Application of reaction-diffusion equations for modeling human and breeding site attraction movement behavior of Aedes aegypti mosquito.

This paper shows how biological population dynamic models in the form of coupled reaction-diffusion equations with nonlinear reaction terms can be applied to heterogeneous landscapes. The presented systems of coupled partial differential equations (PDEs) combine the dispersal of disease-vector mosquitoes and the spread of the disease in a human population. Realistic biological dispersal behavior is taken into account by applying chemotaxis terms for the attraction to the human host and the attraction of suitable breeding sites. These terms are capable of generating the complex active movement patterns of mosquitoes along the gradients of the attractants. The nonlinear initial boundary value problems are solved numerically for geometries of heterogeneous landscapes, which have been imported from geographic information system data to construct a general-purpose finite-element solver for systems of coupled PDEs. The method is applied to the dispersal of the dengue disease vector for Aedes aegypti in a small-scale rural setting consisting of small houses and different breeding sites, and to a large-scale section of the suburban zone of a metropolitan area in Vietnam. Numerical simulations illustrate how the setup of model equations and geographic information can be used for the assessment of control measures, including the spraying patterns of pesticides and biological control by inducing male sterility.

Long-Term Heavy Metal Retention by Mangroves and Effect on Its Growth: A Field Inventory and Scenario Simulation.

The ability of mangroves in taking up and storing heavy metal (HM) helps in reducing HM pollution. However, HMs likewise adversely affect the growth of mangroves. We assess the effects of the long-term soil HMs enrichment on the growth of Rhizophora apiculata forest in the Can Gio Mangrove Forest (Southern Vietnam) in different environmental conditions of soil salinity, ground elevation, and tree density based on a novel set of measured data. These data were analyzed and were used to calibrate and validate for a tree growth model with influencing factors salinity, elevation, tree density, and heavy metals content. Three scenario simulations were performed to predict the mangrove dynamics under different levels of heavy metal pollution in combined environmental conditions of salinity and elevation. Simulation results show the decline of total forest biomass from 1,750,000 tons (baseline scenario with no HM pollution) down to 850,000 tons and 350,000 tons for the current HM pollution and double HM pollution scenarios, respectively. Both data analysis and simulations have shown that although mangroves can assist in reducing HM pollution, the quality and health of this ecosystem will be severely affected if the environment is excessively polluted. In addition, a data-and-model driven management tool is devised for the sustainable management of the mangrove environmental resources.

The Role of Mangroves in the Retention of Heavy Metal (Chromium): A Simulation Study in the Thi Vai River Catchment, Vietnam.

In this study, chromium (Cr) retention by the mangroves in the Thi Vai catchment located in the south of Vietnam was simulated using a coupled model of the hydrodynamic model Delft3D with Cr transport and a model for the uptake of Cr by mangroves. This coupled model was calibrated and validated using data from four hydrodynamic stations and data from phytoremediation studies. To analyze the effect of mangroves on reducing Cr pollution, three scenarios were run by the model. Scenario 1 (SC1) is based on the actual situation concerning discharges and the distribution of mangroves. Scenario 2 (SC2) simulates the deterioration of the actual situation by deforestation on the west bank and the establishment of more industrial zones on the east bank. Scenario 3 (SC3) simulates an eco-friendly development comprising the channeling of wastewater through constructed wetlands with mangroves prior to the discharge into the river. Simulation results showed that the total Cr uptake by mangroves in SC3 was higher than in the other two scenarios. In total, 33 kg Cr in water were absorbed by the constructed wetlands in SC3 within one month. The simulation results helped in overcoming the difficulties and challenges in assessing the capacity of mangrove forests on the retention of chromium at catchment scale.

Ecophysiological responses of young mangrove species Rhizophora apiculata (Blume) to different chromium contaminated environments.

Many mangrove forests have suffered from the contaminated environments near industrial areas. This study addresses the question how these environments influence the renewal of mangrove forests. To this end ecophysiological responses of the young mangrove species Rhizophora apiculata (Blume) grown under combinations of the factors heavy metals (here chromium), nutrition and soil/water environment were analyzed. We tested the hypothesis that soil/water conditions and nutrient status of the soil strongly influence the toxic effect of chromium. Seedlings of R. apiculata were grown in three different soil/water environments (natural saline soil with brackish water, salt-leached soil with fresh water and salt-leached-sterilized soil with fresh water) treated with different levels of chromium and NPK fertilizer. The system was inundated twice a day as similar to natural tidal condition in the mangrove wetland in the south of Vietnam. The experiments were carried out for 6months. Growth data of root, leaf and stem, root cell number and stomata number were recorded and analyzed. Results showed that growth of R. apiculata is slower in natural saline soil/water condition. The effect of chromium and of nutrients respectively depends on the soil/water condition. Under high concentrations of chromium, NPK fertilizer amplifies the toxic effect of chromium. Stomata density increases under chromium stress and is largest under the combination of chromium and salty soil/water condition. From the data a nonlinear multivariate regression model was derived capturing the toxicity threshold of R. apiculata under different treatment combinations.

Ecological risk assessment of a coastal zone in Southern Vietnam: Spatial distribution and content of heavy metals in water and surface sediments of the Thi Vai Estuary and Can Gio Mangrove Forest.

Enrichment of heavy metals was assessed in the Thi Vai Estuary and in the Can Gio Mangrove Forest (SE, Vietnam). Cd, Co, Cr, Cu, Mn, Ni, Pb and Zn contents in water and in sediments were measured. Total organic carbon, nitrogen, phosphorus and C/N ratios were determined. Cu and Cr values were higher than threshold effect level of toxicity, while Ni exceeded probable effect level, indicating the risk of probable toxicity effects. Enrichment factors (EF), contamination factor (CF) and Geo-accumulation index (I-geo) were determined. CF reveals moderate to considerable pollution with Cr and Ni. EF suggests anthropogenic sources of Cr, Cu and Ni. I-geo indicates low contamination with Co, Cu and Zn and moderate contamination with Cr and Ni. Overall metal contents were lower than expected for this highly industrialized region, probably due to dilution, suggesting that erosion rates and hydrodynamics may also play a role in metal contents distribution.

Genetics of metabolic resistance.

Herbicide resistance has become a major issue for many weeds. Metabolic resistance refers to the biochemical processes within organisms that degrade herbicides to less toxic compounds, resulting in a shift of the dose response curve. This type of resistance involves polygenic inheritance. A model is presented linking the biochemical pathway of amino acid synthesis and the detoxifying pathway of an inhibitor of the key enzyme ALS. From this model, resistance factors for each biotype are derived, which are then applied to a polygenic population genetic model for an annual weed plant. Polygenic inheritance is described by a new approach based on tensor products of heredity matrices. Important results from the model are that low dose regimes favour fast emergence of resistant biotypes and that the emergence of resistant biotypes occurs as abrupt outbreaks. The model is used to evaluate strategies for the management of metabolic resistance.

Triple test as predictive screen for unilateral weakness on caloric testing in routine practice.

OBJECTIVE: To investigate in vertigo patients in routine practice to what extent a rapid and straightforward triple bedside test (spontaneous nystagmus, head-shaking nystagmus, and the head impulse test) can predict a normal result on caloric testing. STUDY DESIGN: Prospective, single-blind, diagnostic study. SETTING: Tertiary referral center. PATIENTS: 151 patients (78 male and 73 female subjects; mean age, 52.5 +/- 16.4 yr) presenting with acute or recent symptoms of vertigo. INTERVENTION: Diagnostic evaluation. MAIN OUTCOME MEASURE: The negative predictive value (NPV) of the triple test in relation to a normal caloric test response. RESULTS: In unilateral weakness (UW) on caloric testing (UW, >=25%), the triple test had sensitivity of 63.6%, specificity of 85.4%, a positive predictive value (PPV) of 71.4%, and an NPV of 80.4%. In other words, 80.4% of patients with a negative triple test also had a normal response on caloric testing. In pronounced canal paresis (UW, >=50%), the triple test had sensitivity of 81.8%, specificity of 81.4%, a PPV of 55.1%, and an NPV of 94.1%. Significant differences were found between 2 subgroups assessed by examiners with differing levels of experience (p < 0.05). CONCLUSION: The triple test represents a good screening tool that quickly and reliably excludes unilateral weakness and in particular pronounced canal paresis on caloric testing.

Multi-gene-loci inheritance in resistance modeling.

The ability of an organism to degrade harmful substances to less toxic compounds is referred to as metabolic resistance. The biochemical processes result in a shift of dose-response curves associated with the toxic substances. Hence, the development of metabolic resistance may cause great problems of managing pests and diseases by pesticides. We develop a polygenic fitness model capable of simulating the emergence of metabolic resistance. Within the model, polygenic inheritance is described by a new approach based on tensor products of heredity matrices. This is included as genetic submodel into the time-continuous population model for all possible biotypes. Evolution is acting on the parameters of dose-response curves, i.e., on the mortality rates and thus on the ED(50)-value. The resulting system of differential equations is analyzed with respect to polymorphic equilibria. Under a longterm application of only one mode of action the model produces a gradual shift of the mean dose-response curve of the population which is frequently observed in the field. Different scenarios of the development of metabolic resistance are demonstrated in numerical experiments.

Modelling the effect of temperature on the range expansion of species by reaction-diffusion equations.

The spatial dynamics of range expansion is studied in dependence of temperature. The main elements population dynamics, competition and dispersal are combined in a coherent approach based on a system of coupled partial differential equations of the reaction-diffusion type. The nonlinear reaction terms comprise population dynamic models with temperature dependent reproduction rates subject to an Allee effect and mutual competition. The effect of temperature on travelling wave solutions is investigated for a one dimensional model version. One main result is the importance of the Allee effect for the crossing of regions with unsuitable habitats. The nonlinearities of the interaction terms give rise to a richness of spatio-temporal dynamic patterns. In two dimensions, the resulting non-linear initial boundary value problems are solved over geometries of heterogeneous landscapes. Geo referenced model parameters such as mean temperature and elevation are imported into the finite element tool COMSOL Multiphysics from a geographical information system. The model is applied to the range expansion of species at the scale of middle Europe.

From population-level effects to individual response: modelling temperature dependence in Gammarus pulex.

Population-level effects of global warming result from concurrent direct and indirect processes. They are typically described by physiologically structured population models (PSPMs). Therefore, inverse modelling offers a tool to identify parameters of individual physiological processes through population-level data analysis, e.g. the temperature dependence of growth from size-frequency data of a field population. Here, we make use of experiments under laboratory conditions, in mesocosms and field monitoring to determine the temperature dependence of growth and mortality of Gammarus pulex. We found an optimum temperature for growth of approximately 17°C and a related temperature coefficient, Q(10), of 1.5°C(-1), irrespective of whether we classically fitted individual growth curves or applied inverse modelling based on PSPMs to laboratory data. From a comparison of underlying data sets we conclude that applying inverse modelling techniques to population-level data results in meaningful response parameters for physiological processes if additional temperature-driven effects, including within-population interaction, can be excluded or determined independently. If this is not the case, parameter estimates describe a cumulative response, e.g. comprising temperature-dependent resource dynamics. Finally, fluctuating temperatures in natural habitats increased the uncertainty in parameter values. Here, PSPM should be applied for virtual monitoring in order to determine a sampling scheme that comprises important dates to reduce parameter uncertainty.

Process dominance analysis for fate modeling of flubendazole and fenbendazole in liquid manure and manured soil.

Fate monitoring data on anaerobic transformation of the benzimidazole anthelmintics flubendazole (FLU) and fenbendazole (FEN) in liquid pig manure and aerobic transformation and sorption in soil and manured soil under laboratory conditions were used for corresponding fate modeling. Processes considered were reversible and irreversible sequestration, mineralization, and metabolization, from which a set of up to 50 different models, both nested and concurrent, was assembled. Five selection criteria served for model selection after parameter fitting: the coefficient of determination, modeling efficiency, a likelihood ratio test, an information criterion, and a determinability measure. From the set of models selected, processes were classified as essential or sufficient. This strategy to identify process dominance was corroborated through application to data from analogous experiments for sulfadiazine and a comparison with established fate models for this substance. For both, FLU and FEN, model selection performance was fine, including indication of weak data support where observed. For FLU reversible and irreversible sequestration in a nonextractable fraction was determined. In particular, both the extractable and the nonextractable fraction were equally sufficient sources for irreversible sequestration. For FEN generally reversible formation of the extractable sulfoxide metabolite and reversible sequestration of both the parent and the metabolite were dominant. Similar to FLU, irreversible sequestration in the nonextractable fraction was determined for which both the extractable or the nonextractable fraction were equally sufficient sources. Formation of the sulfone metabolite was determined as irreversible, originating from the first metabolite.

Spatio-temporal patterns of gene flow and dispersal under temperature increase.

Recent data show that the Earth climate is undergoing a change at a rate which is outstanding in geologic history. Temperature is one of the major driving forces of gene flow and dispersal. In this paper the spatial dynamics of genetic dispersal is studied under the auspices of temperature increase by means of a mathematical model. The main elements genetics, competition and dispersal are combined in a coherent approach by a system of coupled partial differential equations with non-linear reaction terms describing population dynamics, genetic exchange and competition. Temperature reaction norms are conferred by a two allele system. The non-linearities of the interaction terms give rise to a richness of spatio-temporal dynamic patterns. Here we show how invasion processes in form of travelling waves are initiated by a temperature rise.

Meteorological input data requirements to predict cross-pollination of GMO maize with Lagrangian approaches.

Modeling pollen dispersal to predict cross-pollination is of great importance for the ongoing discussion of adventitious presence of genetically modified material in food and feed. Two different modeling approaches for pollen dispersal were used to simulate two years of data for the rate of cross-pollination of non-GM maize (Zea mays (L.)) fields by pollen from a central 1 ha transgenic field. The models combine the processes of wind pollen dispersal (transport) and pollen competition. Both models used for the simulation of pollen dispersal were Lagrangian approaches: a stochastic particle Lagrange model and a Lagrangian transfer function model. Both modeling approaches proved to be appropriate for the simulation of the cross-pollination rates. However, model performance differed significantly between years. We considered different complexity in meteorological input data. Predictions compare well with experimental results for all simplification steps, except that systematic deviations occurred when only main wind direction was used. Concluding, it can be pointed out that both models might be adapted to other pollen dispersal experiments of different crops and plot sizes, when wind direction statistics are available. However, calibration of certain model parameters is necessary.

Modelling approaches to compare sorption and degradation of metsulfuron-methyl in laboratory micro-lysimeter and batch experiments.

Results of laboratory batch studies often differ from those of outdoor lysimeter or field plot experiments--with respect to degradation as well as sorption. Laboratory micro-lysimeters are a useful device for closing the gap between laboratory and field by both including relevant transport processes in undisturbed soil columns and allowing controlled boundary conditions. In this study, sorption and degradation of the herbicide metsulfuron-methyl in a loamy silt soil were investigated by applying inverse modelling techniques to data sets from different experimental approaches under laboratory conditions at a temperature of 10 degrees C: first, batch-degradation studies and, second, column experiments with undisturbed soil cores (28 cm length x 21 cm diameter). The column experiments included leachate and soil profile analysis at two different run times. A sequential extraction method was applied in both study parts in order to determine different binding states of the test item within the soil. Data were modelled using ModelMaker and Hydrus-1D/2D. Metsulfuron-methyl half-life in the batch-experiments (t1/2 = 66 days) was shown to be about four times higher than in the micro-lysimeter studies (t1/2 about 17 days). Kinetic sorption was found to be a significant process both in batch and column experiments. Applying the one-rate-two-site kinetic sorption model to the sequential extraction data, it was possible to associate the stronger bonded fraction of metsulfuron-methyl with its kinetically sorbed fraction in the model. Although the columns exhibited strong significance of multi-domain flow (soil heterogeneity), the comparison between bromide and metsulfuron-methyl leaching and profile data showed clear evidence for kinetic sorption effects. The use of soil profile data had significant impact on parameter estimates concerning sorption and degradation. The simulated leaching of metsulfuron-methyl as it resulted from parameter estimation was shown to decrease when soil profile data were considered in the parameter estimation procedure. Moreover, it was shown that the significance of kinetic sorption can only be demonstrated by the additional use of soil profile data in parameter estimation. Thus, the exclusive use of efflux data from leaching experiments at any scale can lead to fundamental misunderstandings of the underlying processes.

Spatially explicit modelling of transgenic maize pollen dispersal and cross-pollination.

Modelling of pollen dispersal and cross-pollination is of great importance for the ongoing discussion on thresholds for the adventitious presence of genetically modified material in food and feed. Two different modelling approaches for pollen dispersal are used to simulate the cross-pollination rate of pollen emerged from an adjacent transgenic crop field. The models are applied to cross-pollination data from field experiments with transgenic maize (Zea mays). The data were generated by an experimental setup specifically designed to suit the demands of mathematical modelling. First a Gaussian plume model is used for the simulation of pollen transport in and from plant canopies. This is a semiempirical approach combining the atmospheric diffusion equation and Lagrangian methodology. The second model is derived from the localised near field (LNF) theory and based on the physical processes in the canopy. Both modelling approaches prove to be appropriate for the simulation of the cross-pollination rates at distances of about 7.5m and more from the transgene source. The simulation of the cross-pollination rate is less precise at the edge of the source plot especially with the LNF theory. However, the simulation results lie within the range of variability of the observations. Concluding can be pointed out that both models might be adapted to other pollen dispersal experiments of different crops and plot sizes.