Formulation and testing of a novel river nitrification model

The nitrification process in many river water quality models has been approximated by a simple first order dependency on the water column ammonia concentration, while the benthic contribution has routinely been neglected. In this study a mathematical framework was developed for sediment bed nitrification based on mass transfer theory and Monod bacterial growth kinetics. The model describes ammonia transport across the boundary layer and consumption within the biofilm to quantify the overall nitrification flux. Model results suggest that nitrification is usually controlled by the boundary layer thickness, and we estimated a nitrification velocity range between 0.14 and 0.97 m d⁻¹, assuming typical boundary thicknesses of 0.1–1.0 mm. These ranges compared favorably with reported literature values, including our own measurements. The model was applied to several river systems of different depths where nitrification rates and river depths were available. Assuming that nitrification is exclusively a benthic process, the average velocity of all the rivers evaluated was 0.85 m d⁻¹ (r² = 0.72).     

Application of a spatial meta-population model with stochastic parameters to the management of the invasive grass Nassella trichotoma in North Canterbury, New Zealand

Optimising the management of invasive plants requires the identification of the population size outcomes for alternative management strategies. Mathematical models can be useful tools for making such management strategy comparisons. In this paper we develop a generic landscape meta-population model and apply it to the weedy grass, Nassella trichotoma, an invasive species occupying approximately 800 land parcels, predominantly pastoral farms, in the Hurunui district, North Canterbury, New Zealand. Empirical evidence reveals that this meta-population is currently stable (at a median density of 6 plants ha⁻¹) under a community strategy requiring manual removal (termed ‘grubbing’) of plants annually from all land parcels. Reduction in population size requires an alternative management strategy. Field data, collected over a 12 year period, were used to provide stochastic parameter values for land parcel size, carrying capacity, rates of local population growth and grubbing.The model reveals that at steady state, the most significant contribution to population growth on a land parcel comes from within the land parcel itself; the expected annual per capita growth on an individual land parcel is 4 orders of magnitude greater than the expected annual contribution from plants arising from other land parcels. This result implies that many of the farms currently supporting N. trichotoma may pose little or no threat to, nor are threatened themselves by, other farms infested by the weed. However, the steady state distribution (of the weed's population density) was sensitive to the spread rate, revealing a need for data on this process. It was also sensitive to how any increase in the grubbing rate is distributed; increasing it via a uniform distribution U(0, 1) where all rates between 0 and 100% year⁻¹ are equally probable did not affect the steady state, whereas increasing the rates via the uniform distribution U(0.25, 0.75) resulted in fewer farms with high population densities. In general the model provides a basis for exploring the effects of a wide range of alternative grubbing strategies on population growth in N. trichotoma.     

Development of TRIPLEX-Management model for simulating the response of forest growth to pre-commercial thinning

In order to simulate forest growth response to pre-commercial thinning (PCT), TRIPLEX1.0 - a process-based model designed to predict forest growth as well as carbon (C) and nitrogen (N) dynamics - was modified and improved to also simulate managed forest ecosystem thinning practices. A three-parameter Weibull distribution model was integrated to simulate thinning treatments within the newly developed TRIPLEX-Management model. The thinning intensity component within the model allows users to simulate thinning treatments by applying basal area, stand density and volume to quantify thinning intensity. Natural mortality decreased following thinning due to an increase in growing space for residual stems. Predicted litterfall pools also increased after thinning events took place. The TRIPLEX-Management model was tested against published observational data for Jack Pine (Pinus banksiana Lamb.) stands subjected to PCT in Northwestern Ontario, Canada. The coefficients of determination (R²) between the predicted and observed variables including stand density, mean DBH (diameter at breast height), the quadratic mean DBH, total volume and merchantable volume as well as belowground, aboveground, and total biomass ranged from 0.50 to 0.88 (n = 20, P < 0.001) with the exception of mean tree height (R² = 0.25, n = 20, P < 0.05). Overall, the Willmott index of agreement between predicted and observed variables ranged from 0.97 to 1.00. Results show that the TRIPLEX-Management model is generally capable of simulating growth response to PCT for Jack Pine stands.     

The MONICA model: Testing predictability for crop growth, soil moisture and nitrogen dynamics

A fundamentally revised version of the HERMES agro-ecosystem model, released under the name of MONICA, was calibrated and tested to predict crop growth, soil moisture and nitrogen dynamics for various experimental crop rotations across Germany, including major cereals, sugar beet and maize. The calibration procedure also included crops grown experimentally under elevated atmospheric CO₂ concentration. The calibrated MONICA simulations yielded a median normalised mean absolute error (nMAE) of 0.20 across all observed target variables (n = 42) and a median Willmott's Index of Agreement (d) of 0.91 (median modelling efficiency (ME): 0.75). Although the crop biomass, habitus and soil moisture variables were all within an acceptable range, the model often underperformed for variables related to nitrogen. Uncalibrated MONICA simulations yielded a median nMAE of 0.27 across all observed target variables (n = 85) and a median d of 0.76 (median ME: 0.30), also showing predominantly acceptable results for the crop biomass, habitus and soil moisture variables. Based on the convincing performance of the model under uncalibrated conditions, MONICA can be regarded as a suitable simulation model for use in regional applications. Furthermore, its ability to reproduce the observed crop growth results in free-air carbon enrichment experiments makes it suited to predict agro-ecosystem behaviour under expected future climate conditions.     

Modeling amphibian energetics, habitat suitability, and movements of western toads, Anaxyrus (=Bufo) boreas, across present and future landscapes

Effective conservation of amphibian populations requires the prediction of how amphibians use and move through a landscape. Amphibians are closely coupled to their physical environment. Thus an approach that uses the physiological attributes of amphibians, together with knowledge of their natural history, should be helpful. We used Niche Mapper™ to model the known movements and habitat use patterns of a population of Western toads (Anaxyrus (=Bufo) boreas) occupying forested habitats in southeastern Idaho. Niche Mapper uses first principles of environmental biophysics to combine features of topography, climate, land cover, and animal features to model microclimates and animal physiology and behavior across landscapes. Niche Mapper reproduced core body temperatures (T_c) and evaporation rates of live toads with average errors of 1.6 ± 0.4 °C and 0.8 ± 0.2 g/h, respectively. For four different habitat types, it reproduced similar mid-summer daily temperature patterns as those measured in the field and calculated evaporation rates (g/h) with an average error rate of 7.2 ± 5.5%. Sensitivity analyses indicate these errors do not significantly affect estimates of food consumption or activity. Using Niche Mapper we predicted the daily habitats used by free-ranging toads; our accuracy for female toads was greater than for male toads (74.2 ± 6.8% and 53.6 ± 15.8%, respectively), reflecting the stronger patterns of habitat selection among females. Using these changing to construct a cost surface, we also reconstructed movement paths that were consistent with field observations. The effect of climate warming on toads depends on the interaction of temperature and atmospheric moisture. If climate change occurs as predicted, results from Niche Mapper suggests that climate warming will increase the physiological cost of landscapes thereby limiting the activity for toads in different habitats.     

Epidemiological risk assessment using linked network and grid based modelling: Phytophthora ramorum and Phytophthora kernoviae in the UK

We developed a stochastic simulation model incorporating most processes likely to be important in the spread of Phytophthora ramorum and similar diseases across the British landscape (covering Rhododendron ponticum in woodland and nurseries, and Vaccinium myrtillus in heathland). The simulation allows for movements of diseased plants within a realistically modelled trade network and long-distance natural dispersal. A series of simulation experiments were run with the model, representing an experiment varying the epidemic pressure and linkage between natural vegetation and horticultural trade, with or without disease spread in commercial trade, and with or without inspections-with-eradication, to give a 2 × 2 × 2 × 2 factorial started at 10 arbitrary locations spread across England. Fifty replicate simulations were made at each set of parameter values. Individual epidemics varied dramatically in size due to stochastic effects throughout the model. Across a range of epidemic pressures, the size of the epidemic was 5–13 times larger when commercial movement of plants was included. A key unknown factor in the system is the area of susceptible habitat outside the nursery system. Inspections, with a probability of detection and efficiency of infected-plant removal of 80% and made at 90-day intervals, reduced the size of epidemics by about 60% across the three sectors with a density of 1% susceptible plants in broadleaf woodland and heathland. Reducing this density to 0.1% largely isolated the trade network, so that inspections reduced the final epidemic size by over 90%, and most epidemics ended without escape into nature. Even in this case, however, major wild epidemics developed in a few percent of cases. Provided the number of new introductions remains low, the current inspection policy will control most epidemics. However, as the rate of introduction increases, it can overwhelm any reasonable inspection regime, largely due to spread prior to detection.     

Application of a Random Forest algorithm to predict spatial distribution of the potential yield of Ruditapes philippinarum in the Venice lagoon, Italy

We present a modelling framework that combines machine learning techniques and Geographic Information Systems to support the management of an important aquaculture species, Manila clam (Ruditapes philippinarum). We use the Venice lagoon (Italy), the first site in Europe for the production of R. philippinarum, to illustrate the potential of this modelling approach. To investigate the relationship between the yield of R. philippinarum and a set of environmental factors, we used a Random Forest (RF) algorithm. The RF model was tuned with a large data set (n = 1698) and validated by an independent data set (n = 841). Overall, the model provided good predictions of site-specific yields and the analysis of marginal effect of predictors showed substantial agreement among the modelled responses and available ecological knowledge for R. philippinarum. The most influent environmental factors for yield estimation were percentage of sand in the sediment, salinity, and water depth. Our results agree with findings from other North Adriatic lagoons. The application of the fitted RF model to continuous maps of all the environmental variables allowed estimates of the potential yield for the whole basin. Such a spatial representation enabled site-specific estimates of yield in different farming areas within the lagoon. We present a possible management application of our model by estimating the potential yield under the current farming distribution and comparing it to a proposed re-organization of the farming areas. Our analysis suggests a reduction of total yield is likely to result from the proposed re-organization.     

Dynamics of a chemostat with three competitive hydrogen oxidizing denitrifying microbial populations and their efficiency for denitrification

In this work, competition for two nitrogen resources (nitrate-, nitrite-nitrogen) between three hydrogen oxidizing denitrifying populations (Acidovorax sp. strain Ic3 (X₁), Paracoccus sp. strain Ic1 (X₂), and Acinetobacter sp. strain Ic2 (X₃)) was examined. The dynamics of three systems of microbial populations (system I: X₁ − X₃, system II: X₂ − X₃, and system III: X₁ − X₂ − X₃), grown in a chemostat, was studied using bifurcation analysis. The chemostat is the most common type of biological reactor used for the study of microbial growth under controlled conditions. The effect of the operating parameters (i.e., dilution rate and feed nitrate nitrogen concentration) on the long-term behavior of the systems showed that X₃ was the predominant population for a wide range of combinations of dilution rate and feed nitrate nitrogen concentration. Also, coexistence of two populations (X₂X₃, X₁X₃) was observed. The results of the bifurcation analysis were also used to determine the denitrification rate and the nitrite nitrogen accumulation for each of the three systems as a function of the dilution rate (up to 0.17 h⁻¹) and the feed nitrate nitrogen concentration (up to 300 mg/L). The highest denitrification rate was achieved by system I (28 mg/Lh). A comparison between the three systems showed that the nitrite nitrogen concentration in system I was less than the one in system III, while the two systems gave similar denitrification rates. The second system had the greatest accumulation of nitrites with the lowest denitrification rate.     

Identification of important factors for water vapor flux and CO2 exchange in a cropland

Water vapor flux and carbon dioxide (CO₂) exchange in croplands are crucial to water and carbon cycle research as well as to global warming evaluation. In this study, a standard three-layer feed-forward back propagation neural network technique associated with the Bayesian technique of automatic relevance determination (ARD) was employed to investigate water vapor and CO₂ exchange between the canopy of summer maize and atmosphere in responses to variations of environmental and physiological factors. These factors, namely the photosynthetically active radiation (PAR), air temperature (T), vapor pressure deficient (VPD), leaf-area index (LAI), soil water content in root zone (W), and friction velocity (U*), were used as inputs in neural network analysis. Results showed that PAR, VPD, T and LAI were the primary factors regulating both water vapor and CO₂ fluxes with VPD and W more critical to water vapor flux and PAR and T more crucial to CO₂ exchange. Furthermore, two time variables “day of the year (DOY)” and “time of the day (TOD)” could also improve the simulation results of neural network analysis. The important factors identified by the neural network technique used in this study were in the order of PAR > T > VPD > LAI > U* > TOD for water vapor flux and in the order of VPD > W > LAI > T > PAR > DOY for CO₂ exchange. This study suggests that neural network technique associated with ARD could be a useful tool for identifying important factors regulating water vapor and CO₂ fluxes in terrestrial ecosystem.     

Residual levels and health risk of polycyclic aromatic hydrocarbons in freshwater fishes from Lake Small Bai-Yang-Dian, Northern China

The residual levels of polycyclic aromatic hydrocarbons (PAHs) in the liver, brain, gill and muscle tissues of four common edible freshwater fish species including crucian carp, snakehead fish, grass carp and silver carp collected from Lake Small Bai-Yang-Dian in northern China were measured by GC-MS. The distribution and composition pattern of PAHs in the fish tissues, and the effects of lipid contents in fish tissues and the octanol-water partition coefficient (Kow) of PAHs congeners on them were analyzed. The human health risk of PAHs though fish consumptions was estimated. The following results were obtained: (1) The average residual levels of total PAHs (PAH₁₆) on wet weight base in the different tissues of each fish species ranged from 4.764 to 144.254 ng/g ww. The differences in the average residual levels on wet weight base for PAH₁₆ within four fish species were not statistically significant (P > 0.05); however, these within four fish tissues were statistically significant (P < 0.01). (2) There were very similar distribution patterns of PAH congeners among both the fish tissues and the fish species, as indicated by statistically significant positive interrelationships (R = 0.58-0.97, P < 0.01 or P < 0.05). Low molecular weight (LMW) PAHs predominated the distribution in the fish tissues, accounting for 89.97% of total PAHs. Phe was the most dominant component, according for 37.79% of total PAHs, followed by Ant (18.59%), Flo (12.59%), Nap (10.79%), Fla (9.82%) and Pyr (6.43%). (3) The PAHs residues and distribution in the fish tissues are dependent on both the Kow of PAH congeners and the lipid contents in the fish tissues. There was a significant positive relationship (R = 0.7116, P < 0.0001) between lipid contents and PAHs residual levels. The statistically significant negative relationships (P < 0.05) were found between LogKow and log-transformed PAHs contents on wet weight base for all fish tissues except for the muscle tissue of snakehead fish, the brain and liver tissues of crucian carp. (4) The risk levels of total PAHs were lower than 10⁻⁵ for the muscle tissues of four studied fish species and for the brain tissues of grass carp and snakehead fish; while these were higher than 10⁻⁵ for the brain tissues of crucian carp and silver carp. The risk levels of total PAHs in the liver tissues of four studied fish species except for snakehead fish exceeded 10⁻⁵ for 2-4.5 times. However, the potency equivalent concentration (PEC) of total PAHs in four studied fish tissues were still lower than the maximum permissible BaP limits for crops and baked meat and for plants in the national criterions. The distributions of PAH congeners in fish were well simulated by a level III fugacity model, especially for low molecule weight PAHs.     

Estimation of annual potential evapotranspiration at regional scale based on the effect of moisture on soil respiration

Potential evapotranspiration (PET) is an important component of water cycle. For traditional models derived from the principle of aerodynamics and the surface energy balance, its calculation always includes many parameters, such as net radiation, water vapor pressure, air temperature and wind speed. We found that it can be acquired in an easier way in specific regions. In this study, a new PET model (PETP model) derived from two empirical models of soil respiration was evaluated using the Penman-Monteith equation as a standard method. The results indicate that the PETP model estimation concur with the Penman-Monteith equation in sites where annual precipitation ranges from 717.71 mm to 1727.37 mm (R² = 0.68, p = 0.0002), but show large discrepancies in all sites (R² = 0.07, p = 0.1280). Then we applied our PETP model at the global scale to the regions with precipitation higher than 700 mm using 2.5° CMAP data to obtain the annual PET for 2006. As expected, the spatial pattern is satisfactory overall, with the highest PET values distributed in the lower latitudes or coastal regions, and with an average of 1292.60 ± 540.15 mm year⁻¹. This PETP model provides a convenient approach to estimate PET at regional scales.     

Foliage profiles of individual trees determine competition,self-thinning,biomass and NPP of a Cryptomeria japonica forest stand: A simulation study based on a stand-scale process-based forest model

A simulation study was carried out to investigate simultaneously the effects of eco-physiological parameters on competitive asymmetry, self-thinning, stand biomass and NPP in a temperate forest using an atmosphere–vegetation dynamics interactive model (MINoSGI). In this study, we selected three eco-physiological relevant parameters as foliage profiles (i.e. vertical distribution of leaf area density) of individual trees (distribution pattern is described by the parameter η), biomass allocation pattern in individual tree growth (χ) and the maximum carboxylation velocity (V_max). The position of the maximal leaf area density shifts upward in the canopy with increasing η. For scenarios with η < 4 (foliage concentrated in the lowest canopy layer) or η > 12 (foliage concentrated in the uppermost canopy layer), a low degree of competitive asymmetry was produced. These scenarios resulted in the survival of subordinate trees due to a brighter lower canopy environment when η < 4 or the generation of spatially separated foliage profiles between dominant and subordinate trees when η > 12. In contrast, competition between trees was most asymmetric when 4 ≤ η ≤ 12 (vertically widespread foliage profile in the canopy), especially when η = 8. In such cases, vertically widespread foliage of dominant trees lowered the opportunity of light acquisition for subordinate trees and reduced their carbon gain. The resulting reduction in carbon gain of subordinate trees yielded a higher degree of competitive asymmetry and ultimately higher mortality of subordinate trees. It was also shown that 4 ≤ η ≤ 12 generated higher self-thinning speed, smaller accumulated NPP, litter-fall and potential stand biomass as compared with the scenarios with η < 4 or η > 12. In contrast, our simulation revealed small effects of χ or V_max on the above-mentioned variables as compared with those of η. In particular, it is notable that greater V_max would not produce greater potential stand biomass and accumulated NPP although it has been thought that physiological parameters relevant to photosynthesis such as V_max influence dynamic changes in forest stand biomass and NPP (e.g. the greater the V_max, the greater the NPP). Overall, it is suggested that foliage profiles rather than biomass allocation or maximum carboxylation velocity greatly govern forest dynamics, stand biomass, NPP and litter-fall.     

Local calibration of coliforms parameters of water quality problem at Igapó I Lake, Londrina, Paraná, Brazil

This article presents results concerning the local calibration of the transport parameters (longitudinal and transversal diffusions and decay coefficient) for a two-dimensional problem of water quality at Igapó I Lake, located in Londrina, Paraná, Brazil, using fecal coliforms as an indicator of water quality. The simulation of fecal coliforms concentrations all over the water body is conducted by means of a structured discretization of the geometry of Igapó I Lake, together with the finite difference and finite element methods. By using the velocity field, modeled by the Navier-Stokes and Poisson equations, the flow of fecal coliforms is described by means of a transport model, which considers advective and diffusive processes, as well as a process of fecal coliforms decay. In the checkpoint, the longitudinal and transversal diffusion coefficients and the coliforms decay coefficient that best fitted the value of the fecal coliforms concentration were D_x = D_y = 0.001 m²/h and k = 0.5 d⁻¹ = 0.02083 h⁻¹. A qualitative and quantitative analysis of the numerical simulations conducted in function of the diffusion coefficients and of the coliforms decay parameter provided a better understanding of the local water quality at Igapó I Lake.     

Inter-annual variability of ecosystem production in boreal jack pine forests (1975-2004) estimated from tree-ring data using CBM-CFS3

We describe and apply a method of using tree-ring data and an ecosystem model to reconstruct past annual rates of ecosystem production. Annual data on merchantable wood volume increment and mortality obtained by dendrochronological stand reconstruction were used as input to the Carbon Budget Model of the Canadian Forest Sector (CBM-CFS3) to estimate net ecosystem production (NEP), net primary production (NPP), and heterotrophic respiration (Rh) annually from 1975 to 2004 at 10 boreal jack pine (Pinus banksiana Lamb.) stands in Saskatchewan and Manitoba, Canada. From 1975 (when sites aged 41-60 years) to 2004 (when they aged 70-89 years), all sites were moderate C sinks except during some warmer than average years where estimated Rh increased. Across all sites and years, estimated annual NEP averaged 57 g Cm⁻² yr⁻¹ (range −31 to 176 g Cm⁻² yr⁻¹), NPP 244 g Cm⁻² yr⁻¹ (147-376 g Cm⁻² yr⁻¹), and Rh 187 g Cm⁻² yr⁻¹ (124-270 g Cm⁻² yr⁻¹). Across all sites, NPP was related to stand age and density, which are proxies for successional changes in leaf area. Regionally, warm spring temperature increased NPP and defoliation by jack pine budworm 1 year previously reduced NPP. Our estimates of NPP, Rh, and NEP were plausible when compared to regional eddy covariance and carbon stock measurements. Inter-annual variability in ecosystem productivity contributes uncertainty to inventory-based assessments of regional forest C budgets that use yield curves predicting averaged growth over time. Our method could expand the spatial and temporal coverage of annual forest productivity estimates, providing additional data for the development of empirical models accounting for factors not presently considered by these models.     

Estimating soil carbon turnover using radiocarbon data: A case-study for European Russia

Turnover rates of soil carbon for 20 soil types typical for a 3.7 million km² area of European Russia were estimated based on ¹⁴C data. The rates are corrected for bomb radiocarbon which strongly affects the topsoil ¹⁴C balance. The approach is applied for carbon stored in the organic and mineral layers of the upper 1 m of the soil profile. The turnover rates of carbon in the upper 20 cm are relatively high for forest soils (0.16–0.78% year⁻¹), intermediate for tundra soils (0.25% year⁻¹), and low for grassland soils (0.02–0.08% year⁻¹) with the exception of southern Chernozems (0.32% year⁻¹). In the soil layer of 20–100 cm depth, the turnover rates were much lower for all soil types (0.01–0.06% year⁻¹) except for peat bog soils of the southern taiga (0.14% year⁻¹). Combined with a map of soil type distribution and a dataset of several hundred soil carbon profiles, the method provides annual fluxes for the slowest components of soil carbon assuming that the latter is in equilibrium with climate and vegetation cover. The estimated carbon flux from the soil is highest for forest soils (12–147 gC/(m² year)), intermediate for tundra soils (33 gC/(m² year)), and lowest for grassland soils (1–26 gC/(m² year)). The approach does not distinguish active and recalcitrant carbon fractions and this explains the low turnover rates in the top layer. Since changes in soil types will follow changes in climate and land cover, we suggest that pedogenesis is an important factor influencing the future dynamics of soil carbon fluxes. Up to now, both the effect of soil type changes and the clear evidence from ¹⁴C measurements that most soil organic carbon has a millennial time scale, are basically neglected in the global carbon cycle models used for projections of atmospheric CO₂ in 21st century and beyond.     

Modelling llama population development under environmental and market constraints in the Bolivian highlands

Changes in the size of animal populations over time are mainly determined by demographic and environmental factors. Livestock population dynamics are additionally influenced by harvesting decisions taken by herders. In Bolivia, not much is known about current llama husbandry and the main influencing factors determining population sizes. We collected data on demography, environmental factors and market values affecting the current and future llama population in three different regions in Bolivia. We generated a population model and assessed the future development of the llama population including environmental factors (rangeland carrying capacity, disturbance phenomena), herd structure and dynamics, and economic market demands. We calibrated and validated the llama model on the basis of 20-year data sets of the regions of Oruro, Potosi and La Paz, respectively. Model calibration by means of the Gauss-Marquardt-Levenberg algorithm yielded a model efficiency of 0.94. For model validation, however, the simulation slightly overestimated the observed llama population yielding model efficiencies of 0.91 and 0.87 for Potosi and La Paz, respectively. Model outcomes were most sensitive to death and birth rates of juveniles and death rate of females compared to environmental or other demographic factors. Population trajectories approached an overall carrying capacity for Oruro, Potosi and La Paz of 8.8 × 10⁵, 9.1 × 10⁵, and 9.0 × 10⁵ llama individuals after 100 years of simulation. Hence, detailed monitoring of demographic, environmental, and economic factors can improve predictions of llama population development over time. Further management should focus on improving birth rates and lowering female mortality through providing supplemental food and shelters against the harsh environmental conditions of the Andean highlands.     

Spatio-temporal modelling of ground vegetation development in mountain spruce forests

More complex models of forest ecosystems are required to understand how land-cover changes can impact vegetation dynamics and spatial pattern. In order to document spatio-temporal modelling abilities, the observations conducted in the declined climax mountain Norway spruce forest during the recovery period (1995-2006) are used for simulation and spatial analysis in the GIS environment. The developed spatio-temporal model is used for simulation of forest vegetation dynamics in a mountain spruce forest in the framework of regeneration processes after stress from air pollution. In order to explore the spatial and temporal phenomena of regeneration processes, the spatio-temporal model is based on a large set of ordinary differential equations that solve dynamic processes in sets of microsites arranged in grids for each ground vegetation species and each age group of Norway spruce seedlings. The spatial extent of the explored site is composed of a set of 50 × 50 microsites. Each microsite is represented by a square with dimensions of 1 m × 1 m. The presented simulation studies are mainly focused on seedlings from the seed year 1992, in order to explore the longest monitored time series of survival. It is based on exponential growth models that are related to the environmental conditions for each microsite. The canopy gaps based on estimates of the local crown projected area, the soil type layer, and the dominant grass density are used to provide case simulation studies. The first case study simulates the influence of microsite positions in relation to the local tree crown projections on the survival of spruce seedlings. It is assumed that the density of the trees is the main factor that determines the light and heat supply to the ground level of the Norway spruce seedlings. The second case study extends the previous study to include terms that determine the growth ratio in dependence on the crown projection area. The third case study provides further extensions in order to simulate growth ratio relations to the local soil type. The fourth case study demonstrates the local influence of the dominant grasses, such as Avenella flexuosa and Calamagrostis villosa, on the natural regeneration of Norway spruce. Starting from the conditions at the sites before the recovery period, the case simulation studies are able to project the short-term succession for a regeneration decade and the approximate long-term development. In addition to the standard simulation procedures based on solution of ordinary differential equations, spatio-temporal modelling in the GIS environment is able to provide spatial data management, analysis and visualization of the data.     

Estimating dyad association probability under imperfect and heterogeneous detection

In animal behaviour studies, association indices estimate the proportion of time two individuals (i.e. a dyad) spend in association. In terms of dyads, all association indices can be interpreted as estimators of the probability that a dyad is associated. However, traditional indices rely on the assumptions that the probability to detect a particular individual (p) is either approximately one and/or homogeneous between associated and not associated individuals. Based on marked individuals we develop a likelihood based model to estimate the probability a dyad is associated (ψ) accounting for p < 1 and possibly varying between associated and not associated individuals. The proposed likelihood based model allows for both individual and dyadic missing observations. In addition, the model can easily be extended to incorporate covariate information for modeling p and ψ. A simulation study showed that the likelihood based model approach yield reasonably unbiased estimates, even for low and heterogeneous individual detection probabilities, while, in contrast, traditional indices showed moderate to strong biases. The application of the proposed approach is illustrated using a real data set collected from a population of Commerson's dolphin (Cephalorhynchus commersonii) in Patagonia Argentina. Finally, we discuss possible extensions of the proposed model and its applicability in animal behaviour and ecological studies.     

A dynamic programming implemented resource competition game theoretic model

Resource competition is commonly occurred in animal populations and studied intensively by researchers. Previous studies have applied game theoretic model by finding Nash equilibrium to investigate this phenomenon. However computation of the Nash equilibrium requires an understanding of the payoff matrix that allocates the rewards received by players when they adopt each of the strategies in the game. In our study we present a dynamic programming implemented framework to compute 2 × 2 intraspecific finite resource allocation game's payoff matrix explicitly. We assume that two distinct types of individuals, aggressive and non-aggressive, are in the population. Then we divide the entire animal development period into three different stages: initialization, quasilinear growth and termination. Each stage for each type of players is specified with their own development coefficient, which determines how resource consumption could convert into strength as reward. Each player has equal and finite resource at the beginning of their development and fights against other players in the population to maximize its own potential reward. Based on these assumptions it is reasonable to use backward induction dynamic programming to compute payoff matrix. We present numerical examples for three different types of aggressive individuals and compute the payoff matrices correspondingly. Then we use the derived payoff matrices to determine the Nash equilibrium and Evolutionary Stable Strategy. Our research provide a framework for future quantitative studies on animal resource competition problems and could be expanded to n-players interspecific stochastic asymmetric resource allocation problem by changing some settings of dynamic programming formulation.