山西毛榛植物构型特征分析

以山西省中条山大河林场、太岳山绵山林场、兴唐寺林场和七里峪林场、五台山金岗库林场、恒山王庄堡林场的毛榛（Corylus mandshurica Maxim.）为研究对象,采用样方调查方法,系统研究了毛榛在不同生境中的构型和分形维数特征。结果显示,大河林场毛榛的总体分枝率和枝径比（RBD_2：1、RBD_3：2）均大于其它地区,逐步分枝率（SBR_1：2、SBR_2：3）与总体分枝率呈现出相反的趋势,五台山金岗库林场毛榛的逐步分枝率最大;山西省各研究地毛榛的分枝角度差异显著,北部地区从1级到3级有减小的趋势,金岗库林场的毛榛1级分枝角度最大;分枝长度也呈现出从1级到3级逐渐减小的趋势,其各级分枝长度排序为：金岗库林场 > 王庄堡林场 > 七里峪林场 > 兴唐寺林场 > 绵山林场 > 大河林场;从分形维数来看,金岗库林场毛榛的树冠分维数和分枝分维数均为最大;各研究地毛榛的叶面积和地上生物量从北到南均表现为逐渐减小;金岗库林场毛榛叶面积的平均值、叶生物量和枝生物量均最大。研究结果表明6个研究区中金岗库林场的毛榛长势最好,该地的气候条件最适宜毛榛生长。     

分形及其在植物研究中的应用

本文着重介绍了非线性科学热点之一的分形理论,并综述了分形理论在植物结构模拟、植物群落研究、景观格局研究、树木冠层特征研究、木材学研究、作物根系研究等方面的应用进展以及分维数求算方法研究进展,最后,对非线性理论在植物研究领域应用前景进行了展望。     

Development,persistence and regeneration of foraging ectomycorrhizal mycelial systems in soil microcosms

Development of extraradical mycelia of two strains each of Paxillus involutus and Suillus bovinus in ectomycorrhizal association with Pinus sylvestris seedlings was studied in two dimensions in non-sterile soil microcosms. There were significant inter- and intra-specific differences in extraradical mycelial growth and morphology. The mycelial systems of both strains of P. involutus were diffuse and extended more rapidly than those of S. bovinus. Depending on the strain, P. involutus mycelia were either highly plane filled, with high mass fractal dimension (a measure of space filling) or sparse, low mass fractal dimension systems. Older mycelial systems persisted as linear cords interlinking ectomycorrhizal tips. S. bovinus produced either a mycelium with a mixture of mycelial cords and diffuse fans that rapidly filled explorable area, or a predominately corded mycelium of minimal area cover. In the soil microcosms, mass fractal dimension and mycelial cover tended to increase with time, mycelia encountering litter having significantly greater values. Results are discussed in terms of the ecology of these fungi, their foraging activities and functional importance in forest ecosystems.     

Self-similar mitochondrial DNA

We show that repeated sequences, like palindromes (local repetitions) and homologies between two different nucleotide sequences (motifs along the genome), compose a self-similar (fractal) pattern in mitochondrial DNA. This self-similarity comes from the looplike structures distributed along the genome. The looplike structures generate scaling laws in a pseudorandom DNA walk constructed from the sequence, called a Lévy flight. We measure the scaling laws from the generalized fractal dimension and singularity spectrum for mitochondrial DNA walks for 35 different species. In particular, we report characteristic loop distributions for mammal mitochondrial genomes.     

Implications of Fluctuations in Substitution Rates: Impact on the Uncertainty of Branch Lengths and on Relative-Rate Tests

Many tests of the lineage dependence of substitution rates, computations of the error of evolutionary distances, and simulations of molecular evolution assume that the rate of evolution is constant in time within each lineage descended from a common ancestor. However, estimates of the index of dispersion of numbers of mammalian substitutions suggest that the rate has time-dependent variations consistent with a fractal-Gaussian-rate Poisson process, which assumes common descent without assuming rate constancy. While this model does not affect certain relative-rate tests, it substantially increases the uncertainty of branch lengths. Thus, fluctuations in the rate of substitution cannot be neglected in calculations that rely on evolutionary distances, such as the confidence intervals of divergence times and certain phylogenetic reconstructions. The fractal-Gaussian-rate Poisson process is compared and contrasted with previous models of molecular evolution, including other Poisson processes, the fractal renewal process, a Lévy-stable process, a fractional-difference process, and a log-Brownian process. The fractal models are more compatible with mammalian data than the nonfractal models considered, and they may also be better supported by Darwinian theory. Although the fractal-Gaussian-rate Poisson process has not been proven to have better agreement with data or theory than the other fractal models, its Gaussian nature simplifies the exploration of its impact on evolutionary distance errors and relative-rate tests. Received: 29 September 1999 / Accepted: 20 January 2000     

A self-similarity model for the occupancy frequency distribution

The shapes of interspecific range-size distributions at scales finer than the geographic range are highly variable. However, no numerical model has been developed as a basis for understanding this variation. Using self-similarity conditions, we present an occupancy probability transition (OPT) model to investigate the effect of sampling scale (i.e. sample grain) and species saturation (strongly positively correlated with the fractal dimension) on the shape of occupancy frequency distributions (fine scale expression of range-size distributions). In accordance with empirical observations, the model showed that core-modes are likely to be rare in occupancy frequency distributions. The modal occupancy shifted from core to satellite with an increase in sample grain (from coarse scale to fine scale) at a linear rate after log-transformation of occupancy. Saturation coefficients above a particular threshold generated multimodality. Bimodal distributions arose from a combination of different occupancy probability distributions (OPDs), with species-specific saturation coefficients generating occupancy frequency distributions of the shape commonly observed empirically, i.e. bimodal with a dominant satellite mode. This is a consequence of the statistical properties of the OPD, and is also largely insensitive to species richness. The OPT model thus provides a null model for the shape of occupancy frequency distributions. Furthermore, it demonstrates that the sample grain of a study, sampling adequacy (based on a linear sampling assumption) and the distribution of species saturation coefficients in a community are together largely able to explain the patterns observed in empirical occupancy frequency distributions.     

A dynamically changing intracellular water network serves as a universal regulator of the cell: the water-governed cycle

The functioning of enzymes and protein folding are well known to be assisted by the surrounding chaperoning water molecules, which are connected to the protein via non-covalent, dynamically changing chemical bonds. A molecular intracellular network of weak non-covalent connections may be presumed to exist in living cells. The roles of such non-covalent networks are examined in terms of a molecular model which postulates a universal enzyme and biochemical mechanism regulating the maintenance of chemical stability in living cells.     

Fractal Dimension in Butterflies’ Wings: a novel approach to understanding wing patterns ?

The geometrical complexity in the wings of several, taxonomically different butterflies, is analyzed in terms of their fractal dimension. Preliminary results provide some evidence on important questions about the (dis)similarity of the wing patterns in terms of their fractal dimension. The analysis is restricted to two groups which are widely used in the literature as typical examples of mimicry, and a small number of unrelated species, thus implying the consideration of only a fraction of the wing pattern diversity. The members of the first mimicry ring, composed by the species Danaus plexippus (better known as the monarch butterfly), and the two subspecies Basilarchia archippus obsoleta (or northern viceroy) and Basilarchia archippus hoffmanni (or tropical viceroy), are found to have a very similar value for the fractal dimension of their wing patterns, even though they do not look very similar at first sight. It is also found that the female of another species (Neophasia terlootii), which looks similar to the members of the previous group, does not share the same feature, while the Lycorea ilione albescens does share it. For the members of the second group of mimicry related butterflies, the Greta nero nero and the Hypoleria cassotis, it is shown that they also have very close values for the fractal dimension of their wing patterns. Finally, it is shown that other species, which apparently have very similar wing patterns, do not have the same fractal dimension. A possible, not completely tested hypothesis is then conjectured: the formation of groups by individuals whose wing patterns have an almost equal fractal dimension may be due to the fact that they do share the same developmental raw material, and that this common feature is posteriorly modified by natural selection, possibly through predation.We sincerely acknowledge the invaluable help of Adolfo Ibarra Vázquez, senior curator of the Lepidopterous collection at the Instituto de Biología, Universidad Nacional Autónoma de México, and the comments made by two anonymous referees     

Evo-devo and the search for homology (“sameness”) in biological systems

Developmental biology and evolutionary studies have merged into evolutionary developmental biology (“evo-devo”). This synthesis already influenced and still continues to change the conceptual framework of structural biology. One of the cornerstones of structural biology is the concept of homology. But the search for homology (“sameness”) of biological structures depends on our favourite perspectives (axioms, paradigms). Five levels of homology (“sameness”) can be identified in the literature, although they overlap to some degree: (i) serial homology (homonomy) within modular organisms, (ii) historical homology (synapomorphy), which is taken as the only acceptable homology by many biologists, (iii) underlying homology (i.e., parallelism) in closely related taxa, (iv) deep evolutionary homology due to the “same” master genes in distantly related phyla, and (v) molecular homology exclusively at gene level. The following essay gives emphasis on the heuristic advantages of seemingly opposing perspectives in structural biology, with examples mainly from comparative plant morphology. The organization of the plant body in the majority of angiosperms led to the recognition of the classical root–shoot model. In some lineages bauplan rules were transcended during evolution and development. This resulted in morphological misfits such as the Podostemaceae, peculiar eudicots adapted to submerged river rocks. Their transformed “roots” and “shoots” fit only to a limited degree into the classical model which is based on either–or thinking. It has to be widened into a continuum model by taking over elements of fuzzy logic and fractal geometry to accommodate for lineages such as the Podostemaceae.