé les effets d'échelle sur les variables prédictives et sur les projections des modèles de distribution. J'ai aussi développé un cadre méthodologique pour tester la robustesse potentielle des modèles lors de projections pour le futur. Finalement, j'ai utilisé un automate cellulaire pour simuler de manière dynamique la migration future des plantes dans le paysage et dans quatre scénarios de changement climatique pour le 21ème siècle. J'ai intégré dans ces simulations des mécanismes et des distances plus réalistes de dispersion de graines. J'ai pu montrer, avec les simulations les plus réalistes, que près du tiers des 284 espèces considérées (28.5%) pourraient être menacées d'extinction en 2100 dans le cas du plus sévère scénario de changement climatique A1. Pour le moins sévère des scénarios B1, seulement 4.6% des espèces sont menacées d'extinctions, mais 54% (153 espèces) risquent de perdre plus 80% de leur habitat initial. Les résultats de monitoring des changements de végétation dans le passé montrent que les plantes peuvent réagir rapidement au réchauffement climatique si la compétition est faible. Dans les prairies subalpines, les espèces déjà présentes limitent certainement l'arrivée de nouvelles espèces par effet de compétition. Les résultats de simulation pour le futur prédisent le début d'extinctions massives dans les Préalpes à partir de 2040, au plus tard en 2080. Mon travail démontre aussi l'importance d'études régionales à échelle fine pour évaluer l'impact des changements climatiques sur la végétation, en intégrant des variables plus directes. En effet, les études à échelle continentale ne tiennent pas compte des micro-refuges, des extinctions locales ni des pertes de connectivité entre populations locales. Malgré cela, la migration des plantes de basses altitudes reste difficile à prédire à l'échelle locale sans modélisation plus globale.

Do stacked species distribution models reflect altitudinal diversity patterns?

The objective of this study was to evaluate the performance of stacked species distribution models in predicting the alpha and gamma species diversity patterns of two important plant clades along elevation in the Andes. We modelled the distribution of the species in the Anthurium genus (53 species) and the Bromeliaceae family (89 species) using six modelling techniques. We combined all of the predictions for the same species in ensemble models based on two different criteria: the average of the rescaled predictions by all techniques and the average of the best techniques. The rescaled predictions were then reclassified into binary predictions (presence/absence). By stacking either the original predictions or binary predictions for both ensemble procedures, we obtained four different species richness models per taxa. The gamma and alpha diversity per elevation band (500 m) was also computed. To evaluate the prediction abilities for the four predictions of species richness and gamma diversity, the models were compared with the real data along an elevation gradient that was independently compiled by specialists. Finally, we also tested whether our richness models performed better than a null model of altitudinal changes of diversity based on the literature. Stacking of the ensemble prediction of the individual species models generated richness models that proved to be well correlated with the observed alpha diversity richness patterns along elevation and with the gamma diversity derived from the literature. Overall, these models tend to overpredict species richness. The use of the ensemble predictions from the species models built with different techniques seems very promising for modelling of species assemblages. Stacking of the binary models reduced the over-prediction, although more research is needed. The randomisation test proved to be a promising method for testing the performance of the stacked models, but other implementations may still be developed.

Evidence for adaptive radiation from a phylogenetic study of plant defenses.

One signature of adaptive radiation is a high level of trait change early during the diversification process and a plateau toward the end of the radiation. Although the study of the tempo of evolution has historically been the domain of paleontologists, recently developed phylogenetic tools allow for the rigorous examination of trait evolution in a tremendous diversity of organisms. Enemy-driven adaptive radiation was a key prediction of Ehrlich and Raven's coevolutionary hypothesis [Ehrlich PR, Raven PH (1964) Evolution 18:586-608], yet has remained largely untested. Here we examine patterns of trait evolution in 51 North American milkweed species (Asclepias), using maximum likelihood methods. We study 7 traits of the milkweeds, ranging from seed size and foliar physiological traits to defense traits (cardenolides, latex, and trichomes) previously shown to impact herbivores, including the monarch butterfly. We compare the fit of simple random-walk models of trait evolution to models that incorporate stabilizing selection (Ornstein-Ulenbeck process), as well as time-varying rates of trait evolution. Early bursts of trait evolution were implicated for 2 traits, while stabilizing selection was implicated for several others. We further modeled the relationship between trait change and species diversification while allowing rates of trait evolution to vary during the radiation. Species-rich lineages underwent a proportionately greater decline in latex and cardenolides relative to species-poor lineages, and the rate of trait change was most rapid early in the radiation. An interpretation of this result is that reduced investment in defensive traits accelerated diversification, and disproportionately so, early in the adaptive radiation of milkweeds.

Prediction of plant species distributions across six millennia.

The usefulness of species distribution models (SDMs) in predicting impacts of climate change on biodiversity is difficult to assess because changes in species ranges may take decades or centuries to occur. One alternative way to evaluate the predictive ability of SDMs across time is to compare their predictions with data on past species distributions. We use data on plant distributions, fossil pollen and current and mid-Holocene climate to test the ability of SDMs to predict past climate-change impacts. We find that species showing little change in the estimated position of their realized niche, with resulting good model performance, tend to be dominant competitors for light. Different mechanisms appear to be responsible for among-species differences in model performance. Confidence in predictions of the impacts of climate change could be improved by selecting species with characteristics that suggest little change is expected in the relationships between species occurrence and climate patterns.

Prediction of crude protein and classification of the growth stage of wheat plant samples from NIR spectra

Near-infrared spectroscopy (NIRS) was used to analyse the crude protein content of dried and milled samples of wheat and to discriminate samples according to their stage of growth. A calibration set of 72 samples from three growth stages of wheat (tillering, heading and harvest) and a validation set of 28 samples was collected for this purpose. Principal components analysis (PCA) of the calibration set discriminated groups of samples according to the growth stage of the wheat. Based on these differences, a classification procedure (SIMCA) showed a very accurate classification of the validation set samples : all of them were successfully classified in each group using this procedure when both the residual and the leverage were used in the classification criteria. Looking only at the residuals all the samples were also correctly classified except one of tillering stage that was assigned to both tillering and heading stages. Finally, the determination of the crude protein content of these samples was considered in two ways: building up a global model for all the growth stages, and building up local models for each stage, separately. The best prediction results for crude protein were obtained using a global model for samples in the two first growth stages (tillering and heading), and using a local model for the harvest stage samples.

Tree cover at fine and coarse spatial grains interacts with shade tolerance to shape plant species distributions across the Alps

The role of competition for light among plants has long been recognized at local scales, but its potential importance for plant species' distribution at larger spatial scales has largely been ignored. Tree cover acts as a modulator of local abiotic conditions, notably by reducing light availability below the canopy and thus the performance of species that are not adapted to low-light conditions. However, this local effect may propagate to coarser spatial grains. Using 6,935 vegetation plots located across the European Alps, we fit Generalized Linear Models (GLM) for the distribution of 960 herbs and shrubs species to assess the effect of tree cover at both plot and landscape grain sizes (~ 10-m and 1-km, respectively). We ran four models with different combinations of variables (climate, soil and tree cover) for each species at both spatial grains. We used partial regressions to evaluate the independent effects of plot- and landscape-scale tree cover on plant communities. Finally, the effects on species' elevational range limits were assessed by simulating a removal experiment comparing the species' distribution under high and low tree cover. Accounting for tree cover improved model performance, with shade-tolerant species increasing their probability of presence at high tree cover whereas shade-intolerant species showed the opposite pattern. The tree cover effect occurred consistently at both plot and landscape spatial grains, albeit strongest at the former. Importantly, tree cover at the two grain sizes had partially independent effects on plot-scale plant communities, suggesting that the effects may be transmitted to coarser grains through meta-community dynamics. At high tree cover, shade-intolerant species exhibited elevational range contractions, especially at their upper limit, whereas shade-tolerant species showed elevational range expansions at both limits. Our findings suggest that the range shifts for herb and shrub species may be modulated by tree cover dynamics.