大明山云贵山茉莉群落物种多度分布的Weibull模型

物种多度分布的分析对于了解群落物种多样性具有重要意义。Weibull模型是拟合物种多度分布的重要模型之一。在采用倍程对物种多度分组的基础上,用Weibull模型分别拟合广西大明山保护区云贵山茉莉群落乔木层、灌木层以及乔木+灌木物种的多度分布,结果三者均符合Weibull分布。由此表明所提出的方法应用于物种多度分布研究是理想的,从而完善了Weibull模型在物种多度分布上的应用。     

Forecasting of the flowering time for wild species observed at Guidonia, central Italy

It is well known that forecasting the flowering time of wild vegetation is useful for various sectors of human activity, particularly for all agricultural practices. Therefore, continuing previous work by Cenci et al., we will present here three new phenoclimatic models of the flowering time for a set of wild species, based on an original data sample of flowering dates for more than 500 species, observed at Guidonia (42° N in central Italy) by Montelucci in the period 1960–1982. However, on applying the bootstrap technique to each species sample to check its basic statistical parameters, we found only about 200 to have data samples with an approximately Gaussian distribution. Eventually only 57 species (subdivided into eight monthly subsets from February to September) were used to formulate the models satisfactorily. The flowering date (represented by the z variable), is expressed in terms of two variables x and y by a nonlinear equation of the form z=αx ^β +γy. The x variable represents either the degree-day sum (in model 1), or the daily-maximum-temperature sum (in model 2), or the daily-global-insolation sum (in model 3), while y for all three models corresponds to the rainy-day sum. Note that all summations involved in the computation of the variables x and y take place over a certain period of time (preceding the flowering phase), which is a parameter to be determined by the fitting procedure. This parameter, together with the threshold temperature (needed to compute the degree-days in model 1), represents the two implicit parameters of the process, thus the total number of parameters (including these last two) becomes respectively, five for model 1, and four for the other two models. The preliminary results of this work were reported at the XVI International Botanical Congress (1–7 August 1999, St. Louis, Missouri USA). Received: 4 November 1999 / Revised: 10 May 2000 / Accepted: 10 May 2000     

Theory of ligand binding to heterogeneous receptor populations: Characterization of the free-energy distribution function

We present a method for characterizing the free-energy and affinity distributions of a heterogeneous population of molecules interacting with a homogeneous population of ligands, by driving expressions for the moments as functions of experimental binding curve characteristics, and then constructing the distribution as an expansion over a Gaussian basis set. Although the method provides the complete distribution in principle, in practice it is restricted by experimental noise, inaccuracies in data fitting, and the severity with which the distribution deviates from a Gaussian. Limitations imposed by experimental inaccuracies and the requirement of an appropriate analytic function for data fitting were evaluated by Monte Carlo simulations of binding experiments with various degrees of error in the data. Thus a distribution was assumed, binding curves with random errors were generated, and the technique was applied in order to determine the extent to which the characteristics of the assumed distribution could be recovered. Typical inaccuracies in the first two moments fell within experimental error, whereas inaccuracies in the third and fourth were generally larger than standard deviations in the data. The accuracy of these higher-order moments was invarient for experimental errors ranging from 2 to 10% and may thus be limited, within this range, primarily by the curve fitting procedure. The other aspect of the problem, accurate inference of the distribution, is limited in part by inaccuracies in the moments but more importantly by the extent to which the distribution deviates from a Gaussian. The extensive statistical literature on the problem of inference enables the delineation of specific criteria for estimating the efficiency of construction, as well as for deciding whether certain features of the inferred distribution, such as bimodality, are artifacts of the procedure. In spite of the limitations of the method, the results indicate that the mean and standard deviation are obtainable with greater accuracy than by a Sipsian analysis. This difference is particularly important when the distribution is narrow and width detection is beyond the sensitivity of the Sips plot. The method should be more accurate than the latter as an assay for homogeneity as well as for characterizing the moments, though equally easy to apply.     

Spatial scaling of species abundance distributions

Species abundance distributions are an essential tool in describing the biodiversity of ecological communities. We now know that their shape changes as a function of the size of area sampled. Here we analyze the scaling properties of species abundance distributions by using the moments of the logarithmically transformed number of individuals. We find that the moments as a function of area size are well fitted by power laws and we use this pattern to estimate the species abundance distribution for areas larger than those sampled. To reconstruct the species abundance distribution from its moments, we use discrete Tchebichef polynomials. We exemplify the method with data on tree and shrub species from a 50 ha plot of tropical rain forest on Barro Colorado Island, Panama. We test the method within the 50 ha plot, and then we extrapolate the species abundance distribution for areas up to 5 km². Our results project that for areas above 50 ha the species abundance distributions have a bimodal shape with a local maximum occurring for the singleton classes and that this maximum increases with sampled area size.     

The MIAmaxent R package: Variable transformation and model selection for species distribution models

The widely used “Maxent” software for modeling species distributions from presence‐only data (Phillips et al., Ecological Modelling, 190, 2006, 231) tends to produce models with high‐predictive performance but low‐ecological interpretability, and implications of Maxent's statistical approach to variable transformation, model fitting, and model selection remain underappreciated. In particular, Maxent's approach to model selection through lasso regularization has been shown to give less parsimonious distribution models—that is, models which are more complex but not necessarily predictively better—than subset selection. In this paper, we introduce the MIAmaxent R package, which provides a statistical approach to modeling species distributions similar to Maxent's, but with subset selection instead of lasso regularization. The simpler models typically produced by subset selection are ecologically more interpretable, and making distribution models more grounded in ecological theory is a fundamental motivation for using MIAmaxent. To that end, the package executes variable transformation based on expected occurrence–environment relationships and contains tools for exploring data and interrogating models in light of knowledge of the modeled system. Additionally, MIAmaxent implements two different kinds of model fitting: maximum entropy fitting for presence‐only data and logistic regression (GLM) for presence–absence data. Unlike Maxent, MIAmaxent decouples variable transformation, model fitting, and model selection, which facilitates methodological comparisons and gives the modeler greater flexibility when choosing a statistical approach to a given distribution modeling problem.     

A model of the species rank-abundance relation for a community in an open habitat

A mathematical model is proposed to describe the relationship between the abundance and the rank of species in order from the most abundant to the least in a community in an open habitat. This model is derived as a corollary of a species-area equation (Kobayashi , 1975) which could be expected in the case where the individuals of each species are uniformly distributed over a habitat area. Numerical simulation reveals that a rank-abundance curve for a universe results in different species-area or species-individual curves according to the spatial distribution of individuals, and that the relative abundance of each species in a sample varies with sample size unless the spatial distribution of individuals is uniform. A species-individual curve obtained bySanders 's (1968) rarefaction method agrees with that observed actually only for the spatially uniform distribution. Change in the pattern of rank-abundance curve with species diversity and with sample size is discussed in relation to the present model.     

The gambin model provides a superior fit to species abundance distributions with a single free parameter: evidence,implementation and interpretation

The species abundance distribution (SAD) has been a central focus of community ecology for over fifty years, and is currently the subject of widespread renewed interest. The gambin model has recently been proposed as a model that provides a superior fit to commonly preferred SAD models. It has also been argued that the model's single parameter (α) presents a potentially informative ecological diversity metric, because it summarises the shape of the SAD in a single number. Despite this potential, few empirical tests of the model have been undertaken, perhaps because the necessary methods and software for fitting the model have not existed. Here, we derive a maximum likelihood method to fit the model, and use it to undertake a comprehensive comparative analysis of the fit of the gambin model. The functions and computational code to fit the model are incorporated in a newly developed free‐to‐download R package (gambin). We test the gambin model using a variety of datasets and compare the fit of the gambin model to fits obtained using the Poisson lognormal, logseries and zero‐sum multinomial distributions. We found that gambin almost universally provided a better fit to the data and that the fit was consistent for a variety of sample grain sizes. We demonstrate how α can be used to differentiate intelligibly between community structures of Azorean arthropods sampled in different land use types. We conclude that gambin presents a flexible model capable of fitting a wide variety of observed SAD data, while providing a useful index of SAD form in its single fitted parameter. As such, gambin has wide potential applicability in the study of SADs, and ecology more generally.     

Predicting the species composition of Nardus stricta communities by logistic regression modelling

Question: Predictive models in plant ecology usually deal with single species or community types. Little effort has so far been made to predict the species composition of a community explicitly. The modelling approach presented here provides a conceptual framework on how to achieve this by combining habitat models for a large number of species to an additive community model. Our approach is exemplified by Nardus stricta communities (acidophilous, low‐productive grassland). Location: Large areas of Germany, 0–2040 m a.s.l. Methods: Logistic regression is applied for individual species models which are subsequently combined for an explicit prediction of species composition. Several parameters reflecting soil, management and climatic conditions serve as predictor variables. For validation, bootstrap and jackknife resampling procedures are used as well as ordination techniques (DCA, CCA). Results: We calculated significant models for 138 individual species. The predictions of species composition and species richness yield good agreements with the observed data. DCA and CCA results show that the community model preserves the main patterns in floristic space. Conclusions: Our approach of predicting species composition is an effective tool that can be applied in nature conservation, e.g. to assess the effects of different site conditions and alternative management scenarios on species composition and richness.     

Prediction of species composition of plant communities in a rural landscape based on species traits

The species composition of a community is a subset of the regional species pool, and predicting the species composition of a community from ecological traits of organisms is an important objective in ecology. If such a prediction can be made feasible, we could assess the risk of invasion of locally new species (alien species and genetically modified species) into natural communities. We developed and tested statistical models to predict a community’s species composition from ecological traits of the species pool. Various types of communities (forest, meadow, and weed communities) exist in a small area of traditional rural landscape in Japan, and have been maintained by human activities. These communities and the tracheophytes species pool in the 1-km² research area were considered. We used logistic regression and decision-tree analysis to construct predictive models of community species composition based on plant traits, using the presence or absence of species in a community as the dependent variable and ecological traits as independent variables. Plant traits were grouped by cluster analysis, and the average in each trait group was used for model building to avoid multiple collinearity. Statistical prediction models were significant in all communities. About 60–75% of species composition could be predicted from the measured plant traits in forest communities, but 33–56% in the meadow and weed communities. Our results showed the possibility of predicting the species composition of plant communities from the ecological traits of the plant species together with the information on local species pool.     

State vector models of the cell cycle II: The first three moments of the transit time distribution.

A discrete time state vector model (the Hahn model) has been used to simulate many experiments in cell kinetics. In the first paper in this series the authors described a new method to define the parameters of the Hahn model suitable for use in automatic fitting of fraction of labelled mitoses (FLM) experiments. In this paper it is shown how to compute the first three moments of the transit time distribution which arises from a Hahn model. These moments are compared analytically and numerically to the corresponding moments of the distribution the authors used to define the Hahn model. Finally, the problems involved in estimating the moments of the transit time distribution observed in fitting FLM data using a Hahn model are discussed.     

Regularities in the variability of species structure of costal littoral kelp: the model analysis

The model describes species structure of competitive community, inhabiting stochastically variable environment. Species list of this community, rearranged accordingly decreasing species abundance, can be described by decreasing geometrical series. According to the model, the value of coefficient of this progression q should be q = exp(-1) = 0.368. The actual data do not contradict statistically to this model constant. Seasonal variability of species structure in biotopes is observed. These biotopes differ one from another by the stability and heterogeneity levels of environmental conditions, estimated with the help of expert evaluation. Total community biomass shows two seasonal peaks; at winter and at spring - summer. Maximal values of total biomass are observed in the biotope with intermediate level of environment stability. The number of species is increased simultaneously with the growth of environmental stability. The level of species abundance equitability grows up too in these conditions. The model of geometric series describes the species structure of the macroalgae community quite adequately. At the same time, the positive correlation between sample's species richness and equitability of species structure results in the outcome that after all samples averaging the biomass distribution of species is approximately more accurately not by geometrical series but by power model. The new statistical method is offered in the application to this work. It allows the expose of statistically significant not monotone essential non-linear relations of nonquantitative (order-type) arguments.     

Assessing the performance of nonparametric estimators of species richness in meadows

To accurately measure the number of species in a biological community, a complete inventory should be performed, which is generally unfeasible; hopefully, estimators of species richness can help. Our main objectives were (i) to assess the performance of nonparametric estimators of plant species richness with real data from a small set of meadows located in the Basque campiña (northern Spain), and (ii) to apply the best estimator to a larger dataset to test the effects on plant species richness caused by environmental conditions and human practices. Two non-asymptotic and seven asymptotic accumulation functions were fitted to a randomized sample-based rarefaction curve computed with data from three well sampled meadows, and information theoretic methods were used to select the best fitting model; this was the Morgan-Mercer-Flodin, and its asymptote was taken as our best guess of true richness. Then, five nonparametric estimators were computed: ICE, Chao 2, Jackknife 1 and 2, and Bootstrap; MMRuns and MMMeans were also assessed. According to the criteria set for our performance assessment (i.e., bias, precision, and accuracy), the best estimator was Jackknife 1. Finally, Jackknife 1 was applied to assess the effects of terrain slope and soil parent material, and also fertilization, grazing, and mowing, on plant species richness from a larger dataset (20 meadows). Results suggested that grass cutting was causing a loss of richness close to 30%, as compared to unmowed meadows. It is concluded that the use of nonparametric estimators of species richness can improve the evaluation of biodiversity responses to human management practices.     

Lag‐phases in alien plant invasions: separating the facts from the artefacts

Temporal trends in biological invasions are often described by a lag‐phase of little or no increase in species occurrence followed by an increase‐phase in which species occurrence rises rapidly. While several biological and environmental mechanisms may underlie lag‐phases, they may also represent statistical artefacts or temporal changes in sampling effort. To date, distinguishing the facts from these artefacts has not been possible. Here we describe a method for estimating the lag‐phase in cumulative records of species occurrence, using a piecewise regression model that explicitly differentiates the lag and increase phases. We used the von Bertalanffy, logistic, linear and exponential functions to model the increase phase, and identified the best‐fitting function using model selection techniques. We confirmed the accuracy of our method using simulated data and then estimated the length of the lag‐phase (t_lag), the maximum collection rate (r) and the projected asymptotic number of records (K) using herbarium records for 105 weed species in New Zealand, while accounting for changes in sampling effort. Nearly all the New Zealand weed species had a lag‐phase, which averaged around 20–30 years, with 4% of species having a lag‐phase greater than 40 years. In more than two thirds of the cases, the accumulation of records was best modelled with the decelerating von Bertalanffy function, despite the tendency for temporal variation in sampling effort to force cumulative herbarium records to follow the sigmoidal shape of a logistic curve. A positive correlation between r and K is consistent with the assumption that the final distribution of an alien plant species reflects its rate of spread. Seemingly rare but fast‐spreading aliens may thus become tomorrow's noxious weeds. A positive correlation between inflection year and r warns that the weeds that have only begun to spread relatively recently may spread faster than previously known invaders.     

An evaluation of randomization models for nested species subsets analysis

Randomization models, often termed “null” models, have been widely used since the 1970s in studies of species community and biogeographic patterns. More recently they have been used to test for nested species subset patterns (or nestedness) among assemblages of species occupying spatially subdivided habitats, such as island archipelagoes and terrestrial habitat patches. Nestedness occurs when the species occupying small or species-poor sites have a strong tendency to form proper subsets of richer species assemblages. In this paper, we examine the ability of several published simulation models to detect, in an unbiased way, nested subset patterns from a simple matrix of site-by-species presence-absence data. Each approach attempts to build in biological realism by following the assumption that the ecological processes that generated the patterns observed in nature would, if they could be repeated many times over using the same species and landscape configuration, produce islands with the same number of species and species present on the same number of islands as observed. In mathematical terms, the mean marginal totals (column and row sums) of many simulated matrices would match those of the observed matrix. Results of model simulations suggest that the true probability of a species occupying any given site cannot be estimated unambiguously. Nearly all of the models tested were shown to bias simulation matrices toward low levels of nestedness, increasing the probability of a Type I statistical error. Further, desired marginal totals could be obtained only through ad-hoc manipulation of the calculated probabilities. Paradoxically, when such results are achieved, the model is shown to have little statistical power to detect nestedness. This is because nestedness is determined largely by the marginal totals of the matrix themselves, as suggested earlier by Wright and Reeves. We conclude that at the present time, the best null model for nested subset patterns may be one based on equal probabilities of occurrence for all species. Examples of such models are readily available in the literature. Received: 3 February 1997 / Accepted: 21 September 1997     

Frequent and occasional species and the shape of relative-abundance distributions

Recently, three different models have been proposed to explain the distribution of abundances in natural communities: the self‐similarity model; the zero‐sum ecological drift model; and the occasional–frequent species model of Magurran and Henderson. Here we study patterns of relative abundance in a large community of forest Hymenoptera and show that it is indeed possible to divide the community into a group of frequent species and a group of occasional species. In accordance with the third model, frequent species followed a lognormal distribution. Relative abundances of the occasional species could be described by the self‐similarity model, but did not follow a log‐series as proposed by the occasional–frequent model. The zero‐sum ecological drift model makes no explicit predictions about frequent and occasional species but the abundance distributions of the hymenopteran species did not show the excess of rare species predicted by this model. Separate fits of this model to the frequent and to the occasional species were worse than the respective fits of the lognormal and the self‐similarity model.     

Rank Distributions in Community Ecology from the Statistical Viewpoint

Traditional statistical methods for definition of empirical functions of abundance distribution (population, biomass, production, etc.) of species in a community are applicable for processing of multivariate data contained in the above quantitative indices of the communities. In particular, evaluation of moments of distribution suffices for convolution of the data contained in a list of species and their abundance. At the same time, the species should be ranked in the list in ascending rather than descending population and the distribution models should be analyzed on the basis of the data on abundant species only.     

The implicit assumption of symmetry and the species abundance distribution

Species abundance distributions (SADs) have played a historical role in the development of community ecology. They summarize information about the number and the relative abundance of the species encountered in a sample from a given community. For years ecologists have developed theory to characterize species abundance patterns, and the study of these patterns has received special attention in recent years. In particular, ecologists have developed statistical sampling theories to predict the SAD expected in a sample taken from a region. Here, we emphasize an important limitation of all current sampling theories: they ignore species identity. We present an alternative formulation of statistical sampling theory that incorporates species asymmetries in sampling and dynamics, and relate, in a general way, the community-level SAD to the distribution of population abundances of the species integrating the community. We illustrate the theory on a stochastic community model that can accommodate species asymmetry. Finally, we discuss the potentially important role of species asymmetries in shaping recently observed multi-humped SADs and in comparisons of the relative success of niche and neutral theories at predicting SADs.     

Modeling species distributions by breaking the assumption of self-similarity

Species distributions are commonly measured as the number of sites, or geographic grid cells occupied. These data may then be used to model species distributions and to examine patterns in both intraspecific and interspecific distributions. Harte et al. (1999) used a model based on a bisection rule and assuming self-similarity in species distributions to do so. However, this approach has also been criticized for several reasons. Here we show that the self-similarity in species distributions breaks down according to a power relationship with spatial scales, and we therefore adopt a power-scaling assumption for modeling species occupancy distributions. The outcomes of models based on these two assumptions (self-similar and power-scaling) have not previously been compared. Based on Harte's bisection method and an occupancy probability transition model under these two assumptions (self-similar and power-scaling), we compared the scaling pattern of occupancy (also known as the area-of-occupancy) and the spatial distribution of species. The two assumptions of species distribution lead to a relatively similar interspecific occupancy frequency distribution pattern, although the spatial distribution of individual species and the scaling pattern of occupancy differ significantly. The bimodality in occupancy frequency distributions that is common in species communities, is confirmed to a result for certain mathematical and statistical properties of the probability distribution of occupancy. The results thus demonstrate that the use of the bisection method in combination with a power-scaling assumption is more appropriate for modeling species distributions than the use of a self-similarity assumption, particularly at fine scales.