Temporal Changes in the Inequality of Early Growth of Cunninghamia lanceolata (Lamb.) Hook.: A Novel Application of the Gini Coefficient and Lorenz Asymmetry

Growth within tree populations varies among individuals due to changes in biotic and abiotic factors. The degree of such variation, defined as growth inequality, serves as a useful indicator of the uniformity of growth within a population in response to the prevalent environmental conditions. By application of the Gini coefficient (G), an index for inequality, we characterized the early growth inequality of ninety crosses of Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) and their open-pollinated parental lines. Tree cumulative height was measured annually for 8 consecutive years. Both the crosses and parental lines exhibited temporal changes in growth inequality. The inequality of total height among the crosses decreased logarithmically with age by nearly 3-fold after 13 growing seasons, suggesting that tree height became less variable among the crosses as trees grew larger. Interestingly, the Lorenz asymmetry, an index reflecting the shape of the Lorenze curve from which G is derived, revealed that the inequality of annual height increment among the crosses resulted from an alternate contribution of the fast-growing and slow-growing trees. Among parental lines, two provenances with the smallest and the largest overall inequality in total height showed a similar pattern of changes in annual growth inequality, and the provenance differences were consistent over time. Compared to the other provinces, a local provenance exhibited less variation in total height among individual trees as reflected by a smaller value of inequality, and was better adapted to the field conditions. Our results demonstrated the sensitivity and usefulness of the Gini coefficient and Lorenz asymmetry for the analysis of growth inequality in non-natural populations. Growth inequality is a potentially useful evaluation criterion for early selection. Given comparable initial growth, provenances/families with lower growth inequality values would likely outperform those with higher growth inequality, and eventually tree size of the latter would be more variable due to greater variations among individual trees. Assessment of growth inequality at early ages will advance our understanding of variability of tree growth within a population, facilitate forest genetics improvement programs, and enhance the efficiency of tree breeding.     

林木个体大小不一致性指标对人工林间伐方式的即时性响应

以广西14年生杉木和马尾松人工林为对象,设同一疏伐强度的下层疏伐、上层疏伐、机械疏伐和干扰树间伐4种处理,分别用标准差、变异系数、偏度、Gini系数、库兹涅茨系数和洛伦茨不对称系数6种指标对4种间伐方式下采伐前后林木个体大小差异进行评价.结果表明: 与间伐前相比,马尾松和杉木人工林下层疏伐或上层疏伐后,林木个体材积的标准差、变异系数、Gini系数和库兹涅茨系数均变小,偏度变大;干扰树间伐后标准差、变异系数、Gini系数和库兹涅茨系数均变大,偏度则不一定.马尾松林和杉木林下层疏伐后洛伦茨不对称系数变大,上层疏伐或干扰树间伐后则变小.机械疏伐后各指标无明显变化规律.干扰树间伐后林木个体大小差异性增加,上层疏伐和下层疏伐后林木个体大小差异性减小.洛伦茨曲线、Gini系数和洛伦茨不对称系数均能较好地反映林木个体大小不一致性,可以进行不同林分间个体差异程度静态和动态比较,较好地反映不同间伐方式引起的林木个体差异.洛伦茨不对称系数可以判断林木个体大小不一致性的来源是大树还是小树.近自然森林经营中干扰树间伐措施可以在减小目标树竞争压力的同时拉大林木个体大小差距,有助于保持目标树在林分中的优势地位.
     

The meaning and measurement of size hierarchies in plant populations

Summary The term size hierarchy has been used frequently by plant population biologists but it has not been defined. Positive skewness of the size distribution, which has been used to evaluate size hierarchies, is inappropriate. We suggest that size hierarchy is equivalent to size inequality. Methods developed by economists to evaluate inequalities in wealth and income, the Lorenz curve and Gini Coefficient, provide a useful quantification of inequality and allow us to compare populations. A measure of inequality such as the Gini Coefficient will usually be more appropriate than a measure of skewness for addressing questions concerning plant population structure.     

Comparative application of the coefficient of variation and range-based statistics for assessing the taxonomic composition of fossil samples

Dental variation has been used commonly to assess taxonomic composition in morphologically homogeneous fossil samples. While the coefficient of variation (CV) has been used traditionally, range-based measures of variation, such as the range as a percentage of the mean (R%) and the maximum/minimum index (I_max/min) have recently become popular alternatives. The current study compares the performance of these statistics when applied to single- and pooled-species dental samples of extant Cercopithecus species. A common methodology for such problems of species discrimination has been to simply compare the maximum value of a variation statistic observed in extant samples with that observed in the fossil sample. However, regardless of what statistic is used, this approach has an unknowable Type I error rate, and usually has low power to detect multiple species. A more appropriate method involves a formal hypothesis test. The null hypothesis is that the level of variation in the fossil sample does not exceed what might be expected in a sample drawn randomly from a reference population, taking into account sampling error and the size of the fossil sample. Previous research using this method with the CV has indicated that it offers considerable power at an acceptable Type I error rate. In the current study, the data of primary interest were posterior dental dimensions for single- and pooled species samples from extant Cercopithecus species. In addition, the study also investigated the relative performance of variation statistics when applied to highly dimorphic canine dimensions, since much recent work has employed sexually dimorphic dental dimensions for assessing single-species hypotheses. The results indicate that the CV consistently out-performed the range-based statistics when using posterior dental dimensions to test a single-species hypothesis. Regardless of which statistic was used, tests on sexually dimorphic dimensions offered minimal power. In consideration of these results and the problem of studywise Type I error rates, we recommend against the use of multiple measures of variation to test for multiple species composition, and advocate the CV as the statistic of choice when using the method of Cope & Lacy (1992). For similar reasons, we argue for careful selection of dental variables for inclusion in such analyses, and in particular recommend against including sexually dimorphic dimensions when testing for multiple species composition.     

Size and fecundity hierarchies in an herbaceous perennial

Summary Inequalities in size in populations have potentially important effects on fitness but have rarely been examined in natural populations. I measured size (number of culms) and fecundity (number of spikelets) in five populations of the grass Danthonia spicata from 1981 to 1985. The populations were in sites in a Pinus-Quercus-Populus forest in northern lower Michigan, USA comprising a secondary succession sequence. The sites had been burned in 1980, 1954, 1948, 1936, and 1911, respectively. Mean sizes and fecundities and the amount of hierarchy in size and fecundity, measured by the Gini coefficient, were compared between the YOUNG population, 1980 burn site, and the OLD populations, 1954, 1948, 1936, and 1911 burn sites. I found large differences in mean size and fecundity between the YOUNG and OLD populations with much larger individuals in the YOUNG population. No differences in size hierarchies were found in either the first year of measurement or after five years. The fecundity hierarchies showed no significant difference among the populations in the first year but after five years the YOUNG population showed a significant decrease in amount of inequality. The longterm patterns of size and fecundity hierarchies differed because fecundity was a cumulative trait while size was not. Size inequalities may not always be a good measure of fecundity inequalities. Short-term measures of inequality in perennials may not be a good indicator of long-term values. In contrast to greenhouse studies, habitat light levels did not affect size hierarchies although they did affect fecundity hierarchies.     

Differentiation and frequency distributions of body weights in plants and animals

The basic and simplest system that one can consider in ecology is a group of individuals of equal age and representing one species, that is, a cohort. This paper is an attempt to show that analysis of such a system may be of great importance to understanding basic ecological problems, such as, intraspecific competition and the dynamics of a single population. It is easy to observe that in even-aged populations individuals differ in weights. A close look can show that weight distributions in even-aged populations may have different skewness. Most common are distributions with coefficients of skewness greater than zero. Sometimes weight distributions are symmetrical or with skewness coefficients less than zero. In a cohort of growing individuals the coefficient of skewness changes with time: most often starting from zero (symmetrical distribution), it increases in time; sometimes after an initial increase it can decrease in the final stage of growth, which is related to an increased mortality of individuals. The rate of change in skewness, and the skewness itself depend on the density of individuals in a cohort and on food conditions. They are greater at higher densities and increase with deteriorating food conditions. Weight distributions are symmetrical at low densities and optimal food conditions. The differences in individual weights measured by variance of weight distributions or coefficient of variation follow the same pattern, but observed changes with time, density and food conditions are not so clear. These conclusions rest upon the review of numerous papers concerning both plants and animals, which is presented in this paper. In the past, the properties of weight distributions in even-aged populations were explained not by interactions between individuals, but rather as a natural outcome of the growth process of non-interacting individuals. The exponential equation of growth, with relative growth rate having a normal distribution in populations, was used to support this hypothesis. Obtained weight distributions were of positive skewness; however, this model, which in fact is able to describe the growth process only in its initial stage, cannot explain the changes of skewness of weight distributions with density and food conditions. A model has been developed which includes competitive interactions among members of even-aged populations to explain observed properties of weight distributions in them. The basic assumption is that intraspecific competition leads to uneven partitioning of resources, which are the object of competition. Functions describing resource partitioning among individuals are included into the model.(ABSTRACT TRUNCATED AT 400 WORDS)     

Geographic structuring of chloroplast DNA genotypes inTiarella trifoliata (Saxifragaceae)

Tiarella trifoliata comprises varietieslaciniata, trifoliata, andunifoliata, and is distributed from southeastern Alaska to northern California. We analyzed restriction site variation of chloroplast DNA (cpDNA) using 23 endonucleases in 76 populations representing the entire geographic range of the species and the three recognized varieties. We also employed comparative restriction site mapping of PCR-amplified chloroplast DNA fragments using 16 restriction endonucleases. This species exhibits low cpDNA restriction site variation. No differentiation is evident among varieties of this species based on cpDNA data; some plants of each variety were characterized by each of the two major cpDNA types detected. The two major cpDNA clades, which differ by only a single restriction site mutation, are geographically structured. A northern clade comprises populations from Alaska to central Oregon; most populations analyzed from southern Oregon and California form a southern clade. Populations that possess the typical northern cpDNA type also occur disjunctly to the south at high elevations in the Siskiyou—Klamath Mountain area of southern Oregon and northern California. Conversely, the southern cpDNA type is found disjunctly to the north in the Olympic Peninsula of Washington. Both geographic areas characterized by disjunct cytoplasms are considered glacial refugia.Tiarella trifoliata joins two other species,Tolmiea menziesii andTellima grandiflora, in having well-demarcated northern and southern cpDNA lineages. All three species have similar life-history traits and geographic distributions. We suggest that glaciation may have played a major role in the formation of the cpDNA discontinuities present in these three taxa. The pronounced relationship between cpDNA variation and geographic distribution suggests the potential applicability of intraspecific phylogeography to plants via the analysis of intraspecific cpDNA variation. These three examples also join a rapidly growing data base which indicates that cytoplasms are often geographically structured within species and species complexes.     

Drawing inferences about the coancestry coefficient

The coancestry coefficient, also known as the population structure parameter, is of great interest in population genetics. It can be thought of as the intraclass correlation of pairs of alleles within populations and it can serve as a measure of genetic distance between populations. For a general class of evolutionary models it determines the distribution of allele frequencies among populations. Under more restrictive models it can be regarded as the probability of identity by descent of any pair of alleles at a locus within a random mating population. In this paper we review estimation procedures that use the method of moments or are maximum likelihood under the assumption of normally distributed allele frequencies. We then consider the problem of testing hypotheses about this parameter. In addition to parametric and non-parametric bootstrap tests we present an asymptotically-distributed chi-square test. This test reduces to the contingency-table test for equal sample sizes across populations. Our new test appears to be more powerful than previous tests, especially for loci with multiple alleles. We apply our methods to HapMap SNP data to confirm that the coancestry coefficient for humans is strictly positive.     

Patterns of genetic differentiation in two annual bromegrasses,Bromus lanceolatus andB. hordeaceus (Poaceae)

Infraspecific genetic differentiation was analysed in two tetraploid annual bromegrasses,Bromus lanceolatus (from N Africa) andB. hordeaceus (from N Africa and France). Genetic analysis of populations was based on allozyme polymorphisms at 17 loci. Different fixed heterozygous phenotypes were scored in both species, according to their allopolyploid origin. In N Africa, more variation occurred among populations ofB. lanceolatus than ofB. hordeaceus. The variation was not randomly distributed among populations of both species. InB. lanceolatus, differentiation was correlated with climatic variables rather than with geographic distance between populations. Higher correlation of genetic differentiation with geographic distance occurred inB. hordeaceus, particularly at large geographic scale, between French and N African populations. Within each region, the populations appeared weakly genetically differentiated, even when belonging to different subspecies.     

基于多角度基尼系数的江西省资源环境公平性研究

资源环境基尼系数是衡量和评价资源消耗、污染物排放在各个城市或地区间的公平性与合理性的有效途径。对基于GDP(gross domestic product)、人口、国土面积等角度推算的资源环境基尼系数方法的优劣性进行了评价,提出了"生态负荷系数"的概念,界定了"生态容量"的概念与内容,并从GDP、人口和生态容量的角度出发,以江西省11地市作为评价对象,选取2009年能源消耗、水资源消耗、COD(chemical oxygen demand)排放及SO2排放等4个评价因子,构建了江西省资源环境基尼系数、生态负荷系数的计算与评价方法,并对计算结果进行了对比分析。结果表明:(1)不同角度计算的基尼系数不尽相同,从生态负荷系数来看,在江西11个城市中,南昌、鹰潭、萍乡、景德镇、新余等经济发达城市是引起能源消耗、SO2排放主要的不公平因子,是需要转变经济发展模式的城市,更须注重经济与环境的协调发展;(2)从生态容量的角度推算的资源环境基尼系数普遍高于从GDP和人口角度推算的资源环境基尼系数,且都高于"警戒线";(3)从理论上看,基于生态容量角度的资源环境基尼系数比基于GDP和人口角度的资源环境基尼系数更为科学与合理。文章最后讨论了不同角度的资源环境基尼系数及生态负荷系数的科学性与合理性的问题。     

On fluctuation analysis: a new,simple and efficient method for computing the expected number of mutants

Fluctuation analysis, which is often used to demonstrate random mutagenesis in cell lines (and to estimate mutation rates), is based on the properties of a probability distribution known as the Luria-Delbrück distribution (and its generalizations). The two main new results reported in this paper are (i) a simple, completely general, and computationally efficient procedure for calculating probability distributions arising from fluctuation analysis and (ii) the formula for this procedure when cells in a colony have only grown for a finite number of generations after initial seeding. It is also shown that the procedure reduces to one that was developed earlier when an infinite number of generations is assumed. The derivation of the generating function of the distribution is also clarified. The results obtained should also be useful to experimentalists when only a relatively short time elapses between seeding and harvestint cultures for fluctuation analysis.     

Food web stability and weighted connectance: the complexity-stability debate revisited

How the complexity of food webs relates to stability has been a subject of many studies. Often, unweighted connectance is used to express complexity. Unweighted connectance is measured as the proportion of realized links in the network. Weighted connectance, on the other hand, takes link weights (fluxes or feeding rates) into account and captures the shape of the flux distribution. Here, we used weighted connectance to revisit the relation between complexity and stability. We used 15 real soil food webs and determined the feeding rates and the interaction strength matrices. We calculated both versions of connectance, and related these structural properties to food web stability. We also determined the skewness of both flux and interaction strength distributions with the Gini coefficient. We found no relation between unweighted connectance and food web stability, but weighted connectance was positively correlated with stability. This finding challenges the notion that complexity may constrain stability, and supports the ‘complexity begets stability’ notion. The positive correlation between weighted connectance and stability implies that the more evenly flux rates were distributed over links, the more stable the webs were. This was confirmed by the Gini coefficients of both fluxes and interaction strengths. However, the most even distributions of this dataset still were strongly skewed towards small fluxes or weak interaction strengths. Thus, incorporating these distribution with many weak links via weighted instead of unweighted food web measures can shed new light on classical theories.     

The impact of species-specific traits and phylogenetic relatedness on allozyme diversity inCarex sect.Phyllostachys (Cyperaceae)

Allozyme variation was examined inCarex sect.Phyllostachys (Cyperaceae) to study the effects of species-specific traits and phylogenetic relatedness on genetic structure. In contrast to the findings of similar studies, genetic variability in thePhyllostachys is poorly correlated with geographic range and putative differences in breeding systems (as inferred from morphology). This suggests that other patterns of evolution, colonization, and gene flow characterize the species found in this section. Fixation indices are negative for all populations suggesting that mechanisms such as disassortative mating and selection are maintaining heterozygous excess within populations. Closely related taxa often exhibit different genetic variability statistics. In some instances, however, clades (e.g.C. jamesii andC. juniperorum) display very similar levels of genetic variability despite marked differences in species-specific traits. Recent speciation coupled with the ability to maintain historical levels of variation within populations may be factors accounting for this phenomenon. Contrary to similar studies, species restricted to known glacial refugia have lower genetic diversity than those species that underwent mass migrations in response to deglaciation. Narrowly endemic species were found to partition their genetic diversity within, as opposed to between populations. The opposite trend was evident in wider ranging congeners.     

Complexity of species conservation in managed habitats: interaction betweenMaculinea butterflies and their ant hosts

Europe's five species ofMaculinea butterfly are examples of endangered species adapted to live in traditional, cultural landscapes. All are threatened with extinction in Western Europe because of recent changes in land use. This is illustrated by an historical account of the extinction of the BritishMaculinea arion populations, despite many conservation attempts. It is shown how the failures proved to be due to ignorance of the key factor forM. arion, its specialization on a single ant host,Myrmica sabuleti. A brief account is given of research that shows how each of the five species is similarly dependent upon a separate hostMyrmica ant species and how each has an interesting and rare specific parasitoid. Steps for the practical conservation of existingMaculinea populations including the obligation, under the Bern Convention, to re-establish nationally extinct species are outlined. The procedure and problems involved in re-establishment are illustrated with reference to the successful programme forM. arion in Britain. The best way of ensuring robust populations ofMaculinea butterflies is to manage habitats to optimize the density and distribution of the required species ofMyrmica host and, secondarily, the distribution of the larval food plant. The value of single species conservation in cultural habitats is discussed. It is concluded that this is possible to achieve and that other rare organisms also often benefit, but only when conservation measures are based on the results of detailed autecological research.     

Branching process results in terms of moments of the generation-time distribution

A number of simple formulae concerning the growth rate, doubling time, and age distribution of cell populations are in common usage. Many of these are invalid unless the generation times have no variation, a situation which occurs rarely. The correct formulae, which are available from the theory of age-dependent branching processes, are often ignored in the biological literature, perhaps due to their complexity. In this paper the major formulae from the theory of age-dependent branching processes are reorganised in terms of the mean, coefficient of variation, and skewness of the generation times. This leads to a greater insight into the theory and some simple formulae which account for the variability.     

Invasive Mahonia plants outgrow their native relatives

Invasive populations often grow more vigorously than conspecific populations in the native range. This has frequently been attributed to evolutionary changes resulting either from founder effects, or from natural selection owing to enemy release. Another mechanism contributing to evolutionary change has largely been neglected in the past: Many invasive plant species do actually descend from cultivated plants and were therefore subject to breeding, including hybridization and artificial selection. In a common garden experiment, we compared invasive Central European populations of the ornamental shrub, Mahonia, with native populations of its putative parental species, Mahonia aquifolium and M. repens, from North America. We hypothesized that plants of invasive populations show increased growth and retained high levels of heritable variation in phenotypic traits. Indeed, invasive Mahonia plants grew larger in terms of stem length, number of leaves and above-ground biomass than either of the two native species, which did not differ significantly from each other. Since there are no hints on release of invasive Mahonia populations from natural enemies, it is likely that hybridization and subsequent selection by breeders have lead to an evolutionary increase of plant vigour in the introduced range. Further on, heritable variation was not consistently reduced in invasive populations compared with populations of the two native species. We suggest that interspecific hybridization among the Mahonia species has counteracted the harmful effects of genetic bottlenecks often associated with species introductions. Based on this case study, we conclude that, more attention has to be paid on the role of plant breeding when assessing the mechanisms behind successful plant invasions in future.     

野生玫瑰种群表型变异

在野生玫瑰(Rosa rugosa)自然分布区内选取5个代表种群,选择24个表型性状作为研究对象,运用方差分析、多重比较、主成分分析、相关分析、聚类分析等方法,得出野生玫瑰种群表型变异程度和变异规律。结果显示:(1)24个表型性状在种群间和种群内均存在极显著差异,变异非常丰富;种群内变异(0.2718)大于种群间变异(0.1679),种群内变异是表型变异的主要来源,种群间平均表型分化系数(VST)为0.2952,分化水平相对较大;表型性状平均变异系数(CV)为18.48%(6.67—26.79%),叶片、果实、花、种子的变异系数依次为21.40%、17.42%、12.54%、6.67%;主成分分析表明叶片、果实的表型变异对种群变异起主要的贡献作用。(2)托叶长与年平均气温、7月平均气温呈显著正相关,与经、纬度呈显著负相关;果实横径与年降水量呈显著正相关;千粒重与经、纬度呈显著正相关,与7月平均气温呈显著负相关。(3)利用欧氏距离进行系统聚类分析,可以将5个种群划分为3类,表型性状主要依地理位置聚类。     

紫距淫羊藿的地理分布新记录及形态描述

淫羊藿属依据少量栽培个体命名的类群普遍存在,往往缺乏足够的野外调查和形态性状统计,对其性状变异幅度、变异式样和分类价值研究不够。紫距淫羊藿(Epimedium epsteinii)由Stearn于1997年依据引种个体命名,为掌握其资源分布及形态性状变异,该研究基于居群概念,对淫羊藿属分布区展开调查,在各分布区选择一个居群(30个体/居群)于花期进行形态观察、统计和描述。结果表明:紫距淫羊藿以往被认为狭域分布于湖南天平山,该研究调查发现广东省和湖北省均有分布,为新分布记录。此两处新分布分别位于天平山的南部和北部,将其自然分布区显著扩大。基于居群观测的形态变异较原描述更广泛。6个主要数量性状(株高、序轴长、小花数、叶长、叶宽和根茎)和花部颜色在居群间和个体间均呈现丰富的变异。生物种的分布范围并非完全连续,而是由若干个多少间断的居群组成,任何一个居群都存在不同程度的连续性变异,要更好地认识各物种,就应当足够重视这些居群系统。紫距淫羊藿的新分布记录对淫羊藿属的资源利用、扩散机制和系统地理学研究具有重要意义。     

Studies in the Melica ciliata – complex: 1. Distribution of allozyme variation within and among individuals, populations and geographic regions

Allozyme variation in 83 European populations of the Melica ciliata/ transsilvanica species complex has been investigated. In spite of a diploid chromosome number, most loci were duplicated and patterns of within-population variation were not explainable unless apomixis or uncommon patterns of chromosomal segregation were assumed. Allelic richness and genetic diversity were very high but most of the variation (55-98%) was due to population differentiation. Geographic patterns were analysed both using phenetic, based on allele frequencies within populations, and cladistic, based on multi-locus genotypes, methods. Both methods congruently recognised three large groups of populations with discrete geographic distributions, in addition to a number of smaller groups. Of the three main groups, one was distributed in eastern and central Europe, one was restricted to western Europe north of the Alps and one was distributed in Iberia, Brittany and along the western shores of the Mediterranean. These groups are likely to have had separate histories but there appears to have been significant gene-flow among them. Among the less distinct groups, it was suggestive that some, e.g. the group containing all populations from the disjunct distribution in the Baltic basin, have been formed by introgression between the three major groups, whereas other deviating populations may represent additional distinct entities.