生物群落多样性的测度方法VI：与多样性测度中有关的统计问题

物种多样性测度是(群落的)总体参数,它们常常是未知的,需要通过抽样将它们估计出来,因此,必须了解估计量的抽样性质。本文对与一些多样性测度的均值、方差的估计和假设检验以及大、小样本分布等有关的问题作了综述。可以看出大多数多样性测度的抽样性质还不清楚,有些甚至根本就没有研究过。Pielou的合并样方法和刀切法是两个比较通用的方法,用它们可以解决其中的一些问题。但相比之下,刀切法更实用。     

Are Plant Censuses Carried Out on Small Quadrats More Reliable than on Larger Ones?

Plant censuses are known to be significantly affected by observers’ biases. In this study, we checked whether the magnitude of observer effects (defined as the % of total variance) varied with quadrat size: we expected the census repeatability (% of the total variance that is not due to measurement errors) to be higher for small quadrats than for larger ones. Variations according to quadrat size of the repeatability of species richness, Simpson equitability and reciprocal diversity indices, Ellenberg indicator values, plant cover and plant frequency were assessed using 359 censuses of vascular plants. These were carried out independently by four professional botanists during spring 2002 on the same 18 forest plots, each comprising one 400-m² quadrat, four 4-m² and four 2-m² quadrats. Time expenditure was controlled for. General Linear Models using random effects only were applied to the ecological indices to estimate variance components and magnitude of the following effects (if possible): plot, quadrat, observer, plant species and two-way interactions. High repeatability was obtained for species richness and Ellenberg indicator values. Species richness and Ellenberg indicator values were generally more accurate but also more biased in large quadrats. Simpson reciprocal diversity and equitability indices were poorly repeatable (especially equitability) probably because plant cover estimates varied widely among observers, irrespective of quadrat size. Grouping small quadrats usually increased the repeatability of the variable considered (e.g. species richness, Simpson diversity, plant cover) but the number of plant species found on those pooled 16 m² was much lower than if large plots were sampled. We therefore recommend to use large, single quadrats for forest vegetation monitoring.     

塔里木河中下游地区荒漠河岸林群落种间关系分析

采用 2× 2列联表, 应用Fisher精确检验法研究了新疆塔里木河中下游荒漠河岸林群落种间关系, 测定了16种植物、共 12 0个种对的种间联结性。研究结果表明 :1) 12 0个种对中有 17个种对分别在不同的样方尺度中表现出显著或极显著的种间联结, 约占总数的 14.2 % ;其中 13个种对为正关联, 4个种对为负关联 ;2 ) 不同取样面积对种间联结性分析的有效性有影响, 不同种对表现出种间联结的最小样方尺度不同 ;3) 随着样方面积的增大, 各种对自有不同的种间联结变化规律, 可归纳为 4种类型 ;4 ) 17个具种间联结的种对以灌木草本和草本草本的种对居多, 占总数的 76.5 % ;主要乔木树种胡杨 (Populuseuphratica) 与灌木之间、灌木和灌木之间趋向独立分布。     

An estimator of number of species from quadrat sampling

We consider the problem of estimating the number of distinct species S in a study area from the recorded presence or absence of species in each of a sample of quadrats. A generalized jackknife estimator of S is derived, along with an estimate of its variance. It is compared with the jackknife estimator for S proposed by Heltshe and Forrester and the empirical Bayes estimator of Mingoti and Meeden. We show that the empirical Bayes estimator has the form of a generalized jackknife estimator under a specific model for species distribution. We compare the new estimators of S to the empirical Bayes estimator via simulation. We characterize circumstances under which each is superior.     

The energetic equivalence rule rejected because of a potentially common sampling error: evidence from carabid beetles

Abundance data from pitfall traps are widely used to estimate the relationship between beetle body size and abundance. Such data probably overestimate densities of large bodied species and may overestimate slopes of size‐abundance relationships. Here, we test this idea by comparing size‐abundance patterns found using data from pitfall trapping with those found with data from a quantitative method of estimating abundance, quadrat sampling. We use data from a total of 47 communities. As expected, slopes of size‐abundance relationships are significantly more positive when estimated using data from pitfall traps compared to when using quadrat sampling data. This was seen when looking across different communities, within communities sampled by both methods and when focusing on the set of species found by both methods within a community. These results were also generally found regardless of method of analysis, which were done using regression with species values as independent data points and using the independent contrast method, and with slopes estimated using ordinary least square regression or the structural relation. Most important, slopes of size‐abundance relationships based on data from pitfall traps were on average significantly more positive than ?0.75 on log–log scales, and thus inconsistent with the energetic equivalence rule. Slopes based on quadrat sampling, on the other hand, were on average not significantly different from ?0.75. The rejection of the energetic equivalence rule based on data from pitfall traps here is therefore a sampling artefact. Similar problems may apply to abundance data from virtually all insect trapping methods, and should make us consider re‐examining many of the size‐abundance patterns documented so far. As a large proportion of all animal species are insects, and traps are widely used to estimate abundance, this is a potentially important problem for our general understanding of the relationship between species body size and abundance.     

The species-area relation I. A model for discrete sampling

A simple mathematical model describing the species-area relation was developed. This paper dealt with the case that discrete random samples are combined. Modelling was made on the assumption that the occurrence probability of a species in a quadrat has a continuous density distribution. The model, given by the equation (6), holds only for a particular size of quadrat (i.e. the characteristic area). More general form applicable to the quadrats the size of which is near to the characteristic area was represented by the equation (9). Validity of the model was examined for the data of plant and insect communities, and it was concluded that the observation can be predicted by the model unless the size of sampling unit considerably differs from the characteristic area. The uniformity of specific density (i. e. the number of species per quadrat) and the size of characteristic area were discussed as being important in an understanding of community structure.     

Accurate determination of vegetational change in meadows by successive point quadrat analysis

The point quadrat method can be used for determination of vegetational change in meadows of great species diversity. An appropriate sampling technique is described comprehending an apparatus of high rigidity and a shelter to keep off wind and rain. Sample size related to sampling time expense affects the number of species recorded and methodical error which is empirically determined by repetitive sampling. A setup of fixed points leads to higher accuracy than random sampling. When methodical error is quantitatively known, significant vegetational change can be detected by sampling at successive times.For fluctuation studies of plant populations in meadows the point quadrat technique should be preferred to visual estimates of plant cover because of its higher accuracy.Abbreviations f= frequency - s= standard deviation - Sr= variation coefficient - DWLS= distance weighted least squares     

Developing methods for quantifying the apparent abundance of fiddler crabs (Ocypodidae: Uca) in mangrove habitats

Counting the number of individuals emerging from burrows is the most practical method for estimating the apparent abundance of Australian Uca species living in mangrove habitats. Experiments were conducted to investigate the effect on counts of quadrat design, distance of observer, quadrat size, recovery time and observational technique. Significant differences in the apparent abundance of one species were found when the subjects were within 2 m of the observer, and when a conspicuous quadrat was used. The largest quadrat tested provided the least variability in counts but an intermediate size (0.56 m²) was more practical. Most Uca active within a 30-min period emerged during the first 10 min regardless of site, species, sex or season. There was a linear correlation between scanning and continuous observation indicating that the former method could be useful when sampling time was limited. Temporal changes in the apparent abundance of Uca suggest that long-term sampling and more detailed studies will be worthwhile.     

A probability distribution model of small -scale species richness in plant communities

We devised a probability distribution model that best expressed species richness per quadrat in grassland communities, and clarified the mechanism by which the mean richness per quadrat was always larger than the variance among quadrats. Our model will aid in the understanding of community structures, and allow comparisons among different communities. The model was constructed based on relatively simple theoretical assumptions about the mechanisms in play in target communities. We assumed in the model that the number of species occurring in an actual quadrat, j, is the sum of “the fundamental number of species”, k (constant), and “a fluctuating number of species”, i (a Poisson variate with the mean of μ); that is, j = k + i, where i, j and k are non-negative integers. The probability that j species occur in a quadrat is given by a Poisson-like distribution (extended Poisson), with two parameters k and μ. The mean species richness in the probability distribution is expressed by λ (= k + μ), and the variance is λ − k. The proposed model afforded a good fit for the observed frequency distribution of species richness per quadrat. If even one species is common among many quadrats, the mean number of species per quadrat is greater than the variance. The greater the number of common species among quadrats is, the larger is the value of k, and then the more pronounced is the difference between the mean and the variance (although the variance does not change). We fitted the model to 55 datasets collected by ourselves from grasslands in various locations (Tibet, Inner Mongolia, Slovakia, or Japan), with varying quadrat size (0.25, 0.0625, or 0.01 m²), and under differing management status (various stocking densities).     

Analyzing spatial structure of communities using the two-dimensional poisson lognormal species abundance model

The joint spatial and temporal fluctuations in the community structure of tropical butterflies are analyzed by fitting the bivariate Poisson lognormal distribution to a large number of observations in space and time. By applying multivariate dependent diffusions for describing the fluctuations in the abundances, the environmental variance is estimated to be very large and so is the strength of local density regulation. The variance in the lognormal species abundance distribution is partitioned into components expressing the heterogeneity between the species, independent noise components for the different species, a demographic stochastic component, and a component due to overdispersion in the sampling. In disagreement with the neutral theory, the estimates show that the heterogeneity component is the dominating one, representing 81% of the total variance in the lognormal model. Different spatial components of diversity, the alpha, beta, and gamma diversity, are also estimated. The spatial scale of the autocorrelation function for the community is of order 1 km, while sampling of a quadrat would need to be 10 km on a side to yield the total diversity for the community.     

A Jackknife Variance Estimator for Unistage Stratified Samples with Unequal Probabilities

Existing jackknife variance estimators used with sample surveyscan seriously overestimate the true variance under unistagestratified sampling without replacement with unequal probabilities.A novel jackknife variance estimator is proposed which is asnumerically simple as existing jackknife variance estimators.Under certain regularity conditions, the proposed variance estimatoris consistent under stratified sampling without replacementwith unequal probabilities. The high entropy regularity conditionnecessary for consistency is shown to hold for the Rao–Sampforddesign. An empirical study of three unequal probability samplingdesigns supports our findings.     

Sampling strategies for assessing the overall density of the cassava green mite (Mononychellus tanajoa)

Six different sampling methods to estimate the density of the cassava green mite, Mononychellus tanajoa, are categorized according to whether leaves or leaflets are used as secondary sampling units and whether the number of leaves on the sampled plants are enumerated, estimated from an independent plant sample, or not censused at all. In the last case, sampling can provide information only on the average number of mites per leaf and its variance, while information on stratum sizes is necessary to estimate the mean number of mites per plant as well. It is shown that leaflet-sampling is as reliable as leaf-sampling for the same number of sampling units. When stratum sizes are estimated from a separate plant sample, sampling time may also be reduced, but the estimated mean density and its variance may be biased if mite density and plant size are correlated. Sampling data show that the within-plant variance contributes relatively little to the overall variance of the population density estimates. It points at a sampling strategy in which the number of primary units (plants) is as large as possible at the expense of secondary units (leaflets) per plant. Mean-variance relationships may be applied to estimate sample variances and can be used even when only one leaflet is taken per plant per stratum. An unequal allocation of primary units among strata can increase precision, but the gain is small compared with an equal allocation. Leaf area can be predicted from the length of the longest leaflet and the number of leaflets.     

Book reviews

The variance test, originally proposed for testing species associations, is used to test whether species richness is more or less variable than expected under the null model of no species interactions. Species richness is more variable than expected in some fields, and less variable than expected in other fields at the Cedar Creek Natural History Area in Minnesota. High variance in species richness may be caused by variability in competitive exclusion rates or small-scale environmental heterogeneity. Low variance in species richess may occur if the community is saturated with species, or if species-rich areas have high local competitive exclusion rates. Results of the variance test depend somewhat on quadrat size, and can be used to select study sites and quadrat sizes for further research on the nature of variation in species richness.     

栽培药材川续断地上部分体积估算的最优样方选择

以贵州省黔南州龙里县内人工栽培的川续断(Dipsacus asperoides)为研究对象, 就如何选择最优样方的面积和数目来估算川续断地上部分体积进行了研究。首先运用球缺模型计算栽培川续断的地上体积, 然后利用基于套状样方的样带调查法研究估算川续断体积时的最优样方面积, 最后利用方差法计算最优采样数目。结果表明: (1)在只考虑相对平均值和相对消耗时, 25 m × 25 m是最优样方面积; 在此基础上进一步考虑到样方的边界效应和单位面积地上体积相对平均值的变化, 得出25 m × 50 m是最优样方面积。(2)如果预计置信度1-α是0.9, 绝对误差限度d是0.12, 总体方差S²按照常规取0.25, 则25 m × 50 m对应的最佳样方数目是25。(3)该研究实际采集了25个25 m × 50 m的样方, 计算后得到整个栽培园地(面积为72696.24 m ²)川续断的总体积90%的近似置信区间为[1909.798 m³, 2214.762 m³]。     

Estimating genetic correlations in natural populations in the absence of pedigree information: accuracy and precision of the Lynch method

Usually, genetic correlations are estimated from breeding designs in the laboratory or greenhouse. However, estimates of the genetic correlation for natural populations are lacking, mostly because pedigrees of wild individuals are rarely known. Recently Lynch (1999) proposed a formula to estimate the genetic correlation in the absence of data on pedigree. This method has been shown to be particularly accurate provided a large sample size and a minimum (20%) proportion of relatives. Lynch (1999) proposed the use of the bootstrap to estimate standard errors associated with genetic correlations, but did not test the reliability of such a method. We tested the bootstrap and showed the jackknife can provide valid estimates of the genetic correlation calculated with the Lynch formula. The occurrence of undefined estimates, combined with the high number of replicates involved in the bootstrap, means there is a high probability of obtaining a biased upward, incomplete bootstrap, even when there is a high fraction of related pairs in a sample. It is easier to obtain complete jackknife estimates for which all the pseudovalues have been defined. We therefore recommend the use of the jackknife to estimate the genetic correlation with the Lynch formula. Provided data can be collected for more than two individuals at each location, we propose a group sampling method that produces low standard errors associated with the jackknife, even when there is a low fraction of relatives in a sample.     

Variance and spatial scales in a tropical rain forest: changing the size of sampling units

The size of a sampling unit has a critical effect on our perception of ecological phenomena; it influences the variance and correlation structure estimates of the data. Classical statistical theory works well to predict the changes in variance when there is no autocorrelation structure, but it is not applicable when the data are spatially autocorrelated. Geostatistical theory, on the other hand, uses analytical relationships to predict the variance and autocorrelation structure that would be observed if a survey was conducted using sampling units of a different size. To test the geostatistical predictions, we used information about individual tree locations in the tropical rain forest of the Pasoh Reserve, Malaysia. This allowed us to simulate and compare various sampling designs. The original data were reorganised into three artificial data sets, computing tree densities (number of trees per square meter in each quadrat) corresponding to three quadrat sizes (5×5, 10×10 and 20×20 m⁽²⁾). Based upon the 5×5 m⁽²⁾ data set, the spatial structure was modelled using a random component (nugget effect) plus an exponential model for the spatially structured component. Using the within-quadrat variances inferred from the variogram model, the change of support relationships predicted the spatial autocorrelation structure and new variances corresponding to 10×10 m⁽²⁾ and 20×20 m⁽²⁾ quadrats. The theoretical and empirical results agreed closely, while the classical approach would have largely underestimated the variance. As quadrat size increases, the range of the autocorrelation model increases, while the variance and proportion of noise in the data decrease. Large quadrats filter out the spatial variation occurring at scales smaller than the size of their sampling units, thus increasing the proportion of spatially structured component with range larger than the size of the sampling units.     

Use of the regression of mean crowding on mean density for estimating sample size and the transformation of data for the analysis of variance

An approximate method for estimating the sample size in simple random sampling and a systematic way of transformation of sample data are derived by using the parameters α and β of the regression of mean crowding on mean density in the spatial distribution per quadrat of animal populations (Iwao , 1968). If the values of α and β have been known for the species concerned, the sample size needed to attain a desired precision can be estimated by simply knowing the approximate level of mean density of the population to be sampled. Also, an appropriate variance stabilizing transformation of sample data can be obtained by the method given here without restrictions on the distribution pattern of the frequency counts.     

A comparison of two methods for making statistical inferences on Nei's measure of genetic distance

The delta and jackknife methods can be used to estimate Nei's measure of genetic distance and calculate confidence intervals for this estimate. Computer stimulations were used to study the bias and variance of each estimator and the accuracy of the corresponding approximate 95% confidence intervals. The simulations were conducted using 3 sets of data and several sample sizes. The results showed: (1) the jackknife reduced bias; (2) in 8 out of 9 cases the variance and mean square error of the jackknife estimator were less; (3) a second order jackknife reduced the bias the most but suffered a corresponding increase in variance; (4) both the first order jackknife and delta methods yielded intervals whose confidence levels were approximately equal but less than 95%.     

Similarities between rarefaction methods

The number of species in a community is one of the most commonly used measures of diversity. This measure is, however, affected by sample size. The rarefaction method attempts to correct sample size bias by assuming an underlying sampling model. Several rarefaction models are shown to be similar analytically. This similarity holds not only for the expected number of species but also for the variance of the number of species.     

Scale specific determinants of tree diversity in an old growth temperate forest in China

The major processes generating pattern in plant community composition depend upon the spatial scale and resolution of observation, therefore understanding the role played by spatial scale on species patterns is of major concern. In this study, we investigate how well environmental (topography and soil variables) and spatial variables explain variation in species composition in a 25-ha temperate forest in northeastern China. We used new variation partitioning approaches to discover the spatial scale (using multi-scale spatial PCNM variables) at which environmental heterogeneity and other spatially structured processes influence tree community composition. We also test the effect of changing grain of the study (i.e. quadrat size) on the variation partitioning results. Our results indicate that (1) species composition in the Changbai mixed broadleaf-conifer forest was controlled mainly by spatially structured soil variation at broad scales, while at finer scales most of the explained variation was of a spatial nature, pointing to the importance of biotic processes. (2) These results held at all sampling grains. However, reducing quadrat size progressively reduced both spatially and environmentally explained variance. This probably partly reflects increasing stochasticity in species abundances, and the smaller proportion of quadrats occupied by each species, when quadrat size is reduced. The results suggest that environmental heterogeneity (i.e. niche processes) and other biotic processes such as dispersal work together, but at different spatial scales, to build up diversity patterns.