Measurable notions of complexity and their relationship to biological complexity

Complexity is often invoked as a motivation for a systems approach to biology. We review three measurable notions of complexity from the areas of computation and data analysis. These measures have each led to mathematical theory and to further insight on the complexity of objects, demonstrating the benefits of having a well-defined measure of complexity. Each measure is applicable in the study of particular biological systems; however, none is satisfactory to serve as a universal measure of biological complexity. The study of biological systems will likely require numerous measures of complexity, each appropriate for analysis in specific settings.     

基于Huffman编码的群落结构复杂性

Anand和Orlóci (1996)提出用Huffman编码的平均码长来衡量群落结构总复杂性,用12阶Rényi熵测度群落无序结构复杂性,用两者之差测度群落有序结构复杂性。这是一种与基于生物多样性的复杂性测度完全不同,至少在思路上不同的结构复杂性测度,但对于这种测度的性质研究还不多。该文模拟建立了具有代表性的各种结构的群落400多万个,计算了这些群落的复杂性测度,对其性质进行了研究。结果表明:1)群落结构总复杂性、无序结构复杂性和有序结构复杂性受群落多样性、变异程度、优势种组成等影响。其中,群落结构总复杂性与Shannon-Wiener指数高度相关(决定系数>0.99),完全可由群落组成的多样性决定。群落无序结构复杂性与群落优势种对数比例或变异系数关系最大,与群落优势种对数比例之间的决定系数>0.99。2)该群落有序结构复杂性可表示为群落生物多样性和优势种对数比例的线性组合。在生态意义上可看作主要由群落中非优势种的组成比例决定,而组成多样性能解释41%~46%的群落有序结构复杂性。3)群落组成物种总数的增加会导致群落复杂性的测度有所增加,但没有像文献(Anand & Orlóci,1996)中描述的那么大,且组成总数对结构复杂性与多样性和优势种的关系等没有影响。     

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.     

群落结构复杂性的测度方法研究进展

该文对群落结构复杂性的测度方法的研究进展状况进行了综述。根据测度方法建立的方法基础,将现有的方法分成3类:基于多样性的复杂性测度、基于计算复杂性的测度和基于几何学特征的复杂性测度。对每类测度方法进行了介绍,对其优缺点进行了评述。同时提出了未来研究中应给予重视的问题。结果表明,现有群落结构复杂性的测度方法普遍存在区分能力差的问题,对于基于多样性的结构复杂性测度,目前还缺乏确定各测度属性权重的客观方法;现有的一些基于计算复杂性的结构测度与多样性指标关系过于密切,还不完善,同时其生态学的意义还不明确,而另一些计算复杂性指标还缺乏实际检验。今后,如何建立既具有区分力、又与多样性在概念和数值上都有一定区别的群落结构的计算复杂性的测度方法、如何科学合理地确定复杂性测度中的属性权重以及如何建立结构复杂性的测度和功能过程之间的联系等都是需要深入和系统研究的。由于方法的相似性,有关群落结构复杂性的测度方法也可以应用到其它尺度上的结构复杂性的研究中。     

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。     

中国东北样带（NECT）植物群落复杂性与多样性研究

在更广的意义上考虑群落复杂性的概念,将群落总复杂性分离为基于无序的复杂性和结构复杂性,并以群落的两个原始数据－群落组分（例如种群）数和各组分个体的比例分布为基础,用描述群落的最小剩余码的平均码长Ｌ（Ｓ）＝ｑ／∑／ｊ＝１ｐｊｌｊ（其中ｌｊ为物种Ｓ的相对多度的Ｈｕｆｆｍａｎ码字长度,ｑ是物种数,ｐｊ满ｑ／∑／ｊ＝１ｐｊ＝１）测度群落总复杂性,用Ｓｈａｎｎｏｎ－Ｗｉｅｎｅｒ熵Ｈ（Ｓ）＝－ｑ／∑／ｊ＝１ｐ     

基于二阶C0复杂度的癫痫发作预测

癫痫发作的预测是近年来在临床医学和神经系统科学研究领域中备受关注的问题。如果癫痫发作能够被可靠地预测,则可以提前采取有效的临床预防措施,从而能较大程度地改善癫痫患者的生活质量。文章提出了一种基于二阶C0复杂度的预测算法用于预测癫痫发作。该算法通过分析癫痫患者颅内脑电信号的二阶C0复杂度,利用发作前期复杂度曲线的变化特征预测癫痫发作。作者运用该算法对21组癫痫病人87次发作的临床颅内脑电数据和4组大鼠4次发作的颅内脑电数据进行分析计算,预测准确率分别为94.3%和100%。实验结果表明该算法可以有效地预测癫痫发作,具有潜在的重要临床应用价值。     

The Complexity and Diversity of Typical Plant Communities Along the Northeast China Transect (NECT)

This study examine the notion of plant community complexity in a broad sense and develop a new measure based on the average length L(S) (L(S)=∑ qj=1p jl j ) of the communication-theoretical parsimonious code required to describe the community (S). Total complexity may be differentiated into organized and unorganized complexity. The author refers to Shannon-Wiener entropy H(S) (H(S)=-∑ qj=1 p j log 2 p j ) and Renyi entropy H 12 (S) (H α(S)=11-αlog 2∑ qj=1 p α j , where α =12) as “disorder-based complexity", L(S) as “total complexity" and the difference Δ(S)=L(S)-H(S) and Δ 12 (S)=L(S)-H 12 (S) as “structural complexity". The complexity and diversity of typical plant communities along the NECT (Northeast China Transect) were discussed. The results suggest that structural complexity is higher in the lightly grazed grassland than the heavily grazed grassland. Clearly, structural complexity and disorder-based diversity are not substitutes for one another and should be considered as autonomous, equally important properties. Δ 12(S) measures a community complexity distinct form the disorder-based complexity H 12 (S) .     

Relationship of Sponge Macrofauna with the Morphology of their Hosts in the North Aegean Sea

The associated macrofauna of four Aegean Sea sponge species (Agelas oroides, Petrosia ficiformis, Ircinia variabilis and Aplysina aerophoba) was compared. The total number of individuals and species was found to be related to sponge volume for all sponge species. The associated macrofaunal weight per individual on all sponge species was negatively correlated with sponge volume. Sponge complexity, as measured by sponge surface area to biomass ratio, was not a consistent predictor of associated macrofauna abundance or diversity. Sponge macrofauna species were not host specific and their relative abundances differed among sponge species.     

Evaluation of the complexity of treatment plans from a national IMRT/VMAT audit – Towards a plan complexity score

PurposeThis work aimed to characterize and compare the complexity of the plans created in the context of a national IMRT/VMAT audit. A plan complexity score is proposed to summarize all the evaluated complexity features.Materials and methodsNine complexity metrics have been computed for the audit plans, evaluating different complexity aspects. An approach based on Principal Component Analysis was followed to explore the correlation between the metrics and derive a smaller set of new uncorrelated variables (principal components, PCs). The resulting PCs were then used to calculate a plan complexity score. Plan quality was also assessed and the correlation between plan complexity, quality and deliverability investigated using the Spearman's rank correlation coefficient.ResultsThe first two PCs explained over 90% of the total variance in the original dataset. Their representation allowed to identify patterns in the data, namely a clear separation between plans created using different technologies/techniques. The calculated plan complexity score quantified these differences. Sliding window Eclipse plans were found to be the most complex and VMAT Eclipse group presented the highest complexity variability, for the evaluated parameters. Concerning plan quality, no differences between treatment technology/technique have been identified. However, plans with larger number of monitor units tended to be associated with higher deviations between calculated and measured doses.ConclusionsThe proposed plan complexity score allowed to summarize the differences not only inter- but also intra-groups of technologies/techniques, paving the way for improvement of the planning strategies at the national level through knowledge sharing.     

Solving the SAT problem using a DNA computing algorithm based on ligase chain reaction

A new DNA computing algorithm based on a ligase chain reaction is demonstrated to solve an SAT problem. The proposed DNA algorithm can solve an n-variable m-clause SAT problem in m steps and the computation time required is O (3m+n). Instead of generating the full-solution DNA library, we start with an empty test tube and then generate solutions that partially satisfy the SAT formula. These partial solutions are then extended step by step by the ligation of new variables using Taq DNA ligase. Correct strands are amplified and false strands are pruned by a ligase chain reaction (LCR) as soon as they fail to satisfy the conditions. If we score and sort the clauses, we can use this algorithm to markedly reduce the number of DNA strands required throughout the computing process. In a computer simulation, the maximum number of DNA strands required was 2(0.48n) when n=50, and the exponent ratio varied inversely with the number of variables n and the clause/variable ratio m/n. This algorithm is highly space-efficient and error-tolerant compared to conventional brute-force searching, and thus can be scaled-up to solve large and hard SAT problems.     

Plant community complexity in the arid valley of Minjiang River, southwestern China

Biocomplexity theory is becoming increasingly important in understanding natural vegetation dynamics and interrelation among all components of the ecosystem. In this study, based on the field investigation of plant species and environmental factors (altitude, microtopography, soil water content, and soil nutrients) in an arid valley of the upper reaches of Minjiang River, Sichuan Province, southwestern China, plant community complexity and its relationship with environmental factors, community diversity, species evenness and richness were studied. Both total and structural complexities of the communities showed a “high- low-high” tendency with the increase in altitude of the area, which meant that the complexity of communities was the highest at the sites of low and high altitude, whereas it was the lowest at the sites of intermediate altitude. It was found that the total community complexity had significant quadratic correlations with soil organic matter (SOM) content, total nitrogen (N), hydrolyzable N, soil water content, and available potassium (K), whereas it had no significant correlations with soil total K, total phosphorus (P), available P, and pH value. The total community complexity positively correlated with community diversity, species evenness and species richness, whereas the structural complexity negatively correlated with the community evenness. Of the two components of the total community complexity, namely, the structural complexity and the structural diversity, the structural complexity was more sensitive than the structural diversity to the changes of species in the community, which was not only related to the community evenness but also to the community richness. The relative contribution of both the structural complexity and the structural diversity to the total complexity would be different for different study areas or ecosystems.     

Plant community complexity in the arid valley of Minjiang River, southwestern China

Biocomplexity theory is becoming increasingly important in understanding natural vegetation dynamics and interrelation among all components of the ecosystem. In this study, based on the field investigation of plant species and environmental factors (altitude, microtopography, soil water content, and soil nutrients) in an arid valley of the upper reaches of Minjiang River, Sichuan Province, southwestern China, plant community complexity and its relationship with environmental factors, community diversity, species evenness and richness were studied. Both total and structural complexities of the communities showed a “high- low-high” tendency with the increase in altitude of the area, which meant that the complexity of communities was the highest at the sites of low and high altitude, whereas it was the lowest at the sites of intermediate altitude. It was found that the total community complexity had significant quadratic correlations with soil organic matter (SOM) content, total nitrogen (N), hydrolyzable N, soil water content, and available potassium (K), whereas it had no significant correlations with soil total K, total phosphorus (P), available P, and pH value. The total community complexity positively correlated with community diversity, species evenness and species richness, whereas the structural complexity negatively correlated with the community evenness. Of the two components of the total community complexity, namely, the structural complexity and the structural diversity, the structural complexity was more sensitive than the structural diversity to the changes of species in the community, which was not only related to the community evenness but also to the community richness. The relative contribution of both the structural complexity and the structural diversity to the total complexity would be different for different study areas or ecosystems.     

岷江干旱河谷植物群落的复杂性

通过对岷江干旱河谷植被及环境因子的系统取样调查,研究了该地区植物群落复杂性及其与环境因子的关系,探讨了群落复杂性与多样性、均匀度、物种丰富度之间的关系.随着海拔的增加,群落总复杂性和结构复杂性均表现为“高-低-高”的变化趋势,表明高海拔和低海拔段有较高的复杂性,中海拔段复杂性较低;位于干旱河谷核心区的样带3、4较北部过渡区样带1、2和南部过渡区样带5、6有着较低的群落总复杂性;不同坡位、坡形及坡向,群落总复杂性和结构复杂性,均表现为上坡位＞下坡位＞中坡位,凹坡＞平破＞凸坡,阴坡＞半阴半阳坡＞阳坡.华帚菊-小黄素馨灌丛的总复杂性最高,西南野丁香灌丛、驼绒藜灌丛的总复杂性最低,橿子栎灌丛和群小花滇紫草灌丛的结构复杂性较高; 群落总复杂性与有机质、全N、土壤含水量、水解N、速效K呈现出显著的二次曲线关系,与全K、全P、速效P、pH值没有明显的相关关系.总复杂性与多样性、均匀度、物种丰富度的关系密切,均呈现显著的线性正相关关系.均匀度和结构复杂性呈现极显著的线性负相关,表明结构复杂性随均匀度的增加而减小.作为群落总复杂性与多样性的区分,结构复杂性对群落内物种数的变化较为敏感,不仅与均匀度有关,还与群落物种数量有关.结构复杂性和多样性作为群落总复杂性的两个组成部分,对总复杂性的影响随着研究区域和群落的不同而不同.     

Dynamical properties of model gene networks and implications for the inverse problem

We study the inverse problem, or the "reverse-engineering" problem, for two abstract models of gene expression dynamics, discrete-time Boolean networks and continuous-time switching networks. Formally, the inverse problem is similar for both types of networks. For each gene, its regulators and its Boolean dynamics function must be identified. However, differences in the dynamical properties of these two types of networks affect the amount of data that is necessary for solving the inverse problem. We derive estimates for the average amounts of time series data required to solve the inverse problem for randomly generated Boolean and continuous-time switching networks. We also derive a lower bound on the amount of data needed that holds for both types of networks. We find that the amount of data required is logarithmic in the number of genes for Boolean networks, matching the general lower bound and previous theory, but are superlinear in the number of genes for continuous-time switching networks. We also find that the amount of data needed scales as 2(K), where K is the number of regulators per gene, rather than 2(2K), as previous theory suggests.     

Mammals with Small Populations Do Not Exhibit Larger Genomes

Genome size in cellular organisms varies by six orders of magnitude, yet the cause of this large variation remains unexplained. The influential Drift-Barrier Hypothesis proposes that large genomes tend to evolve in small populations due to inefficient selection. However, to our knowledge no explicit tests of the Drift-Barrier Hypothesis have been reported. We performed the first explicit test, by comparing estimated census population size and genome size in mammals while incorporating potential covariates and the effect of shared evolutionary history. We found a lack of correlation between census population size and genome size among 199 species of mammals. These results suggest that population size is not the predominant factor influencing genome size and that the Drift-Barrier Hypothesis should be considered provisional.     

Protein Connectivity and Protein Complexity Promotes Human Gene Duplicability in a Mutually Exclusive Manner

It has previously been reported that protein complexity (i.e. number of subunits in a protein complex) is negatively correlated to gene duplicability in yeast as well as in humans. However, unlike in yeast, protein connectivity in a protein–protein interaction network has a positive correlation with gene duplicability in human genes. In the present study, we have analyzed 1732 human and 1269 yeast proteins that are present both in a protein–protein interaction network as well as in a protein complex network. In the human case, we observed that both protein connectivity and protein complexity complement each other in a mutually exclusive manner over gene duplicability in a positive direction. Analysis of human haploinsufficient proteins and large protein complexes (complex size >10) shows that when protein connectivity does not have any direct association with gene duplicability, there exists a positive correlation between gene duplicability and protein complexity. The same trend, however, is not found in case of yeast, where both protein connectivity and protein complexity independently guide gene duplicability in the negative direction. We conclude that the higher rate of duplication of human genes may be attributed to organismal complexity either by increasing connectivity in the protein–protein interaction network or by increasing protein complexity.     

Habitat-specific predation susceptibilities of a littoral rotifer to two invertebrate predators

The rotifer Euchlanis dilatata lives associated with submerged vegetation in the littoral zone of freshwater lakes and ponds. I assessed habitat-specific predation susceptibilities for this rotifer in the presence of three aquatic macrophytes (Myriophyllum exalbescens, Elodea canadensis, and Ceratophyllum demersum) and two predators (damselfly nymphs — Enallagma carunculata; and cnidarians — Hydra). Rotifer survival was greatest on Myriophyllum in the presence of both predators. Conversely, the presence of the other macrophyte species actually increase rotifer suspectibility to predation by damselfly nymphs. I also manipulated plant structural complexity. As predicted, decreasing the relative complexity of each plant resulted in lower rotifer survival.