Nikolay Strigul

SCALING FROM TREES TO FORESTS: TRACTABLE MACROSCOPIC EQUATIONS FOR FOREST DYNAMICS

Individual-based forest simulators, such as TASS and SORTIE, are spatial stochastic processes that predict properties of populations and communities by simulating the fate of every plant throughout its life cycle. Although they are used for forest management and are able to predict dynamics of real forests, they are also analytically intractable, which limits their usefulness to basic scientists. We have developed a new spatial individual-based forest model that includes a perfect plasticity formulation for crown shape. Its structure allows us to derive an accurate approximation for the individual-based model that predicts mean densities and size structures using the same parameter values and functional forms, and also it is analytically tractable. The approximation is represented by a system of von Foerster partial differential equations coupled with an integral equation that we call the perfect plasticity approximation (PPA). We have derived a series of analytical results including equilibrium abundances for trees of different crown shapes, stability conditions, transient behaviors, such as the constant yield law and self-thinning exponents, and two species coexistence conditions.

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 (≤15-year) inventory data from individual trees. We implemented 100-year PPA simulations given these parameters and compared these predictions to chronosequences of stand development. Predictions for the timing and magnitude of basal area dynamics and ecological succession on each soil were accurate, and predictions for the diameter distribution of 100-year-old stands were correct in form and slope. For a given species, the PPA provides analytical metrics for early-successional performance (H20, height of a 20-year-old open-grown tree) and late-successional performance (Ẑ*, equilibrium canopy height in monoculture). These metrics predicted which species were early or late successional on each soil type. Decomposing Ẑ* showed that (i) succession is driven both by superior understory performance and superior canopy performance of late-successional species, and (ii) performance differences primarily reflect differences in mortality rather than growth. The predicted late-successional dominants matched chronosequences on xeromesic (Quercus rubra) and mesic (codominance by Acer rubrum and Acer saccharum) soil. On hydromesic and hydric soils, the literature reports that the current dominant species in old stands (Thuja occidentalis) is now failing to regenerate. Consistent with this, the PPA predicted that, on these soils, stands are now succeeding to dominance by other late-successional species (e.g., Fraxinus nigra, A. rubrum).

Solubility, Sorption, and Soil Respiration Effects of Tungsten and Tungsten Alloys

This laboratory study addresses issues related to the fate and transport of tungsten and tungsten oxides in the environment (soil-water). Tungsten dioxide and tungsten trioxide were dissolved in aqueous solutions whose pH had been adjusted from 4.0 to 11.0. For initial pH smaller than 10.0, dissolved tungsten concentration remained fairly constant at around 10.0 mg/L for WO2 and increased from 0.3 mg/L to 2.0 mg/L for WO3 with increasing values of initial pH. Large amounts of dissolved tungsten were found when tungsten powder or alloy pieces were exposed to aqueous solutions. The dissolution occurs along depletion in solution pH and dissolved oxygen concentration. Depending upon the alloying elements present, the final dissolved tungsten concentration varied from 70 to 475 mg/L. Reduction in pH, dissolved oxygen depletion, and high levels of dissolved tungsten may be of relevance to environmental forensics. In the presence of alloying elements such as iron, nickel, and cobalt, tungsten strongly sorbed to well-characterized model soils. Sorption of tungsten to illite and montmorillonite clays occurs with an increase in pH and appears to be nonreversible. This behavior may significantly retard tungsten mobility. The mixing of tungsten powder with soils at rates higher than 3% (w/w) resulted in acidification of the soil matrix and had a significant impact on soil microbial community as determined by soil respiration.

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.

Mathematical modeling of PGPR inoculation into the rhizosphere

Abstract One of the main problems when introducing beneficial microbes to the plant rhizosphere is that the plant growth promoting rhizobacteria (PGPR) do not survive or do not execute their specific function. The goal of our research was to evaluate microbial inoculant survival in rhizospheres, using mathematical modeling and computer-based simulations. We tested several abiotic factors effects on PGPR survival: the availability of soluble organic compounds and molecular oxygen, and the concentration of mineral nitrogen in soil. The principal biotic factors considered were the direct and indirect interactions between PGPR and resident microorganisms, protozoan predation, and bacterial parasitism. A model system of four non-linear ordinary differential equations was developed to simulate the growth of PGPR populations in the rhizosphere. Simulation results indicated that the competition for limiting resources between the introduced population and the resident microorganisms was the most important factor determining PGPR survival. The most effective PGPR inoculation was expected in organic and mineral poor soils or stressed soils, when development of the resident microflora was inhibited. Another important factor for PGPR survival was compatibility between the composition of the host plant root exudates, and ability of the PGPR to utilize those compounds.

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.

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.

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.

Individual-Based Models and Scaling Methods for Ecological Forestry: Implications of Tree Phenotypic Plasticity

The concept of sustainable forest management (SFM) has been developed across traditional disciplinary boundaries, including natural resource management, environmental, social, political, economical, climatic sciences and ecology. The Montreal process (www.mpci.org) has established multidisciplinary criteria for the SFM of temperate and boreal forests. In parallel with the Montreal process, the pan-European forest policy process (www.foresteurope.org, Forest Europe, The Ministerial Conference on the Protection of Forests in Europe, MCPFE) has developed criteria for SFM in Europe. Practical implementation of SFM criteria requires the development of scaling methods to link individual-level processes, pollution effects, climatic changes and silvicultural operations to large-scale ecosystem patterns and processes. A general problem is that data obtained in numerous experimental studies that address effects at the individual level cannot be translated to the ecosystem level without a large amount of uncertainty. Forested ecosystems have a complicated spatially heterogeneous hierarchical structure emerging from numerous interdependent individual processes. The fundamental ecological questions are how macroscopic patterns emerge as a result of self-organization of individuals and how ecosystems respond to different types of environmental disturbances occurring at different scales (Levin, 1999). The SFM employs the ecological forestry (EF) silvicultural approach, which is significantly distinct from the intensive (traditional) forestry and, therefore, requires different modeling tools than traditional forestry models. Traditional or intensive forestry is focused on wood production to maximize productivity of land use and usually involves tree plantations of commercially important trees (Nyland, 1996; Perry, 1998). Different silvicultural tools help increase wood fiber production. In particular, use is made of fast growing and disease resistant cultivars, vegetation control via thinning and regeneration harvesting techniques, soil management, and forest pests and noncrop vegetation control. Intermediate cutting operations include low, crown and mechanical thinning target future stand growth on higher valued trees to improve the stand yield at final harvest while providing some financial return on the shorter time scales. Traditional forestry also employs prescribed fire, cutting and application of herbicides for regulation of species composition and promoting growth of economically important tree species in the mixed stands. 20

Modelling of forest stand dynamics using Markov chains

Understanding forest complexity and self-organization across multiple scales is essential for both ecology and natural resource management. In this paper, we develop a Markov chain approach for the modelling of forest stand dynamics. The aim of this work is to generalize the recently developed Perfect Plasticity Approximation (PPA) model for scaling of vegetation dynamics from individual level to the landscape level through the ecosystem hierarchical structure. Our basic assumption is that the forested ecosystem and disturbance regimes can be modelled on 3 hierarchical scales (levels): individual trees, forest stand (or patch, defined as a spatial unit about 0.5-1 ha of the same forest at one successional stage.) and landscape (collection of forest patches of different forest/soil types at different successional stages) levels. In our modelling approach the PPA model is an intermediate step for scaling from the individual level to the forest stand level (or patch level). In this paper we develop a Markov chain model for stage-structured dynamics of forest stands (patches). In order to determine the structure of the Markov chain model and estimate parameters, we analyze the patch-mosaic patterns of forest stands of the Lake States (MI, WI, and MN) recorded in the USDA FIA database as well as data for other US states and Canada. The distribution of macroscopic characteristics of a large collection of forest patches is considered as an estimate of the stationary distribution of the underlying Markov chain. The data demonstrates that this distribution is unimodal and skewed to the right. We identify the simplest Markov chain that produces such a distribution and estimate the upper bound of the probability of disaster for this Markov chain.