Multilevel Nonlinear Mixed-Effect Crown Ratio Models for Individual Trees of Mongolian Oak (Quercus mongolica) in Northeast China

In this study, an individual tree crown ratio (CR) model was developed with a data set from a total of 3134 Mongolian oak (Quercus mongolica) trees within 112 sample plots allocated in Wangqing Forest Bureau of northeast China. Because of high correlation among the observations taken from the same sampling plots, the random effects at levels of both blocks defined as stands that have different site conditions and plots were taken into account to develop a nested two-level nonlinear mixed-effect model. Various stand and tree characteristics were assessed to explore their contributions to improvement of model prediction. Diameter at breast height, plot dominant tree height and plot dominant tree diameter were found to be significant predictors. Exponential model with plot dominant tree height as a predictor had a stronger ability to account for the heteroskedasticity. When random effects were modeled at block level alone, the correlations among the residuals remained significant. These correlations were successfully reduced when random effects were modeled at both block and plot levels. The random effects from the interaction of blocks and sample plots on tree CR were substantially large. The model that took into account both the block effect and the interaction of blocks and sample plots had higher prediction accuracy than the one with the block effect and population average considered alone. Introducing stand density into the model through dummy variables could further improve its prediction. This implied that the developed method for developing tree CR models of Mongolian oak is promising and can be applied to similar studies for other tree species.     

Effects of plot size on the ordination of vegetation samples

Questions: Do ordination patterns differ when based on vegetation samples recorded in plots of different size? If so, how large is the effect of plot size relative to the effects of data set heterogeneity and of using presence/absence or cover‐abundance data? Can we combine plots of different size in a single ordination? Methods: Two homogeneous and two heterogeneous data sets were sampled in Czech forests and grasslands. Cover‐abundances of plant species were recorded in series of five or six nested quadrats of increasing size (forest 49‐961 m2; grassland 1‐49 m²). Separate ordinations were computed for plots of each size for each data set, using either species presences/absences or cover‐abundances recorded on an ordinal scale. Ordination patterns were compared with Procrustean analysis. Also, ordinations of data sets jointly containing plots of different size were calculated; effects of plot size were evaluated using a Monte Carlo test in constrained ordination. Results: The results were consistent between forest and grassland data sets. In homogeneous data sets, the effect of presence/absence vs. cover‐abundance was similar to, or larger than, the effect of plot size; for presence/absence data the differences between ordinations of differently sized plots were smaller than for cover‐abundance data. In heterogeneous data sets, the effect of plot size was larger than the effect of presence‐absence vs. cover‐abundance. The plots of smaller size (= 100 m2 in forests, = 4 m² in grasslands) yielded the most deviating ordination patterns. Joint ordinations of differently sized plots mostly did not yield patterns that would be artifacts of different plot size, except for plots from the homogeneous data sets that differed in size by a factor of four or higher. Conclusions: Variation in plot size does influence ordination patterns. Smaller plots tend to produce less stable ordination patterns, especially in data sets with low ß‐diversity and species cover‐abundances. Data sets containing samples from plots of different sizes can be used for ordination if they represent vegetation with large ß‐diversity. However, if data sets are homogeneous, i.e. with low ß‐diversity, the differences in plot sizes should not be very large, in order to avoid the danger of plot size differences distorting the real vegetation differentiation in ordination patterns.     

The influence of sample plot size on evaluations with Ellenberg indicator values

The effect of plot size was tested on heterogeneous and homogeneous data sets that were obtained by sampling grassland and forest vegetation on plots differing in size. Mean EIV for relevés revealed no differences among data sets from various plot sizes or between homogeneous and heterogeneous data sets. This is probably due to a similar indicator value for species newly occurring in plots with increasing plot size. Using EIV is thus a robust method even for data sets associated with wide range of plot sizes.     

Selection system efficiencies for computer simulated progeny test field designs in loblolly pine

Summary Six simulated progeny test field designs in combination with three within-family selection systems were tested on three loblolly pine (Pinus taeda L.) progeny test sites in southeastern Oklahoma and southwestern Arkansas, to compare genetic gains for the single trait, height. Residual deviations obtained by subtraction of family and plantation mean effects for each plantation were combined with simulated genetic effects with known family variance structure. The simulated genetic populations, arranged in the following progeny test field designs — large square or almost square plots, five- and ten-tree row plots, five-tree noncontiguous plots, two tree row plots, and single-tree plots — were superimposed on the residual data for each plantation. Within-family selection methods based on deviations from block means, deviations from neighborhood means and deviations from plot means were built into the model. Realized genetic gain attained by each design — selection system combination was compared with the genetic gain theoretically possible if selection accuracy were perfect, and with expected gain estimated using the general linear model. In general, average realized genetic gain compared well with expected gain. Differences between designs with large versus small plots were generally lower than expected, although the single-tree plot design always yielded highest realized gain. Realized gain was generally higher than expected when within-family selection was based on deviations from block or neighborhood means, but equal to or lower than expected when selection was based on deviations from plot means.     

Residual plots for log odds ratio regression models.

This article describes graphical diagnostic methods for log odds ratio regression models. To study the effects of an additional covariate on log odds ratio regression analysis, three types of residual plots based on weighted least squares (WLS) are discussed: (i) added variable plot (partial regression plot), (ii) partial residual plot, and (iii) augmented partial residual plot. These plots provide diagnostic procedures for identifying heterogeneity of error variances, outliers, or nonlinearity of the model. They are especially useful for clarifying whether including a covariate as a linear term is appropriate, or whether quadratic or other nonlinear transformations are preferable. A well-known data set for case-control studies is analyzed to illustrate the residual plots.     

Defining a Target Map of Native Species Assemblages for Restoration

Vegetation restoration is usually based on predefined species assemblages from large‐scale maps of potential vegetation. However, most restoration plans apply to smaller spatial scales, so a homogeneous species assemblage is usually assigned to the target site. We propose defining species assemblages for restoration by modeling the distribution of individual target species. The example presented here is about postfire restoration, but it can be used in other types of disturbed areas. We surveyed 212 plots in well‐preserved vegetation around the burned area to obtain a list of target species and physical parameters of the plots. The burned area was divided in a grid of 723 squares, 1 ha each, and then characterized according to the same physical parameters. From these data, we modeled the distribution of 23 target species. A target map of predicted species assemblages was built combining species maps. This map largely resembles the native vegetation in terms of species richness per plot, environmental gradients in α‐diversity, spatial variation in β‐diversity, and frequency of species occurrence. Comparison between the target map and the current vegetation (recovery status) indicated that, on average, only half of the potential set of species is already present in each plot. Analysis of the recovery status suggested that both rock outcrops and areas at lower altitude, with gentle slope and deeper soil, recover faster. This illustrates the utility of target maps to outline plots in more need of restoration.     

Diagnostic plots in Cox's regression model.

Two diagnostic plots are presented for validating the fitting of a Cox proportional hazards model. The added variable plot is developed to assess the effect of adding a covariate to the model. The constructed variable plot is applied to detect nonlinearity of a fitted covariate. Both plots are also useful for identifying influential observations on the issues of interest. The methods are illustrated on examples of multiple myeloma and lung cancer data.     

Finescale species associations in alvar limestone grasslands

To examine the importance of positive or negative interactions of plant species on a micro‐scale, species associations were studied in 38 1 m² ‐plots in alvar limestone grasslands on Öland, Sweden. Each plot was assumed to be homogeneous as to its environmental conditions and spatial distribution of dominant species, and was divided into 25 sub‐plots of 100 cm² size arranged in a regular grid. Presence‐absence data of rooted vascular plants were recorded for each sub‐plot. Significant positive or negative associations were observed in all plots. The number of significant interactions was positively related to the within‐plot variation in soil depth. In seven and nine cases, respectively, there were more positive or negative associations than expected on the basis of a random distribution of species over the sub‐plots. The ratio of the number of positive associations to the potential number of positive associations increased with increasing species richness. There was a significant spatial autocorrelation in species composition in most plots, but the coefficients of determination were on average very low, indicating a minor importance of spatial dependence in the data set. Correspondingly, the ratio of observed to potential species associations was unrelated to the extent of spatial autocorrelation. About 2/3 of all species encountered were at least once involved in a significant interaction. We found differences in the proportion of positive to negative associations between species with different habitat requirements and attributes. In general, species with predominantly negative associations were mostly relatively tall and competitive, long‐lived hemicryptophytes characteristic of Festuco‐Brometea and more mesotrophic grasslands, for example Filipendula vulgaris and Achillea millefolium. In contrast, species with largely positive associations were mostly smaller and shortlived stress‐tolerators and stress‐tolerant ruderals, preferring more shallow and exposed soils, such as Cerastium semidecandrum and Trifolium arvense. While the negative associations prevailing among the dominant species in the alvar grasslands are likely to be the outcome of interspecific competition for space and resources, the positive associations may be the result of facilitative relations between the dominant and sub‐ordinate species.     

Detection of errors of interpretation in experiments in enzyme kinetics

Although modern statistical computing will often be the method of choice for analyzing kinetic data, graphic methods provide an important supplement that ought not to be neglected. Residual plots, or plots of differences between observed and calculated values against variables not expected to be correlated with these differences, permit a rapid judgment of whether data have been correctly interpreted and analyzed. The rapid increase in the frequency with which artificially modified or mutated enzymes are studied is making it less and less safe to assume that enzymes are stable under assay conditions, and there is thus an increased need for methods to check for enzyme stability, and a method for doing this is briefly described. Finally, the Scatchard plot (together with the Eadie-Hofstee plot) is used as an example to discuss the dangers of publishing derived information unaccompanied by any primary data.     

Explained variation in a fully specified model for data-grouped survival data

An additive hazards model may be used to quantify the effect of genetic and environmental predictors on flowering of sugar beet plants recorded as data-grouped time-to-event data. Estimated predictor effects have an intuitive interpretation rooted in the underlying time dynamics of the flowering process. However, agricultural experiments are often designed using several plots containing a large number of plants that are subsequently being monitored. In this article, we consider an additive hazards model with an additional plot structure induced by latent shared frailty variables. This approach enables us to derive a method to assess the quality of predictors in terms of how much plot variation they explain. We apply the method to a large data set exploring flowering of sugar beet and conclude that the genetic predictor biotype, which has a strong effect, also explains a substantial amount of the plot variation. The method is also applied to a data set from medical research concerning days to virus positivity of serum samples in AIDS patients.     

Pteridophyte diversity and species composition in four Amazonian rain forests

Abstract. Local variation in individual density, species composition, species richness and species diversity of terrestrial pteridophytes were studied at four sites in the tropical lowland rain forest of western Amazonia. 15 568 pteridophyte individuals representing 40 species were recorded in four plots. The variability among subplots within the same plot was considerable in all the characteristics measured (number of individuals, number of species, species diversity); the square 1‐ha plot was more homogeneous in these respects than any of the three 5 m by 1300 m transects. Species richness was affected by the density of individuals both within and among plots. Density of individuals was not affected by topographical position within any of the plots, whereas in some of the plots both species richness and species diversity were. Clustering and ordination analyses showed that floristically similar subplots could be found in different plots: although there was a tendency for subplots from the same plot to be floristically similar and therefore to group together, many recognized groups included subplots from two or more plots. Both within and among plots, the floristic differences corresponded to topographic position and were probably related to soil drainage. This was also evident in that the abundance patterns of many species followed the topography.     

Validity of f-test in a randomized block design with missing data

In this paper the first two moments of the test criterion (Treat. S.S.)/(Treat.S.S. + Error S.S.) have been derived assuming that one observation corresponding to the first plot of the first block which is under treatment ‘m’ (say), is missing in a randomized block design with ‘V’ treatments and ‘r’ blocks. To keep the analysis simple the case of one missing observation has been considered. It is concluded that in general the design is not unbiased in YATES (1951) sense and the usual F-test is satisfactory iff /(vr - r - 1)=(S - S₁)/(v - 1) (r-1), the block errors are homogeneous and (vr - r - 1) is large. The analysis of three unifornity trial data indicates that the first condition is the most important for the F-test to be satisfactory. However, if one observation is missing at random from some plot of some block, the F-test is unbiased. If the block errors are homogeneous and (vr - r - 1) GT96, the F-test also provides a good approximation to the corresponding randomization test in this case.     

Environmental constraints at the edge of a species distribution, the Eurasian badger (Meles meles L.): a biogeographic approach

Aim This paper describes the distribution pattern (occurrence) of badgers (Meles meles L. 1758) in a Mediterranean mountain area of central Spain, in relation to landscape characteristics and climatic data. We test the fit of the badger occurrence pattern to the niche hypothesis predictions. Location We sampled twenty-four survey plots randomly distributed in the mountains of central Spain (Sierra de Guadarrama, Madrid): ten in the north and fourteen in the south slopes. All habitat types and climatic conditions typical of central Spain can be found. Methods The ocurrence of badgers in the plots were recorded through an exhaustive search of setts and latrines in four different (and evenly spaced) points in each plot. The index of occurrence was made by dividing the number of positive points (badger presence) by the total number of points sampled (four in all plots). Landscape patterns (% type of habitat in each plot) were obtained from detailed maps and climate data from meteorological stations placed in the plot. We analyse the contribution of landscape variables and climate data to explain the differences in badger occurrence through Pearson correlations and fixed one-way ANCOVA with climatic data as fixed factor, vegetation cover as covariates and badger occurrence as response variable. Additionally, we use an one-way ANOVA to check the differences in occurrence between north and south plots with the location of each plot as fixed factor. Results The results indicate that the badger is more abundant in rainy areas of the mountains, and in open landscapes vegetated by ash-tree forests than in closed landscapes vegetated by holm oak forests. In addition, the species is more abundant in the northern plots than in the southern ones. Northern plots were homogeneous areas characterized by their open landscape and wet climate, while southern plots were characterized by their dry climate and closed landscapes. In addition, climate (measured as summer rain) is more determinant than habitat type (holm oak cover) to explain the pattern of badger occurrence. Main conclusions Overall, we consider that the typical Mediterranean landscapes are poor habitats for badgers due to changes in the environmental conditions associated with concomitant changes in food resources. These data support the niche hypothesis to explain the changes in abundance or occurrence close to the edge of the distribution of species, and in particular, in Palearctic species in the Mediterranean area.     

Detecting spatial patterns in species composition with multiple plot similarity coefficients and singularity measures

Recently, several multiple plot similarity indices have been presented that cure some of the problems associated with the approaches for the calculation of compositional similarity for groups of plots by averaging pairwise similarities. These new indices calculate the similarity between more than two plots whilst considering the species composition on all compared plots. The resulting similarity value is true for the whole group of plots considered (called neighborhood in the following). Here, we review the possibilities for multiple plot similarity calculation and additionally explore coefficients that examine multiple plot similarity between a reference plot (named focal plot in the following) and any number of surrounding plots. The latter represent measures of singularity. Further, we establish a framework for applying these two kinds of multiple plot measures to gridded data including an algorithm for testing the significance of calculated values against random expectations. The capability of multiple plot measures for detecting species compositional gradients and local/regional hotspots within this framework is tested. For this purpose, several artificial data sets with known gradients in species composition (random, gradient, central hotspot, hotspot bottom right) are constructed on the basis of a real data set from a Tundra ecosystem in northern Sweden (Abisko). The coefficients that best reflect the positions of the plots on the realized gradients in species composition are considered as performing best with regard to pattern detection. The tested measures of multiple plot similarity and singularity produced considerably different results when applied to one real and 4 artificial data sets. The newly proposed symmetric singularity coefficient has the best overall performance which makes it suitable for local/regional hotspot detection and for incorporating local to regional similarity analyses in reserve selection procedures.     

Early succession on lahars spawned by Mount St. Helens

The effects of isolation on primary succession are poorly documented. I monitored vegetation recovery on two Mount St. Helens lahars (mud flows) with different degrees of isolation using contiguous plots. Seventeen years after the eruption, species richness was stable, but cover continued to increase. That isolation affects community structure was confirmed in several ways. The dominance hierarchies of the lahars differed sharply. Detrended correspondence analysis on Lahar I showed a trend related to distance from an adjacent woodland, whereas vegetation on Lahar II was relatively homogeneous. Spectra of growth forms and dispersal types also differed. Lahar I was dominated by species with modest dispersal ability, while Lahar II was dominated by species with better dispersal. Variation between plots should decline through time, a prediction confirmed on Lahar II. Lahar I remained heterogeneous despite having developed significantly higher cover. Here, the increasing distance from the forest has prevented plots from becoming more homogeneous. At this stage of early primary succession, neither lahar is converging towards the species composition of adjacent vegetation. This study shows that isolation and differential dispersal ability combine to determine initial vegetation structure. Stochastic effects resulting from dispersal limitations may resist the more deterministic effects of competition that could lead to floristic convergence.     

Permanent plots as tools for plant community ecology

Abstract. Permanent plots provide information on spatio-temporal patterns in plant communities, which could be analyzed to yield correlated changes in pairs of species and information on species replacements in space. The potential use of permanent plots to study underlying processes of interspecific interactions (namely competition) is discussed. Two examples (one simulated, using a cellular automaton model, and one from a removal experiment in grasslands) are used to demonstrate that this use is not straightforward, since (1) radically different underlying mechanisms (symmetric founder control with little competitive replacement vs. asymmetric dominance control strongly structured by competition) may produce very similar spatio-temporal patterns; and (2) topology of species replacements in space may be very different from the competitive hierarchy as determined by the removal experiment. Permanent plot data can be used to study interspecific interactions in the following ways: (1) if there is additional information to decide which of the potential underlying models is acceptable, permanent plot data may enable further articulation of the model, such as estimation of the model parameters; this approach is similar to that used in many other plant ecology fields (fine scale patterns, chronosequences, plant size distribution and dynamics); (2) data from permanent plots constrain the number of feasible underlying models; (3) permanent plot data provide verification of predictions of experimental studies; in this respect, they are much superior to non-repeated studies of pattern.     

Experimental evidence for density dependence of reproduction in great tits

1. Density dependence of avian reproduction has often been analysed using correlations between annual mean reproductive output and population density. Experiments are necessary to prove that density is the cause of the observed patterns, but so far, three out of four experimental studies do not support a direct causal effect of density on reproduction.
2. This paper presents experimental evidence that reproductive decisions in great tits, Parus major L., are causally affected by breeding density. The breeding density of great tits was manipulated by providing nest-boxes at different densities in an ecologically homogeneous area.
3. Within years the densities in the high and low density plots differed approximately 8-fold. During the 11 years of the experiment, clutch size, nestling mass and the proportion of birds starting a second brood were all lower in the high density plot. In 5 years with equal breeding densities in both parts, clutch size did not differ between the plots. The patterns found were consistent with the density effects as predicted from the non-experimental data.     

基于抚育间伐效应的长白落叶松人工林两阶段枯死模型

1972和1974年分别在黑龙江省江山娇林场及孟家岗林场设置10块长白落叶松人工林固定样地(8块抚育间伐样地、2块对照样地),采用连年复测数据,分析抚育间伐对人工长白落叶松样地枯死与单木枯死的影响.基于二分类变量Logistic回归,建立了样地枯死及样地内单木枯死概率的两阶段模型(Ⅰ:抚育间伐后样地水平枯死概率模型;Ⅱ:枯死样地中单木水平枯死概率模型),采用广义估计方程(GEE)方法对模型参数进行估计.根据敏感度和特异度曲线相交点确定枯死概率最优临界点.结果表明: 样地数据按照抚育间伐次数分为4组分别建模(模型1～模型4).在模型1中,地位指数、林分年龄的自然对数、抚育间伐年龄及强度为显著自变量;模型2～模型4采用主成分分析法建模,主成分包含林分年龄、每公顷株数、平均胸径及抚育间伐因子,说明抚育间伐因子对样地枯死概率有显著影响.抚育间伐对枯死样地中单木枯死概率无显著影响,单木枯死概率模型中显著性自变量为林分初植密度、年龄、林木胸径的倒数及林分中大于对象木的所有林木断面积之和.样地枯死概率模型及单木枯死概率模型Hosmer和Lemeshow拟合优度检验均不显著,模型AUC均在0.91以上,估计正确率均超过80%,说明模型拟合效果较好.     

Implications of epidermal growth factor (EGF) induced egf receptor aggregation.

To investigate the role of receptor aggregation in EGF binding, we construct a mathematical model describing receptor dimerization (and higher levels of aggregation) that permits an analysis of the influence of receptor aggregation on ligand binding. We answer two questions: (a) Can Scatchard plots of EGF binding data be analyzed productively in terms of two noninteracting receptor populations with different affinities if EGF induced receptor aggregation occurs? No. If two affinities characterize aggregated and monomeric EGF receptors, we show that the Scatchard plot should have curvature characteristic of positively cooperative binding, the opposite of that observed. Thus, the interpretation that the high affinity population represents aggregated receptors and the low affinity population nonaggregated receptors is wrong. If the two populations are interpreted without reference to receptor aggregation, an important determinant of Scatchard plot shape is ignored. (b) Can a model for EGF receptor aggregation and EGF binding be consistent with the "negative curvature" (i.e., curvature characteristic of negatively cooperative binding) observed in most Scatchard plots of EGF binding data? Yes. In addition, the restrictions on the model parameters required to obtain negatively curved Scatchard plots provide new information about binding and aggregation. In particular, EGF binding to aggregated receptors must be negatively cooperative, i.e., binding to a receptor in a dimer (or higher oligomer) having one receptor already bound occurs with lower affinity than the initial binding event. A third question we consider is whether the model we present can be used to detect the presence of mechanisms other than receptor aggregation that are contributing to Scatchard plot curvature. For the membrane and cell binding data we analyzed, the best least squares fits of the model to each of the four data sets deviate systematically from the data, indicating that additional factors are also important in shaping the binding curves. Because we have controlled experimentally for many sources of receptor heterogeneity, we have limited the potential explanations for residual Scatchard plot curvature.     

Plot size matters: Toward comparable species richness estimates across plot‐based inventories

To understand the state and trends in biodiversity beyond the scope of monitoring programs, biodiversity indicators must be comparable across inventories. Species richness (SR) is one of the most widely used biodiversity indicators. However, as SR increases with the size of the area sampled, inventories using different plot sizes are hardly comparable. This study aims at producing a methodological framework that enables SR comparisons across plot‐based inventories with differing plot sizes. We used National Forest Inventory (NFI) data from Norway, Slovakia, Spain, and Switzerland to build sample‐based rarefaction curves by randomly incrementally aggregating plots, representing the relationship between SR and sampled area. As aggregated plots can be far apart and subject to different environmental conditions, we estimated the amount of environmental heterogeneity (EH) introduced in the aggregation process. By correcting for this EH, we produced adjusted rarefaction curves mimicking the sampling of environmentally homogeneous forest stands, thus reducing the effect of plot size and enabling reliable SR comparisons between inventories. Models were built using the Conway–Maxell–Poisson distribution to account for the underdispersed SR data. Our method successfully corrected for the EH introduced during the aggregation process in all countries, with better performances in Norway and Switzerland. We further found that SR comparisons across countries based on the country‐specific NFI plot sizes are misleading, and that our approach offers an opportunity to harmonize pan‐European SR monitoring. Our method provides reliable and comparable SR estimates for inventories that use different plot sizes. Our approach can be applied to any plot‐based inventory and count data other than SR, thus allowing a more comprehensive assessment of biodiversity across various scales and ecosystems.