Modeling the Complex Impacts of Timber Harvests to Find Optimal Management Regimes for Amazon Tidal Floodplain Forests

At the Amazon estuary, the oldest logging frontier in the Amazon, no studies have comprehensively explored the potential long-term population and yield consequences of multiple timber harvests over time. Matrix population modeling is one way to simulate long-term impacts of tree harvests, but this approach has often ignored common impacts of tree harvests including incidental damage, changes in post-harvest demography, shifts in the distribution of merchantable trees, and shifts in stand composition. We designed a matrix-based forest management model that incorporates these harvest-related impacts so resulting simulations reflect forest stand dynamics under repeated timber harvests as well as the realities of local smallholder timber management systems. Using a wide range of values for management criteria (e.g., length of cutting cycle, minimum cut diameter), we projected the long-term population dynamics and yields of hundreds of timber management regimes in the Amazon estuary, where small-scale, unmechanized logging is an important economic activity. These results were then compared to find optimal stand-level and species-specific sustainable timber management (STM) regimes using a set of timber yield and population growth indicators. Prospects for STM in Amazonian tidal floodplain forests are better than for many other tropical forests. However, generally high stock recovery rates between harvests are due to the comparatively high projected mean annualized yields from fast-growing species that effectively counterbalance the projected yield declines from other species. For Amazonian tidal floodplain forests, national management guidelines provide neither the highest yields nor the highest sustained population growth for species under management. Our research shows that management guidelines specific to a region’s ecological settings can be further refined to consider differences in species demographic responses to repeated harvests. In principle, such fine-tuned management guidelines could make management more attractive, thus bridging the currently prevalent gap between tropical timber management practice and regulation.     

Mixed‐Effects State‐Space Models for Analysis of Longitudinal Dynamic Systems

Summary The rapid development of new biotechnologies allows us to deeply understand biomedical dynamic systems in more detail and at a cellular level. Many of the subject‐specific biomedical systems can be described by a set of differential or difference equations that are similar to engineering dynamic systems. In this article, motivated by HIV dynamic studies, we propose a class of mixed‐effects state‐space models based on the longitudinal feature of dynamic systems. State‐space models with mixed‐effects components are very flexible in modeling the serial correlation of within‐subject observations and between‐subject variations. The Bayesian approach and the maximum likelihood method for standard mixed‐effects models and state‐space models are modified and investigated for estimating unknown parameters in the proposed models. In the Bayesian approach, full conditional distributions are derived and the Gibbs sampler is constructed to explore the posterior distributions. For the maximum likelihood method, we develop a Monte Carlo EM algorithm with a Gibbs sampler step to approximate the conditional expectations in the E‐step. Simulation studies are conducted to compare the two proposed methods. We apply the mixed‐effects state‐space model to a data set from an AIDS clinical trial to illustrate the proposed methodologies. The proposed models and methods may also have potential applications in other biomedical system analyses such as tumor dynamics in cancer research and genetic regulatory network modeling.     

A mixed model QTL analysis for sugarcane multiple-harvest-location trial data

Sugarcane-breeding programs take at least 12 years to develop new commercial cultivars. Molecular markers offer a possibility to study the genetic architecture of quantitative traits in sugarcane, and they may be used in marker-assisted selection to speed up artificial selection. Although the performance of sugarcane progenies in breeding programs are commonly evaluated across a range of locations and harvest years, many of the QTL detection methods ignore two- and three-way interactions between QTL, harvest, and location. In this work, a strategy for QTL detection in multi-harvest-location trial data, based on interval mapping and mixed models, is proposed and applied to map QTL effects on a segregating progeny from a biparental cross of pre-commercial Brazilian cultivars, evaluated at two locations and three consecutive harvest years for cane yield (tonnes per hectare), sugar yield (tonnes per hectare), fiber percent, and sucrose content. In the mixed model, we have included appropriate (co)variance structures for modeling heterogeneity and correlation of genetic effects and non-genetic residual effects. Forty-six QTLs were found: 13 QTLs for cane yield, 14 for sugar yield, 11 for fiber percent, and 8 for sucrose content. In addition, QTL by harvest, QTL by location, and QTL by harvest by location interaction effects were significant for all evaluated traits (30 QTLs showed some interaction, and 16 none). Our results contribute to a better understanding of the genetic architecture of complex traits related to biomass production and sucrose content in sugarcane.     

A mixed-model quantitative trait loci (QTL) analysis for multiple-environment trial data using environmental covariables for QTL-by-environment interactions, with an example in maize

Complex quantitative traits of plants as measured on collections of genotypes across multiple environments are the outcome of processes that depend in intricate ways on genotype and environment simultaneously. For a better understanding of the genetic architecture of such traits as observed across environments, genotype-by-environment interaction should be modeled with statistical models that use explicit information on genotypes and environments. The modeling approach we propose explains genotype-by-environment interaction by differential quantitative trait locus (QTL) expression in relation to environmental variables. We analyzed grain yield and grain moisture for an experimental data set composed of 976 F(5) maize testcross progenies evaluated across 12 environments in the U.S. corn belt during 1994 and 1995. The strategy we used was based on mixed models and started with a phenotypic analysis of multi-environment data, modeling genotype-by-environment interactions and associated genetic correlations between environments, while taking into account intraenvironmental error structures. The phenotypic mixed models were then extended to QTL models via the incorporation of marker information as genotypic covariables. A majority of the detected QTL showed significant QTL-by-environment interactions (QEI). The QEI were further analyzed by including environmental covariates into the mixed model. Most QEI could be understood as differential QTL expression conditional on longitude or year, both consequences of temperature differences during critical stages of the growth.     

同龄纯林密度效应新模型的研究

根据植物种群生物量增长模式和最终产量恒定理论,提出一种新的同龄纯林密度效应模型：V^-β=AN^β B。这里N和V分别为林分密度和平均单株材积;A、B、β分别是随生长阶段而变化的参数。采用杉木人工林密度试验材料进行验证,表明该模型能很好地拟合实际的观测资料,明显优于目前常用的密度效应倒数模型和二次效应模型,显示了较大的优越性和较高的准确性。在新的密度效应模型中,取β=1可得密度效应倒数模型,即密度效应倒数模型仅为本文新模型的一个特例。     

Phenomenological modeling of tumor diameter growth based on a mixed effects model

Over the last few years, taking advantage of the linear kinetics of the tumor growth during the steady-state phase, tumor diameter-based rather than tumor volume-based models have been developed for the phenomenological modeling of tumor growth. In this study, we propose a new tumor diameter growth model characterizing early, late and steady-state treatment effects. Model parameters consist of growth rhythms, growth delays and time constants and are meaningful for biologists. Biological experiments provide in vivo longitudinal data. The latter are analyzed using a mixed effects model based on the new diameter growth function, to take into account inter-mouse variability and treatment factors. The relevance of the tumor growth mixed model is firstly assessed by analyzing the effects of three therapeutic strategies for cancer treatment (radiotherapy, concomitant radiochemotherapy and photodynamic therapy) administered on mice. Then, effects of the radiochemotherapy treatment duration are estimated within the mixed model. The results highlight the model suitability for analyzing therapeutic efficiency, comparing treatment responses and optimizing, when used in combination with optimal experiment design, anti-cancer treatment modalities.     

Biometrical modeling of twin and family data using standard mixed model software

Summary .   Biometrical genetic modeling of twin or other family data can be used to decompose the variance of an observed response or 'phenotype' into genetic and environmental components. Convenient parameterizations requiring few random effects are proposed, which allow such models to be estimated using widely available software for linear mixed models (continuous phenotypes) or generalized linear mixed models (categorical phenotypes). We illustrate the proposed approach by modeling family data on the continuous phenotype birth weight and twin data on the dichotomous phenotype depression. The example data sets and commands for Stata and R/S-PLUS are available at the Biometrics website.     

Hierarchical Bayesian modeling of random and residual variance–covariance matrices in bivariate mixed effects models

Bivariate mixed effects models are often used to jointly infer upon covariance matrices for both random effects ( u ) and residuals ( e ) between two different phenotypes in order to investigate the architecture of their relationship. However, these (co)variances themselves may additionally depend upon covariates as well as additional sets of exchangeable random effects that facilitate borrowing of strength across a large number of clusters. We propose a hierarchical Bayesian extension of the classical bivariate mixed effects model by embedding additional levels of mixed effects modeling of reparameterizations of u‐ level and e ‐level (co)variances between two traits. These parameters are based upon a recently popularized square‐root‐free Cholesky decomposition and are readily interpretable, each conveniently facilitating a generalized linear model characterization. Using Markov Chain Monte Carlo methods, we validate our model based on a simulation study and apply it to a joint analysis of milk yield and calving interval phenotypes in Michigan dairy cows. This analysis indicates that the e ‐level relationship between the two traits is highly heterogeneous across herds and depends upon systematic herd management factors.     

Water temperature and fish growth: otoliths predict growth patterns of a marine fish in a changing climate

Ecological modeling shows that even small, gradual changes in body size in a fish population can have large effects on natural mortality, biomass, and catch. However, efforts to model the impact of climate change on fish growth have been hampered by a lack of long‐term (multidecadal) data needed to understand the effects of temperature on growth rates in natural environments. We used a combination of dendrochronology techniques and additive mixed‐effects modeling to examine the sensitivity of growth in a long‐lived (up to 70 years), endemic marine fish, the western blue groper (Achoerodus gouldii), to changes in water temperature. A multi‐decadal biochronology (1952–2003) of growth was constructed from the otoliths of 56 fish collected off the southwestern coast of Western Australia, and we tested for correlations between the mean index chronology and a range of potential environmental drivers. The chronology was significantly correlated with sea surface temperature in the region, but common variance among individuals was low. This suggests that this species has been relatively insensitive to past variations in climate. Growth increment and age data were also used in an additive mixed model to predict otolith growth and body size later this century. Although growth was relatively insensitive to changes in temperature, the model results suggested that a fish aged 20 in 2099 would have an otolith about 10% larger and a body size about 5% larger than a fish aged 20 in 1977. Our study shows that species or populations regarded as relatively insensitive to climate change could still undergo significant changes in growth rate and body size that are likely to have important effects on the productivity and yield of fisheries.     

竹林坡地径流中泥沙及氮磷载荷特征模拟

采用人工模拟降雨的试验手段,设定6个降雨强度(31.8～114.0 mm·h-1),通过测试径流量、泥沙量、径流中总氮(TN)和总磷(TP)浓度,研究了浙江省2种不同经营方式竹林(用材竹林和笋竹林)坡地(坡度20°)径流的载荷特征及机理.结果表明:用材竹林地的总径流量和径流系数均高于笋竹林地;笋竹林地的径流含沙量和总产沙量远大于用材竹林地;相同雨强下,笋竹林地降雨径流中的TN浓度为用材竹林地的5～6倍,笋竹林坡地径流中TN浓度随雨强增大而减小;用材竹林地降雨径流中TP浓度高于笋竹林地,笋竹林地泥沙中TP流失量是用材竹林地的数百倍;在TN和TP随径流泥沙的流失过程中,产流前期浓度起主要作用,后期径流量和产沙量起决定作用.     

Neural networks for clustered and longitudinal data using mixed effects models

Although most statistical methods for the analysis of longitudinal data have focused on retrospective models of association, new advances in mobile health data have presented opportunities for predicting future health status by leveraging an individual's behavioral history alongside data from similar patients. Methods that incorporate both individual-level and sample-level effects are critical to using these data to its full predictive capacity. Neural networks are powerful tools for prediction, but many assume input observations are independent even when they are clustered or correlated in some way, such as in longitudinal data. Generalized linear mixed models (GLMM) provide a flexible framework for modeling longitudinal data but have poor predictive power particularly when the data are highly nonlinear. We propose a generalized neural network mixed model that replaces the linear fixed effect in a GLMM with the output of a feed-forward neural network. The model simultaneously accounts for the correlation structure and complex nonlinear relationship between input variables and outcomes, and it utilizes the predictive power of neural networks. We apply this approach to predict depression and anxiety levels of schizophrenic patients using longitudinal data collected from passive smartphone sensor data.     

A Study of Stand Growth Model for Pinus yunnanensis (Pinaceae) Based on Plots Data——A Case Study in Yangliu Township,Baoshan, Yunnan Province

Pinus yunnanensis is one of most important timber species in Yunnan Province, and widely distributed in southwest China. Studies on growth model have been reported, however, most of which focused on a specific part of growth model. To build detailed, easily used and accurate empirical stand growth model from the same dataset, a case study was conducted in Yangliu Township, Baoshan, Yunnan Province. A total of 86 sample plots data were collected using two stages sampling design. Several popular non-linear growth functions were fitted and compared, including Chapman-Richards, Mitscherlich, Schumacher, Gompertz, Logistic, Korf and Allometric function. Models of site index, density index, average diameter at breast height (DBH) and stock volume growth model were fitted respectively. The different models performed more or less similarly in terms of coefficients of determination and root mean square error (RMSE). However, empirical growth function “Schumacher” had lower coefficient of variation for all parameters than other models. Schumacher function was the most suitable one for site index, average DBH and stock volume growth model in all alternative functions.     

Mathematical approach to modeling of the treatment of suppurative processes

Consideration of an inflammation focus as an "open system" provided analogy between microbiological processes in inflamed wounds and in systems of continuous cultivation of microorganisms. Mathematical modeling of such systems is widely used. Some of the methods for the mathematical modeling were applied to chemoprophylaxis and chemotherapy of postoperative wounds. In modeling continuous cultivation of microorganisms it is usually necessary to determine optimal conditions for the maximum yield of their biomass. In modeling of wound treatment the aim was to determine the process parameters providing the minimum biomass. The described simple models showed that there could be certain optimal flow rate of the washing fluid in the aspiration-washing procedure for wound treatment at which the drug was not completely washed out while the growth rate of the microbial population was minimal. Such mathematical models were shown valuable in optimizing the use of bactericidal and bacteriostatic antibiotics.     

Nonlinear mixed-effects branch diameter and length models for natural Dahurian larch (<Emphasis Type="Italic">Larix gmelini</Emphasis>) forest in northeast China

Key message

We developed the generalized branch diameter and length models using the multi-level nonlinear mixed-effects techniques for the natural Dahurian larch ( Larix gmelini ) forest in northeast China.

Abstract

Dahurian larch (Larix gmelini) is the most commercially cultivated timber species in northeastern China due to its ecological prevalence and its superior wood attribute. However, its timber quality was largely driven by the crown architecture, i.e., the number, size and distribution of branches. The majority of branch-level models in the literature are focused on planted forests, which have substantially different crown architecture than that grown in natural mixed forests. Therefore, the goal of this investigation was to develop branch diameter and length models for Dahurian larch that are grown in natural mixed forests. A multi-level nonlinear mixed-effects model technique, including the fixed-effects, random-effects, variance functions and correlation structures, was employed to develop the branch growth models. The results suggested that the cumulative branch diameter and length were both increased with the increases of branch depth into the crown. Diameter at breast height (DBH) had significant positive influences on the branch size; however, tree height (HT) produced negative influences on the branch size, i.e., larger DBH and smaller HT could lead to larger branch size. Model fitting and validation results confirmed that we should avoid developing over-complex models from the perspective of application. As for the branch diameter and length models in our study, addressing the stand and tree level effects as random component were quite reliable and accurate for predicting the branch growth process of Dahurian larch in northeastern China.

     

The effects of alternate optimal solutions in constraint-based genome-scale metabolic models

Genome-scale constraint-based models of several organisms have now been constructed and are being used for model driven research. A key issue that may arise in the use of such models is the existence of alternate optimal solutions wherein the same maximal objective (e.g., growth rate) can be achieved through different flux distributions. Herein, we investigate the effects that alternate optimal solutions may have on the predicted range of flux values calculated using currently practiced linear (LP) and quadratic programming (QP) methods. An efficient LP-based strategy is described to calculate the range of flux variability that can be present in order to achieve optimal as well as suboptimal objective states. Sample results are provided for growth predictions of E. coli using glucose, acetate, and lactate as carbon substrates. These results demonstrate the extent of flux variability to be highly dependent on environmental conditions and network composition. In addition we examined the impact of alternate optima for growth under gene knockout conditions as calculated using QP-based methods. It was observed that calculations using QP-based methods can show significant variation in growth rate if the flux variability among alternate optima is high. The underlying biological significance and general source of such flux variability is further investigated through the identification of redundancies in the network (equivalent reaction sets) that lead to alternate solutions. Collectively, these results illustrate the variability inherent in metabolic flux distributions and the possible implications of this heterogeneity for constraint-based modeling approaches. These methods also provide an efficient and robust method to calculate the range of flux distributions that can be derived from quantitative fermentation data.     

Low-rank scale-invariant tensor product smooths for generalized additive mixed models

A general method for constructing low-rank tensor product smooths for use as components of generalized additive models or generalized additive mixed models is presented. A penalized regression approach is adopted in which tensor product smooths of several variables are constructed from smooths of each variable separately, these "marginal" smooths being represented using a low-rank basis with an associated quadratic wiggliness penalty. The smooths offer several advantages: (i) they have one wiggliness penalty per covariate and are hence invariant to linear rescaling of covariates, making them useful when there is no "natural" way to scale covariates relative to each other; (ii) they have a useful tuneable range of smoothness, unlike single-penalty tensor product smooths that are scale invariant; (iii) the relatively low rank of the smooths means that they are computationally efficient; (iv) the penalties on the smooths are easily interpretable in terms of function shape; (v) the smooths can be generated completely automatically from any marginal smoothing bases and associated quadratic penalties, giving the modeler considerable flexibility to choose the basis penalty combination most appropriate to each modeling task; and (vi) the smooths can easily be written as components of a standard linear or generalized linear mixed model, allowing them to be used as components of the rich family of such models implemented in standard software, and to take advantage of the efficient and stable computational methods that have been developed for such models. A small simulation study shows that the methods can compare favorably with recently developed smoothing spline ANOVA methods.     

Markov and Semi‐Markov Switching Linear Mixed Models Used to Identify Forest Tree Growth Components

Summary Tree growth is assumed to be mainly the result of three components: (i) an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous among individuals, (ii) a time‐varying environmental component assumed to take the form of synchronous fluctuations among individuals, and (iii) an individual component corresponding mainly to the local environment of each tree. To identify and characterize these three components, we propose to use semi‐Markov switching linear mixed models, i.e., models that combine linear mixed models in a semi‐Markovian manner. The underlying semi‐Markov chain represents the succession of growth phases and their lengths (endogenous component) whereas the linear mixed models attached to each state of the underlying semi‐Markov chain represent—in the corresponding growth phase—both the influence of time‐varying climatic covariates (environmental component) as fixed effects, and interindividual heterogeneity (individual component) as random effects. In this article, we address the estimation of Markov and semi‐Markov switching linear mixed models in a general framework. We propose a Monte Carlo expectation–maximization like algorithm whose iterations decompose into three steps: (i) sampling of state sequences given random effects, (ii) prediction of random effects given state sequences, and (iii) maximization. The proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along Corsican pine trunks influenced by climatic covariates.     

Increased growth rates of stream salamanders following forest harvesting

Timber harvesting can influence headwater streams by altering stream productivity, with cascading effects on the food web and predators within, including stream salamanders. Although studies have examined shifts in salamander occupancy or abundance following timber harvest, few examine sublethal effects such as changes in growth and demography. To examine the effect of upland harvesting on growth of the stream‐associated Ouachita dusky salamander (Desmognathus brimleyorum), we used capture–mark–recapture over three years at three headwater streams embedded in intensely managed pine forests in west‐central Arkansas. The pine stands surrounding two of the streams were harvested, with retention of a 14‐ and 21‐m‐wide forested stream buffer on each side of the stream, whereas the third stream was an unharvested control. At the two treatment sites, measurements of newly metamorphosed salamanders were on average 4.0 and 5.7 mm larger post‐harvest compared with pre‐harvest. We next assessed the influence of timber harvest on growth of post‐metamorphic salamanders with a hierarchical von Bertalanffy growth model that included an effect of harvest on growth rate. Using measurements from 839 individual D. brimleyorum recaptured between 1 and 6 times (total captures, n = 1229), we found growth rates to be 40% higher post‐harvest. Our study is among the first to examine responses of individual stream salamanders to timber harvesting, and we discuss mechanisms that may be responsible for observed shifts in growth. Our results suggest timber harvest that includes retention of a riparian buffer (i.e., streamside management zone) may have short‐term positive effects on juvenile stream salamander growth, potentially offsetting negative sublethal effects associated with harvest.