On the latent state estimation of nonlinear population dynamics using Bayesian and non-Bayesian state-space models

Nonlinear state-space models have been increasingly applied to study population dynamics and data assimilation in environmental sciences. State-space models can account for process error and measurement error simultaneously to correct for the bias in the estimates of system state and model parameters. However, few studies have compared the performance of different nonlinear state-space models for reconstructing the state of population dynamics from noisy time series. This study compared the performance of the extended Kalman filter (EKF), unscented Kalman filter (UKF) and Bayesian nonlinear state-space models (BNSSM) through simulations. Synthetic population time series were generated using the theta logistic model with known parameters, and normally distributed process and measurement errors were introduced using the Monte Carlo simulations. At higher levels of nonlinearity, the UKF and BNSSM had lower root mean square error (RMSE) than the EKF. The BNSSM performed reliably across all levels of nonlinearity, whereas increased levels of nonlinearity resulted in higher RMSE of the EKF. The Metropolis–Hastings algorithm within the Gibbs algorithm was used to fit the theta logistic model to synthetic time series to estimate model parameters. The estimated posterior distribution of the parameter θ indicated that the 95% credible intervals included the true values of θ (=0.5 and 1.5), but did not include 1.0 and 0.0. Future studies need to incorporate the adaptive Metropolis algorithm to estimate unknown model parameters for broad applications of Bayesian nonlinear state-space models in ecological studies.     

Validation of a multispecies forest dynamics model using 50-year growth from Eucalyptus forests in eastern Australia

One of the key problems confronting ecological forecasting is the validation of computer models. Here we report successful validation of a forest dynamics model Ecosystem Dynamics Simulator (EDS), adapted from the JABOWA-II forest succession model. This model and many variants derived from it have successfully simulated growth dynamics of uneven-aged mixed forests under changing environment with a moderate amount of input data. But rarely are adequate time-series data available for quantitative model validation. This study tested the performance of EDS in projecting the tree density, tree diameter at breast height (dbh), tree height, basal area and aboveground biomass of uneven-aged, mixed species sclerophyll forests in St. Mary state forests of eastern Australia. The test data were collected between 1951 and 2005. Every tree was uniquely numbered, tagged and measured in consecutive re-measurements. Projected growth attributes were compared with those observed in an independent validation dataset. The model produced satisfactory projections of tree density (91.7%), dbh (92.3%), total tree height (82.8%), basal area (89.3%) and aboveground biomass (87.6%) compared to the observed attributes. These results suggest that the EDS model can provide reasonable capability in projecting growth dynamics of uneven-aged, mixed species sclerophyll forests.     

Statistical inference on patch-specific survival and movement rates from marked animals

Empirical estimates of patch-specific survival and movement rates are needed to parametrize spatially explicit population models, and for inference on the effects of habitat quality and fragmentation on populations. Data from radio-marked animals, in which both the fates and habitat locations of animals are known over time, can be used in conjunction with continuous-time proportional hazards models to obtain inferences on survival rates. Discrete-time conditional logistic models may provide inference on both survival and movement rates. We use Monte Carlo simulation to investigate accuracy of estimates of survival from both approaches, and movement rates from conditional logistic regression, for two habitats. Bias was low (relative bias < 0.04) and interval coverage accurate (close to the nominal 0.95) for estimates of habitat effect on survival based on proportional hazards. Bias was high ( relative bias 0.60) and interval coverage poor ( = 0.26 vs. nominal 0.95) for estimates of habitat effect based on conditional logistic regression; bias was especially influenced by heterogeneity in survival and the shape of the hazard function, whereas both bias and coverage were affected by ‘memory’ effects in movement patterns. Bias estimates of movement rate was low ( relative bias < 0.05), but interval coverage was poor ( = 0.48–0.80), possibly as a result of poor performance of a Taylor series estimate of variance. An example is provided from a radio-telemetry study of 47 wintering American woodcock (Scolopax minor), illustrating practical difficulties in field studies to parametrize these models. We also discuss extensions of continuous-time models to explicitly include a movement process, and further examine tradeoffs between continuous and discrete models.     

扁刺栲在两种类型林分中的生长过程分析

通过对扁刺栲—华木荷林区针阔混交林、次生阔叶林的群落调查以及扁刺栲的树干解析．研究结果表明：(1)扁刺栲在针阔混交林与次生阔叶林中,胸径快速生长期分别在a8～12和a10～14之间,生长高峰值分别出现在a10和a12,最大值分别为1．07cm和0．85cm．(2)扁刺栲在针阔混交林与次生阔叶林中,树高快速生长期分别在a6～10和a10～14之间,生长高峰值分别出现在a8和a10,最大值分别为0．55m和0．56m．(3)在针阔混交林中,16a生扁刺栲单株材积达0．0134m^3,而在次生阔叶林中只有0．0103m^3．在分析不同林分中扁刺栲生长差异及其原因的基础上,建议对次生阔叶林经营应采用动态管理．     

A diameter increment model for Crimean pine (Pinus nigra Arnold) and Calabrian pine (Pinus brutia Ten.) stands in Isparta region, Turkey

The purpose of this research was to test the precision of a diameter increment model for the estimation of future periodic diameter increment. Individual trees of Crimean pine (Pinus nigra Arnold) and Calabrian pine (Pinus brutia Ten.) located in both natural and plantation stands were selected. For that reason, normal closed canopy, pure, even-aged and undisturbed stands were examined. In 2002, plots were sampled in three natural and three plantation stands in Isparta region of Turkey. The number of sampling points in sample plots ranged from 19 to 55. In each sampling point, a subject tree and six competitors were selected. In each sampling point, subject tree and competitor trees were stem mapped (x and y coordinate system), and diameter (dbh), total height, age, and 10-yrs radial increment recorded. The predictors of a distance dependent diameter increment model were chosen that included tree level (diameter (d), competition index (CI), and age (t)) and stand level (basal area (G), and site index (SI)) characteristics as well as their transformations. The best fit index of the regression model was pursued in trials with variable combinations. The models explained 65%, 60%, 68% and 50% of the variation in individual tree diameter increment of Crimean pine and Calabrian pine for both natural and plantations stands, respectively. These models can be estimated diameter increment of individual trees at highly significant level (p<0.001).     

Dynamic growth model for Scots pine (Pinus sylvestris L.) plantations in Galicia (north-western Spain)

In this study we developed a dynamic growth model for Scots pine (Pinus sylvestris L.) plantations in Galicia (north-western Spain). The data used to develop the model were obtained from a network of permanent plots, of between 10 and 55-year-old, which the Unidade de Xestión Forestal Sostible (Sustainable Forest Management Unit) of the University of Santiago de Compostela has set up in pure plantations of this species of pine in its area of distribution in Galicia. In this model, the initial stand conditions at any point in time are defined by three state variables (number of trees per hectare, stand basal area and dominant height), and are used to estimate stand volume, classified by commercial classes, for a given projection age. The model uses three transition functions expressed as algebraic difference equations of the three corresponding state variables used to project the stand state at any point in time. In addition, the model incorporates a function for predicting initial stand basal area, which can be used to establish the starting point for the simulation. This alternative should only be used when the stand is not yet established or when no inventory data are available. Once the state variables are known for a specific moment, a distribution function is used to estimate the number of trees in each diameter class, by recovering the parameters of the Weibull function, using the moments of first and second order of the distribution (arithmetic mean diameter and variance, respectively). By using a generalized height–diameter function to estimate the height of the average tree in each diameter class, combined with a taper function that uses the above predicted diameter and height, it is then possible to estimate total or merchantable stand volume.     

Spatially explicit modeling of overstory manipulations in young forests: Effects on stand structure and light

Young forests can be manipulated in diverse ways to enhance their ecological values. We used stem maps from two dense, second-growth stands in western Washington and a spatially explicit light model (tRAYci) to simulate effects of five silvicultural manipulations on diameter distribution, species composition, spatial patterning, and light availability. Each treatment removed 30% of the basal area, but differed in how trees were selected for removal. Three primary treatments were thin from below (removing the smallest trees), random thin (removing trees randomly), and gap creation (removing all trees in circles ∼1 tree height in diameter). Two additional treatments combined elements of these approaches: random ecological thin (a mixture of thin from below and random thin) and structured ecological thin (a mixture of thin from below and gap creation).     

A universal approach to estimate biomass and carbon stock in tropical forests using generic allometric models

Allometric equations allow aboveground tree biomass and carbon stock to be estimated from tree size. The allometric scaling theory suggests the existence of a universal power-law relationship between tree biomass and tree diameter with a fixed scaling exponent close to 8/3. In addition, generic empirical models, like Chave's or Brown's models, have been proposed for tropical forests in America and Asia. These generic models have been used to estimate forest biomass and carbon worldwide. However, tree allometry depends on environmental and genetic factors that vary from region to region. Consequently, theoretical models that include too few ecological explicative variables or empirical generic models that have been calibrated at particular sites are unlikely to yield accurate tree biomass estimates at other sites. In this study, we based our analysis on a destructive sample of 481 trees in Madagascar spiny dry and moist forests characterized by a high rate of endemism (> 95%). We show that, among the available generic allometric models, Chave's model including diameter, height, and wood specific gravity as explicative variables for a particular forest type (dry, moist, or wet tropical forest) was the only one that gave accurate tree biomass estimates for Madagascar (R2 > 83%, bias < 6%), with estimates comparable to those obtained with regional allometric models. When biomass allometric models are not available for a given forest site, this result shows that a simple height-diameter allometry is needed to accurately estimate biomass and carbon stock from plot inventories.     

Crown ratio influences allometric scaling in trees

Allometric theories suggest that the size and shape of organisms follow universal rules, with a tendency toward quarter-power scaling. In woody plants, however, structure is influenced by branch death and shedding, which leads to decreasing crown ratios, accumulation of heartwood, and stem and branch tapering. This paper examines the impacts on allometric scaling of these aspects, which so far have been largely ignored in the scaling theory. Tree structure is described in terms of active and disused pipes arranged as an infinite branching network in the crown, and as a tapering bundle of pipes below the crown. Importantly, crown ratio is allowed to vary independently of crown size, the size of the trunk relative to the crown deriving from empirical results that relate crown base diameter to breast height diameter through crown ratio. The model implies a scaling relationship in the crown which reduces to quarter-power scaling under restrictive assumptions but would generally yield a scaling exponent somewhat less than three-quarters. For the whole tree, the model predicts that scaling between woody mass and foliage depends on crown ratio. Measurements on three boreal tree species are consistent with the model predictions.     

3 forest simulation model

The 3 forest simulation model is a process model of tree growth, carbon and nitrogen dynamics in a single-species, even-aged forest stand. It is based on the model. Major changes include the computation of sun angle and radiation as a function of latitude and day of the year, the closed-form integration of canopy production as a function of day and hour, the introduction of tree number, height, and diameter as separate state variables, and different growth strategies, mortalities, and resulting self-thinning as function of crowding competition.The tree/soil system is described by a set of nonlinear ordinary differential equations for the state variables: tree number, base diameter, tree height, wood biomass, nitrogen in wood, leaf mass, fine root mass, fruit biomass, assimilate, carbon and nitrogen in litter, carbon and nitrogen in soil organic matter, and plant-available nitrogen. The model includes explicit formulations of all relevant ecophysiological processes such as: computation of radiation as a function of seasonal time, daytime and cloudiness, light attenuation in the canopy, and canopy photosynthesis as function of latitude, seasonal time, and daytime, respiration of all parts, assimilate allocation, increment formation, nitrogen fixation, mineralization, humification and leaching, forest management (thinning, felling, litter removal, fertilization etc.), temperature effects on respiration and decomposition, and environmental effects (pollution damage to photosynthesis, leaves, and fine roots). Only ecophysiological parameters which can be either directly measured or estimated with reasonable certainty are used. 3 is a generic process model which requires species- and site-specific parametrization. It can be applied to deciduous and coniferous forests under tropical, as well as temperate or boreal conditions.The paper presents a full documentation of the mathematical model as well as representative simulation results for spruce and acacia.     

treedyn3 forest simulation model

The treedyn3 forest simulation model is a process model of tree growth, carbon and nitrogen dynamics in a single-species, even-aged forest stand. It is based on the treedyn model. Major changes include the computation of sun angle and radiation as a function of latitude and day of the year, the closed-form integration of canopy production as a function of day and hour, the introduction of tree number, height, and diameter as separate state variables, and different growth strategies, mortalities, and resulting self-thinning as function of crowding competition.The tree/soil system is described by a set of nonlinear ordinary differential equations for the state variables: tree number, base diameter, tree height, wood biomass, nitrogen in wood, leaf mass, fine root mass, fruit biomass, assimilate, carbon and nitrogen in litter, carbon and nitrogen in soil organic matter, and plant-available nitrogen. The model includes explicit formulations of all relevant ecophysiological processes such as: computation of radiation as a function of seasonal time, daytime and cloudiness, light attenuation in the canopy, and canopy photosynthesis as function of latitude, seasonal time, and daytime, respiration of all parts, assimilate allocation, increment formation, nitrogen fixation, mineralization, humification and leaching, forest management (thinning, felling, litter removal, fertilization etc.), temperature effects on respiration and decomposition, and environmental effects (pollution damage to photosynthesis, leaves, and fine roots). Only ecophysiological parameters which can be either directly measured or estimated with reasonable certainty are used. treedyn3 is a generic process model which requires species- and site-specific parametrization. It can be applied to deciduous and coniferous forests under tropical, as well as temperate or boreal conditions.The paper presents a full documentation of the mathematical model as well as representative simulation results for spruce and acacia.     

Tsunami mitigation by coastal vegetation considering the effect of tree breaking

Damage to vegetation by tsunami moment and reduction of potential tsunami force are discussed based on a numerical simulation. A numerical model based on two-dimensional nonlinear long-wave equations that include drag forces and turbulence-induced shear force due to the presence of vegetation was developed to estimate tree breaking. The numerical model was then applied to a coastal forest where two dominant tropical vegetation species, Pandanus odoratissimus and Casuarina equisetifolia, were considered. The threshold water depth for tree breaking increased with increasing forest width, and the analysis was consistent with the field investigation results that the critical tsunami water depth for breaking is around 80% of the tree height for P. odoratissimus. C. equisetifolia is stronger than P. odoratissimus against tsunami action, but P. odoratissimus can reduce a greater tsunami force than C. equisetifolia due to its complex of aerial root structures. Even if breakage occurs, P. odoratissimus still has high potential to reduce the tsunami force due to its dense aerial root structures. Previous numerical models that do not include the breaking phenomena may overestimate the vegetation effect for reducing tsunami force. The combination of P. odoratissimus and C. equisetifolia is recommended as a vegetation bioshield to protect coastal areas from tsunami hazards.     

基于植被指数和神经网络的热带人工林地上蓄积量遥感估测

热带森林作为陆地生态系统的组成成分之一,研究其蓄积量估测对我们了解其在全球碳循环中的地位和作用有很重要的意义.但遥感估测森林生态参数的精度如何,还是个不确定的问题.利用LANDSAT-TM数据,基于森林清查数据和遥感技术,以尾叶桉和加勒比松为例,对中国南方地区人工林蓄积量估测进行了尝试研究.首先,通过测量样方胸径、树高,建立森林蓄积量估算模型.其次,通过对比分析不同植被指数与森林蓄积量之间的关系,选择合适植被指数组合,建立多元回归和神经网络模型.结果表明:单波段TM数据和大多数植被指数与蓄积量相关性并不好.神经网络比回归分析模拟效果好.而多元回归和神经网络模型大大提高预测精度.本研究方法对大面积的森林蓄积量估测具有一定的参考价值.     

Introducing effects of temperature and CO2 elevation on tree growth into a statistical growth and yield model

Impacts of elevated temperature and CO₂ on tree growth were introduced into a statistical growth and yield model for Finnish conditions based on corresponding predictions obtained from a physiological growth model. This one-way link between models was made by means of species-specific transfer functions describing the increase in stem volume growth of trees as a function of elevated temperature and CO₂, stand density and the tree's competition status in a stand of Scots pine (Pinus sylvestris), silver birch (Betula pendula) and Norway spruce (Picea abies). This method allows the inner dynamics of the statistical model to be followed when the impacts of temperature and CO₂ elevation on tree growth are introduced into the calculation of volume growth and further allocated between diameter and height growth. In this way compatibility with previous predictions of tree growth by means of statistical models and related model systems under current climatic conditions could be retained.The performance of the statistical model with species-specific transfer functions was evaluated by comparing its predictions with corresponding predictions given by a physiological model under conditions of elevated temperature and CO₂. These calculations revealed that the growth response of individual trees to elevated temperature and CO₂ can be introduced into the statistical model from a physiological growth model with an outcome that results in fairly satisfactory growth responses at the stand level as well.     

Statistical treatment for the wet bias in tree-ring chronologies: a case study from the Interior West,USA

Dendroclimatic research has long assumed a linear relationship between tree-ring increment and climate variables. However, ring width frequently underestimates extremely wet years, a phenomenon we refer to as ‘wet bias’. In this paper, we present statistical evidence for wet bias that is obscured by the assumption of linearity. To improve tree-ring-climate modeling, we take into account wet bias by introducing two modified linear regression models: a linear spline regression (LSR) and a likelihood-based wet bias adjusted linear regression (WBALR), in comparison with a quadratic regression (QR) model. Using gridded precipitation data and tree-ring indices of multiple species from various sites in Utah, both LSR and WBALR show a significant improvement over the linear regression model and out-perform QR in terms of in-sample \({R}^{2}\) and out-of-sample MSE. This further shows that the wet bias emerges from nonlinearity of tree-ring chronologies in reconstructing precipitation. The pattern and extent of wet bias varies by species, by site, and by precipitation regime, making it difficult to generalize the mechanisms behind its cause. However, it is likely that dis-coupling between precipitation amounts (e.g., percent received as rain/snow or percent infiltrating the soil) and its availability to trees (e.g., root zone dynamics), is the primary mechanism driving wet bias.     

Modeling individual tree mortality for crimean pine plantations

Individual tree mortality model was developed for crimean pine (Pinus nigra subsp. pallasiana) plantations in Turkey. Data came from 5 year remeasurements of the permanent sample plots. The data comprises of 115 sample plots with 5029 individual trees. Parameters of the logistic equation were estimated using weighted nonlinear regression analysis. Approximately 80% of the observations were used for model development and 20% for validation. The explicatory variables in the model were ratio of diameter of the subject tree and basal area mean diameter of the sample plot as measure of competition index for individual trees, basal area and site index. All parameter estimates were found highly significant (p < 0.001) in predicting mortality model. Chi-square statistics indicate that the most important variable is d / d(q), the second most important is site index, and the third most important predictor is stand basal area. Examination of graphs of observed vs. predicted mortality rates reveals that the mortality model is well behaved and match the observed mortality rates quite well. Although the phenomenon of mortality is a stochastic, rare and irregular event, the model fit was fairly good. The logistic mortality model passed a validation test on independent data not used in parameter estimation. The key ingredient for obtaining a good mortality model is a data set that is both large and representative of the population under study and the data satisfy both requirements. The mortality model presented in this paper is considered to have an appropriate level of reliability.     

Correcting climate model simulations in Heihe River using the multivariate bias correction package

The simulations from climate models require bias correction prior to use in impact assessments or when used as predictors in statistical or dynamic downscaling models. Recent works have sought to address each of these limitations and the results are the Multivariate Recursive Nesting Bias Correction (MRNBC) and Multivariate recursive Quantile-matching Nested Bias Correction (MRQNBC) methods. The model was applied to a mountain region of Heihe River. A comparison of the historical and generated statistics shows that the model preserves all the important characteristics of meteorological variables at daily, monthly, seasonally and annual time scales. This study has documented the performance of Multivariate Recursive Nesting Bias Correction to remove the discrepancy between the predictors in the simulated GCM and the reanalysis NCEP data and assess the projected future precipitation accuracy in the headwater region of Heihe River. A relatively high spatial resolution GCM outputs—ACCESS1-3—from the CMIP5 Earth System Models (ESMs) was employed to downscale for the historical 1960–2005 and the future period 2010–2100 under the scenarios of Representative Concentration Pathways RCP4.5 and RCP8.5. The MRNBC method can dramatically increase the performance of the simulated precipitation data. Verified by statistical score metrics applied for evaluation of the results, the developed method appears to be an important statistical tool in the correction of the bias between the GCM output and the reanalysis data, leading to significant improvements in the predictive performance accuracy of the precipitation projections. The projected precipitation under RCP8.5 appeared to exhibit the significant increasing trend relative to the RCP4.5 scenario in the headwater region of Heihe River. Future precipitation will increasing by 8% and 20% for near and long term period under RCP4.5 and increasing 14% and 37% for near and long term period, under RCP8.5, respectively.     

长白山暗针叶林建群种竞争关系的研究

根据野外调查数据,利用Hegyi单木竞争指数模型,定量地研究了长白山暗针叶内主要建群种（以鱼鳞云杉为例）的种内、种间竞争关系,结果表明：暗针叶林中鱼鳞云杉种内竞争强度随着林木径级的增大而迅速减小,也就是说,在暗叶叶林内,鱼鳞云杉种群由于自然调节的作用,随着林木径级的增大,林木因自然稀疏过程导致部分个体死亡,加大了株间距离,因此对光、温、水等生态条件及资源的竞争强度降低,暗针叶林内鱼鳞云杉种内种间竞争强度的顺序为：鱼鳞云杉－鱼鳞云杉＞鱼鳞云杉－臭冷杉＞鱼鳞云杉－红松＞鱼鳞云杉－长白落叶松＞鱼鳞云杉－岳桦＞鱼鳞云杉－杂木,鱼鳞云杉种内种间竞争强度可用幂函数关系CI＝AD－B（其中CI为竞争强度：D为对象木胸径;A、B为参数）表示,并可模拟和预测鱼鳞云杉种内种间竞争强度,从预测结果中发现：当鱼鳞云杉胸径达到35cm后,竞争强度变得小,且变化幅度不大,说明此时该生态系统已基本上达到稳定状态,这可为暗叶林的经营管理提供依据,即在鱼鳞云杉胸径达到35cm之间辅以必要的人工管理措施,以期使得该生态系统尽快达到稳定状态,图2表4参10     

细叶桉造林密度试验初报

在细叶桉造林试验中，设计了7种密度，结果表明，在造林的当年，高密度林分能较早形成林分环境，有利于早期生长，而后来其个体间较早开始进行营养空间的竞争，部分个体生长受到抑制。随着时间的推移，高密度林分不利于冠径的发展。相应地低密度林分呈现出径生长较快的趋势，并且这种趋势随着树木长大而愈来愈明显。单株材积随密度的变化趋势与径的变化规律相一致。林分的蓄积量更大程度地受株数的作用，密度越大，蓄积量越大。建议细叶桉小径材和纸浆材的造林密度为2500株／hm^2。     

Modeling patterns of nonlinearity in ecosystem responses to temperature, CO2, and precipitation changes.

It is commonly acknowledged that ecosystem responses to global climate change are nonlinear. However, patterns of the nonlinearity have not been well characterized on ecosystem carbon and water processes. We used a terrestrial ecosystem (TECO) model to examine nonlinear patterns of ecosystem responses to changes in temperature, CO2, and precipitation individually or in combination. The TECO model was calibrated against experimental data obtained from a grassland ecosystem in the central United States and ran for 100 years with gradual change at 252 different scenarios. We primarily used the 100th-year results to explore nonlinearity of ecosystem responses. Variables examined in this study are net primary production (NPP), heterotrophic respiration (R(h)), net ecosystem carbon exchange (NEE), runoff, and evapotranspiration (ET). Our modeling results show that nonlinear patterns were parabolic, asymptotic, and threshold-like in response to temperature, CO2, and precipitation anomalies, respectively, for NPP, NEE, and R(h). Runoff and ET exhibited threshold-like pattern in response to both temperature and precipitation anomalies but were less sensitive to CO2 changes. Ecosystem responses to combined temperature, CO2, and precipitation anomalies differed considerably from the responses to individual factors in terms of response patterns and/or critical points of nonlinearity. Our results suggest that nonlinear patterns in response to multiple global-change factors were diverse and were considerably affected by combined climate anomalies on ecosystem carbon and water processes. The diverse response patterns in nonlinearity have profound implications for both experimental design and theoretical development.