Quantifying habitat complexity in aquatic ecosystems

1. Many aquatic studies have attempted to relate biological features, such as species diversity, abundance, brain size and behaviour, to measures of habitat complexity. Previous measures of habitat complexity have ranged from simple, habitat‐specific variables, such as the number of twigs in a stream, to quantitative parameters of surface topography, such as rugosity. 2. We present a new video‐based technique, called optical intensity, for assaying habitat complexity in aquatic ecosystems. Optical intensity is a visual, quantitative technique modifiable for any scale or for a nested analysis. We field‐tested the technique in Lake Tanganyika, Tanzania, on 38 quadrats (5 × 5 m) to determine if three freshwater habitats (sand, rock and intermediate) were quantitatively different. 3. A comparison of the values obtained from optical intensity with a previous measure of surface topography (rugosity) showed that the two corresponded well and revealed clear differences among habitats. Both the new measure and rugosity were positively correlated with species diversity, species richness and abundance. Finally, whether used alone or in combination, both measures had predictive value for fish community parameters. 4. This new measure should prove useful to researchers exploring habitat complexity in both marine and freshwater systems.     

Evolution of structure,order and complexity in biological systems: Part III of a general theory

In this, Part III of a general theory, the large-scale features of evolution of structure, order, and complexity are considered as characteristic features of the biological state of matter. This starts with a rigorous formal definition of structure, classes of structural order, complexity, measures of complexity, and how these arise through evolution by a cumulative process of storing information in memory systems. Three such memory systems have evolved: the genetic memory, the immune memory, and the memories of the nervous system. The evolution, characteristic parameters and the limitations of these memory systems are explored. From these considerations emerge the large-scale features of the evolutionary pathways of biological structure, function, and complexity.     

LZ complexity distance of DNA sequences and its application in phylogenetic tree reconstruction

DNA sequences can be treated as finite-length symbol strings over a four-letter alphabet （A, C, T, G）. As a universal and computable complexity measure, LZ complexity is valid to describe the complexity of DNA sequences. In this study, a concept of conditional LZ complexity between two sequences is proposed according to the principle of LZ complexity measure. An LZ complexity distance metric between two nonnull sequences is defined by utilizing conditional LZ complexity. Based on LZ complexity distance, a phylogenetic tree of 26 species of placental mammals （Eutheria） with three outgroup species was reconstructed from their complete mitochondrial genomes. On the debate that which two of the three main groups of placental mammals, namely Primates, Ferungulates, and Rodents, are more closely related, the phylogenetic tree reconstructed based on LZ complexity distance supports the suggestion that Primates and Ferungulates are more closely related.     

The structural complexity of DNA templates—Implications on cellular complexity

A previously formulated procedure for the quantitative evaluation of the complexities of molecules and biostructures is applied to assess the complexities of selected genomic DNA sequences. These include: (1) Several E. coli genes, including lacI, as examples of DNA sequences which are nearly as complex as possible (relative complexity=∼1). This is verified by the Lempel-Ziv (LZ) complexity analysis. (2) The telomere of a yeast chromosome, which has a considerable number of regular features that reduce complexity; the telomere shows indeed a lower structural complexity value. (3) A segment of human DNA, gene p53, which has a certain number of regular features such as 29 interspersed alu elements; these features cause a certain reduction in the complexity of the p53 gene, but do not invalidate the (previous) overall conclusion that template complexity is very high. The close to maximal complexity of the transcribed regions of p53 is validated by the LZ compression analysis. The general conclusion is that DNA base sequence composition is the dominant factor determining cellular complexity. The high complexity of DNA arrived at is a direct consequence of the template character of DNA and reflects the role of genomic DNA as a principal regulating element of a cell. It will be a challenge to find systems of lower complexity with the ability to respond to challenges from the environment to the extent that DNA templated systems do. Cellular complexity and template directed activity are thus highly intertwined properties, at the heart of many developmental, behavioral and evolutionary processes.     

Investigating the evolution and development of biological complexity under the framework of epigenetics

Biological complexity is a key component of evolvability, yet its study has been hampered by a focus on evolutionary trends of complexification and inconsistent definitions. Here, we demonstrate the utility of bringing complexity into the framework of epigenetics to better investigate its utility as a concept in evolutionary biology. We first analyze the existing metrics of complexity and explore the link between complexity and adaptation. Although recently developed metrics allow for a unified framework, they omit developmental mechanisms. We argue that a better approach to the empirical study of complexity and its evolution includes developmental mechanisms. We then consider epigenetic mechanisms and their role in shaping developmental and evolutionary trajectories, as well as the development and organization of complexity. We argue that epigenetics itself could have emerged from complexity because of a need to self‐regulate. Finally, we explore hybridization complexes and hybrid organisms as potential models for studying the association between epigenetics and complexity. Our goal is not to explain trends in biological complexity but to help develop and elucidate novel questions in the investigation of biological complexity and its evolution.     

The performances of the chi-square test and complexity measures for signal recognition in biological sequences

With large amounts of experimental data, modern molecular biology needs appropriate methods to deal with biological sequences. In this work, we apply a statistical method (Pearson's chi-square test) to recognize the signals appear in the whole genome of the Escherichia coli. To show the effectiveness of the method, we compare the Pearson's chi-square test with linguistic complexity on the complete genome of E. coli. The results suggest that Pearson's chi-square test is an efficient method for distinguishing genes (coding regions) form pseudogenes (noncoding regions). On the other hand, the performance of the linguistic complexity is much lower than the chi-square test method. We also use the Pearson's chi-square test method to determine which parts of the Open Reading Frame (ORF) have significant effect on discriminating genes form pseudogenes. Moreover, different complexity measures and Pearson's chi-square test applied on the genes with high value of Pearson's chi-square statistic. We also compute the measures on homologous of these genes. The results illustrate that there is a region near the start codon with high value of chi-square statistic and low complexity that is conserve between homologous genes.     

基于替代数据思想的复杂度归一化方法及其在心电信号分析中的应用

基于替代数据(Surrogate)思想的复杂度归一化方法,克服了一般复杂度对信号采样长度与采样频率的敏感性。文章对在生物医学信号复杂度分析中最有潜在应用价值的近似熵和C0复杂度进行了归一化。应用该方法可以有效地反映人体心脏某些病理状态之间的差别。同时,通过比较各种复杂度指标发现,C0复杂度和近似熵对采样长度的敏感性最弱,适用于短数据量的信号分析。     

Path lengths in protein-protein interaction networks and biological complexity

We investigated the biological significance of path lengths in 12 protein-protein interaction (PPI) networks. We put forward three predictions, based on the idea that biological complexity influences path lengths. First, at the network level, path lengths are generally longer in PPIs than in random networks. Second, this pattern is more pronounced in more complex organisms. Third, within a PPI network, path lengths of individual proteins are biologically significant. We found that in 11 of the 12 species, average path lengths in PPI networks are significantly longer than those in randomly rewired networks. The PPI network of the malaria parasite Plasmodium falciparum, however, does not exhibit deviation from rewired networks. Furthermore, eukaryotic PPIs exhibit significantly greater deviation from randomly rewired networks than prokaryotic PPIs. Thus our study highlights the potentially meaningful variation in path lengths of PPI networks. Moreover, node eccentricity, defined as the longest path from a protein to others, is significantly correlated with the levels of gene expression and dispensability in the yeast PPI network. We conclude that biological complexity influences both global and local properties of path lengths in PPI networks. Investigating variation of path lengths may provide new tools to analyze the evolution of functional modules in biological systems.     

Exploring statistical and population aspects of network complexity

The characterization and the definition of the complexity of objects is an important but very difficult problem that attracted much interest in many different fields. In this paper we introduce a new measure, called network diversity score (NDS), which allows us to quantify structural properties of networks. We demonstrate numerically that our diversity score is capable of distinguishing ordered, random and complex networks from each other and, hence, allowing us to categorize networks with respect to their structural complexity. We study 16 additional network complexity measures and find that none of these measures has similar good categorization capabilities. In contrast to many other measures suggested so far aiming for a characterization of the structural complexity of networks, our score is different for a variety of reasons. First, our score is multiplicatively composed of four individual scores, each assessing different structural properties of a network. That means our composite score reflects the structural diversity of a network. Second, our score is defined for a population of networks instead of individual networks. We will show that this removes an unwanted ambiguity, inherently present in measures that are based on single networks. In order to apply our measure practically, we provide a statistical estimator for the diversity score, which is based on a finite number of samples.     

Food web structure and biocontrol in a four-trophic level system across a landscape complexity gradient

Decline in landscape complexity owing to agricultural intensification may affect biodiversity, food web complexity and associated ecological processes such as biological control, but such relationships are poorly understood. Here, we analysed food webs of cereal aphids, their primary parasitoids and hyperparasitoids in 18 agricultural landscapes differing in structural complexity (42-93% arable land). Despite little variation in the richness of each trophic group, we found considerable changes in trophic link properties across the landscape complexity gradient. Unexpectedly, aphid-parasitoid food webs exhibited a lower complexity (lower linkage density, interaction diversity and generality) in structurally complex landscapes, which was related to the dominance of one aphid species in complex landscapes. Nevertheless, primary parasitism, as well as hyperparasitism, was higher in complex landscapes, with primary parasitism reaching levels for potentially successful biological control. In conclusion, landscape complexity appeared to foster higher parasitism rates, but simpler food webs, thereby casting doubt on the general importance of food web complexity for ecosystem functioning.     

On modeling and complexity of developing systems

We consider the general properties of developing systems, the approaches to their modeling, and the question of their complexity. The notion “complex system” is vague; somewhat more distinct is the complexity of the model describing a phenomenon. We propose to discuss two pertinent issues. (i) The complexity of basic models is minimal; in other words, complicated basic models are needless. (ii) Living systems are simpler than inanimate ones. Though developing systems are seen in abiotic as well as in biotic nature, the fundamental difference is that living beings are capable of goal-setting and purposeful development; hence they can be described with simpler basic models.     

害虫灾害研究的复杂性理论框架

害虫灾害是高度复杂的大系统 ,表现出不均匀性、差异性、多样性、突发性、随机性、可预测性和周期性等复杂性特征 ,使得经典的理论和方法已不适用于害虫灾害的研究。依据复杂性科学和分形、神经网络、混沌及小波等非线性科学的发展及其近期在害虫灾害中的部分研究成果 ,该文从复杂大系统出发 ,构建了害虫灾害研究的复杂性理论框架 ,为深入研究害虫灾害的成因、机制与预测提供理论依据。     

On the complexity measures of genetic sequences

MOTIVATION: It is well known that the regulatory regions of genomes are highly repetitive. They are rich in direct, symmetric and complemented repeats, and there is no doubt about the functional significance of these repeats. Among known measures of complexity, the Ziv-Lempel complexity measure reflects most adequately repeats occurring in the text. But this measure does not take into account isomorphic repeats. By isomorphic repeats we mean fragments that are identical (or symmetric) modulo some permutation of the alphabet letters. RESULTS: In this paper, two complexity measures of symbolic sequences are proposed that generalize the Ziv-Lempel complexity measure by taking into account any isomorphic repeats in the text (rather than just direct repeats as in Ziv-Lempel). The first of them, the complexity vector, is designed for small alphabets such as the alphabet of nucleotides. The second is based on a search for the longest isomorphic fragment in the history of sequence synthesis and can be used for alphabets of arbitrary cardinality. These measures have been used for recognition of structural regularities in DNA sequences. Some interesting structures related to the regulatory region of the human growth hormone are reported.     

Measuring complexity of environmental gradients

Analysis of vegetation response to environmental gradients should take into account the spatial complexity of the environmental property itself. Whether a gradient exists on the landscape or in abstract space, the spatial variability of environmental factors often invalidates the implicit assumption that the gradient is continuous. There is a need to know how variable the spatial pattern of a gradient is and how much deviation from the general trend may be expected. Geostatistics is shown to provide a useful method for analyzing spatial variability. If the assumptions for its use can be met, the fractal dimension can be used in combination with geostatistics to provide a quantitative index of gradient complexity. An example is given, showing that an hypothesized gradient of shoreline erosion disturbance along Delaware Bay either does not exist or is so complicated by short-range, local factors that any longer-range gradient is relatively unimportant. Such complex environmental patterns are thought to be common in nature. Geostatistics, fractals, or similar spatial methods can be utilized to detect and measure such complexity.This work was conducted while the author was a research assistant at the Center for Coastal and Environmental Studies, Rutgers University, New Brunswick, N.J. The support of the Center is gratefully acknowledged.     

Fractal dimension and vessel complexity in patients with cerebral arteriovenous malformations

The fractal dimension (FD) can be used as a measure for morphological complexity in biological systems. The aim of this study was to test the usefulness of this quantitative parameter in the context of cerebral vascular complexity. Fractal analysis was applied on ten patients with cerebral arteriovenous malformations (AVM) and ten healthy controls. Maximum intensity projections from Time-of-Flight MRI scans were analyzed using different measurements of FD, the Box-counting dimension, the Minkowski dimension and generalized dimensions evaluated by means of multifractal analysis. The physiological significance of this parameter was investigated by comparing values of FD first, with the maximum slope of contrast media transit obtained from dynamic contrast-enhanced MRI data and second, with the nidus size obtained from X-ray angiography data. We found that for all methods, the Box-counting dimension, the Minkowski dimension and the generalized dimensions FD was significantly higher in the hemisphere with AVM compared to the hemisphere without AVM indicating that FD is a sensitive parameter to capture vascular complexity. Furthermore we found a high correlation between FD and the maximum slope of contrast media transit and between FD and the size of the central nidus pointing out the physiological relevance of FD. The proposed method may therefore serve as an additional objective parameter, which can be assessed automatically and might assist in the complex workup of AVMs.     

A novel approach to measuring subtidal habitat complexity

Habitat complexity plays an important role in determining benthic community structure. A diverse range of methods for its measurement have been adopted but none are convenient for use underwater where access time is at a premium. We describe a novel, calibrated, tool for rapidly measuring scale-dependent habitat complexity developed, primarily, for use underwater. This tool is based on a distance-wheel with interchangeable wheels of different sizes to allow a scale-dependent measure of distance. This technique was calibrated against a profile of known complexity, at relevant scales, and then trialed on the Loch Linnhe Artificial Reef, a replicated artificial substratum offering two different scale-dependent habitat complexities. The distance-wheel was cost-effective, simple to fabricate and enabled the rapid and straightforward measurement of perceived distance over the step-length range of 133-1020 mm.     

一种统计复杂性测度及在心率变异信号分析中的应用

统计复杂性率量方法是作为结构或关联的一般性指示被提出来的。最近,Ｌｏｐｅｚ－Ｒｕｉｚ等提出一种称为ＣＬＭＣ的统计复杂性测度,满足在秩序和随机两个极端情况下测度为０的边界条件。Ｄａｖｉｄ详细研究了ＣＬＭＣ的特性,发现它既不是一个热力学集中变量也不是一个热力学扩张变量,并提出一种满足热力学扩张特性的补偿形式,但最后证明ＣＬＭＣ只是熵密度的普通解,不能作为结构测度。因此统计复杂性度量不仅应满足有序－随机     

Calculating structural complexity in phylogenies using ancestral ontologies

Complexity is an important aspect of evolutionary biology, but there are many reasonable concepts of complexity, and its objective measurement is an elusive matter. Here we develop a simple measure of complexity based on counts of elements, incorporating the hierarchical information as represented in anatomical ontologies. Neomorphic and transformational characters are used to identify novelties and individuated morphological regions, respectively. By linking the characters to terms in an anatomical ontology a node‐driven approach is implemented, where a node ontology and a complexity score are inferred from the optimization of individual characters on each ancestral or terminal node. From the atomized vector of character scorings, the anatomical ontology is used to integrate the hierarchical structure of morphology in terminals and ancestors. These node ontologies are used to calculate a measure of complexity that can be traced on phylogenetic trees and is harmonious with usual phylogenetic operations. This strategy is compared with a terminal‐driven approach, in which the complexity scores are calculated only for terminals, and optimized as a continuous character on the internal nodes. These ideas are applied to a real dataset of 166 araneomorph spider species scored for 393 characters, using Spider Ontology (SPD, https://bioportal.bioontology.org/ontologies/SPD ); complexity scores and transitions are calculated for each node and branch, respectively. This result in a distribution of transitions skewed towards simplification; the transitions in complexity have no apparent correlation with character branch lengths. The node‐driven and terminal‐driven estimations are generally correlated in the complexity scores, but have higher divergence in the transition values. The structure of the ontology is used to provide complexity scores for organ systems and body parts of the focal groups.