A stochastic forest fire growth model

We consider a stochastic fire growth model, with the aim of predicting the behaviour of large forest fires. Such a model can describe not only average growth, but also the variability of the growth. Implementing such a model in a computing environment allows one to obtain probability contour plots, burn size distributions, and distributions of time to specified events. Such a model also allows the incorporation of a stochastic spotting mechanism.

A stochastic weather generation model for Alaska

A specific problem encountered in ecosystem-level simulation of Arctic ecosystems is the depth and extent of the driving variable record. Often, climate records are of short duration, gathered at locations different from the area to be simulated, or do not contain all the variables required by a given model. This paper addresses this problem for ecosystem simulation in Alaska with the development of a weather generator. The generator, called WGENAL, is based on the WGEN climate generator developed and validated in the 48 conterminous states. Because of the extreme variability of weather in Alaska that is not accommodated by the statistical metrics in the earlier model, a new climate generator was developed. WGENAL generates daily values of precipitation, maximum temperature, minimum temperature, solar radiation, and wind run. Precipitation is generated using a Markov chain-gamma model. A two-parameter gamma distribution is used to generate wind run. Temperatures and solar radiation are generated using procedures developed in the earlier study. Validation of the generator shows it provides adequate diurnal and seasonal weather records for Fairbanks. Other comparisons of synthetic weather with observed weather for sites north of the Brooks Range in Alaska are also within the error of the original data.     

A stochastic bioeconomic model for the management of clam farming

The Manila clam Tapes philippinarum is one of the most important commercial mollusc species in Europe. Intensive clam farming takes place in several coastal lagoons of the Northern Adriatic Sea, supporting local economy but raising the problem of the environmental sustainability of this activity. In this work, we propose a bioeconomic model that provides guidelines for an efficient management of intensive clam farming. Clam demography is described by a stochastic model of growth and survival, accounting for the effect of water temperature, seeding substratum and density dependence of vital rates. The model is calibrated on and applied to the case of Sacca di Goro, a lagoon located in the Po River Delta (Northern Italy). We consider two distinct management criteria: the optimisation of the marketable yield and the optimisation of monetary benefits, respectively. The use of a stochastic formulation allows us to reveal the existing trade-off between maximizing the median yield or profit and minimizing its variance. A Pareto analysis shows that seeding in spring or fall on sandy substrata and harvesting 18 months later provides the best compromise between these two contrasting objectives, maximizing profits while minimizing the associated uncertainty level. Finally, we show that seeding clams at high densities (more than 750 clams m⁻² on muddy substrata and more than 1500 elsewhere) can have not only a potentially negative impact on the ecological sustainability of clam farming, but also a negative economic effect.     

A stochastic model for the use of a country park

The subject of this theoretical study is a country park with a very delicate natural environment, located near large urban areas, as a result of which it receives a heavy inflow of visitors.The problem is that of determining the best organization of the park to achieve a distribution of visitors which is compatible with the protection of the natural environment. Therefore a mathematical model is sought which describes the distribution of visitors in relation to the various zones within the park.In this paper the mathematical model and its subsequent calibration are described.     

A two-dimensional simulation model of phosphorus uptake including crop growth and P-response

Modelling nutrient uptake by crops implies considering and integrating the processes controlling the soil nutrient supply, the uptake by the root system and relationships between the crop growth response and the amount of nutrient absorbed. We developed a model that integrates both dynamics of maize growth and phosphorus (P) uptake. The crop part of the model was derived from Monteith's model. A complete regulation of P-uptake by the roots according to crop P-demand and soil P-supply was assumed. The soil P-supply to the roots was calculated using a diffusion equation and assuming that roots behave as zero-sinks. The actual P-uptake and crop growth were calculated at each time step by comparing phosphate and carbohydrate supply–demand ratios. Model calculations for P-uptake and crop growth were compared to field measurements on a long term P-fertilization trial. Three P-fertilization regimes (no P-fertilization, 42.8 kg P ha⁻¹ year⁻¹ and 94.3 kg P ha⁻¹ year⁻¹) have led to a range of P-supply. Our model correctly simulated both the crop development and growth for all P-treatments. P-uptake was correctly predicted for the two non-limiting P-treatments. Nevertheless, for the limiting P-treatment, P-uptake was correctly predicted during the early period of growth but it was underestimated at the last sampling date (61 day after sowing). Several arguments for under-prediction were considered. However, most of them cannot explain the observed magnitude in discrepancy. The most likely reason might be the fact that biomass allocation between shoot and root must be modelled more precisely. Despite this mismatch, the model appears to provide realistic simulations of the soil–plant dynamic of P in field conditions.     

A two-dimensional inviscid model of the gravity-current head by Lagrangian block simulation

A two-dimensional inviscid model of the gravity-current head produced by the release of a relatively small volume of dense fluid from behind a tall lock gate is constructed by Lagrangian block simulation. Three numerical experiments are conducted for the lock’s height-to-length aspect ratios H/L _o  = 8, 4 and 2. The front speeds obtained by the simulations agree with the laboratory observation for a similar range of aspect ratios. The floor velocity in the wake behind these heads is found to be greater than their front speed. The high floor velocity is caused by the impingement of the coherent wake vortex on the floor. It is a condition that permits these gravity-current heads to maintain their structural integrity so that the fine sediments can travel with the head over long distances on the ocean floor. The structural coherence of the current head depends on the lock aspect ratio. The gravity-current head produced by the release from the lock with the highest aspect ratio of H/L _o  = 8 is most coherent and relatively has the greatest floor velocity and the least trailing current behind the head.     

Analytical methods for a stochastic mainland-island metapopulation model

We study a class of chain-binomial metapopulation models, giving special attention to the ‘mainland-island’ configuration, where patches receive immigrants from an external source. We evaluate the distribution of the number n_t of occupied patches at any census time t and establish a law of large numbers that identifies a deterministic trajectory which can be used to approximate the process when the number of patches is large. We also establish a central limit law, which shows that the fluctuations about this trajectory are approximately normally distributed. We describe briefly much finer results that can be used for model calibration.     

A semi-coupled model for determining the distribution of two-dimensional coherent structures in open channel flow

Environmental Fluid Mechanics - Mixing layers and associated large-scale turbulent structures are some of the most common features of turbulent shallow water flow. Due to their...     

Model correlation in stochastic forest simulators—A case of multilevel multivariate model for seedling establishment

Forest development can be predicted by the use of forest simulators based on various statistical models describing the forest and its dynamics. One potential approach to study the reliability of the simulators is to utilise Monte Carlo simulation techniques to generate a predictive distribution of a forest characteristic. One problem in examining the effect of model uncertainty in forestry decision making, however, is correlation between the models. If this is not taken into account, predictions of the model systems may become biased, and the effect of errors on decision making may be underestimated. In reality, the models often are interdependent, but the correlations usually are not known because the models have been estimated in separate studies. The aim of this paper is to study the impacts of between-model dependencies on the predictive distribution of forest characteristics by Monte Carlo simulation techniques. We utilise a case of predicting seedling establishment of planted Norway spruce (Picea abies (L.) Karst.) stands as an example with multivariate multilevel model structures. Regardless of low cross-correlations between the models, ignoring them led to significant underestimation of the amount of competing broadleaves to be removed in pre-commercial thinning. Therefore, we recommend that between-model dependencies are clarified and considered in stochastic simulations. In our case, between-model interdependencies can be reliably estimated with a limited dataset. In addition, estimating the models separately and using the model residuals to estimate interdependencies between models were also sufficient to take the between-model dependencies into account when producing stochastic predictions for silvicultural decision making.     

Throughflow analysis: A stochastic approach

Ecological network analysis (ENA), predicated on systems theory and Leontiev input–output analysis, is a method widely used in ecology to reveal ecosystem properties. An important ecosystem property computed in ENA is throughflows, the amount of matter/energy leaving each compartment of the ecosystem. Throughflows are analyzed via a matrix representing their relationships to the driving input at the boundary. Network particle tracking (NPT) builds on ENA to offer a Lagrangian particle method that describes the activity of the ecosystem at the microscopic level. This paper introduces a Lagrangian throughflow analysis methodology using NPT and shows that the NPT throughflow matrix, , agrees with the conventional ENA throughflow matrix, , for ecosystems at steady-state with donor-controlled flows. The matrix is computed solely from the pathways (particles’ histories) generated by NPT simulations and its average over multiple runs of the algorithm with longer simulation time agrees with the Eulerian matrix (Law of Large Numbers). While the traditional NEA throughflow analysis is mostly used with steady-state ecosystem models, the Lagrangian throughflow analysis that we propose can be used with non-steady-state models and paves the way for the development of dynamic throughflow analysis.     

Local population dynamics of an invasive tree species with a complex life-history cycle: A stochastic matrix model

Biological invasions are widely accepted as having a major impact on ecosystem functioning worldwide, giving urgency to a better understanding of the factors that control their spread. Modelling tools have been developed for this purpose but are often discrete-space, discrete-time spatial-mechanistic models that adopt a computer simulation approach and resist mathematical analysis. We constructed a simple demographic matrix model to explore the local population dynamics of an invasive species with a complex life history and whose invasive success depends on resource availability, which occurs stochastically. As a case study we focused on the American black cherry (Prunus serotina Ehrh.), a gap-dependent tree able both to constitute a long-living seedling bank under unfavourable light conditions and to resprout vigorously once cut-down, which is invading European temperate forests. The model used was a stage-classified matrix population model (i.e., Lefkovitch matrix), integrating environmental stochasticity. Stochastic matrix projection analysis was combined with elasticity analysis and stochastic simulations to search for the species’ ‘Achille heel’. As expected, the population growth rate (i.e., Lyapunov exponent), which measures the risk of P. serotina invasion at the stand scale, increased with light frequency. There was a critical value above which the population of P. serotina explodes and below which it locally goes extinct. The resprouting capacity usually speed up the invasion but appeared to play a minor role. The mean duration of stand invasion was measured and important life stage transitions that mostly contribute to the local stochastic growth rate were identified. Some relevant management implications are discussed and the interest of such models for the understanding of demographic characteristics of invasive species is stressed.     

Simulation of small bird populations. I. Development of a stochastic model

A computer model was developed to simulate the fate of small populations of birds. It uses general and easily available data as input. Monte-Carlo techniques are used and a survival probability is calculated for every population member four times per simulated year. The model allows for density-dependence in winter survival and also in fecundity.Simulation results are used to compile standard age-specific life-tables for all complete cohorts generated. A mean life-table is also made. The survivor functions, both accumulated and mean, are contrasted with control functions and tested for significance.The model has been applied to classical population data in ornithology, namely those for the great tit and the tawny owl in Wytham Woods (Oxford, UK). There was a fair agreement between simulation results and field data.     

Migration effects in a stochastic multipopulation model for African bee population dynamics

The rate of northern migration of the Africanized honey bee (AHB) in the United States has recently slowed dramatically. This paper investigates the impact of migration on the equilibrium size distributions of a particular stochastic multipopulation model, namely a coupled logistic power law model. The bivariate equilibrium size distribution of the model is derived and illustrated with parameter values used to describe AHB population dynamics. In the model, the difference between the equilibrium sizes of the two populations is a measure of the effect of migration. The distribution of this difference may be approximated by a normal distribution. The mean and variance parameters for the normal are predicted accurately by a second-order regression model based on the migration rate and the maximum size of the first population. The methodology is general, and should be useful in studying the migration effect in many other applications with one-way migration.     

Automatic sensitivity analysis of a finite volume model for two-dimensional shallow water flows

Given a numerical model for solving two-dimensional shallow water equations, we are interested in the robustness of the simulation by identifying the rate of change of the water depths and discharges with respect to a change in the bottom friction coefficients. Such a sensitivity analysis can be carried out by computing the corresponding derivatives. Automatic differentiation (AD) is an efficient numerical method, free of approximation errors, to evaluate derivatives of the objective function specified by the computer program, Rubar20 for example. In this paper AD software tool Tapenade is used to compute forward derivatives. Numerical tests were done to show the robustness of the model and to demonstrate the efficiency of these AD-derivatives.     

Deducing an upper bound to the horizontal eddy diffusivity using a stochastic Lagrangian model

We present a method for estimating the upper bound of the horizontal eddy diffusivity using a non-stationary Lagrangian stochastic model. First, we identify a mixing barrier using a priori evidence (e.g., aerial photographs or satellite imagery) and using a Lagrangian diagnostic calculated from observed or modeled spatially non-trivial, time-dependent velocities [for instance, the relative dispersion (RD) or finite time Lyapunov exponent (FDLE)]. Second, we add a stochastic component to the observed (or modeled) velocity field. The stochastic component represents sub-grid stochastic diffusion and its mean magnitude is related to the eddy diffusivity. The RD of Lagrangian trajectories is computed for increasing values of the eddy diffusivity until the mixing barrier is no longer present. The value at which the mixing barrier disappears provides a dynamical estimate of the upper bound of the eddy diffusivity. The erosion of the mixing barrier is visually observed in numerical simulations, and is quantified by computing the kurtosis of the RD at each value of the eddy diffusivity. We demonstrate our method using the double gyre circulation model and apply it to high frequency (HF) radar observations of surface currents in the Gulf of Eilat.     

Coupling soil water and shoot dynamics in three grass species: A spatial stochastic model on water competition in Neotropical savanna

Savannas are ecosystems known for their high environmental and economic value. They cover at least 20% of the global land surface and, in some cases, can act as a boundary between tropical rainforest and deserts. Water is an important determinant of savanna ecosystems.In this paper, we present a theoretical stochastic model of root competition for water, which couples, soil water availability, phenology, and root and shoot architecture applied to three Neotropical savanna grasses. Soil moisture was simulated using a daily balance, as proposed by Rodriguez-Iturbe et al. [Rodriguez-Iturbe, I., Porporato, A., Ridolfi, L., Isham, V., Cox, D.R., 1999. Probabilistic modelling of water balance at a point: the role of climate, soil and vegetation. Proc. R. Soc. London, Ser. A 455, 3789–3805.]. To simulate rainfall stochasticity, we used daily precipitation data from the airport weather station in the State of Barinas, Venezuela, for the period 1991–2007. Competition among neighbouring plants took into account the spatial distribution of the individuals. As a final step, the model allowed us to calculate the shoot dynamic of the species as a function of soil water availability.Using these data, we compared the behaviour of isolated plants, pairs and trios, and we found below-ground competition to be a fundamental component of global (shoot + root) competition. Finally, our model suggests various circumstances that allow poor competitor plants to coexist in competition for water with more successful competitors. Apparently, this is not only due to transpiration rates, but also to differences in shoot emergence and shoot growth.     

The pattern of species turnover resulting from stochastic population dynamics: The model and field data

The model of random population dynamics in a sampling site returns geometric distribution of longevities of continuous presence (=persistence) and Poisson distribution of the presence–absence transitions. This discrete-time stochastic process describes the presence–absence pattern observed in the beetles surveyed 6 years on Mount Carmel, Israel. Homogeneous pools of species mostly on the Families rank, exhibit the predicted by the model patterns. Conformity to an ergodic hypothesis is the criterion of ecological homogeneity. This criterion assumes the equivalence of short-term behavior of entire pool and long-term behavior of any species from this pool. The pool of all 801 species of Order Coleoptera does not match the model. Thus a taxon of an arbitrary rank may not be considered a priory as a unit of ecological study. Determined from field data parameters of the model are biased and magnitude of the bias depends on longevity of the survey. Parameter of distribution depends also on species tolerance, which is the level adaptation of given species to given environment in given time interval. Random process of species turnover may be considered as a game of species to gain their presence against deteriorative fluctuations of environmental conditions.     

On interacting bee/mite populations: a stochastic model with analysis using cumulant truncation

Parasitism by the Varroa mite has had recent drastic impact on both managed and feral bee colonies. This paper proposes a stochastic population dynamics model for interacting African bee colony and Varroa mite populations. Cumulant truncation procedures are used to obtain approximate transient cumulant functions, unconstrained by the usual assumption of bivariate Normality, for an assumed large-scale model. The apparent size of the variance and skewness functions suggest the importance of the proposed truncation procedure which retains some higher-order cumulants, but determining the accuracy of the approximations is problematical. A smaller-scale bee/Varroa mite model is hence proposed and investigated. The accuracy for the means is exceptional, for the second-order cumulants is moderate, and for some third-order cumulants is poor. Notwithstanding the poor accuracy of a skewness approximation, the saddlepoint approximations for the marginal transient population size distributions are excellent. The cumulant truncation methodology is very general, and research is continuing in its application to this new class of host-parasite models.     

A stochastic simulation model of brown shrimp (Penaeus aztecus ives) growth,movement, and survival in Galveston Bay,Texas

A stochastic simulation model of brown shrimp (Penaeus aztecus Ives) population dynamics in Galveston Bay, Texas, is described, validated, and used to evaluate the effects of management alternatives and changing environmental conditions on shrimp dynamics. The model is composed of submodels representing: (1) recruitment, (2) growth, (3) natural mortality, (4) fishing mortality, and (5) emigration of brown shrimp. The model predicts significant changes in total annual harvest from the food shrimp, bait, and recreational fisheries resulting from (1) closure of the bay system to all fishing except during the spring and fall open seasons, (2) two-week postponement of the opening and closing of the open seasons for the food shrimp fishery, (3) a 2.5°C increase and (4) a 2.5°C decrease in mean water temperature, (5) an 80% increase and (6) an 80% decrease in fishing effort. No significant change in the total annual harvest is predicted when the food shrimp fishing season is extended from May 15 through December 15. Sensitivity analysis suggests that field experimentation designed specifically to test the hypothesis of a 60-day time lag between brown shrimp recruitment into the bays and exposure to the fishery should receive high priority. Simulation results are discussed within a management framework.     

稻草型生物有机肥对萝卜的作用效果

为推广应用稻草型生物有机肥,采用田间小区试验研究了稻草型生物有机肥对萝卜(Raphanus sativus)功能叶叶绿素含量、碳氮代谢关键酶活性、萝卜产量和品质的影响.结果表明:稻草型生物有机肥处理Ⅰ与等NPK养分施用量的纯化肥处理Ⅱ和菜枯肥处理Ⅲ相比,可提高萝卜功能叶叶绿素含量、防止功能叶早衰;提高硝酸还原酶、蔗糖合成酶、蔗糖磷酸合成酶三种碳氮代谢关键酶活性.处理Ⅰ使萝卜的产量分别比处理Ⅱ和处理Ⅲ提高4.48%、6.01%,维生素C分别提高22.48%、28.24%,可溶性糖含量分别提高10.39%、19.91%,萝卜硝酸盐含量分别下降8.78%和16.67%,且以上4个指标处理Ⅰ与处理Ⅱ和处理Ⅲ的差异均达极显著水平,此外亚硝酸盐含量也明显降低.