Is spread of COVID-19 a chaotic epidemic?

The COVID-19 epidemic challenges humanity in 2020. It has already taken an enormous number of human lives and had a substantial negative economic impact. Traditional compartmental epidemiological models demonstrated limited ability to predict the scale and dynamics of COVID-19 epidemic in different countries. In order to gain a deeper understanding of its behavior, we turn to chaotic dynamics, which proved fruitful in analyzing previous diseases such as measles. We hypothesize that the unpredictability of the pandemic could be a fundamental property if the disease spread is a chaotic dynamical system. Our mathematical examination of COVID-19 epidemic data in different countries reveals similarity of this dynamic to the chaotic behavior of many dynamics systems, such as logistic maps. We conclude that the data does suggest that the COVID-19 epidemic demonstrates chaotic behavior, which should be taken into account by public policy makers. Furthermore, the scale and behavior of the epidemic may be essentially unpredictable due to the properties of chaotic systems, rather than due to the limited data available for model parameterization.

US forest response to projected climate-related stress: a tolerance perspective.

Although it is widely recognized that climate change will require a major spatial reorganization of forests, our ability to predict exactly how and where forest characteristics and distributions will change has been rather limited. Current efforts to predict future distribution of forested ecosystems as a function of climate include species distribution models (for fine-scale predictions) and potential vegetation climate envelope models (for coarse-grained, large-scale predictions). Here, we develop and apply an intermediate approach wherein we use stand-level tolerances of environmental stressors to understand forest distributions and vulnerabilities to anticipated climate change. In contrast to other existing models, this approach can be applied at a continental scale while maintaining a direct link to ecologically relevant, climate-related stressors. We first demonstrate that shade, drought, and waterlogging tolerances of forest stands are strongly correlated with climate and edaphic conditions in the conterminous United States. This discovery allows the development of a tolerance distribution model (TDM), a novel quantitative tool to assess landscape level impacts of climate change. We then focus on evaluating the implications of the drought TDM. Using an ensemble of 17 climate change models to drive this TDM, we estimate that 18% of US ecosystems are vulnerable to drought-related stress over the coming century. Vulnerable areas include mostly the Midwest United States and Northeast United States, as well as high-elevation areas of the Rocky Mountains. We also infer stress incurred by shifting climate should create an opening for the establishment of forest types not currently seen in the conterminous United States.

Cross-scale integration of knowledge for predicting species ranges: a metamodeling framework.

AIM: Current interest in forecasting changes to species ranges have resulted in a multitude of approaches to species distribution models (SDMs). However, most approaches include only a small subset of the available information, and many ignore smaller-scale processes such as growth, fecundity, and dispersal. Furthermore, different approaches often produce divergent predictions with no simple method to reconcile them. Here, we present a flexible framework for integrating models at multiple scales using hierarchical Bayesian methods. LOCATION: Eastern North America (as an example). METHODS: Our framework builds a metamodel that is constrained by the results of multiple sub-models and provides probabilistic estimates of species presence. We applied our approach to a simulated dataset to demonstrate the integration of a correlative SDM with a theoretical model. In a second example, we built an integrated model combining the results of a physiological model with presence-absence data for sugar maple (Acer saccharum), an abundant tree native to eastern North America. RESULTS: For both examples, the integrated models successfully included information from all data sources and substantially improved the characterization of uncertainty. For the second example, the integrated model outperformed the source models with respect to uncertainty when modelling the present range of the species. When projecting into the future, the model provided a consensus view of two models that differed substantially in their predictions. Uncertainty was reduced where the models agreed and was greater where they diverged, providing a more realistic view of the state of knowledge than either source model. MAIN CONCLUSIONS: We conclude by discussing the potential applications of our method and its accessibility to applied ecologists. In ideal cases, our framework can be easily implemented using off-the-shelf software. The framework has wide potential for use in species distribution modelling and can drive better integration of multi-source and multi-scale data into ecological decision-making.

Predicting and understanding forest dynamics using a simple tractable model.

The perfect-plasticity approximation (PPA) is an analytically tractable model of forest dynamics, defined in terms of parameters for individual trees, including allometry, growth, and mortality. We estimated these parameters for the eight most common species on each of four soil types in the US Lake states (Michigan, Wisconsin, and Minnesota) by using short-term (

Does speciation matter for tungsten ecotoxicology?

Tungsten is a widely used transition metal that has not been thoroughly investigated with regards to its ecotoxicological effects. Tungsten anions polymerize in environmental systems as well as under physiological conditions in living organisms. These polymerization/condensation reactions result in the development of several types of stable polyoxoanions. Certain chemical properties (in particular redox and acidic properties) differentiate these polyanions from monotungstates. However, our current state of knowledge on tungsten toxicology, biological and environmental effects is based entirely on experiments where monotungstates were used and assumed by the authors to be the form of tungsten that was present and that produced the observed effect. Recent discoveries indicate that tungsten speciation may be important to ecotoxicology. New results obtained by different research groups demonstrate that polytungstates develop and persist in environmental systems, and that polyoxotungstates are much more toxic than monotungstates. This paper reviews the available toxicological information from the standpoint of tungsten speciation and identifies knowledge gaps and pertinent future research directions.

Does speciation matter for tungsten ecotoxicology?

Tungsten is a widely used transition metal that has not been thoroughly investigated with regards to its ecotoxicological effects. Tungsten anions polymerize in environmental systems as well as under physiological conditions in living organisms. These polymerization/condensation reactions result in the development of several types of stable polyoxoanions. Certain chemical properties (in particular redox and acidic properties) differentiate these polyanions from monotungstates. However, our current state of knowledge on tungsten toxicology, biological and environmental effects is based entirely on experiments where monotungstates were used and assumed by the authors to be the form of tungsten that was present and that produced the observed effect. Recent discoveries indicate that tungsten speciation may be important to ecotoxicology. New results obtained by different research groups demonstrate that polytungstates develop and persist in environmental systems, and that polyoxotungstates are much more toxic than monotungstates. This paper reviews the available toxicological information from the standpoint of tungsten speciation and identifies knowledge gaps and pertinent future research directions.

Tungsten speciation and toxicity: acute toxicity of mono- and poly-tungstates to fish.

Tungsten is a widely used transition metal for which very limited information on environmental and toxicological effects is available. Of particular interest is the lack of information linking tungsten speciation and environmental effects. Tungsten anions may polymerize (depending upon concentration, pH, and aquatic geochemistry) in aquatic and soil systems. However, to this date, of all soluble tungstate species only monotungstates have been scrutinized to a fair extent in toxicological studies. The objective of this work is a comparative assessment of the acute toxicity of monotungstates (sodium tungstate, Na(2)WO(4)) and polytungstates (sodium metatungstate, 3Na(2)WO(4).9WO(3)) to Poecilia reticulate. The experiments have been performed according to the OEDC protocols 203 and 204. LD50 values for 1-14 days show that sodium metatungstate is significantly more toxic to fish than sodium tungstate. Based on LD50 (0.86-3.88gL(-1) or 4.67-21.1x10(-3)molNa(2)WO(4)L(-1)), sodium tungstate may be classified as a chemical of low toxicity to fish. Sodium metatungstate caused similar fish mortality to sodium tungstate when it was introduced in 55-80 times lower concentrations (in terms of molL(-1)) than sodium tungstate. LD50 values for sodium metatungstate range from 0.13 to 0.85gWL(-1) or 5.69 to 38.71x10(-5)mol 3Na(2)WO(4).9WO(3)L(-1). Based on these values sodium metatungstate can be classified as a moderate toxic agent to fish.

Tungsten in Washington State surface waters.

At high concentrations, tungsten can be toxic to humans, animals, and the environment, though little is known about natural, aqueous tungsten in surface waters. To improve understanding and develop a model predicting tungsten concentrations, we collected water and sediment from 77 water bodies in 20 watersheds in Washington State, USA. We found aqueous tungsten concentrations spanning two orders of magnitude (10.3 ng L-1 - 2.05 µg L-1) with average tungsten concentrations in both water and sediments more than two-fold higher in watersheds with tungsten-bearing underlying rock types (average: 0.217 µg L-1, 0.669 mg kg-1; range: 0.010-2.05 µg L-1, 0.0713-4.691 mg kg-1 for surface waters and sediments, respectively) than in watersheds without such underlying geology (average: 0.068 µg L-1, 0.352 mg kg-1; range: 0.010-0.211 µg L-1, 0.0349-2.399 mg kg-1 for surface waters and sediments, respectively). Aqueous concentrations of tungsten significantly correlated with beryllium (Be) and copper (Cu) (R2 = 0.31, 0.41, respectively) and a multiple linear regression model using Be and Cu explained 65% of the variance in measured aqueous tungsten concentrations. Applying this model to existing Be and Cu data from 19 sites across the Pacific Northwest resulted in predicted tungsten concentrations ranging from 0.116 to 0.458 µg L-1. These predicted concentrations along with our measured concentrations indicate none of these sites were close to the drinking water standard for tungsten set by the former Soviet Union-the only country so far to set limits for tungsten in drinking water (50 µg L-1).

Intercomparison of photogrammetry software for three-dimensional vegetation modelling.

Photogrammetry-based three-dimensional reconstruction of objects is becoming increasingly appealing in research areas unrelated to computer vision. It has the potential to facilitate the assessment of forest inventory-related parameters by enabling or expediting resource measurements in the field. We hereby compare several implementations of photogrammetric algorithms (CMVS/PMVS, CMPMVS, MVE, OpenMVS, SURE and Agisoft PhotoScan) with respect to their performance in vegetation assessment. The evaluation is based on (i) a virtual scene where the precise location and dimensionality of objects is known a priori and is thus conducive to a quantitative comparison and (ii) using series of in situ acquired photographs of vegetation with overlapping field of view where the photogrammetric outcomes are compared qualitatively. Performance is quantified by computing receiver operating characteristic curves that summarize the type-I and type-II errors between the reference and reconstructed tree models. Similar artefacts are observed in synthetic- and in situ-based reconstructions.

Correction to: 'Intercomparison of photogrammetry software for three-dimensional vegetation modelling'.

[This corrects the article DOI: 10.1098/rsos.172192.].

The assessment of the energetic compound 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-Hexaazaisowurtzitane (CL-20) degradability in soil.

CL-20 is a relatively new energetic compound with applications in explosive and propellant formulations. Currently, information about the fate of CL-20 in ecological systems is scarce. The aim of this study is to evaluate the biodegradability of CL-20 in soil environments. Four soils were used where initial CL-20 concentrations (above water solubility) ranged from 125 to 1500 mg of CL-20 per kg dry soil (corresponding to the concentrations derived from unexploded ordnance, low order detonation, or manufacturing spills). CL-20 appears to be biodegradable in soil under anaerobic conditions, and additions of organic substrates can substantially accelerate this process. However, CL-20 is not degraded in soil under aerobic conditions kept in the dark at temperatures up to 30 degrees C without organic amendments. Additions of starch or cellulose promote the biodegradation of CL-20 under aerobic conditions. Soil microbial community mediated biodegradation and plant uptake appears to enhance CL-20 biodegradation, the latter suggesting a possible route for CL-20 to entry in the food chain.

An individual-based forest model links canopy dynamics and shade tolerances along a soil moisture gradient.

Understanding how forested ecosystems respond to climatic changes is a challenging problem as forest self-organization occurs simultaneously across multiple scales. Here, we explore the hypothesis that soil water availability shapes above-ground competition and gap dynamics, and ultimately alters the dominance of shade tolerant and intolerant species along the moisture gradient. We adapt a spatially explicit individual-based model with simultaneous crown and root competitions. Simulations show that the transition from xeric to mesic soils is accompanied by an increase in shade-tolerant species similar to the patterns documented in the North American forests. This transition is accompanied by a change from water to sunlight competitions, and happens at three successive stages: (i) mostly water-limited parkland, (ii) simultaneously water- and sunlight-limited closed canopy forests featuring a very sparse understory, and (iii) mostly sunlight-limited forests with a populated understory. This pattern is caused by contrasting successional dynamics that favour either shade-tolerant or shade-intolerant species, depending on soil moisture and understory density. This work demonstrates that forest patterns along environmental gradients can emerge from spatial competition without physiological trade-offs between shade and growth tolerance. Mechanistic understanding of population processes involved in the forest-parkland-desert transition will improve our ability to explain species distributions and predict forest responses to climatic changes.

Effects of tungsten on environmental systems.

Tungsten is a metal with many industrial and military applications, including manufacturing of commercial and military ammunition. Despite its widespread use, the potential environmental effects of tungsten are essentially unknown. This study addresses environmental effects of particulate and soluble forms of tungsten, and to a minor extent certain tungsten alloy components, present in some munitions formulations. Dissolution of tungsten powder significantly acidifies soils. Tungsten powder mixed with soils at rates higher than 1% on a mass basis, trigger changes in soil microbial communities resulting in the death of a substantial portion of the bacterial component and an increase of the fungal biomass. It also induces the death of red worms and plants. These effects appear to be related with the soil acidification occurring during tungsten dissolution. Dissolved tungsten species significantly decrease microbial yields by as much as 38% for a tungsten media concentration of 89 mg l(-1). Soluble tungsten concentrations as low as 10(-5) mg l(-1), cause a decrease in biomass production by 8% which is possibly related to production of stress proteins. Plants and worms take up tungsten ions from soil in significant amounts while an enrichment of tungsten in the plant rhizosphere is observed. These results provide an indication that tungsten compounds may be introduced into the food chain and suggest the possibility of development of phytoremediation-based technologies for the cleanup of tungsten contaminated sites.

An appraisal of the classic forest succession paradigm with the shade tolerance index.

In this paper we revisit the classic theory of forest succession that relates shade tolerance and species replacement and assess its validity to understand patch-mosaic patterns of forested ecosystems of the USA. We introduce a macroscopic parameter called the "shade tolerance index" and compare it to the classic continuum index in southern Wisconsin forests. We exemplify shade tolerance driven succession in White Pine-Eastern Hemlock forests using computer simulations and analyzing approximated chronosequence data from the USDA FIA forest inventory. We describe this parameter across the last 50 years in the ecoregions of mainland USA, and demonstrate that it does not correlate with the usual macroscopic characteristics of stand age, biomass, basal area, and biodiversity measures. We characterize the dynamics of shade tolerance index using transition matrices and delimit geographical areas based on the relevance of shade tolerance to explain forest succession. We conclude that shade tolerance driven succession is linked to climatic variables and can be considered as a primary driving factor of forest dynamics mostly in central-north and northeastern areas in the USA. Overall, the shade tolerance index constitutes a new quantitative approach that can be used to understand and predict succession of forested ecosystems and biogeographic patterns.

3D Tree Dimensionality Assessment Using Photogrammetry and Small Unmanned Aerial Vehicles.

Detailed, precise, three-dimensional (3D) representations of individual trees are a prerequisite for an accurate assessment of tree competition, growth, and morphological plasticity. Until recently, our ability to measure the dimensionality, spatial arrangement, shape of trees, and shape of tree components with precision has been constrained by technological and logistical limitations and cost. Traditional methods of forest biometrics provide only partial measurements and are labor intensive. Active remote technologies such as LiDAR operated from airborne platforms provide only partial crown reconstructions. The use of terrestrial LiDAR is laborious, has portability limitations and high cost. In this work we capitalized on recent improvements in the capabilities and availability of small unmanned aerial vehicles (UAVs), light and inexpensive cameras, and developed an affordable method for obtaining precise and comprehensive 3D models of trees and small groups of trees. The method employs slow-moving UAVs that acquire images along predefined trajectories near and around targeted trees, and computer vision-based approaches that process the images to obtain detailed tree reconstructions. After we confirmed the potential of the methodology via simulation we evaluated several UAV platforms, strategies for image acquisition, and image processing algorithms. We present an original, step-by-step workflow which utilizes open source programs and original software. We anticipate that future development and applications of our method will improve our understanding of forest self-organization emerging from the competition among trees, and will lead to a refined generation of individual-tree-based forest models.

Extrapolating phosphorus production to estimate resource reserves.

Various indicators of resource scarcity and methods for extrapolating resource availability are examined for phosphorus. These include resource lifetime, and trends in resource price, ore grade and discovery rates, and Hubbert curve extrapolation. Several of these indicate increasing scarcity of phosphate resources. Calculated resource lifetime is subject to a number of caveats such as unanticipated future changes in resource discovery, mining and beneficiation technology, population growth or per-capita demand. Thus it should be used only as a rough planning index or as a relative indicator of potential scarcity. This paper examines the uncertainty in one method for estimating available resources from historical production data. The confidence intervals for the parameters and predictions of the Hubbert curves are computed as they relate to the amount of information available. These show that Hubbert-type extrapolations are not robust for predicting the ultimately recoverable reserves or year of peak production of phosphate rock. Previous successes of the Hubbert curve are for cases in which there exist alternative resources, which is not the situation for phosphate. It is suggested that data other than historical production, such as population growth, identified resources and economic factors, should be included in making such forecasts.

Robust and efficient design of experiments for the Monod model.

In this paper the problem of designing experiments for the Monod model, which is frequently used in microbiology, is studied. The model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, environmental research, pharmacokinetics, and plant physiology. The designs presented so far in the literature are local optimal designs, which depend sensitively on a preliminary guess of the unknown parameters, and are for this reason in many cases not robust with respect to their misspecification. Uniform designs and maximin optimal designs are considered as a strategy to obtain robust and efficient designs for parameter estimation. In particular, standardized maximin D- and E-optimal designs are determined and compared with uniform designs, which are usually applied in these microbiological models. It is demonstrated that maximin optimal designs are substantially more efficient than uniform designs. Parameter variances can be decreased by a factor of two by simply sampling at optimal times during the experiment. Moreover, the maximin optimal designs usually provide the possibility for the experimenter to check the model assumptions, because they have more support points than parameters in the Monod model.