The persistence exponent of DNA

Using the complete genome of Thermoplasma volcanium, as an example, we have examined the distribution functions for the amount of C or G in consecutive, non-overlapping blocks of m bases in this system. We find that these distributions are very much broader (by many factors) than those expected for a random distribution of bases. If we plot the widths of the C-G distributions relative to the widths expected for random distributions, as a function of the block size used, we obtain a power law with a characteristic exponent. The broadening of the C-G distributions follows from the empirical finding that blocks containing a given C-G content tend to be followed by blocks of similar C-G content thus indicating a statistical persistence of composition. The exponent associated with the power law thus measures the strength of persistence in a given DNA. This behavior can be understood using Mandelbrot's model of a fractional Brownian walk. In this model there is a hierarchy of persistence (correlation between blocks) between all parts of the system. The model gives us a way to scale the C-G distributions such that all these functions are collapsed onto a master curve. For a fractional Brownian walk, the fractal dimension of the C-G distribution is simply related to the persistence exponent for the power law. The persistence exponent for T. volcanium is found to be gamma = 0.29 while for a 10 million base segment of the human genome we obtain gamma = 0.39, similar to but not identical with the value found for the microbe.     

The fundamental organization of cardiac mitochondria as a network of coupled oscillators

Mitochondria can behave as individual oscillators whose dynamics may obey collective, network properties. We have shown that cardiomyocytes exhibit high-amplitude, self-sustained, and synchronous oscillations of bioenergetic parameters when the mitochondrial network is stressed to a critical state. Computational studies suggested that additional low-amplitude, high-frequency oscillations were also possible. Herein, employing power spectral analysis, we show that the temporal behavior of mitochondrial membrane potential (DeltaPsi(m)) in cardiomyocytes under physiological conditions is oscillatory and characterized by a broad frequency distribution that obeys a homogeneous power law (1/f(beta)) with a spectral exponent, beta = 1.74. Additionally, relative dispersional analysis shows that mitochondrial oscillatory dynamics exhibits long-term memory, characterized by an inverse power law that scales with a fractal dimension (D(f)) of 1.008, distinct from random behavior (D(f) = 1.5), over at least three orders of magnitude. Analysis of a computational model of the mitochondrial oscillator suggests that the mechanistic origin of the power law behavior is based on the inverse dependence of amplitude versus frequency of oscillation related to the balance between reactive oxygen species production and scavenging. The results demonstrate that cardiac mitochondria behave as a network of coupled oscillators under both physiological and pathophysiological conditions.     

Statistical analyses support power law distributions found in neuronal avalanches

The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling ("finite size" effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to -1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.     

Taylor's law and related allometric power laws in New Zealand mountain beech forests: the roles of space,time and environment

Taylor's law says that the variance of population density of a species is proportional to a power of mean population density. Density–mass allometry says that mean population density is proportional to a power of mean biomass per individual. These power laws predict a third, variance–mass allometry: the variance of population density of a species is proportional to a power of mean biomass per individual. We tested these laws using 10 censuses of New Zealand mountain beech trees in 250 plots over 30 years at spatial scales from 5 m to kilometers. We found that: 1) a single‐species forest not disrupted by humans obeyed all three laws; 2) random sampling explained the parameters of Taylor's law at a large spatial scale in 8 of 10 censuses, but not at a fine spatial scale; 3) larger spatial scale increased the exponent of Taylor's law and decreased the exponent of variance–mass allometry (this is the first empirical demonstration that the latter exponent depends on spatial scale), but affected the exponent of density–mass allometry slightly; 4) despite varying natural disturbance, the three laws varied relatively little over the 30 years; 5) self‐thinning and recruiting plots had significantly different intercepts and slopes of density–mass allometry and variance–mass allometry, but the parameters of Taylor's law were not usually significantly affected; and 6) higher soil calcium was associated with higher variance of population density in all censuses but not with a difference in the exponent of Taylor's law, while elevation above sea level and soil carbon‐to‐nitrogen ratios had little effect on the parameters of Taylor's law. In general, the three laws were remarkably robust. When their parameters were influenced by spatial scale and environmental factors, the parameters could not be species‐specific indicators. We suggest biological mechanisms that may explain some of these findings.     

The Evolution of the Exponent of Zipf's Law in Language Ontogeny

It is well-known that word frequencies arrange themselves according to Zipf''s law. However, little is known about the dependency of the parameters of the law and the complexity of a communication system. Many models of the evolution of language assume that the exponent of the law remains constant as the complexity of a communication systems increases. Using longitudinal studies of child language, we analysed the word rank distribution for the speech of children and adults participating in conversations. The adults typically included family members (e.g., parents) or the investigators conducting the research. Our analysis of the evolution of Zipf''s law yields two main unexpected results. First, in children the exponent of the law tends to decrease over time while this tendency is weaker in adults, thus suggesting this is not a mere mirror effect of adult speech. Second, although the exponent of the law is more stable in adults, their exponents fall below 1 which is the typical value of the exponent assumed in both children and adults. Our analysis also shows a tendency of the mean length of utterances (MLU), a simple estimate of syntactic complexity, to increase as the exponent decreases. The parallel evolution of the exponent and a simple indicator of syntactic complexity (MLU) supports the hypothesis that the exponent of Zipf''s law and linguistic complexity are inter-related. The assumption that Zipf''s law for word ranks is a power-law with a constant exponent of one in both adults and children needs to be revised.     

EVOLUTION OF STATIC ALLOMETRIES: ADAPTIVE CHANGE IN ALLOMETRIC SLOPES OF EYE SPAN IN STALK‐EYED FLIES

Julian Huxley showed that within‐species (static) allometric (power‐law) relations can arise from proportional growth regulation with the exponent in the power law equaling the factor of proportionality. Allometric exponents may therefore be hard to change and act as constraints on the independent evolution of traits. In apparent contradiction to this, many empirical studies have concluded that static allometries are evolvable. Many of these studies have been based, however, on a broad definition of allometry that includes any monotonic shape change with size, and do not falsify the hypothesis of constrained narrow‐sense allometry. Here, we present the first phylogenetic comparative study of narrow‐sense allometric exponents based on a reanalysis of data on eye span and body size in stalk‐eyed flies (Diopsidae). Consistent with a role in sexual selection, we found strong evidence that male slopes were tracking “optima” based on sexual dimorphism and relative male trait size. This tracking was slow, however, with estimated times of 2–3 million years for adaptation to exceed ancestral influence on the trait. Our results are therefore consistent with adaptive evolution on million‐year time scales, but cannot rule out that static allometry may act as a constraint on eye‐span adaptation at shorter time scales.     

A semiflexible polymer model applied to loop formation in DNA hairpins

A statistical mechanical "zipper" model is applied to describe the equilibrium melting of short DNA hairpins with poly(dT) loops ranging from 4 to 12 bases in the loop. The free energy of loop formation is expressed in terms of the persistence length of the chain. This method provides a new measurement of the persistence length of single-stranded DNA, which is found to be approximately 1.4 nm for poly(dT) strands in 100 mM NaCl. The free energy of the hairpin relative to the random coil state is found to scale with the loop size with an apparent exponent of > or = 7, much larger than the exponent of approximately 1.5-1.8 expected from considerations of loop entropy alone. This result indicates a strong dependence of the excess stability of the hairpins, from stacking interactions of the bases within the loop, on the size of the loop. We interpret this excess stability as arising from favorable hydrophobic interactions among the bases in tight loops and which diminish as the loops get larger. Free energy profiles along a generalized reaction coordinate are calculated from the equilibrium zipper model. The transition state for hairpin formation is identified as an ensemble of looped conformations with one basepair closing the loop, and with a lower enthalpy than the random coil state. The equilibrium model predicts apparent activation energy of approximately -11 kcal/mol for the hairpin closing step, in remarkable agreement with the value obtained from kinetics measurements.     

Conformational analysis of the B and Z forms of the d(m5C-G)3 and d(br5C-G)3 hexamers in solution. A 300-MHz and 500-MHz NMR study

The B and the Z forms of the DNA hexamers d(m5C-G)3 and d(br5C-G)3 were investigated by means of NMR spectroscopy. It is demonstrated that the low-salt form of d(m5C-G)3 is a B DNA structure. The form, which becomes increasingly predominant when increasing amounts of MgCl2 and/or methanol are added to the solution, has Z DNA characteristics. It is shown that the major geometrical features of the Z form of d(m5C-G)3 in the crystal structure are maintained in solution, with the dC residues S sugar conformation, gamma + and the base in the anti orientation and the dG residues N (except the 3'-terminal residue), gamma t and syn. Neither the Z form of the methylated nor that of the brominated compound resembles the Z' form, in which the deoxy guanosine sugar rings adopt a C1'-exo conformation. Substitution of m5C by br5C causes no perceptible conformational changes in either the B or in the Z forms.     

Neutral communities in fragmented landscapes

Habitat fragmentation displays a crucial role in conservation biology. Despite this, little is known about the detailed ecological consequences of habitat fragmentation due to the scarce number of controlled experimental surveys. The species–area relationship, a fundamental concept in ecology, requires the understanding of the fragmentation effects in a long term perspective, which turns this task even harder. Here we address the spatial patterns of species distribution in fragmented landscapes, assuming a neutral community model. We study the species area relationship and how its shape changes as the landscape becomes more fragmented. Recent investigations, based on extensive computer simulation, have contributed to establish some definite conclusions in the study of non‐fragmented landscapes: the existence of a three‐regime or two‐regime scenario for the species–area relationship, the emergence of a power‐law regime at intermediate scales and the augment of the species–area exponent z with the speciation rate. Despite the recent efforts, some other questions remain, such as the dependence of z in the whole range of the speciation rate. Questions like these are currently debated but generalizations cannot be drawn. This is the first paper, to our knowledge, that uses the coalescence method and neutral theory to examine biodiversity on more complex spatial structures. Our simulation results corroborate that the fragmentation plays a crucial role in shaping the species–area relationship, by determining the existence and extension of the power‐law regime associated with small and intermediate areas. On the other hand, when individuals are allowed to disperse over longer distances the species–area relationship now displays the classic triphasic pattern, and the intermediate regime, which is well described by a power‐law, is established even for highly fragmented landscapes.     

MONITORING THE PERSISTENCE OF GIANT KELP AROUND SANTA CATALINA ISLAND USING A GEOGRAPHIC INFORMATION SYSTEM

Geographic information systems (GIS) facilitate monitoring and analysis of population distributions at spatial and temporal scales differing from those employed in conventional field monitoring. This study utilizes a GIS-based gap analysis of a network of marine reserves around Santa Catalina Island relative to the regional ecology, disturbance regime, and persistence of giant kelp ( Macrocystis pyrifera ), a keystone species in the nearshore, marine environment. Catalina's orientation and greatly-dissected coastline create diverse microhabitats with respect to storm exposure, temperature, light regime and topographic factors. GIS overlay methods applied to multi-temporal kelp distribution maps generated a model representing the spatial "persistence" of kelp. Correlations between the kelp's geographic distribution and persistence, the disturbance regime and physical variables conferring resistance to or recovery from it were drawn. This analysis identified regions of persistent kelp under disturbance regimes markedly different from those in the existing reserves, suggesting the designation of additional reserves in unprotected areas is ecologically warranted.     

Body mass, population density, and offspring number in mammals

The negative relationship between population density and body mass with the body mass exponent of -0.75 implies that the energy flow through populations of small- and large-bodied species is the same, for individual metabolism scales to body mass raised to the power of +0.75. This relationship called the energetic equivalence rule, has often been observed for mammal species assemblages studied at regional scales. Here we suggest a demography-based mechanism that may generate it. Having analyzed about 130 literature sources, mostly in Russian, we collected demography and body-mass data for 88 mammalian species from the territory and coastal waters of the former Soviet Union. The data were used to construct a number of interspecific relationships. It is shown that (1) the number of offspring per lifetime is approximately inversely proportional to the relative mass at birth (the exponent is not significantly different from -1), (2) the average lifespan is proportional to body mass to the 0.25 power, (3) body mass at birth is proportional to the adult body mass. We develop a simple theory to demonstrate that relations (1) to (3) entail the energetic equivalence rule. The theory also allows us to explain violation of this rule (in non-flying birds, for example), namely, to predict the exponent of relation (1) for any given exponent of the relation between population density and body mass. This is possible because relations (2) and (3) are likely to more universally hold than relation (1). Finally, since natural selection acts on individual traits rather than on population-level ones such as population density, the theory opens up the way to an evolutionary explanation for the energetic equivalence rule.     

Geographic range, turnover rate and the scaling of species diversity

The study of the relative roles of local and regional processes in determining the scaling of species diversity is a very active field in current ecology. The importance of species turnover and the species‐range‐size frequency distributions in determining how local and regional species diversity are linked has been recognised by recent approaches. Here we present a model, based on a system of fully nested sampling quadrats, to analyse species diversity at several scales. Using a recursive procedure that incorporates increasingly smaller scales and a multiplicative formula for relating local and regional diversity, the model allows the simultaneous depiction of alpha, beta and gamma diversity in a single “species‐scale plot”. Species diversity is defined as the number of ranges that are intersected by sampling quadrats of various sizes. The size, shape and location of individual species ranges determine diversity at any scale, but the average point diversity, measured at hypothetical zero‐area localities, is determined solely by the size of individual ranges, regardless of their shape and location. The model predicts that if the species‐area relationship is a power function, then beta diversity must be scale invariant if measured at constant scale increments. Applying the model to the mammal fauna of four Mexican regions with contrasting environmental conditions, we found that: 1) the species‐range‐size frequency distribution at the scale of the Mexican regions differs from the log‐normal pattern reported for the national and continental scales. 2) Beta diversity is not scale‐invariant within each region, implying that the species‐area relationship (SAR) does not follow a power function. 3) There is geographic variation in beta diversity. 4) The scaling of diversity is directly linked to patterns of species turnover rate, and ultimately determined by patterns in the geographic distribution of species. The model shows that regional species diversity and the average distribution range of species are the two basic data necessary to predict patterns in the scaling of species diversity.     

Statistical mechanics unifies different ecological patterns

Recently there has been growing interest in the use of maximum relative entropy (MaxREnt) as a tool for statistical inference in ecology. In contrast, here we propose MaxREnt as a tool for applying statistical mechanics to ecology. We use MaxREnt to explain and predict species abundance patterns in ecological communities in terms of the most probable behaviour under given environmental constraints, in the same way that statistical mechanics explains and predicts the behaviour of thermodynamic systems. We show that MaxREnt unifies a number of different ecological patterns: (i) at relatively local scales a unimodal biodiversity-productivity relationship is predicted in good agreement with published data on grassland communities, (ii) the predicted relative frequency of rare vs. abundant species is very similar to the empirical lognormal distribution, (iii) both neutral and non-neutral species abundance patterns are explained, (iv) on larger scales a monotonic biodiversity-productivity relationship is predicted in agreement with the species-energy law, (v) energetic equivalence and power law self-thinning behaviour are predicted in resource-rich communities. We identify mathematical similarities between these ecological patterns and the behaviour of thermodynamic systems, and conclude that the explanation of ecological patterns is not unique to ecology but rather reflects the generic statistical behaviour of complex systems with many degrees of freedom under very general types of environmental constraints.     

Exploitation dynamics of fish stocks

I address the question of the fluctuations in fishery landings. Using the fishery statistics time-series collected by the Food and Agriculture Organization of the United Nations since the early 1950s, I here analyze fishing activities and find two scaling features of capture fisheries production: (i) the standard deviation of growth rate of the domestically landed catches decays as a power–law function of country landings with an exponent of value 0.15 and (ii) the average number of fishers in a country scales to the 0.7 power of country landings. I show how these socio-ecological patterns may be related, yielding a scaling relation between these exponents. The predicted scaling relation implies that the width of the annual per capita growth-rate distribution scales to the 0.2 power of country landings, i.e. annual fluctuations in per capita landed catches increase with increased per capita catches in highly producing countries. Beside the scaling behavior, I report that fluctuations in the annual domestic landings have increased in the last 30 years, while the mean of the annual growth rate declined significantly after 1972.     

The Length and Viscosity Dependence of End-to-End Collision Rates in Single-Stranded DNA

Intramolecular dynamics play an essential role in the folding and function of biomolecules and, increasingly, in the operation of many biomimetic technologies. Thus motivated we have employed both experiment and simulation to characterize the end-to-end collision dynamics of unstructured, single-stranded DNAs ranging from 6 to 26 bases. We find that, because of the size and flexibility of the optical reporters employed experimentally, end-to-end collision dynamics exhibit little length dependence at length scales <11 bases. For longer constructs, however, the end-to-end collision rate exhibits a power-law relationship to polymer length with an exponent of −3.49 ± 0.13. This represents a significantly stronger length dependence than observed experimentally for unstructured polypeptides or predicted by polymer scaling arguments. Simulations indicate, however, that the larger exponent stems from electrostatic effects that become important over the rather short length scale of these highly charged polymers. Finally, we have found that the end-to-end collision rate also depends linearly on solvent viscosity, with an experimentally significant, nonzero intercept (the extrapolated rate at zero viscosity) that is independent of chain length—an observation that sheds new light on the origins of the “internal friction” observed in the dynamics of many polymer systems.     

Pyramimonas tychotreta, sp. nov. (prasinophyceae), a new marine species from antarctica: light and electron microscopy of the motile stage and notes on growth rates

An undescribed marine prasinophyte, Pyramimonas tychotreta, sp. nov., was isolated from a water sample collected near the ice edge in the Weddell Sea (Antarctica) and is characterized by means of light and electron microscopy. This is the second described Antarctic species in the genus and it possesses a cell ultrastructure typical for members of the subgenus Vestigifera McFadden. The quadriflagellated cells measure 8–12 μm in length and 6–7 μm in width and are equipped with seven types of organic scales that cover the flagella and cell body. The scale floor of the box scales is ornamented by quadrants of parallel striations running perpendicular to one another. The scale floor is further characterized by a number of randomly positioned perforations. The wall of the box scales may be solid or possess up to five perforations. The base of the crown scales is square with rounded corners. It is formed of two crossed ribs, the extremities of which are interconnected by a peripheral rib. Four upright arms, attached to the peripheral rib in positions slightly offset from its junction with the cross ribs, join up with the distal extremity of a central upright strut. Each arm possesses two spines. The limuloid scales are cross‐striped by 10–12 ribs. Some details of the flagellar apparatus are briefly reported. Pyramimonas tychotreta is compared with other species of the genus. Experiments were conducted to study the response of growth rate to variations in temperature and salinity in the clonal culture. The best growth rate (0.45 divisions·24 h ^{? 1}) was found at 4.6° C; growth ceased at temperatures in excess of 12° C. Growth in salinities ranging from 15 to 35 psu was similar, but was arrested at 10 psu. These studies suggest that P. tychotreta as a cold stenotherm and euryhaline taxon. New observations are presented on the geographic distribution of previously described species of Pyramimonas Schmarda from the Northern Foxe Basin, Canada.     

Quantitative assessments of morphological and functional properties of biological trees based on their fractal nature.

The branching systems in our body (vascular and bronchial trees) and those in the environment (plant trees and river systems) are characterized by a fractal nature: the self-similarity in the bifurcation pattern. They increase their branch density toward terminals according to a power function with the exponent called fractal dimension (D). From a stochastic model based-on this feature, we formulated the fractal-based integrals to calculate such morphological parameters as aggregated branch length, surface area, and content volume for any given range of radius (r). It was followed by the derivation of branch number and cross-sectional area, by virtue of the logarithmic sectioning of the r axis and of the branch radius-length relation also given by a power function of r with an exponent (alpha). These derivatives allowed us to quantify various hydrodynamic parameters of vascular and bronchial trees as fluid conduit systems, including the individual branch flow rate, mean flow velocity, wall shear rate and stress, internal pressure, and circumferential tension. The validity of these expressions was verified by comparing the outcomes with actual data measured in vivo in the vascular beds. From additional analyses of the terminal branch number, we found a simple equation relating the exponent (m) of the empirical power law (Murray's so-called cube law) to the other exponents as (m=D+alpha). Finally, allometric studies of mammalian vascular trees revealed uniform and scale-independent distributions of terminal arterioles in organs, which afforded an infarct index, reflecting the severity of tissue damage following arterial infarction.     

Single-strand stacking free energy from DNA beacon kinetics

DNA beacons are short single-stranded chains which can form closed hairpin shapes through complementary base pairing at their ends. Contrary to the common polymer theory assumption that only their loop length matters, experiments show that their closing kinetics depend on the loop composition. We have modeled the closing kinetics and in so doing have obtained stacking enthalpies and entropies for single-stranded nucleic acids. The resulting change of persistence length with temperature effects the dynamics. With a Monte Carlo study, we answer another polymer question of how the closing time scales with chain length, finding tau approximately N(2.44+/-0.02). There is a significant crossover for shorter chains, bringing the effective exponent into good agreement with experiment.     

<Emphasis Type="Italic">Enneapterygius velatus</Emphasis>, a new deepwater triplefin (Perciformes: Tripterygiidae) from the Ryukyu Islands,southern Japan

A new deepwater species, Enneapterygius velatus sp. nov. (Perciformes: Tripterygiidae), is described from two male specimens from Ryukyu Island, southern Japan, the holotype having been collected at a depth of 55 m and an underwater photograph taken between 30 and 41 m depth. The new species is characterized by an extremely long first dorsal-fin spine (length 31.6–34.0 % of SL), the first dorsal-fin spine bases close together, first dorsal-fin base length less than half the distance between the base of the third spine of the first dorsal-fin and origin of second dorsal-fin, first dorsal-fin spine base with developed inclinator muscles, long pelvic fins (tip of second ray extending beyond anal-fin origin), large body scales (8 circumpeduncular scales), the supratemporal sensory canals deeply U-shaped in dorsal view, snout profile weakly rounded, abdomen from between pelvic-fin bases to anal-fin origin covered by cycloid scales, body lacking significant blackish blotches and caudal-fin base with scattered melanophores in preserved specimens.