A mean field model for competition: from neutral ecology to the Red Queen

Individual species are distributed inhomogeneously over space and time, yet, within large communities of species, aggregated patterns of biodiversity seem to display nearly universal behaviour. Neutral models assume that an individual's demographic prospects are independent of its species identity. They have successfully predicted certain static, time‐independent patterns. But they have generally failed to predict temporal patterns, such as species ages or population dynamics. We construct a new, multispecies framework incorporating competitive differences between species, and assess the impact of this competition on static and dynamic patterns of biodiversity. We solve this model exactly for the special case of a Red Queen hypothesis, where fitter species are continually arising. The model predicts more realistic species ages than neutral models, without greatly changing predictions for static species abundance distributions. Our modelling approach may allow users to incorporate a broad range of ecological mechanisms.     

Correcting for finite spatial scales of self-similarity when calculating fractal dimensions of real-world structures

Fractal geometry is a potentially valuable tool for quantitatively characterizing complex structures. The fractal dimension (D) can be used as a simple, single index for summarizing properties of real and abstract structures in space and time. Applications in the fields of biology and ecology range from neurobiology to plant architecture, landscape structure, taxonomy and species diversity. However, methods to estimate the D have often been applied in an uncritical manner, violating assumptions about the nature of fractal structures. The most common error involves ignoring the fact that ideal, i.e. infinitely nested, fractal structures exhibit self-similarity over any range of scales. Unlike ideal fractals, real-world structures exhibit self-similarity only over a finite range of scales.Here we present a new technique for quantitatively determining the scales over which real-world structures show statistical self-similarity. The new technique uses a combination of curve-fitting and tests of curvilinearity of residuals to identify the largest range of contiguous scales that exhibit statistical self-similarity. Consequently, we estimate D only over the statistically identified region of self-similarity and introduce the finite scale- corrected dimension (FSCD). We demonstrate the use of this method in two steps. First, using mathematical fractal curves with known but variable spatial scales of self-similarity (achieved by varying the iteration level used for creating the curves), we demonstrate that our method can reliably quantify the spatial scales of self-similarity. This technique therefore allows accurate empirical quantification of theoretical Ds. Secondly, we apply the technique to digital images of the rhizome systems of goldenrod (Solidago altissima). The technique significantly reduced variations in estimated fractal dimensions arising from variations in the method of preparing digital images. Overall, the revised method has the potential to significantly improve repeatability and reliability for deriving fractal dimensions of real-world branching structures.     

秦岭太白红杉种群空间分布格局动态及分形特征研究

采用相邻格子样方法采集数据,应用计盒维数和信息维数研究了太白红杉种群空间格局的分形特征,结果表明,太白红杉种群有较高的计盒维数(1.8087)和信息维数(1.7931),表明其对空间占据程度较高.用分布系数法和Morisita格局指数法检验格局类型,发现不同年龄组太白红杉种群均呈聚集分布.运用Greig-Smith的方法研究格局规模,发现太白红杉种群在128m²和512m²处聚集,不同年龄组在不同规模尺度聚集.以区组分布格局强度(PI)检测聚集强度,发现太白红杉种群格局强度随尺度变化程度较高,个体分布不均匀,随着年龄的增大,其聚集强度呈下降趋势.太白红杉种群的空间分布格局特征是其对严酷生境长期适应的结果.     

Hierarchical analysis of the relationship between spatial distribution and abundance of epiphytic lichens (Mt. Olympos-Greece)

The relationship between distribution and abundance of epiphytic lichens on five different substrates (Fagus sylvatica, Pinus nigra, Quercus coccifera, Pinus heldreichii and Quercus pubescens) has been studied. For the first three substrates the above relationship has been studied hierarchically. It was concluded that this relationship is partly represented by the core-satellite distribution. This abundance-distribution pattern could probably be explained by more than one hypothesis and it is probably related with the life strategies of lichen species.     

A frequency distribution approach to hotspot identification

We present a new global method for the identification of hotspots in conservation and ecology. The method is based on the identification of spatial structure properties through cumulative relative frequency distributions curves, and is tested with two case studies, the identification of fish density hotspots and terrestrial vertebrate species diversity hotspots. Results from the frequency distribution method are compared with those from standard techniques among local, partially local and global methods. Our approach offers the main advantage to be independent from the selection of any threshold, neighborhood, or other parameter that affect most of the currently available methods for hotspot analysis. The two case studies show how such elements of arbitrariness of the traditional methods influence both size and location of the identified hotspots, and how this new global method can be used for a more objective selection of hotspots.     

新型降水分布数学模型研究及其应用

在分布式水文模型中,单元栅格内的降水输入是准确模拟各种水文过程的关键因素,寻求产生分布式降水数据的方法是水文模型研究的热点之一.在对国内外降水模型分析基础上,认为流域面上实际降水分布是天气系统降水与下垫面地形影响共同作用的结果,如果不受地形影响,天气系统降水的降水量等值线在平面上的分布近似为一组同心椭圆.根据这一原理,建立了一种能够模拟天气系统降水分布,并利用牛顿插值法对模拟结果进行地形影响修正的新型降水分布数学模型,提出了对降水中心位置及其中心降水量的模型模拟.利用黄土高原西川河流域实测资料对模型进行了检验,结果表明,该模型具有较高精度.由于模型概念简单明晰,且能指明降水中心位置及其中心降水量,因此在流域暴雨分析和洪水预报中具有一定价值.     

Scaling of offspring number and mass to plant and animal size: model and meta-analysis

The scaling of reproductive parameters to body size is important for understanding ecological and evolutionary patterns. Here, we derived allometric relationships for the number and mass of seeds, eggs and neonates from an existing model on population production. In a separate meta-analysis, we collected 79 empirical regressions on offspring mass and number covering different taxa and various habitats. The literature review served as a validation of the model, whereas, vice versa, consistency of isolated regressions with each other and related ecological quantities was checked with the model. The total offspring mass delivered in a reproductive event scaled to adult size with slopes in the range of about 3/4 to 1. Exponents for individual seed, egg and neonate mass varied around 1/2 for most heterotherms and between 3/4 and 1 for most homeotherms. The scaling of the progeny number released in a sowing, clutch or litter was opposite to that of their size. The linear regressions fitted into a triangular envelope where maximum offspring mass is limited by the size of the adult. Minimum seed and egg size scaled with weight exponents of approximately 0 up to 1/4. These patterns can be explained by the influence of parents on the fate of their offspring, covering the continuum of r-strategists (pelagic–aquatic, arial, most invertebrates, heterotherms) and K-strategists (littoral–terrestrial, some invertebrates, homeotherms).     

Fractal analysis of plant spatial patterns: a monitoring tool for vegetation transition shifts

Spatial heterogeneity, like species diversity, is an important ecosystem property. We examine the effects of land use on the diversity and spatial distribution of plants in five semi-arid communities of eastern Spain using non-linear methods to assess the spatialtemporal dynamics of plant populations. Specifically, we are interested in detecting long-term structural changes or drift in an ecosystem before it is too late to prevent irreversible degradation. Fractal analysis is used to characterize the complexity of plant spatial patterns and Information Theory indices are used to measure change in information flow with land use changes and soil substrate. We found that grazing favored diversity and heterogeneity of species distribution on the impoverished gypsum and saline substrate community, as opposed to the detrimental effect of grazing in the Alpha steppe community. Indeed, old-field succession after 30 years of abandonment showed a recovery of species diversity but not the spatial structure of the vegetation. Further, Information Fractal Dimension, representing the unpredictability of plant spatial patterns in the landscape, increased as we moved from a highly diverse to a less diverse community, revealing the change to a more scattered and homogeneous spatial plant distribution. The Information Fractal Dimension is a good estimator of ecosystem disturbance, independent of scale, and thus can be used to monitor ecosystem dynamics.     

k-长DNA子序列频数分布研究

在详细阐述了生成DNA序列分形图像的Hao方法后,提出一种能够直观显示k-长DNA子序列频数分布差异性的三维频数分布图生成方法。把3D频数分布图转化为1D对数频谱图,突出显示了频数分布的局部特征,提出k-长DNA子序列频数区划分准则,并详细研究了甚高频数区的n阶零间隔现象,指出n阶零间隔分布就是基因组进化过程所留痕迹的假设,并给出对数频谱图特征的生物学解释。实验发现许多DNA序列频数概率分布近似服从非中心F分布,对于分布呈多峰现象的基因组序列,可采用多个非中心F分布的叠加来拟合。在比较非中心F分布与Gamma分布后,提出一种结合二者在拟合方面具有互补优势的新分布,实验证明这种新分布能够更好地吻合实际DNA序列的频数分布。最后研究了两种特异出现频数(最高出现频数与出现频数为1的k-长子序列个数)与k值的关系,发现不同物种的这两种关系具有良好的一致性。     

Contrasting spatial heterogeneity of sessile organisms within mussel (Perna perna L.) beds in relation to topographic variability

We examined the spatial heterogeneity in three sessile rocky shore organisms, the mussel Perna perna, the barnacle Octomeris angulosa (Sowerby) and the red alga Gelidium pristoides (Turn.) at a range of continuous local scales along horizontal transects within mid- and upper mussel beds of South African shores. We also examined the relationships between variability of organisms and topographic features (rock depressions, slope, aspect), and between mussel, barnacle and algal variability over the same scales. To estimate spatial heterogeneity, we analyzed scaling properties of semivariograms using a fractal approach. Relationships between different variables at the different scales were examined by cross-semivariograms. Spatial dependence of P. perna variability increased with spatial dependence of topographic variability, so that scaling regions of mussel and topographic distributions corresponded well. This relationship often improved with larger local scales (mussel cover increased with depressions, steeper slope and aspect towards waves), while at smaller spatial scales, variability in mussel cover was less well explained by variability in topography. The variability of the barnacle O. angulosa exhibited spatial dependence, even on topographically unstructured shores. In contrast, the distribution of the alga G. pristoides revealed high fractal dimensions, showing spatial independence on topographically unstructured shores. Algae also showed a very strong negative relationship with mussels at most local scales, and a negative relationship with barnacles in upper zones, especially at larger local scales. Barnacles may show clear spatial dependence because of hydrodynamics (at larger local scales) and the need to find a future mate in close proximity (at smaller local scales), while algae may show a strong negative relationship with mussels because of competition for space.     

The dynamic evolution of the power exponent in a universal growth model of tumors

We have previously reported that a universal growth law, as proposed by West and collaborators for all living organisms, appears to be able to describe also the growth of tumors in vivo after an initial exponential growth phase. In contrast to the assumption of a fixed power exponent p (assumed by West et al. to be equal to 3/4), we propose in this paper a dynamic evolution of p, using experimental data from the cancer literature. In analogy with results obtained by applying scaling laws to the study of fragmentation of solids, the dynamic behaviour of p is related to the evolution of the fractal topology of neoplastic vascular systems. Our model might be applied for diagnostic purposes to mark the emergence of an efficient neo-angiogenetic structure if the results of our in silico experiments are confirmed by clinical observations.     

Evidence for density-dependent habitat occupancy at varying scales in an expanding bird population

Understanding factors shaping the spatial distribution of animals is crucial for the conservation and management of wildlife species. However, few studies have investigated density-dependent habitat selection in wild populations in non-equilibrium conditions and at varying spatial scales. Here, we investigated density-dependent habitat selection at varying spatial scales in an increasing white stork Ciconia ciconia population using a long term data set in western France. During a 16-year study period, the breeding population density increased from 0.66 nests per 100 km² to 6.6 nests per 100 km². At the beginning of the colonisation of the area settlement probability of storks was mainly positively affected by grasslands located near wetlands. Areas with intensive or moderately intensive agriculture were extremely unlikely to be occupied by breeding birds. However, selection for the initially preferred habitats faded as stork density increased although the proportions of habitat types remained unchanged. At the same time selection for initially less favoured habitats had increased. Moreover, we found that the spatial scale of selection for each foraging habitat variable was consistent over time. Our results suggest that snapshot analyses of resource selection in populations at high density may be misleading for population conservation or management. In contrast, a longitudinal approach to resource selection can be a valuable tool for understanding resource limitation.     

A light distribution model for an internally radiating photobioreactor

Analysis of light energy distribution in culture is important for maximizing the growth efficiency of photosynthetic cells and the productivity of a photobioreactor. To characterize the irradiance conditions in a photobioreactor, we developed a light distribution model for a single-radiator system and then extended the model to multiple radiators using the concept of parallel translation. Mathematical expressions for the local light intensity and the average light intensity were derived for a cylindrical photobioreactor with multiple internal radiators. The proposed model was used to predict the irradiance levels inside an internally radiating photobioreactor using Synechococcus sp. PCC 6301 as a model photosynthetic microorganism. The effects of cell density and radiator number were interpreted through photographic and model simulation studies. The predicted light intensity values were found to be very close to those obtained experimentally, which suggests that the proposed model is capable of accurately interpreting the local light energy profiles inside the photobioreactor system. Due to the simplicity and flexibility of the proposed model, it was also possible to predict the light conditions in other complex photobioreactors, including optical-fiber and pond-type photobioreactors.     

Fractal properties of forest spatial structure

The definition of fractal dimension of natural objects, which enables to deal with scale dependence of fractal dimension is discussed. Abrupt changes of fractal dimension of spatial structure of terrestrial ecosystems are considered in the context of hierarchical paradigm. On this ground the procedure is proposed for segmentation of a territory, which takes into account the scale dependence of spatial variability of ecological parameters. Using remotely sensed data — normalized difference vegetation index (NDVI) and thermal radiation in the infrared band — fractal dimensions and critical scales are evaluated for different forest types with the help of software, developed for this purpose. The results obtained corroborate the potentialities of fractal approach in ecology. These methods and results can be used for discrimination of remotely sensed data; but further investigations, including detailed comparison of fractal characteristics of remotely sensed forest images with results of on-site field studies are necessary to validate them.     

Density-dependent habitat selection in muskrats: a test of the ideal free distribution model

Summary Two predictions of the ideal free distribution model, a null hypothesis of habitat selection, were examined using free-ranging muskrats. We rejected the prediction that the proportion of the animals found in each of five habitats was independent of population size. Data on over-winter occupancy of muskrat dwellings tend also to refute the prediction of equal fitness reward among habitats. Habitat type and water-level had a profound effect on the suitability of a site for settlement. We concluded that the observed pattern of muskrat distribution followed more closely an ideal despotic distribution where some individuals benefited from a higher fitness because of resource monopolization. Current theories of density-dependent habitat selection, which assume an ideal free distribution, would not apply to muskrats and possibly to many other mammal species.