The population genetic structure of clonal organisms generated by exponentially bounded and fat-tailed dispersal

Long-distance dispersal (LDD) plays an important role in many population processes like colonization, range expansion, and epidemics. LDD of small particles like fungal spores is often a result of turbulent wind dispersal and is best described by functions with power-law behavior in the tails ("fat tailed"). The influence of fat-tailed LDD on population genetic structure is reported in this article. In computer simulations, the population structure generated by power-law dispersal with exponents in the range of -2 to -1, in distinct contrast to that generated by exponential dispersal, has a fractal structure. As the power-law exponent becomes smaller, the distribution of individual genotypes becomes more self-similar at different scales. Common statistics like GST are not well suited to summarizing differences between the population genetic structures. Instead, fractal and self-similarity statistics demonstrated differences in structure arising from fat-tailed and exponential dispersal. When dispersal is fat tailed, a log-log plot of the Simpson index against distance between subpopulations has an approximately constant gradient over a large range of spatial scales. The fractal dimension D2 is linearly inversely related to the power-law exponent, with a slope of approximately -2. In a large simulation arena, fat-tailed LDD allows colonization of the entire space by all genotypes whereas exponentially bounded dispersal eventually confines all descendants of a single clonal lineage to a relatively small area.     

Fractal species distributions do not produce power-law species-area relationships

We derive the species-area relationship (SAR) expected from an assemblage of fractally distributed species. If species have truly fractal spatial distributions with different fractal dimensions, we show that the expected SAR is not the classical power-law function, as suggested recently in the literature. This analytically derived SAR has a distinctive shape that is not commonly observed in nature: upward-accelerating richness with increasing area (when plotted on log-log axes). This suggests that, in reality, most species depart from true fractal spatial structure. We demonstrate the fitting of a fractal SAR using two plant assemblages (Alaskan trees and British grasses). We show that in both cases, when modelled as fractal patterns, the modelled SAR departs from the observed SAR in the same way, in accord with the theory developed here. The challenge is to identify how species depart from fractality, either individually or within assemblages, and more importantly to suggest reasons why species distributions are not self-similar and what, if anything, this can tell us about the spatial processes involved in their generation.     

Self-similar properties of the spatial structure of intertidal macro- and microbenthic communities

Spatial distribution (SD) of White Sea intertidal soft-bottom communities was studied at scales from decimetres to dozens of kilometres on the basis of an extensive dataset (464 samples of macrofauna, 349 samples of ciliates, and 333 samples of diatoms). We used the information index of structural heterogeneity D(I) (Azovsky et al., 2000 // Mar. Biol. 136 (3): 581-590) to characterize spatial variability in the species composition of the communities at different extent (total area surveyed) and grain (finest spatial resolution). The type of distribution was determined via the relation between D(I) and parameters of the spatial scale (extent and grain). At small scale (in terms of extent), all the communities were distributed randomly (mosaic SD). At larger scales, the estimated spatial variability depended neither on extent nor grain, exclusively on their ratio, i.e., was scale-invariant. This means that at some scale the spatial patterns of communities display self-similar properties (fractal SD). Such SD was found at a rather wide range of scales scales: 10(1)-10(4) m for the macrofauna, 10(0)-10(3) m for the ciliates, and 10(-1)-10(2) m for the diatoms. At still greater scales, patchy or gradient patters were observed. Thus, the ranges of fractal distribution were proportional to the average size of the organisms (approximately 10(4)-10(7) times the body size). We suppose that such spatial pattern reflects community self-organization in a relatively homogeneous environment and may be the most efficient way to realize the highest structural diversity on the basis of pre-formed complexes of predominant species. We also suppose that fractal-like patterns may be a general feature of the spatial organization of communities.     

Spatial patterns and scaling behaviors of Steller sea lion (Eumetopias jubatus) distributions and their environment

Fractal geometry and other multi-scale analyses have become popular tools for investigating spatial patterns of animal distributions in heterogeneous environments. In theory, changes in patterns of animal distributions with changes in scale reflect transitions between the controlling influences of one environmental factor or process over another. In an effort to find linkages between Steller sea lions (Eumetopias jubatus) and their environment, the objective of this study was to determine if the spatial distribution of Steller sea lions at sea displayed similar scaling properties to the variation of two environmental features, including bathymetry and sea surface temperature (SST). Additionally, distributions of Steller sea lion point patterns were examined with respect to measurements of bathymetric complexity. From February 2000 to May 2004, satellite transmitters were deployed on 10 groups of juvenile Steller sea lions (n=52) at eight different locations within the Aleutian Islands and Gulf of Alaska. Indices of fractal dimension were calculated for each group of sea lions using a unit square box-counting method, whereas indices of bathymetry and SST patchiness were derived by conducting a variance ratio analysis over the same scales. Distributions of Steller sea lions at sea displayed self-similar fractal patterns, suggesting that individuals were distributed in a continuous hierarchical set of clumps within clumps across scales, and foraging behavior was likely influenced by a scale invariant mechanism. Patterns of bathymetric variability also were self-similar, whereas patterns of SST variability were scale dependent and failed to retain self-similar spatial structure at larger scales. These results indicate that the distributions of Steller sea lions at sea were more influenced by bathymetry than SST at the scales examined, but scale-dependent patterns in the distribution of Steller sea lions at sea or linkages with SST may have been apparent if analyses were conducted at finer spatial scales.     

The distribution of the macrobenthos of the White Sea littoral in different spatial scales

Spatial distribution of macrobenthos of middle intertidal zone was studied in scale from centimetres to 30 kilometres along the coastline. The community structure and distribution of the 5 most abundant species (Hydrobia ulvae, Mya arenaria, Macoma baltica. Peloscolex benedeni, Arenicola marina) were considered. Spatial heterogeneity of macrobenthos, estimated as mean dissimilarity between samples, kept constant in scale of centimetres--meters, but increased significantly when enlarged area is considered. Patterns of many species changed with scale from random mosaic to more or less pronounced patchiness, whereas the density of H. ulvae and the structure of the whole community demonstrated fractal (self-similar) patch pattern in wide range of scale from dozens of meters to several kilometres. Spatial correlations between species (the composition of assemblages) and between species and environmental factors were also scale dependent. Some possible effects of scale on the observed spatial distribution of benthos are discussed, and multiscaled analysis of biotic heterogeneity is concluded to be very fruitful.     

Spatial scaling of mountain pine beetle infestations

1. The relationship between occupancy and spatial contagion during the spread of eruptive and invasive species demands greater study, as it could lead to improved prediction of ecosystem damage. 2. We applied a recently developed model that links occupancy and its fractal dimension to model the spatial distribution of mountain pine beetle infestations in British Columbia, Canada. We showed that the distribution of infestation was scale-invariant in at least 24 out of 37 years (mostly in epidemic years), and presented some degree of scale-invariance in the rest. There was a general logarithmic relationship between fractal dimension and infestation occupancy. Based on the scale-invariance assumption, we further assessed the interrelationships for several landscape metrics, such as correlation length, maximum cluster size, total edge length and total number of clusters. 3. The scale-invariance assumption allows fitting the above metrics, and provides a framework to establish the scaling relationship between occupancy and spatial contagion. 4. We concluded that scale-invariance dominates the spread of mountain pine beetle. In this context, spatial aggregation can be predicted from occupancy, hence occupancy is the only variable one needs to know in order to predict the spatial distributions of populations. This supports the hypothesis that fractal dispersal kernels may be abundant among outbreaks of pests and invasive species.     

The endogenous circadian pacemaker imparts a scale-invariant pattern of heart rate fluctuations across time scales spanning minutes to 24 hours

Heartbeat fluctuations in mammals display a robust temporal structure characterized by scale-invariant/fractal patterns. These scale-invariant patterns likely confer physiological advantage because they change with cardiovascular disease and these changes are associated with reduced survival. Models of physical systems imply that to produce scale-invariant patterns, factors influencing the system at different time scales must be coupled via a network of feedback interactions. A similar cardiac control network is hypothesized to be responsible for the scale-invariant pattern in heartbeat dynamics, although the essential network components have not been determined. Here is shown that scale-invariant cardiac control occurs across time scales from minutes to approximately 24 h, and that lesioning the mammalian circadian pacemaker (suprachiasmatic nucleus; SCN) completely abolishes the scale-invariant pattern at time scales>or approximately 4 h. At time scales相似文献   

Widespread occurrence of power-law distributions in inter-repeat distances shaped by genome dynamics

Repetitive DNA sequences derived from transposable elements (TE) are distributed in a non-random way, co-clustering with other classes of repeat elements, genes and other genomic components. In a previous work we reported power-law-like size distributions (linearity in log-log scale) in the spatial arrangement of Alu and LINE1 elements in the human genome. Here we investigate the large-scale features of the spatial arrangement of all principal classes of TEs in 14 genomes from phylogenetically distant organisms by studying the size distribution of inter-repeat distances. Power-law-like size distributions are found to be widespread, extending up to several orders of magnitude. In order to understand the emergence of this distributional pattern, we introduce an evolutionary scenario, which includes (i) Insertions of DNA segments (e.g., more recent repeats) into the considered sequence and (ii) Eliminations of members of the studied TE family. In the proposed model we also incorporate the potential for transposition events (characteristic of the DNA transposons' life-cycle) and segmental duplications. Simulations reproduce the main features of the observed size distributions. Furthermore, we investigate the effects of various genomic features on the presence and extent of power-law size distributions including TE class and age, mode of parental TE transmission, GC content, deletion and recombination rates in the studied genomic region, etc. Our observations corroborate the hypothesis that insertions of genomic material and eliminations of repeats are at the basis of power-laws in inter-repeat distances. The existence of these power-laws could facilitate the formation of the recently proposed "fractal globule" for the confined chromatin organization.     

On the Gompertzian growth in the fractal space-time

An analytical approach to determination of time-dependent temporal fractal dimension b(t)(t) and scaling factor a(t)(t) for the Gompertzian growth in the fractal space-time is presented. The derived formulae take into account the proper boundary conditions and permit a calculation of the mean values b(t)(t) and a(t)(t) at any period of time. The formulae derived have been tested on experimental data obtained by Schrek for the Brown-Pearce rabbit's tumor growth. The results obtained confirm a possibility of successful mapping of the experimental Gompertz curve onto the fractal power-law scaling function y(t)=a(t)tb(t) and support a thesis that Gompertzian growth is a self-similar and allometric process of a holistic nature.     

Species richness, endemism, and abundance patterns: tests of two fractal models in a serpentine grassland

Although scaling relationships that characterize fractal species distributions offer an exciting potential for unification in biogeography, empirical support for fractal theory remains the subject of debate. We synthesize and test multiple predictions of two interrelated fractal models and a null model of random placement using Californian serpentine grassland data describing the spatial location of over 37 000 individually identified plants. The endemics–area relationship and species‐abundance distribution recently derived from a community‐level fractal property performed poorly because of an inaccurate assumption of homogeneity among species. In contrast, a species‐level fractal model that incorporates species‐level differences predicted abundances well, but systematically overestimated endemism and predicted a species–area relationship that violated the observed power law. These findings indicate that in order to make predictions based on the existence of a power‐law species–area relationship, ecologists need a unifying theory of how the community‐level fractal property arises in the presence of species‐level distributional differences.     

1/f correlations in viral genomes--a Fast-Fourier Transformation (FFT) Study

We have studied the presence of long-range correlations in the complete genomes of ten different dsDNA viruses and Saccharomyces cerevisiae (bakers' yeast) chromosome I. We have also studied the correlation between the distribution of the gene length and the domain of "1/f region" of their genomes. Linear regression analysis was done for the power-law region of these organisms and the slope values obtained were approximately -1, which signify the existence of "1/f noise" in the low and medium (intermediate) frequency regions. This suggests the presence of long-range correlations in their genomes. The presence of 1/f noise in a given frequency interval indicates the existence of a fractal (self-similar) structure in the corresponding range of wavelengths. The results of our study suggest that genes have correlations within themselves, and the correlations appear to be related with the scaling exponent alpha.     

Temporal fractal in the feeding behavior ofDrosophila melanogaster

A temporal fractal is clearly shown in the feeding behavior ofDrosophila as a self-similar pattern of locomotive velocity and inverse power law distributions of food dwelling time over the time scale range of 10³. The fractality was observed in the dwelling time distribution immediately after the fly was placed to feeding site or on inferior food in a two-choice situation. Fractality may be understood as adaptive, and an intrinsic property of animal behavior that reflects complex information processing in the CNS ofDrosophila.     

Structural complexity in mussel beds: the fractal geometry of surface topography

Seafloor topographic complexity is ecologically important because it provides habitat structure and alters boundary-layer flow over the bottom. Despite its importance, there is little agreement on how to define and measure surface complexity. The purpose of this investigation was to utilize fractal geometry of vertical cross-section profiles to characterize the surface topography of the soft-bottom mussel bed (Mytilus edulis L.) at Bob's Cove, ME, USA. Mussels there have been shown previously to have spatially ordered fractal characteristics in the horizontal plane. Two hypotheses were tested. The first was that the bed surface is fractal over the spatial scale of 1.44-200 mm, with fractal dimension less than or equal to 1.26, the value for the Koch curve, our model for bed profiles. The second was that bed surface topography (i.e., in vertical profile) is less complex than the mussel bed spatial pattern (i.e., aerial view in the horizontal plane). Both hypotheses were supported. Cross-sections of plaster casts of the bed produced 88 surface profiles, all of which were fractal over the entire spatial scale of more two orders of magnitude employed in the analysis. Fractal dimension values (D) for individual profiles ranged from 1.031 to 1.310. Fractal dimensions of entire casts ranged up to mean (1.242+/-0.046) and median (1.251) values similar to 1.26, the theoretical value of the Koch curve. The bed surface was less complex than the bed spatial pattern because every profile had D<1.36, the smallest value previously obtained from aerial views of the bed. The investigation demonstrated for the first time that surface topography of a soft-bottom mussel bed was fractal at a spatial scale relevant to hydrodynamic processes and habitat structure important for benthic organisms. The technique of using cross-section profiles from casts of the bed surface avoided possible underestimates of fractal dimension that can result from other profiling methods reported in the literature. The results demonstrate that fractal dimension can be useful in the analysis of habitat space and water flow over any irregular seafloor surface because it incorporates the size, shape, and scale of roughness elements into a simple, numerical metric.     

The self-organizing fractal theory as a universal discovery method: the phenomenon of life

A universal discovery method potentially applicable to all disciplines studying organizational phenomena has been developed. This method takes advantage of a new form of global symmetry, namely, scale-invariance of self-organizational dynamics of energy/matter at all levels of organizational hierarchy, from elementary particles through cells and organisms to the Universe as a whole. The method is based on an alternative conceptualization of physical reality postulating that the energy/matter comprising the Universe is far from equilibrium, that it exists as a flow, and that it develops via self-organization in accordance with the empirical laws of nonequilibrium thermodynamics. It is postulated that the energy/matter flowing through and comprising the Universe evolves as a multiscale, self-similar structure-process, i.e., as a self-organizing fractal. This means that certain organizational structures and processes are scale-invariant and are reproduced at all levels of the organizational hierarchy. Being a form of symmetry, scale-invariance naturally lends itself to a new discovery method that allows for the deduction of missing information by comparing scale-invariant organizational patterns across different levels of the organizational hierarchy.     

Spatial Analysis of Childhood Cancer: A Case/Control Study

BackgroundChildhood cancer was the leading cause of death among children aged 1-14 years for 2012 in Spain. Leukemia has the highest incidence, followed by tumors of the central nervous system (CNS) and lymphomas (Hodgkin lymphoma, HL, and Non-Hodgkin’s lymphoma, NHL). Spatial distribution of childhood cancer cases has been under concern with the aim of identifying potential risk factors.ObjectiveThe two objectives are to study overall spatial clustering and cluster detection of cases of the three main childhood cancer causes, looking to increase etiological knowledge.MethodsWe ran a case-control study. The cases were children aged 0 to 14 diagnosed with leukemia, lymphomas (HL and NHL) or CNS neoplasm in five Spanish regions for the period 1996-2011. As a control group, we used a sample from the Birth Registry matching every case by year of birth, autonomous region of residence and sex with six controls. We geocoded and validated the address of the cases and controls. For our two objectives we used two different methodologies. For the first, for overall spatial clustering detection, we used the differences of K functions from the spatial point patterns perspective proposed by Diggle and Chetwynd and the second, for cluster detection, we used the spatial scan statistic proposed by Kulldorff with a level for statistical significance of 0.05.ResultsWe had 1062 cases of leukemia, 714 cases of CNS, 92 of HL and 246 of NHL. Accordingly we had 6 times the number of controls, 6372 controls for leukemia, 4284 controls for CNS, 552 controls for HL and 1476 controls for NHL. We found variations in the estimated empirical D(s) for the different regions and cancers, including some overall spatial clustering for specific regions and distances. We did not find statistically significant clusters.ConclusionsThe variations in the estimated empirical D(s) for the different regions and cancers could be partially explained by the differences in the spatial distribution of the population; however, according to the literature, we cannot discard environmental hazards or infections agents in the etiology of these cancers.     

Fractal analysis of surface electromyography signals: A novel power spectrum-based method

This paper presents a novel power spectrum-based method for fractal analysis of surface electromyography signals. This method, named the bi-phase power spectrum method, provides a bi-phase power-law which represents a multi-scale statistically self-affine signal. This form of statistical self-affinity provides an accurate approximation for stochastic signals originating from a strong non-linear combination of a number of similar distributions, such as surface electromyography signals which are formed by the summation of a number of single muscle fiber action potentials. This power-law is characterized by a set of spectral indicators, which are related to distributional and geometrical characteristics of the electromyography signal’s interference pattern. These novel spectral indicators are capable of sensing the effects of motor units’ recruitment and shape separately by exploiting the geometry of the interference pattern. The bi-phase power spectrum method is compared to geometrical techniques and the 1/f^α approach for fractal analysis of electromyography signals. The extracted indicators using the bi-phase power spectrum method are evaluated in the context of force and joint angle and the results of a human study are presented. Results demonstrate that the bi-phase power spectrum method provides reliable information, consisting of components capable of sensing force and joint angle effects separately, which could be used as complementary information for confounded conventional measures.     

Fractal dimensions of cranial sutures and waveforms.

Two quite different shapes of cranial sutures ostensibly yield fractal dimensions. The rare, intricate sutures yield the more valid fractal dimensions because self-similar scaling provides a double-log plot of negative slope. These sutures are fractals over a range of several r values. Some of the highly folded, wavy sutures in humans also fill space except at very tiny values of r, but are nonfractal. A great deal depends on whether the dimension D is > 1 and by how much, whether the curve yields a false fractal dimension, whether the curve scales and shows self-similarity, and whether the scaling occurs regularly in the same pattern. We suggest careful attention to the inverse power law equations, which when misused can yield false fractal values. Cranial sutures vary from the simple wavy sutures to the complex folded ones, and, in rare instances, evolve and develop to the self-similar, scaling, elaborate ones called intricate sutures. The main thing is to express the biology precisely, whether waveform regularity or irregularity or scaling elaboration conserving space and the original shape. D values may not in themselves reliably allow such a distinction, by whatever method used.