Critical-like self-organization and natural selection: Two facets of a single evolutionary process?

We argue that critical-like dynamics self-organize relatively easily in non-equilibrium systems, and that in biological systems such dynamics serve as templates upon which natural selection builds further elaborations. These critical-like states can be modified by natural selection in two fundamental ways, reflecting the selective advantage (if any) of heritable variations either among avalanche participants or among whole systems. First, reproducing (avalanching) units can differentiate, as units adopt systematic behavioural variations. Second, whole systems that are exposed to natural selection can become increasingly or decreasingly critical. We suggest that these interactions between SOC-like dynamics and natural selection have profound consequences for biological systems because they could have facilitated the evolution of division of labour, compartmentalization and computation, key features of biological systems. The logical conclusion of these ideas is that the fractal geometry of nature is anything but coincidental, and that natural selection is itself a fractal process, occurring on many temporal and spatial scales.     

Spectral and Fractal Analysis of Cerebellar Activity After Single and Repeated Brain Injury

The cerebellum, even when not directly damaged, is potentially interesting for understanding the adaptive responses to brain injury. Cerebellar electrocortical activity (ECoG) in rats was studied using spectral and fractal analysis after single and repeated unilateral injury of the parietal cortex. Local field potentials of cerebellar paravermal cortex were recorded before brain injury, in the acute phase (up to 2.5 hours) after a first injury of anesthetized rats, and then before and after second, third, and, in some cases, fourth injury. Relative gamma power (32.1–128.0 Hz) and fractal dimension of ECoGs were temporarily increased after the first injury. However, there was a permanent mild increase in gamma activity and a mild increase in the fractal dimension of cerebellar activity as a chronic change after repeated remote brain injury. There was a negative linear correlation between the normalized difference in fractal dimensions and normalized difference in gamma powers of cerebellar activity only in the case of repeated brain injury. This is the first study showing that correlation between the parameters of spectral and fractal analyses of cerebellar activity can discriminate between single and repeated brain injuries, and is, therefore, a promising approach for identifying specific pathophysiological states.     

放牧和刈割条件下草山草坡群落空间异质性分析

采用变异矩分析和分形方法,研究了草山草坡群落在放牧和刈割条件下的空间异质性及空间自相关性,结果表明,群落空间格局有尺度依赖性,刈割条件下空物异质性及空间相关性弱,多样性梯度即β多样性小,放牧消除地形引起的样地差异,因而使空间异质性简单化。     

一类Julia分形图及其计算机构造

分形理论及其构造方法的研究目前已吸引了包括生物数学家在内的众多领域学者的关注。本文讨论了一类有理函数映射下的Julia分形集的性质,以及构造这类分形集的广义割线方法,并证明了该方法的收敛性,分析并讨论了所构造的新一类分形图谱的特点,并进一步支持了算法的有效性。     

毛竹杉木混交林土壤团粒结构的分形特征研究

运用分形理论对杉木纯林（19年生）、毛竹纯林（19年生）、6种杉木毛竹混交林（杉木19年生）的土壤团粒结构进行研究,建立了土壤团粒结构的分形维数与土壤团聚体含量、土壤结构体破坏率之间的回归模型,在此基础上,运用弹性分析与边际分析法进一步探讨了土壤团粒结构的分形维数对土壤性质变化所产生的影响效应。结果表明:土壤>0.25mm水稳定性团聚体含量越大,团粒结构的分形维数越小,土壤的结构与稳定性就越好;土壤团粒结构分形维数与水稳定性团聚体（>0.25 mm及>5.0mm）含量及结构体破坏率之间均存在极显著的回归关系;土壤团粒结构分形维数对土壤性质的变化产生较大的影响效应。本研究为毛竹杉木混交林的栽培管理,土壤肥力的科学评价提供依据。     

Scaling exponents and rank-size distributions as indicators of landscape character and change

I used a rank-size distribution model and its associated scaling exponents to describe the organization of Yellowstone National Park before and after the 1988 fire season using the statistical distribution of patch sizes. Rank-size distributions indicate the relative effect of patch size on landscape structure, and whether the size of patches differs from what is expected from the model. Scaling exponents describe the distribution and magnitude of change in patch size, and may indicate the effect of fire on ecological processes including succession and resource distribution. The results of my analysis suggest that fires during the 1988 fire-season substantially affected the distribution of patch size in Yellowstone National Park, where large patches have a disproportionate effect on landscape character. For example, patches ≥100 ha occupy a majority of the area even though they represent a minority number of patches in the landscape. Additionally, rank-size distributions indicate fractal properties existed over several orders of magnitude, signifying that processes acting at one level of the landscape hierarchy may be acting similarly at other levels of the hierarchy. This has implications for linking the scaling properties of patch size with other scale-based phenomena including allometry. Finally, the distribution of patch sizes in conjunction with fire-return interval may be useful in assessing the likelihood of landscape-level disturbances.     

水生植物叶片的分形特征研究

应用分形几何理论对保安湖部分水生植物叶的分形特征进行研究 ,以寻找其中的自相似性特征 ,计算其分形维数 ,并力图了解各个分维的生态学含义。计算得到各物种分维平均值 ,马来眼子菜为 1 441(1 3 2 2 -1 52 0 ,sd =0 0 547) ,菹草为 1 472 (1 3 81-1 565,sd =0 0 489) ,大茨藻为 1 3 2 5(1 2 0 9-1 40 6,sd =0 0 470 ) ,轮叶黑藻为 1 10 3(1 0 0 1-1 2 17,sd =0 0 456)。按分维值排序 ,菹草 >金鱼藻 >马来眼子菜 >茨藻 >黑藻。叶片分维的大小 ,说明了不同种类水生植物叶片占据空间的程度和利用生态空间的能力有差异。通过对五种植物叶的空间格局的定量化描述 ,更好地理解水生植物对水环境的适应机理 ,为进一步对更大尺度下的水生植物空间格局研究提供基础信息     

英罗港红树林土壤粒径分布的分形特征

应用分形理论分析了英罗港红树林土壤粒径分布的分形特征。结果表明,红树林土壤的分形维数为2.6837-2.8834,不同质地土壤的分形维数呈现砂壤土＜轻壤土＜中壤土＜重壤土＜轻粘土的规律,外滩红树林土壤的分形维数低于中滩和内滩。土壤分形维数与其盐分和有机质含量呈显著正相关。群落类型、土壤质地、滩位、含盐量、有机质含量等是影响英罗港红树林土壤分形维数的主要因子。     

鱼类体长与体重关系中的分形特征

运用分形理论得到了描述鱼类形态的基本关系式,既扩展了传统上对鱼类形状描述的思路,又回答了鱼类体长-体重关系式Ｗ=ｂＬａ在实际运用中长期存在的量纲不和谐问题。还对体长-体重函数关系的普适性、参数ａ和鱼类生长发育过程的阶段性、鱼类肥满度定义等进行了分析和讨论．     

Shannon-Wiener指数的改进

针对多样性测定的Shannon－Wiener指数缺陷,运用分形理论,建立一个测定多样性的新的Shannon－Wiener指数,并推导了Shannon－Wiener新指数的均匀度公式．应用武夷山国家自然保护区的米储群落多样性调查的100－1500m~2不等的样地资料进行Shannon－Wiener新指数及其均匀度的测定,结果表明,新指数能客观表征多样性特性,是一个可供应用的新模型．