Phylogenetic networks form partial trees
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系统发育树的构建方法,使用的保守蛋白集
生物系统发育树(Phylogenetic tree)是分子生物学研究中最为常用的技术之一。
它可以预测到一组基因的演化过程,以便了解其衍生的生物类别的相对关系。
在构建生物系统发育树的过程中,常常使用保守蛋白集(conserved protein set)。
保守蛋白集是指在不同物种之间具有稳定序列并能够执行特定生物功能的蛋白质。
选择保守蛋白集作为建立生物系统发育树的分子标志物,这是因为它在沿着一个演化过程中保持稳定性,可以为树的构建提供有效的信息和数据。
此外,由于保守蛋白集通常都可以完全鉴定出来,而且序列之间的相似性要大于其它蛋白质,因此可以更加准确地定量表征这些物种的相似性。
在构建生物系统发育树时,首先要收集尽可能多物种的保守蛋白质序列,其次要对所有序列进行比较,然后用这些比较结果来构建一棵生物系统发育树。
其中,比较过程可以基于结构、功能、序列或者综合多种方法来完成,以便更准确地评估物种之间的相关性。
建立完成以后,可以提取从树中获得的信息来进一步研究这些物种的关系。
在生物系统发育树的构建过程中,使用保守蛋白集是一种有效的方法,它可以更准确地反映物种之间的关系,同时也有助于我们理解进化的模式和进程。
trimAl: a tool for automated alignment trimming in large-scale phylogenetics analyses Salvador Capella-Gutiérrez, Jose M. Silla-Martínez and Toni GabaldónTutorialVersion 1.2trimAl tutorialtrimAl is a tool for the automated trimming of Multiple Sequence Alignments. A format inter-conversion tool, called readAl, is included in the package. You can use the program either in the command line or webserver versions. The command line version is faster and has more possibilities,so it is recommended if you are going to use trimAl extensively.The trimAl webserver included in Phylemon 2.0 provides a friendly user interface and the opportunity to perform many different downstream phylogenetic analyses on your trimmed alignment. This document is a short tutorial that will guide you through the different possibilities of the program.Additional information can be obtained from where a more comprehensive documentation is available.If you use trimAl or readAl please cite our paper:trimAl: a tool for automated alignment trimming in large-scale phylogenetic analyses.Salvador Capella-Gutierrez;Jose M.Silla-Martinez;Toni Gabaldon.Bioinformatics 2009 25: 1972-1973.If you use the online webserver phylemon or phylemon2, please cite also this reference:Phylemon:a suite of web tools for molecular evolution,phylogenetics and phylogenomics.Tárraga J, Medina I, Arbiza L, Huerta-Cepas J, Gabaldón T, Dopazo J, Dopazo H. Nucleic Acids Res. 2007 Jul;35 (Web Server issue):W38-42.1. Program Installation.If you have chosen the trimAl command line version you can download the source code from the Download Section in trimAl's wikipage.For Windows OS users, we have prepared a pre-compiled trimAl version to use in this OS. Once the user has uncompressed the package, the user can find a directory,called trimAl/bin, where trimAl and readAl pre-compiled version can be found.Meanwhile for the OS based on Unix platform, e.g. GNU/Linux or MAC OS X, the user should compile the source code before to use these programs. To compile the source code, you have to change your current directory to trimAl/source and just execute "make".Once you have the trimAl and readAl binaries program, you should check if trimAl is running in appropriate way executing trimal program before starting this tutorial.2. trimAl. Multiple Sequence Alignment dataset.In order to follow this tutorial, we have prepared some examples. These examples have been taken from and you can use the codes from these files to get more information about it in this database.You can find three different directories called Api0000038, Api0000040 and Api0000080 with different files. The directory contains these files:A file .seqs with all the unaligned sequences.A file .tce with the Multiple Sequence Alignment produced by T-Coffee1.A file .msl with the Multiple Sequence Alignment produced by Muscle2.A file .mft with the Multiple Sequence Alignment produced by Mafft3.A file .clw with the Multiple Sequence Alignment produced by Clustalw4.A file .cmp with the different names of the MSAs in the directory. This file would be used by trimAl to get the most consistent MSA among the different alignments.You can use any directory to follow the present tutorial.3. Useful trimAl's features.Among the different trimAl parameters, there are some features that can be useful to interpret your alignment results:-htmlout filename. Use this parameter to have the trimAl output in an html file. In this way you can see the columns/sequences that trimAl maintains in the new alignment in grey color while the columns/sequences that have been deleted from the original alignment are in white color.-colnumbering. This parameter will provide you the relationship between the column numbers in the trimmed and the original alignment.-complementary. This parameter lets the user get the complementary alignment, in other words,when the user uses this parameter trimAl will render the columns/sequences that would be deleted from the original alignment.-w number. The user can change the windows size, by default 1, to take into account the surrounding columns in the trimAl's manual methods. When this parameter is fixed, trimAl take into account number columns to the right and to the left from the current position to compute any value, e.g. gap score, similarity score, etc. If the user wants to change a specific windows size value should use the correspond parameter-gw to change window size applied only a gap score assessments, -sc to change window size applied only to similiraty score calculations or -cw to change window size applied only to consistency part.4. Useful trimAl's/readAl's features.Both programs, trimAl and readAl, share common features related to the MSA conversion. It is possible to change the output format for a given alignment, by default the output format is the same than the input one, you can produce an output in different format with these options: -clustal. Output in CLUSTAL format.-fasta. Output in FASTA format.-nbrf. Output in PIR/NBRF format.-nexus. Output in NEXUS format.-mega. Output in MEGA format.-phylip3.2. Output in Phylip NonInterleaved format.-phylip. Output in Phylip Interleaved format.5. Getting Information from Multiple Sequence Alignment.trimAl computes different scores, such as gap score or similarity score distribution, from a given MSA. In order to obtain this information, we can use different parameters through the command line version.To do this part,we are going to use the MSA called Api0000038.msl.This file is in the Api0000038 directory.$ cd Api0000038$ trimal -in Api0000038.msl -sgt$ trimal -in Api0000038.msl -sgc$ trimal -in Api0000038.msl -sct$ trimal -in Api0000038.msl -scc$ trimal -in Api0000038.msl -sidentYou can redirect the trimAl output to a file. This file can be used in subsequent steps as input of other programs, e.g.gnuplot,,microsoft excel,etc,to do plots of this information.$ trimal -in Api0000038.msl -scc > SimilarityColumnsFor instance, in the lines below you can see how to plot the information generated by trimAl using the GNUPLOT program.$ gnuplotplot 'SimilarityColumns' u 1:2 w lp notitleset yrange [-0.05:1.05]set xrange [-1:1210]set xlabel 'Columns'set ylabel 'Residue Similarity Score'plot 'SimilarityColumns' u 1:2 w lp notitleexitIn this other example you can see the gaps distribution from the alignment. This plot also was generated using GNUPLOT$ trimal -in Api0000038.msl -sgt > gapsDistribution$ gnuplotset xlabel '% Alignment'set ylabel 'Gaps Score'plot 'gapsDistribution' u 7:4 w lp notitleexit6. Using user-defined thresholds.If you do not want to use any of the automated procedures included in trimAl (see sections 7 and 8) you can set your own thresholds to trim your alignment. We will use the parameter -htmlout filename for each example so differences can be visualized. In this example, we will use the Api0000038.msl file from the Api0000038 directory.Firstly, we are going to trim the alignment only using the -gt value which is defined in the [0 - 1] range. In this specific example, those columns that do not achieve a gap score, at least, equal to 0.190, meaning that the fraction of gaps on these columns are smaller than this value, will be deleted from the input alignment.$ trimal -in Api0000038.msl -gt 0.190 -htmlout ex01.htmlYou can see different parts of the alignment in the image below.This figure has been generated from the trimAl's HTML file for the previous example.In this other example, we can see the effect to be more strict with our threshold. An usual consequence of higher stringency is that the trimmed MSA has fewer columns. Be careful so you do not remove too much signal$ trimal -in Api0000038.msl -gt 0.8 -htmlout ex02.htmlTo be on the safe side, you can set a minimal fraction of your alignment to be conserved. In this example,we have reproduced the previous example with the difference that here we required to the program that, at least, conserve the 80% of the columns from the original alignment. This will remove the most gappy 20% of the columns or stop at the gap threshold set.$ trimal -in Api0000038.msl -gt 0.8 -cons 80 -htmlout ex03.htmlSecondly,we are going to introduce other manual threshold-st value.In this case,this threshold,also defined in the[0-1]range,is related to the similarity score.This score measures the similarity value for each column from the alignment using the Mean Distance method, by default we use Blosum62 similarity matrix but you can introduce any other matrix (see the manual). In the example below, we have used a smaller threshold to know its effect over the example.$ trimal -in Api0000038.msl -st 0.003 -htmlout ex04.htmlIn this example, similar to the previous example, we have required to conserve a minimum percentage of the original alignment in a independent way to fixed by the similarity threshold.A given threshold maintains a larger number of columns than the cons threshold, trimAl selects this first one.$ trimal -in Api0000038.msl -st 0.003 -cons 30 -htmlout ex05.htmlThirdly, we are going to see the effect of combining two different thresholds. In this case, trimAl only maintains those columns that achieve or pass both thresholds.$ trimal -in Api0000038.msl -st 0.003 -gt 0.19 -htmlout ex06.htmlFinally, we are going to see the effect of combining two different thresholds with the cons parameter. In this case, if the number of columns that achieve or pass both thresholds is equal or greater than the percentage fixed by cons parameter, trimAl chose these columns. However, if the number of columns that achieve or pass both thresholds is less than the number of columns fixed by cons parameter, trimAl relaxes both to thresholds in order to retrieve those columns that lets to achieve this minimum percentage.$ trimal -in Api0000038.msl -st 0.003 -gt 0.19 -cons 60 -htmlout ex07.html7. Selection of the most consistent alignment.trimAl can select the most consistent alignment when more than one alignment is provided for the same sequences (and in the same order) using the -compareset filename parameter. To do this part, we are going to move to Api0000040 directory, we can find there a file calledApi0000040.cmp listing the alignment paths. Using this file, we execute the instruction below to select the most consistent alignment among the alignment provided$ trimal -compareset Api0000040.cmpAs in previous section, once trimAl has selected the most consistent alignment, we can get information about the alignment selected using the appropriate parameters. For example, we can use the follow instructions to know the consistency value for each column in the alignment or its consistency values distribution$ trimal -compareset Api0000040.cmp -sct$ trimal -compareset Api0000040.cmp -sccAlso, we can trim the selected alignment using a specific threshold related to the consistency value. To do that, we should use the -ct value where the value is a number defined in the [0 - 1] range. This number refers to the average conservation of residue pars in that column with respect to the other alignments.$ trimal -compareset Api0000040.cmp -ct 0.6 -htmlout ex08.htmlOn the same way than the previous section, we can define a minimum percentage of columns that should be conserve in the new alignment. For this purpose, we have to use the cons parameter as we explained before.$ trimal -compareset Api0000040.cmp -ct 0.6 -cons 50 -htmlout ex09.htmlFinally, we can combine different thresholds, in fact, we can use all of them as well as we can define a minimum percentage of columns that should be conserve in the output alignment. In the line below, you can see an example of this situation.$ trimal -compareset Api0000040.cmp -ct 0.6 -cons 50 -gt 0.8 -st 0.01-htmlout ex10.html8. Applying automated methods.One of the most powerful aspects of trimAl is that it provides you with several automated options.This option will automatically select the most appropriate thresholds for your alignment after examining the distribution of various parameters along your alignment. Among the alignment features that trimAl takes into account to compute these optimal cut-off are the gap distribution, the similarity distribution, the identity score, etc.You can find a complete explanation about all of these methods in the trimAl's Publications Section.Here,we provide some examples on how to use these methods.The automated methods, gappyout, strict and strictpus, can be used independently if you are working with one or more than one alignment, in the last case, for the same sequences.In the lines below, you can see how to use the gappyout method in both ways. This method will eliminate the most gappy fraction of the columns from your alignment. For this, we are going to continue using the same directory than the previous section.$ trimal -compareset Api0000040.cmp -gappyout -htmlout ex11.html$ trimal -in Api0000040.mft -gappyout -htmlout ex12.htmlIn this case, we are going to use the same files than in the example before but we have changed the method to trim the alignmnet. Now, we are using strict and strictplus methods. These two methods combine the information on the fraction of gaps in a column and their similarity scores, being strictplus for more stringent than strict method.$ trimal -compareset Api0000040.cmp -strict -htmlout ex13.html$ trimal -in Api0000040.clw -strictplus -htmlout ex14.htmling an heuristic method to decide which is the best automated method for a given MSA.Finally, we implemented an heuristic method to decide which is the best automated method to trim a given alignment. The heuristic method takes into account alignment features such as the number of sequences in the alignment as well as some measures about the identity score among the sequences in the alignment or among the best pairwise sequences in that MSA. According to these characteristics trimAl will decide upon one of the two automated methods (gappyout or strictplus).To illustrate how to use this method, we provide a couple of example using the same directory than the section before. First, we used trimAl to selecte the most consistent alignment and then we trimmed that alignmnet using our heuristic method.$ trimal -compareset Api0000040.cmp -automated1 -htmlout ex15.htmlThen, we trim a single MSA using the previously mentioned method.$ trimal -in Api0000040.msl -automated1 -htmlout ex16.html10. Getting more information.We hope that this short introduction to trimAl's features has been useful to you.We advise you to visit periodically the trimAl's wikipage()where you could get the latest news about the program as well as more information, examples, etc, about trimAl's package. You can also subscribe to the mailing list if you want to be updated in new trimAl developing.11. References.1.T-Coffee: A novel method for fast and accurate multiple sequence alignment.Notredame C, Higgins DG, Heringa J. J Mol Biol. 2000 Sep 8;302(1):205-17.2.MUSCLE:multiple sequence alignment with high accuracy and highthroughput. Edgar RC.Nucleic Acids Res. 2004 Mar 19;32(5):1792-7.3.MAFFT: a novel method for rapid multiple sequence alignment based on fastFourier transform. Katoh K, Misawa K, Kuma K, Miyata T. Nucleic Acids Res. 2002 Jul 15;30(14):3059-66.4.CLUSTAL W:improving the sensitivity of progressive multiple sequencealignment through sequence weighting,position-specific gap penalties and weight matrix choice. Thompson JD, Higgins DG, Gibson TJ. Nucleic Acids Res. 1994 Nov 11;22(22):4673-80.。
efficientnet解读-回复什么是EfficientNet?EfficientNet是一种高效的卷积神经网络(Convolutional Neural Network, CNN)架构,由Google研究团队在2019年提出。
它通过优化网络的深度、宽度和分辨率,达到了在图像分类任务上,比目前其他SOTA(State-of-the-Art)的模型具有更高的精度和更好的效能。
EfficientNet的创新点在于使用了一种称为Compound Scaling的方法,该方法为网络的不同维度(深度、宽度和分辨率)选择了合适的比例,从而使网络在三个方面都能够提供良好的性能。
这意味着EfficientNet不仅提升了模型的准确性,同时还减少了可训练参数的数量,使得模型更加高效。
EfficientNet的核心思想是通过在网络的不同层次上相对比例地缩放深度、宽度和分辨率,从而平衡网络的规模和性能。
具体地说,EfficientNet利用了一个复合缩放系数phi(ϕ),它控制了网络的总体缩放比例。
该phi 参数是通过在一定范围内进行搜索和验证,确定出最佳值的。
在EfficientNet的工作中,研究人员通过在Imagenet上进行大规模的实验评估,找到了一个最佳的复合缩放系数phi=1.2。
在EfficientNet的网络结构中,首先进行的是深度方向的缩放。
通过复制某个输入模型(例如ResNet)的某个重复模块,即可扩展EfficientNet的深度。
而深度可以同时扩展子层的数量和整体的网络深度。
然后,进行的是宽度方向的缩放,即扩展通道/特征维度的数量。
为了平衡不同层级的性能,EfficientNet限制了扩展的范围。
这样,即使在更高分辨率的层级中,EfficientNet也能保证较高的计算效率。
最后,进行的是分辨率方向的缩放,即调整图像输入的分辨率。
通过在训练过程中逐渐增加分辨率,EfficientNet能够提高网络对更高分辨率图像的适应能力。
Estimating phylogenetic trees and networks usingSplitsTree4,Daniel H.HusonCenter for Bioinformatics,T¨u bingen University,Sand14,72076T¨u bingen,Germany.E-mail:huson@informatik.uni-tuebingen.deDave BryantCenter for Bioinformatics,McGill University,Montreal,CanadaE-mail:bryant@mcb.mcgill.caSplitsTree4[7,8]is a new Java program for estimating phylogenetic trees and networks.Its main focus is on computing phylogenetic networks[4].It provides methods for con-structing splits networks,such as the consensus network[6]or super network of a set of phylogenetic trees or partial trees[9],distance methods such as Neighbor-Net[3]and split decomposition[1]and direct methods such as median networks[2]and spectral analysis[5].SplitsTree4also provides a large number of distance transformations and implementations of all standard distance-methods for building phylogenetic trees.Moreover,it also provides interfaces to external programs such ClustalW or Phylip.SplitsTree is currently the only available program for computing hybridization networks from gene trees[11]and computing recombination networks from binary sequences[10].The program can be run both in a GUI mode or in a non-interactive command-line mode. The software is freely available for UNix/Linux,Windows and MacOS from:References[1]H.-J.Bandelt and A.W.M.Dress.A canonical decomposition theory for metrics on afinite set.Advances in Mathematics,92:47–105,1992.[2]H.-J.Bandelt,P.Forster,B.C.Sykes,and M.B.Richards.Mitochondrial portraits of human population using median networks.Genetics,141:743–753,1995.[3] D.Bryant and V.Moulton.NeighborNet:An agglomerative method for the construction of planar phylogenetic networks.In R.Guig´o andD.Gusfield,editors,Algorithms in Bioinformatics,WABI2002,volume LNCS2452,pages375–391,2002.[4] A.W.M.Dress and D.H.Huson.Constructing splits graphs.IEEE/ACM Transactions in Computational Biology and Bioinformatics,1(3):109–115,2004.[5]M.D.Hendy and D.Penny.Spectral analysis of phylogentic data.Journal of Classification,10:5–24,1993.[6] B.Holland and V.Moulton.Consensus networks:A method for visualizing incompatibilities in collections of trees.In G.Benson and R.Page,editors,Proceedings of“Workshop on Algorithms in Bioinformatics”,volume2812of LNBI,pages165–176.Springer,2003.[7] D.H.Huson.SplitsTree:A program for analyzing and visualizing evolutionary data.Bioinformatics,14(10):68–73,1998.[8] D.H.Huson and D.Bryant.Estimating phylogenetic trees and networks using SplitsTree4.Manuscript in preparation,software availablefrom ,2005.[9] D.H.Huson,T.Dezulian,T.Kloepper,and M. A.Steel.Phylogenetic super-networks from partial trees.IEEE/ACM Transactions inComputational Biology and Bioinformatics,1(4):151–158,2004.[10] D.H.Huson and puting recombination networks from binary sequences.Submitted,2005.[11] D.H.Huson,T.Kloepper,P.J.Lockhart,and M.A.Steel.Reconstruction of reticulate networks from gene trees.In Proceedings of the NinthInternational Conference on Research in Computational Molecular Biology(RECOMB),2005.。
一种分层图像编码算法
王成儒;司菁菁
【期刊名称】《计算机工程与应用》
【年(卷),期】2005(041)026
【摘要】针对纹理较丰富的图像提出了一种分层编码算法.该算法将图像划分成具有不同特征的两层:平滑层和纹理层,分别基于小波变换和自适应局部余弦变换(ALCT)进行编码.编码平滑层时,仅对原图像一级小波变换后的低频子带进行小波SPIHT编码,在减少计算量的同时,提高了整个算法的性能.该文改进了实现ALCT的折叠算子,并且提出了一种ALCT系数的重组方案,从而利用零树编码获得了嵌入式码流.实验结果表明,本算法在未进行算术编码的情况下,压缩性能优于SPIHT,并且在重建图像中更好地保留了原图像的纹理特征.
【总页数】3页(P78-80)
【作者】王成儒;司菁菁
【作者单位】燕山大学信息科学与工程学院,河北,秦皇岛,066004;燕山大学信息科学与工程学院,河北,秦皇岛,066004
【正文语种】中文
【中图分类】TP391
【相关文献】
1.采用小波与ALCT的分层图像编码算法 [J], 王成儒;司菁菁
2.一种采用分层多阈值的分辨率渐进图像编码算法 [J], 陈仁喜;赵忠明
3.一种基于离散余弦变换的嵌入式图像编码算法 [J], 陈鑫;游敏娟;崔艺君;张勇;王世刚
4.基于改进的正交FRIT的分层图像编码算法 [J], 司菁菁;王成儒;程银波
5.基于小波和匹配跟踪的分层图像编码算法 [J], 刘利雄;廖斌;贾云得;王元全
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⽣物信息学复习题⼀、名词解释1.bioinformatics:⽣物信息学,指从事对基因组研究相关的⽣物信息的获取、加⼯、储存、分配、分析和解释的⼀门科学,是⼀门⽣物学,数学和计算机相互交叉融合⽽产⽣的新兴学科。
2.molecular bioinformatics:指综合应⽤信息科学、数学的理论、⽅法和技术,管理、分析和利⽤⽣物分⼦数据的科学。
3.GenBank:是美国全国卫⽣研究所维护的基因序列数据库,汇集并注释了所有公开的核酸序列,与⽇本的DNA数据库DDBJ以及欧洲分⼦实验室核酸序列数据库EMBL⼀起,都是国际核苷酸序列数据库合作的成员。
4.EMBL:EMBL实验室—欧洲分⼦⽣物学实验室,EMBL数据库—是⾮盈利性学术组织EMBL建⽴的综合性数据库,EMBL核酸数据库是欧洲最重要的核酸序列数据库,它定期地与美国的GenBank、⽇本的DDBJ数据库中的数据进⾏交换,并同步更新。
5.DDBJ:⽇本DNA数据库,主要向研究者收集DNA序列信息并赋予其数据存取号,信息来源主要是⽇本的研究机构,也接受其他国家呈递的序列。
6.BLAST:基本局部⽐对搜索⼯具的缩写,是⼀种序列类似性检索⼯具。
BLAST采⽤统计学⼏分系统,同时采⽤局部⽐对算法, BLAST程序能迅速与公开数据库进⾏相似性序列⽐较。
BLAST结果中的得分是对⼀种对相似性的统计说明。
7.BLASTn:是核酸序列到核酸库中的⼀种查询。
库中存在的每条已知序列都将同所查序列作⼀对⼀地核酸序列⽐对。
8.BLASTp:是蛋⽩序列到蛋⽩库中的⼀种查询。
库中存在的每条已知序列将逐⼀地同每条所查序列作⼀对⼀的序列⽐对。
9.Clustsl X:是CLUSTAL多重序列⽐对程序的Windows版本,是⽤来对核酸与蛋⽩序列进⾏多序列⽐较的程序,也可以对来⾃不同物种的功能或结构相似的序列进⾏⽐对和聚类,通过重建系统发⽣树判断亲缘关系,并对序列在⽣物进化过程中的保守性进⾏估计。
1 SplitsTree4.0-Computation of phylogenetic treesand networksDaniel H.Huson1,Tobias Kloepper2,David Bryant3 Keywords:phylogeny,evolution,trees,networks,graphs.1IntroductionThe goal of phylogenetic analysis is to determine the order and approximate timing of spe-ciation events in the evolution of a given set of species.In the classic theory of phylogenetic analysis the species are assumed to evolve along a(bifucating)X-tree,experiencing point mutations along the way.Recent results from genome wide comparision of gene trees seem to indicate that these models mayfit well for single genes but fail to represent the complex evo-lution of a genome.A natural generalisation of the phylogenetic tree,that seems tofit well with the complex evolution of a genome,is the phylogenetic network.There are two main approches to generate such phylogenetic networks.Thefirst one is the combined analysis approach,and the second one is the individual analysis approach.In thefirst approach the phylogenetic network is generated directly from the given combined information.In the sec-ond approach individual trees are generated for the given information sets and all individual trees are then combined into one network.Bandelt and Dress[BD92]suggested a number of combined analysis methods,such as the split-decomposition method and the parsimony splits.More recently,Bryant and Moulton[BM02]described a new method Neighbor-Net, that brings together both split decomposition and the well-known Neighbor-Joining method [SN87].Holland and Moulton[HM03]presented a method to join individual gene trees for a common set of species.In2004Huson et al.[HDKS04]presented the Z-Super-Network method,which merges individual partial gene trees.2The SplitsTree programThere exist a number of packages for performing phylogenetic analysis,e.g.[Swo00,SvH96, MM02].However,they all use trees as the fundamental data structure.In contrast,the SplitsTree program[HB05]is based on so-called splits and phylogenetic networks.It is aimed at providing a general framework for both tree-and network-oriented phylogenetic analysis.Fundamental data types supported by the program includ unaligned-and aligned sequences,distances,splits,trees,networks and quartets.The package provides commonly used distance-based algorithms.We have also implemented the methods mentioned in the introduction.The package provides numerous visualisation methods for phylogentic trees and networks,examples are split graphs[DH04]and the equal-daylight method[Fel04].We [HKLS05]have recently implemented methods for the reconstruction of reticulation networks and the transformation from split networks to reticulation networks.The main features of the program are:2•it runs on any machine with minimal installation requirements based on Java or Java Web Start.•GUI version for interactive use,command-line version for scripting pipelines.•Flexible frame-work for doing phylogenetic analysis.•De-centralized plug-in concept for adding new methodology.•Fundamental data types include splits and quartets.•Uses Nexusfile format,with one-to-one correspondence between internal data classes and external nexus blocks,and supports most other formats.•Transformations of molecular sequences to distances.•Combined and individual analysis methods.•Visualisation of phylogenetic trees and networks.•Interactive exploration of the visualisation.•Bootstrapping3Availability.The program is freely available from rmatik.uni-tuebingen.de/software References[BD92]H.-J.Bandelt,and A.W.M.Dress,Split Decomposition:A new and useful approach to phylogenetic analysis of distance data.Molecular Phylogenetics and Evolution1(3):242-252, 1992.[BM02] D.Bryant and V.Moulton.NeighborNet:An agglomerative method for the construction of planar phylogenetic networks.In R.Guig´o and D.Gusfield,editors,Algorithms in Bioinfor-matics,WABI2002,volume LNCS2452,pages375,391,2002.[DH04] A.W.M.Dress and D.H.Huson.Constructing splits graphs,IEEE/ACM Transactions in Computational Biology and Bioinformatics,volume1(3),pages109-115,2004.[Fel04]J.Felsenstein.Inferring Phylogenies Sinauer Associates,Inc.,pages582ff,2004.[HM03] B.Holland and V.Moulton.Consensus networks:A method for visualizing incompatibilities in collections of trees.Algorithms in Bioinformatics,WABI2003,volume LNBI2812,pages 165-176,2003[HB05] D.H.Huson and D.Bryant.Estimating phylogenetic trees and networks using SplitsTree4,note=Manuscript in preparation,software available from rmatik.uni-tuebingen.de/software[HDKS04] D.H.Huson,T.Dezulian,T.Kloepper and M.A.Steel.Phylogenetic Super-Networks from Partial Trees.Algorithms in Bioinformatics,WABI2004,in press,2004.[HKLS05] D.H.Huson,T.Kloepper,P.J.Lockhart and M.A.Steel.Reconstruction of Reticulate Networks from Gene Trees accepted for RECOMB2005.[MM02]W.Maddison and D.Maddison.Mesquite-a modular system for evolutionary analysis./mesquite/mesquite.html,2002.[SN87]N.Saitou and M.Nei.The Neighbor-Joining method:a new method for reconstructing phylogenetic trees.Molecular Biology and Evolution,4:406–425,1987.[SvH96]K.Strimmer and A.von Haeseler.Quartet puzzling:a quartet maximum likelihood method for reconstructing tree topologies.Molecular Biology and Evolution,13:964–969,1996. [Swo00] D.L.Swofford.PAUP∗:Phylogenetic analysis using parsimony(∗:and other methods), version4.2,2000.。
作系统进化树的方法系统进化树(Phylogenetic tree)是一种表示生物物种之间进化关系的图形结构。
它基于生物的遗传物质或形态特征等数据,通过一定的算法和模型来构建,以揭示物种之间的亲缘关系和进化历程。
以下是构建系统进化树的一般步骤:1. 数据收集:首先需要收集用于构建进化树的基因或形态特征数据。
这通常涉及从各种来源获取DNA、蛋白质或其他分子序列数据,或者从博物馆和标本馆获取生物形态特征数据。
2. 序列比对:对于DNA或蛋白质序列数据,需要将这些序列进行比对,以确保它们可以一起进行比较和分析。
3. 选择适当的距离度量:在构建系统进化树时,需要计算物种之间的“距离”。
这些距离是基于序列或形态特征的差异来计算的。
有多种方法可以计算这些距离,例如基于遗传物质的p距离(代表两个序列之间的差异比例)或形态特征的欧几里得距离。
4. 选择合适的建树算法:系统进化树可以通过多种算法来构建,包括但不限于UPGMA(Unweighted Pair Group Method with Arithmetic Mean)、WPGMA(Weighted Pair Group Method with Arithmetic Mean)、WPGMC(Weighted Pair Group Method with Centroid Linkage)、Neighbor Joining、Fitch-Margoliash、Maximum Parsimony、Maximum Likelihood等。
选择哪种算法取决于你的具体需求和所处理数据的性质。
5. 构建系统进化树:使用选择的算法和距离度量,将物种按照它们的亲缘关系分组。
这一步通常涉及到一个迭代过程,其中算法会尝试不同的分组方案,直到找到一个最优解。
6. 评估和验证树:一旦构建了系统进化树,就需要对其进行评估和验证,以确保其合理性和可靠性。
这通常涉及使用多种统计测试和可视化工具,例如Bootstrapping、P-distance、Tree-bisection-reconnection (TBR) 操作等。
生物大数据分析中的进化遗传树构建方法与技巧进化遗传树(Phylogenetic Tree)是生物学研究中用于分析物种关系和演化历程的重要工具。
通过构建进化树,我们可以了解不同物种之间的进化关系,揭示物种的演化历史以及预测它们之间的共同祖先。
在生物大数据分析中,构建进化遗传树有着重要的意义,因为它可以帮助我们理解生物的遗传多样性、物种起源以及群体分化等重要生物学问题。
在构建进化遗传树的过程中,我们需要根据生物学数据来推断物种间的关系。
这些生物学数据可以是DNA或RNA序列、蛋白质序列、形态特征等。
为了准确地构建进化遗传树,我们需要选择合适的方法和技巧。
下面将介绍一些常用的进化遗传树构建方法和技巧。
1. 距离法(Distance-based methods):距离法是通过计算物种间的相似度或差异度来构建进化遗传树的方法。
常用的距离法包括最邻近法(Neighbor Joining)、最小进化法(Minimum Evolution)和最大简约法(Maximum Parsimony)等。
这些方法根据不同的算法和模型,通过计算物种间的距离矩阵来构建进化关系。
2. 贝叶斯方法(Bayesian methods):贝叶斯方法是一种基于统计模型和概率推断的进化遗传树构建方法。
它通过采用贝叶斯推断和蒙特卡洛马尔科夫链蒙特卡洛算法(MCMC)来估计进化树的拓扑结构和参数。
贝叶斯方法具有高度灵活性和更准确的模型,适用于复杂的进化树推断问题。
3. 最大似然方法(Maximum likelihood methods):最大似然方法是一种常用的基于概率统计的进化遗传树构建方法。
它通过最大化观测到的数据出现的概率,推断出可能的进化树。
最大似然方法考虑了模型中的参数估计问题,并用参数化的模型来描述进化过程,从而提高了推断结果的准确性。
在进行进化遗传树构建时,还有一些技巧需要注意,以保证结果的准确性和可靠性:1. 数据质量的控制:数据质量是构建进化遗传树的关键因素之一。
专利名称:一种基于深度迁移网络的高光谱图像分类方法专利类型:发明专利
发明人:刘晓敏,桑顺,孙兴建,史珉,王浩宇
申请号:CN202111503748.X
申请日:20211210
公开号:CN114494762A
公开日:
20220513
专利内容由知识产权出版社提供
摘要:本发明公开了一种基于深度迁移网络的高光谱图像分类方法,该方法不仅基于CORAL从整体上对齐了两域的二阶统计量信息,适配了两域的全局分布。
而且基于局部最大均值差异对齐了相关子领域的一阶统计量信息,适配了两域的局部分布。
且所提方法能够提取目标域深层、具判别性特征,仅利用源域标记样本完成对目标域无标签样本的分类。
申请人:南通大学
地址:226019 江苏省南通市崇川区啬园路9号
国籍:CN
更多信息请下载全文后查看。
DOI 10.1007/s00442-014-3035-2Traits and phylogenetic history contribute to network structure across Canadian plant–pollinator communitiesScott A. Chamberlain · Ralph V . Cartar · Anne C. Worley · Sarah J. Semmler ·Grahame Gielens · Sherri Elwell · Megan E. Evans · Jana C. Vamosi · Elizabeth Ellereceived: 26 august 2013 / accepted: 1 august 2014 © springer-Verlag Berlin heidelberg 2014among modules. In addition, larger pollinators tended to be more specialized. as traits mediate interactions and have a phylogenetic signal, we found that phylogenetically close species tend to interact with a similar set of species. at the network level, patterns were weak, but we found increasing functional trait and phylogenetic diversity of plants associ-ated with increased weighted nestedness. these results pro-vide evidence that both specific traits and phylogenetic his-tory can contribute to the nature of mutualistic interactions within networks, but they explain less variation between networks.Keywords mutualism · Interaction webs ·trophic levels · morphological trait · Functional traitIntroductionInteraction webs define how the members of two or more trophic levels interact with one another. Comparisons of the structure of different mutualistic interaction webs reveal some consistent patterns, suggesting common mechanisms by which communities are assembled. For example, the degree distribution (distribution of number of interactions per species) of mutualistic networks has a consistent pat-tern, despite differences in species composition across net-works (Bascompte and Jordano 2007). In addition, a pat-tern of many weak, and few strong species interactions, is pervasive across not only mutualistic networks (Bascompte et al. 2006), but food webs as well (Paine 1980). however, despite consistent structural patterns, there is still no con-sensus on what mediates the production of these patterns. generally, traits of the species within networks are thought to either encourage or prevent interactions (santamaría and rodríguez-gironés 2007; Vázquez et al. 2009; Junker et al.Abstract Interaction webs, or networks, define how the members of two or more trophic levels interact. however, the traits that mediate network structure have not been widely investigated. generally, the mechanism that deter-mines plant-pollinator partnerships is thought to involve the matching of a suite of species traits (such as abundance, phenology, morphology) between trophic levels. these traits are often unknown or hard to measure, but may reflect phylogenetic history. We asked whether morphological traits or phylogenetic history were more important in medi-ating network structure in mutualistic plant-pollinator inter-action networks from Western Canada. at the plant species level, sexual system, growth form, and flower symmetry were the most important traits. For example species with radially symmetrical flowers had more connections within their modules (a subset of species that interact more among one another than outside of the module) than species with bilaterally symmetrical flowers. at the pollinator spe-cies level, social species had more connections within andCommunicated by steven D. Johnson.Electronic supplementary material the online version of this article (doi:10.1007/s00442-014-3035-2) contains supplementary material, which is available to authorized users.s. a. Chamberlain (*) · g. gielens · s. elwell · e. elleDepartment of Biological sciences, simon Fraser university, Burnaby, BC V5a 1s6, Canada e-mail: myrmecocystus@r. V . Cartar · m. e. evans · J. C. VamosiDepartment of Biological sciences, university of Calgary, Calgary, aB t2n 1n4, Canadaa. C. Worley · s. J. semmlerDepartment of Biological sciences, university of manitoba, Winnipeg, mB r3t 2n2, Canada2010; Cagnolo et al. 2011; Donatti et al. 2011; Danieli-silva et al. 2012), yet stochastic processes may also play a role. Because the traits themselves are evolving at varying rates, the phylogenetic history of any given assemblage of species can therefore influence network structure.there are two ways in which traits can mediate link-age rules in a plant-pollinator bipartite community: bar-rier (the difference between traits of plants and pollinators prevents interaction), and complementarity (the degree to which traits are similar allows interaction). traits involved in mediating species interactions are likely to be specific; for example, the maximum length a pollinator’s tongue can extend will determine the nectar tube lengths and there-fore plant species it can visit. Junker et al. (2013) showed that flower traits have a large impact on the pollinators that visit them, and the resulting network structure; how-ever, they did not compare the ability of traits to explain structure compared to other factors (e.g. abundance). stang et al. (2006) showed that both abundance (plant and pol-linator) and flower traits independently contributed to net-work structure, but the combination of the two better pre-dicted network structure. there are few studies that have been able to use many traits of both sides of a network to ask how traits contribute to network structure. Furthermore, a limitation of most studies exploring how traits relate to network structure is small size of data sets: it is difficult to combine a large set of networks with trait data for the com-ponent species. Because of this difficulty, we explore the possibility of using phylogenetic information as a surrogate representing unmeasured differences among species.many species traits are phylogenetically conserved (Blomberg et al. 2003); in which case closely related spe-cies tend to have more similar traits than distantly related species. thus, if species traits are the result, at least in part, of their phylogenetic history, traits and phylogeny should predict network structure to similar degrees. however, dif-ferences can arise because: (1) some important traits are evolutionarily labile and show little phylogenetic signal; and (2) some traits do show a phylogenetic signal, yet may not have been regularly measured, either due to perceptual differences (e.g. ultraviolet (uV) reflectance in flowers that insects can see but humans cannot) or because we simply did not appreciate their importance [e.g. electrical fields (Clarke et al. 2013)]. Considering the possibility for the presence of “unknown” important traits, as well as the large amount of time it takes to collect data on a suite of poten-tially important traits, it would be useful if phylogenetic history could be a proxy for describing a list of traits that mediate species interactions. thus far, several studies have shown that phylogenies do influence network structure and specific species interactions, but the effect of phylog-eny overall appears to be modest relative to traits (rezende et al. 2007; Vázquez et al. 2009).there is a temptation to reduce all of the interactions observed in a community into summary metrics, such as connectance, nestedness and interaction asymmetry, and link these summary metrics to some value of vulnerabil-ity of the community to invasion or disturbance (elle et al. 2012). While these observations are intriguing, the mecha-nisms that may cause these metrics to be associated with stability are often unclear and an investigation of traits can be a good place to begin to tease apart mechanistic influ-ences. here we use 47 mutualistic plant-pollinator interac-tion networks from Western Canada to ask what mediates their structure. specifically, we ask:1. how do phylogeny and traits affect individual speciesinteraction patterns, as measured by several commonly used metrics?2. how do phylogeny and traits affect structural proper-ties of whole networks?We list empirically based predictions, where possible, for question 1 in table 1.Materials and methodsstudy sitesa total of 47 mutualistic plant-pollinator networks were studied in four regions of Western Canada, from west to east: oak savannah (British Columbia; 12 networks), shrub-steppe (British Columbia; eight networks), foothills rough fescue prairie (alberta; 21 networks), and upland tall grass prairie and sedge meadow habitat (manitoba; six networks) [see table a1 (electronic supplementary material; esm) for site information]. Our original data set included 52 networks, but five from very degraded rough fescue prai-rie were excluded because they had less than ten species in total (no. plant + pollinator species).Collection of mutualistic network datatwo sampling methods were used in this study: transects and plots. Plots are generally more appropriate when the plant species in the community are very patchily distributed (gibson et al. 2011). In the plot method, sampling focuses on individual plant species, with an attempt to observe each plant species for an equal amount of time. the transect method is more appropriate for communities in which plant species are relatively homogeneously distributed so that a few transects can capture most of the plant species. an observer walks each transect for an equal amount of time. the tendency of the plot method is to pick up rare polli-nators, while the transect method can be biased towardsobserving common pollinators. We attempt to correct for the different methods by including collection method as a categorical variable in the analyses (see “Data analyses ”). the following are details of collection methods in each region [see appendix table a1 (esms) for details].Oak savannah sitesWe collected data on species interactions in 1-ha plots at each of six sites in both 2009 and 2010. each plot was sur-veyed from ten to 12 times per season between late april and early July, the majority of the flowering period. Over the flowering period we attempted to visit sites morning, midday, and afternoon on different survey dates to reduce bias due to flight-time differences among visiting insects. During each survey, each plant species in flower was observed for a 10-min period by each of two surveyors, on haphazard walks throughout the plot.Shrub‑steppe sitesData were collected in 2010 for eight sites using the same methodology as for oak-savannah sites, but surveys occurred from the beginning of april up to and including the end of July for a total of 12 samples per site.Foothills rough fescue prairieWe collected data on species interactions in six parallel 100-m transects at each of 21 sites. Bees were sampledover a 2-m-wide area centered on each transect. We vis-ited sites twice per survey date (a.m. and p.m.), walking at a pace to cover 600 m in 30 min. each site was sampled from three to eight times (median = 5) during the flowering season, but different sites were sampled in 2009 and 2010.Tall grass prairiesampling occurred in four upland tall grass prairie sites and two sites in sedge meadow. Insect observations took place within two 4 × 90-m parallel belt transects in each site. transects were walked by two researchers for 1 h between 0900 and 1500 hours. start times for observations in each site were rotated over survey dates. each plot was sampled eight times between June and mid-september 2010.With the exception of the tall grass prairie networks, all pollinators were collected for identification in the lab to the lowest taxonomic level possible (species or genus). For the tall grass prairie networks some pollinators could be iden-tified to morphospecies on the wing; all other specimens were collected for identification in the lab.Plant and pollinator traitsusing information in published floras, we collected the fol-lowing traits for plant species: flower symmetry (radial, bilateral); flower colour (blue, pink, white, yellow, green); sexual system (dioecious, gynodioecious, gynomonecious, perfect, and other, which includes monoecy, andromonoecy, androdioecy, etc.); life span [short lived (annual, biennial)Table 1 Description of traits included in this study, and expectations on how each trait should relate to four pollinator or plant network struc-tures Upwards arrows indicate that we expect the value of the network metrics [e.g. among-module connectivity (c ; among-module degree)] to increase if the value of the trait is that listed in the Expectation at column; we expect those with downwards arrows to decrease in value; we do not have a prediction for those with an X .z Within-module degree, ia interaction asymmetry, d ′ specializationtraitDescriptionexpectation atcziad ′Pollinators sociality solitary, socialsocial↑↑↑↓ nest location above- or belowground aboveground X X X X nest type renters or excavators rentersX X X X Parasitism Parasitic, non-parasitic non-parasitic X X X ↓ Body size Intertegular distancelarger size ↑↑↑↓PlantsFlower symmetry Zygomorphic, actinomorphic actinomorphic ↑↑↑↓ Flower colour Flower colouryellow flowers ↑↑↑↓ sexual system Perfect, monoecious, dioecious Perfect X X X X growth form herbaceous, woody herbs ↓↓X ↑ life span short lived, long lived annual ↓↓X ↑ Flower sizeFlower sizelarger size↑↑X↓or long lived (perennial)]; growth form [(herbaceous and other (including sub-shrubs, shrubs, trees, and woody vines)]; and flower size. Flower size was determined by taking the midpoint of the minimum and maximum range of flower size given in each species’ description in the flora (in millimetres). Flower colours available in floras do not include uV reflectance in flowers that insects can see but humans cannot. however, it is worth asking if flower col-our classes do drive any variation in network structures because the spectrum humans see is at least part of the spectrum pollinators can see. Plant trait data were collected from various sources, including the Flora of North America (Flora of north america editorial 2002) and the E‑Flora of British Columbia (Klinkenberg 2012).For pollinators, we collected the following life history traits, also from the literature: sociality (solitary, social, unknown); parasitism (not parasitic, social parasite, clep-toparasite); nest location (aboveground, belowground, above/belowground); and nest type (rent or excavate). rent-ers construct nests within existing tunnels or other cavities regardless of nest location, while excavators dig or bore the chamber/tunnel within existing substrate (michener 2007). life history data were collected from michener (2007). We also estimated body size for some of the bees and flies col-lected in this research. We measured intertegular distance (Itwidth) for bees, which correlates with body size (Cane 1987; greenleaf et al. 2007), and with foraging distance (greenleaf et al. 2007). We calculated bee mass (milli-grams) using the equation: mass = 0.77 × Itwidth0.405, following Cane (1987). For flies, we measured body length (tip of the head to the end of the abdomen), and used the following equation to convert body length to mass (milli-grams): mass = 0.032 × length2.63, following sabo et al. (2002). Body size was not estimated for other taxa.Plant and pollinator phylogenetic reconstructionPlant phylogenies were built using Phylomatic (/phylomatic/; Webb and Donoghue 2004). Phylomatic is an online interface used to retrieve a phylogeny based on a user-defined set of plant species taxonomic names. Branch lengths were estimated for the master plant phylogeny using the algorithm for branch length adjustment (BlaDJ) in the software Phylocom (Webb et al. 2008), which fixes a set of nodes in the tree to specified ages (Wikstrom et al. 2001) and evenly dis-tributes the ages of the remaining nodes. the file (in mul-tiple formats) we used to run the bladj command in Phy-locom is provided in appendix B (esm). see the master plant phylogeny in appendix B (esm) and on (/articles/Canadian_networks/1014346).animal phylogenies were built using a variety of tools, similar to that implemented in Phylomatic for plant phylogenies. First, we built a topology of all animal pol-linators across all networks in the study in mesquite ver-sion 2.75 (maddison and maddison 2011), based on a variety of published phylogenies [appendix B (esm)]. second, we collected 33 node age estimates (in millions of years) from (hedges et al. 2006), which are provided in appendix B (esm). last, we used the algo-rithm for branch length adjustment (BlaDJ) as described above for plants, except that we used our node age esti-mates retrieved from . see the master pollina-tor phylogeny in appendix B (esm) and on (/articles/Canadian_networks/1014346).We pruned the master phylogenies made above for both plants and pollinators for each network, to produce phylog-enies for each site/year combination.species-level network metricsFor species-level metrics of interaction, we calculated direction of interaction strength asymmetry (ia), a meas-ure of specialization [Blüthgen’s d′ (Blüthgen et al. 2006)], degree (number of other species the focal species interacts with), within-module degree (z), among-module connectiv-ity (c), and ecological similarity. We used the species level function in the bipartite r package (Dormann 2011). Posi-tive values of ia show that a focal species affects an interac-tor more than the interactor affects the focal species; nega-tive values of ia indicate that a focal species is, on average, affected more by the interactor than the converse (Vázquez et al. 2007). the d′ metric of specialization measures how specialized a species is with respect to available resources. z is the standardized number of links to other species in the same module, and c is the extent of connections of the spe-cies to other modules (Olesen et al. 2007). ecological simi-larity of any two species was calculated following rezende et al. (2007) as the number of species with which both spe-cies interact divided by the total number of species with which they separately interact. a large value means the two species share interactions with the same species, while a small value indicates they share relatively few of the same species. this measure is necessarily one that depends on comparing two species—thus, this measure is only used when investigating how phylogenetic history relates to spe-cies traits (see below).network structural properties and trait diversityFor both plants and pollinators, we quantified trait diver-sity within each network using a measure of functional dispersion (laliberté and legendre 2010). FDis computes the mean distance of a species in ordination space from the mean for all species, where the ordination space is defined by a set of traits. this is in effect a multidimensionalmeasure of functional diversity. FDis is highly correlated with rao’s quadratic entropy (Q) (Botta-Dukát 2005), but FDis has better properties than Q (laliberté and legendre 2010). FDis can be weighted by the abundance of each spe-cies, but we did not do this because FDis is used in analyses in which the measures of abundance are the sums of cell values in the interaction matrices; this lack of independence would confound analyses. In these network-level analyses, we did not include traits individually because many traits were categorical/nominal, which would leave few residual df and low statistical power.For both plants and pollinators, we calculated one net-work-level measure of phylogenetic diversity: mean pair-wise distance (mPD) (Webb et al. 2008) between all taxa. We calculated four measures of network-level structure: weighted nestedness, modularity, weighted connectance, and network-level specialization (H2′). For nestedness, we used the weighted nestedness metric based on overlap and decreasing fill (nODF), proposed by almeida-neto and ulrich (2011). We used a modified version, nODF2, which sorts the matrix before calculating the measure, ideal for comparisons across different networks as it is independ-ent of the initial matrix. Values of zero indicate non-nest-edness, those of 100 are perfect nesting. modularity meas-ures the extent to which a network is organized into clearly delimited modules, where a module is a subset of species that interact more among one another than outside of the module (Bascompte and Jordano 2007). We used the mod-ularity-detecting algorithm, which maximized modularity using simulated annealing implemented in the command line function netcarto_cl in the C library r graph (guimera and amaral 2005a, b). Weighted connectance is the quanti-tative version of linkage density divided by number of spe-cies in the network, following tylianakis et al. (2007). H2′was introduced by Blüthgen et al. (2006), and characterizes the degree of specialization in a network, while not being affected by network size or sampling intensity. a summary table of these network-level metrics is presented in appen-dix C (esm).Data analysesPhylogenetic signalWe calculated phylogenetic signal for a subset of traits that were either binary (plants–lifespan, growth form, and flower symmetry; pollinators–nest location, parasitic, and sociality) or continuous (plants–flower size; pollinators–body size). For binary traits we calculated the D-statistic proposed by Fritz and Purvis (2010), while for continuous traits we calculated the K-statistic proposed by Blomberg et al. (2003). For both methods we performed 1,000 simu-lations to compare the observed statistic to a distribution of values from species randomized on the tips of each phy-logeny. We calculated phylogenetic signal for each trait in each site, for both plants and pollinators. For D, we deter-mined whether D was significantly greater than 0 (indi-cating that trait is more phylogenetically conserved than under a Brownian motion model), and whether it was sig-nificantly less than 1 (indicating that trait is phylogeneti-cally overdispersed). the K statistic tests whether K is sig-nificantly different from 1; less than 1 indicates that trait is phylogenetically overdispersed, while a value greater than 1 indicates that trait is phylogenetically conserved. We could not calculate signal for some site/organism/trait com-binations because trait values were the same for all species. thus, sample sizes are less than 47 for some tests. We sum-marized these analyses by presenting the proportion of net-works that had D-values significantly greater than 0 or less than 1, and K values significantly less than or greater than 1.a potential source of bias in detecting phylogenetic signal was that some networks had fewer than 20 species, which Blomberg et al. (2003) showed have less than 0.8 statistical power.How do phylogeny and traits affect species‑level interaction metrics?For species-level analyses we tested for a relationship between species-level interaction metrics and phylogenetic history within individual networks, and separately tested for a relationship between species-level network metrics and traits across the entire data set. For phylogenies, we calculated pairwise phylogenetic distance between each species pair in the phylogeny for each network using the cophenetic.phylo function in the ape r package (Paradis et al. 2004) and compared them to distance matrices based on interaction metrics using mantel tests. separate analy-ses were done for plants and pollinators. although there are some drawbacks to mantel tests (harmon and glor 2010), we use them with caution, recognizing that, relative to the alternative K statistic, type I error is unaffected, but that type II error is inflated. We used the function mantel in the vegan r package (Oksanen et al. 2013).For our analysis of trait effects, we used mixed linear models for all variables, some with gaussian error distribu-tions (response variables–ia, and z) and others with bino-mial distributions (d′ and c). models were run separately for plant traits and pollinator traits. all plant models were: network metric ~ symmetry + colour category + flower size + sexual system + life span + growth form + col-lection method. all pollinator models were: network metric ~ sociality + parasitism + nest location + nest type + mass + collection method. In both models, region (e.g. oak savannah, rough fescue) and network (i.e. site) were included as random effects. the explanatory variablemass was log10 transformed to improve assumptions of normality and homoscedasticity of residuals. In the case of significant effects of categorical variables, we performed post hoc tukey tests to determine what levels within a vari-able differ from one another. For the d’ and c response vari-ables, we used generalized linear mixed models with bino-mial error distribution with a logit link function, using the function glmer in the package lme4 (Bates et al. 2012).How do phylogeny and traits affect network structures?to address the extent to which phylogeny and traits influ-ence community-level network structures, we modeled each of the five network structures with the model: network structure ~N tOt+ FDis PO+ FDis Pl+ mPD PO+ mPD Pl, where N tOt is total network size (no. pollinator spe-cies + no. plant species), FDis PO is pollinator functionaltrait dispersion, FDis Pl is plant functional trait dispersion; mPD PO is mean phylogenetic diversity of pollinators, and mPD Pl is mean phylogenetic diversity of plants. as all response variables were continuous and bounded between 0 and 1, we used β regression models for each network met-ric, using the betareg r package (Cribari-neto and Zeileis 2010), which are appropriate for this kind of data. Z-tests were used to perform significance tests of model coeffi-cients. nestedness was calculated as between 0 and 100, but is essentially a proportion by dividing the nestedness value by 100. network-level data used in analyses are pro-vided in appendix C (esm).ResultsPhylogenetic signalPlantsOverall, the two traits that showed phylogenetic signal the most frequently were plant growth form (herb, woody) and flower symmetry (radial, bilateral). life span was phyloge-netically conserved in 17 % (six of 35) of trees, and overd-ispersed in 17 % of trees [see appendix e (esm)]. growth form was phylogenetically conserved in 6 % (two of 34) of trees, and overdispersed in 12 % of trees. Flower symmetry was phylogenetically conserved in 41 % (19 of 46) of trees, and overdispersed in 0 trees. Flower size had a significant phylogenetic signal in 28 % (13 of 47) of trees, with phylo-genetic conservation in seven trees, and overdispersion in six. PollinatorsOverall, the two traits that showed phylogenetic signal most frequently were sociality and nest location (above- vs. belowground). For nest location, 73 % (22 of 30) of trees were phylogenetically conserved, while no trees were overdispersed [see appendix e (esm)]. For parasitism, 38 % (three of eight) of trees were phylogenetically conserved, while 13 % (one of eight) of trees were overdispersed. For sociality, 93 % (38 of 41) of trees were phylogenetically conserved, while no trees were overdispersed. Body size had a significant phylogenetic signal in 55 % (25 of 47) of trees, with two trees showing phy-logenetic conservation, and 24 showing overdispersion. Phylogenetic historyFor plants, ecological similarity was most frequently related to plant phylogenetic distance, with significant relationships in 17 % of networks. specialization (d′) was significantly related to pollinator phylogenetic distance in 10 % of net-works, while z was related to pollinator phylogenetic dis-tance in 5 % of networks. For pollinators, ecological simi-larity was most frequently related to pollinator phylogenetic distance, with significant relationships in 16 % of networks (table 2; Fig. 1). ia was related to pollinator phylogenetic distance in 14 % of networks. z was significantly related to pollinator phylogenetic distance in 5 % of networks.how do phylogeny and traits affect species-level interaction metrics?Plant traitssexual systems, plant growth form, and flower symme-try were important traits for species-level network metrics [appendix table D1 (esm); Fig. 2]. species with a perfect sexual system had greater specialization (d′) and interacted with fewer insect species (lower degree) than did gynomo-necious species. sexual system also significantly influenced z, but post hoc tests showed no differences among levels Table 2 summary of results of species-level analyses of the relation-ship between species-level interaction metrics and phylogenetic dis-tanceNumbers in each cell are the number of networks with significant (P < 0.05) relationships between species-level interaction metrics (ia, d, c, z, and ecosim) and phylogenetic distance; percentages are percent of total networks with significant relationships. For abbrevia-tions, see table 1network structure PhylogeneticPollinators Plantsia13 (14 %) 2 (2 %) d′ 2 (2 %)9 (10 %) c 3 (3 %) 2 (2 %) z 5 (5 %) 5 (5 %) ecosim15 (16 %)16 (17 %)。
全连接层剪枝带权重数值全连接层剪枝是一种常用的神经网络压缩方法,通过减少神经网络中的冗余权重参数,可以使得网络模型更加轻量化和高效。
在深度学习中,神经网络模型通常由多个层组成,其中全连接层是其中的一种常见类型。
全连接层的作用是将前一层的所有神经元与当前层的所有神经元进行连接,每个连接都有一个对应的权重参数。
这些权重参数的数量通常非常庞大,占据了网络模型的大部分存储空间和计算资源。
然而,这些权重参数中并不是所有的都对网络的性能和准确度有贡献,有些权重参数对网络的输出结果影响较小甚至可以近似为零。
因此,剪枝方法的思想就是通过删除这些冗余的权重参数,来减少网络的复杂度和计算量,从而提高网络的推理速度和效率。
全连接层剪枝的方法通常有两种:一种是基于绝对阈值的剪枝方法,另一种是基于相对阈值的剪枝方法。
基于绝对阈值的剪枝方法是根据权重的绝对值大小来判断是否进行剪枝,而基于相对阈值的剪枝方法是根据权重的相对大小来进行剪枝。
在进行全连接层剪枝时,需要先对网络进行训练,然后计算每个权重参数的重要性分数。
这些重要性分数可以通过多种方式来计算,比如权重的绝对值、梯度的绝对值、Hessian矩阵的特征值等。
然后,根据设定的剪枝比例,选择重要性分数最低的一部分权重参数进行剪枝,将其置为零或删除。
进行全连接层剪枝后,网络模型的结构会发生改变,一些神经元之间的连接会被删除,从而减少了计算量和存储空间。
但同时也会带来一定的性能损失,因为删除了一部分权重参数,网络的表达能力可能会下降。
因此,在剪枝之后需要对网络进行微调或者重新训练,以恢复网络的性能。
全连接层剪枝作为一种常见的神经网络压缩方法,已经在实际应用中取得了很好的效果。
通过剪枝可以大幅减少模型的大小和计算量,使得模型可以在嵌入式设备等资源有限的环境下运行。
同时,剪枝也有助于减少过拟合和提高泛化能力,从而提高网络的准确度和鲁棒性。
除了全连接层剪枝之外,还有一些其他的神经网络压缩方法,比如卷积层剪枝、通道剪枝等。
《生物信息学》第四章:分子进化与系统发生系统发生树:系统发生树的样子研究分子进化所要构建的系统发生树(Phylogenetic tree),也叫分子树。
首先来看从系统发生树上我们都能研究出什么?对于一个未知的基因或蛋白质序列,可以利用系统发生树确定与其亲缘关系最近的物种。
比如你得到了一个新发现的细菌的核糖体RNA,你可以把它跟所有已知的核糖体RNA放在一起,然后用他们构建一棵系统发生树。
这样就可以从树上推测出谁和这个新细菌的关系最近。
系统发生树还可以预测一个新发现的基因或蛋白质的功能。
以基因为例,如果在树上与新基因关系十分密切的基因的功能已知,那么这个已知的功能可以被延伸到这个新基因上。
构建系统发生树还有助于预测一个分子功能的走势。
也就是从树上可以看出某个基因是正在走向辉煌还是在逐渐衰落。
最后,系统发生树还能帮助我们追溯一个基因的起源。
甚至当它从一个物种“跳”到另一个物种上,也就是发生了水平基因转移时,系统发生树都可以很好的展示出来。
系统发生树看上去就是很像小朋友画的简笔画(图1)。
虽然简单,但是一点也不简略,一棵树该有的东西,它一个也没少!图1. 系统发生树的样子树是从根(root)长出来的。
从根延伸出的树枝就叫枝(branch/lineage)。
枝上有分叉,分叉的地方就叫节(node)。
枝的顶端顶着的就是叶(leaf)。
根、节和叶都可以叫做节点(node)。
但是叶后面不再有枝了,是最外面的节点,所以叫外节点(outer node)。
而节的前后都有枝,所以叫内节点(inner node)。
根是一切的起源,习惯上就叫根。
根和节都表示理论上曾经存在的祖先,叶子是现存的物种。
这一点很重要!比如我们要研究某个基因,于是搜集了很多物种的这个基因的序列,用它们构建了一棵系统发生树。
搜集到的物种都出现在叶子上,也就是外节点上,没有在内节点上的。
内节点上都是理论上曾经存在过的共同祖先,现在已经不存在了!此外,枝子的长短也是有意义的,我们后面再讲。
随着人工智能技术的不断发展,自然语言生成成为了人们关注的焦点之一。
前馈神经网络作为一种重要的机器学习模型,在自然语言生成领域也扮演着重要的角色。
在本文中,我们将探讨如何使用前馈神经网络进行自然语言生成,从基本原理到应用实践,带您深入了解这一话题。
一、前馈神经网络的基本原理前馈神经网络是一种最基础、最简单的神经网络模型。
它由输入层、隐层和输出层组成,每一层包含多个神经元,每个神经元与上一层的每个神经元都有连接。
在前馈神经网络中,信息是从输入层经过隐层传递到输出层的,不存在循环连接。
这种结构使得前馈神经网络适合处理各种各样的输入数据,并且在自然语言生成领域表现出色。
二、前馈神经网络在自然语言生成中的应用在自然语言生成中,前馈神经网络可以被用来完成多种任务,例如文本摘要、对话系统、文章生成等。
以文本摘要为例,前馈神经网络可以通过学习大量的文章和摘要数据,来理解文章的主题和内容,然后生成简洁准确的摘要。
对话系统中,前馈神经网络可以通过学习大量的对话数据,来生成流畅自然的对话内容。
在文章生成中,前馈神经网络可以通过学习大量的文章数据,来生成具有逻辑连贯性和可读性的文章内容。
三、如何训练前馈神经网络进行自然语言生成要训练前馈神经网络进行自然语言生成,首先需要准备大量的文本数据。
这些数据可以是文章、对话、摘要等形式的文本,数据量越大越有利于网络的学习和生成。
其次,需要对文本数据进行预处理,包括分词、去除停用词、标点符号等。
然后,需要将文本转换成神经网络可以理解和处理的数据形式,例如词向量、词袋等。
接下来,可以选择合适的前馈神经网络模型进行训练,如多层感知机(MLP)、卷积神经网络(CNN)等。
在训练过程中,需要调整网络的超参数,例如学习率、批大小、隐藏层神经元数等,以达到最佳的训练效果。
最后,可以使用生成器来生成自然语言内容,如生成摘要、对话等。
四、如何提高前馈神经网络的自然语言生成效果在实际应用中,为了提高前馈神经网络的自然语言生成效果,可以采取一些策略和方法。
a rXiv:079.283v1[math.CO ]3Se p27Phylogenetic Networks from Partial Trees S.Gr¨u newald Department of Combinatorics and Geometry (DCG),CAS-MPG Partner Institute for Computational Biology (PICB),Shanghai Institutes for Biological Sciences (SIBS),Chinese Academy of Sciences (CAS),China,and K.T.Huber and Q.Wu School of Computing Sciences,University of East Anglia,Norwich,NR57TJ,United Kingdom.February 1,20081K.T.HuberSchool of Computing Sciences,University of East Anglia,Norwich,NR57TJ,United Kingdom.email:katharina.huber@FAX:+44(0)1603593345We would prefer to submit thefinal manuscript in LATEX.2AbstractA contemporary and fundamental problem faced by many evolu-tionary biologists is how to puzzle together a collection P of partialtrees(leaf-labelled trees whose leaves are bijectively labelled by speciesor,more generally,taxa,each supported by e.g.a gene)into an overallparental structure that displays all trees in P.This already difficultproblem is complicated by the fact that the trees in P regularly sup-port conflicting phylogenetic relationships and are not on the samebut only overlapping taxa sets.A desirable requirement on the soughtafter parental structure therefore is that it can accommodate the ob-served conflicts.Phylogenetic networks are a popular tool capableof doing precisely this.However,not much is known about how toconstruct such networks from partial trees,a notable exception beingthe Z-closure super-network approach and the recently introduced Q-imputation approach.Here,we propose the usage of closure rules toobtain such a network.In particular,we introduce the novel Y-closurerule and show that this rule on its own or in combination with oneof Meacham’s closure rules(which we call the M-rule)has some verydesirable theoretical properties.In addition,we use the M-and Y-ruleto explore the dependency of Rivera et al.’s“ring of life”on the factthat the underpinning phylogenetic trees are all on the same data set.Our analysis culminates in the presentation of a collection of inducedsubtrees from which this ring can be reconstructed.1IntroductionPhylogenetic trees have proved an important tool for representing evolution-ary relationships.For a set X of species(or,more generally,taxa)these are formally defined as leaf-labelled trees whose leaves are bijectively labelled by the elements of X.Advances in DNA sequencing have resulted in ever more data on which such trees may be putational limitations however combined with the need to understand species evolution have left biologists with the following fundamental problem which we will refer to as amalgamation problem:given a collection P of phylogenetic trees,how can these trees be amalgamated into an overall parental structure that preserves the phylogenetic relationships supported by the trees in P?The hope is that such a structure might help shed light on the evolution of the underlying genomes(and thus the species).In the ideal case that all trees in P support the same phylogenetic rela-tionships(as is the case for trees T1and T2depicted in Fig.1)this structure is known to be a phylogenetic tree and a supertree method[2]may be used to reconstruct it.For the above example the outcome T∗of such a method is3T2T1Figure1:3phylogenetic trees which appeared in weighted form in[17]on subsets of the7plant species: A.thaliana(A.th),A.suecia(A.su),Turri-tis(Tu)A.arenosa(A.ar),A.cebennensis(A.ce),Crucihimalaya(Cru)and A.halleri(A.ha).T1with species Cru(see Fig.1for full species names)attached via a pendant edge to the vertex labelled v.It should be noted that T∗supports the same phylogenetic relationships as T1and T2in the following sense:For afinite set X,call a bipartition S={A, A}of some subset X′⊆X a partial split on X,or a partial(X)-split for short,and denote it by A| A or,equivalently,by A|A where A:=X′−A.In particular,call S a(full)split of X if X′=X. Furthermore,say that a partial X-split S=A| A extends a partial X-split S′=B| B if either B⊆A and B⊆ A or B⊆ A and A⊆ B.Finally,say that a phylogenetic tree T displays a split S=A| A if S is a partial split on the leaf set L(T)of T induced by deleting an edge of T.Then“supports the same phylogenetic relationships”means that for every split S displayed by T1or T2there exists a split on L(T∗)that extends S and is displayed by T∗.Due to complex evolutionary mechanisms such as incomplete lineage sorting,recombination(in the case of viruses),or lateral gene transfer(in case of bacteria)the trees in P may however support not the same but conflicting phylogenetic relationships.A phylogenetic network in the form of a split network(see[10,19]for overviews)rather than a phylogenetic tree is therefore the structure of choice if one wishes to simultaneously represent all phylogenetic relationships supported by the trees in P.An example in point is the split network pictured in Fig.2which appeared as a weighted network in[17].With replacing“edge”in the definition of displaying by “band of parallel edges”and“L(T)”by“set of network vertices of degree 1”to obtain a definition for when a split network displays a split,it is straight forward to check that the network in Fig.2displays all splits displayed by the3trees pictured in Fig.1.It should be noted that phylogenetic networks such as the one depicted in4Fig.2(see e.g.[7,11,14]for recently introduced other types of phylogeneticnetworks)provide a means to visualize the complexity of a data set andshould not be thought of as an explicit model of evolution.Awareness ofthis complexity does not only allow the exploration of a data set but,as is the case of e.g.hybridization networks[14],can also serve as starting pointfor obtaining an explicit model of evolution(see[12]for more on this).Figure2:A circular phylogenetic network that represents all phylogenetic relationships supported by the trees depicted in Fig.1(see thatfigure forfull species names).Apart from displaying all splits induced by the3trees depicted in Fig.1,the network depicted in Fig.2has a further interesting feature.It is cir-cular.In other words,if X denotes the set of the7plant species underconsideration,then the elements of X can be arranged around a circle C sothat every split S=A| A of X displayed by the network can be obtained by intersecting C with a straight line so that the label set of one of the resulting2connected components is A and the label set of the other is A.Although seemingly a very special type of phylogenetic network,circularphylogenetic networks are a frequently used structure in phylogenetics(seee.g.[3,4,5,6,8])as they do not only naturally generalize the concept of aphylogenetic tree but are also guaranteed to be representable in the plane;a fact that greatly facilitates drawing and thus analyzing them.However,al-though recentlyfirst steps have been made with regards tofinding a solution to the amalgamation problem in terms of a phylogenetic network leading to the attractive Z-closure[13]and Q-imputation[9]approaches,very little is known about a solution of this problem in terms of a circular phylogenetic network.Intrigued by this and motivated by the fact that,from a combinatorialpoint of view,phylogenetic trees and networks are split systems(i.e.collections5of full splits)and that therefore the amalgamation problem boils down to the problem of how to extend partial splits on some set X to splits on X,we wondered whether closure rules for partial splits could not be of help.Es-sentially mechanisms for splits’enlargement,such rules have proved useful for supertree construction and also underpin the above mentioned Z-closure super-network approach.As it turns out,this is indeed the case.As an immediate consequence of our main result(Corollary5.5),we obtain that for a collection of partial splits that can be“displayed”by a circular phy-logenetic network N,the collection of(full)splits generated by the closure rules in the centre of this paper is guaranteed to be displayable by N and also independent of the order in which the rules are applied.In a study aimed at shedding light into the origin of eukaryotes,Rivera et al.[20]put forward the idea of a“ring of life”with the eukaryotic genome being the result of a fusion of two diverse procaryotic genomes(see also [16,20,23]).A natural and interesting question in this context is how dependent Rivera et al.’s ring of life is on the fact that all underpinning trees are on the same taxa set.In the last section of this paper,we provide a partial answer by presenting an example of a collection of induced partial trees from which the ring of life can be reconstructed using the M-and Y-rule.The paper is organized as follows.In Section2,wefirst introduce some more terminology and then restate one of Meacham’s closure rules(our M-rule)and introduce the novel Y-rule.In Section3,we study the relationship between the M-and Y-rule and the closure rule that underpins the afore-mentioned Z-closure super-network approach.In Section4,we introduce the concept of a circular collection of partial splits and show that both the Y-and M-rule preserve circularity(Proposition4.4).In Section5,we in-troduce the concept of a split closure and show that for certain collections of partial splits this closure is independent of the order in which the Y-rule and/or M-rule are/is applied(Theorem5.3).This result lies at the heart of Corollary5.5.In Section6,we explore the dependency of Rivera et al.’s ring of life on the fact that the underpinning trees are all on the same data setThroughout the paper,X denotes afinite set and the terminology and notation largely follows[21].62Closure rulesWe start this section by introducing some additional terminology and nota-tion.Subsequent to this,wefirst restate Meacham’s rule(which we call the M-rule)and then introduce a novel closure rule which we call the Y-rule.LetΣ(X)denote the collection of all partial splits of X and suppose Σ⊆Σ(X).Then a partial split S∈Σthat can be extended by a partial split S′∈Σ−S is called redundant.The set obtained by removing redundant elements fromΣis denoted byΣ−.IfΣ=Σ−thenΣis called irreducible and the set of all irreducible subsets inΣ(X)is denoted by P(X).Note that the relation“ ”defined for any two(partial)split collectionsΣ,Σ′∈P(X) by puttingΣ Σ′if every partial split inΣis extended by a partial split in Σ′is a partial order on P(X)[21].Suppose for the following thatθis a closure rule,that is,a replacement rule that replaces a collection A⊆Σ(X)of partial splits that satisfy some condition Cθby a collectionθ(A)⊆Σ(X)whose elements are generated in some systematic way from the partial splits in A(see e.g.the M-and the Y-closure rules presented below for two such systematic ways).Suppose Σ,Σ′∈P(X)are two irreducible collections of partial splits and Cθ(Σ)is the set of all subsets ofΣthat satisfy Cθ.If there exists some subset A∈Cθ(Σ) such thatΣ′=(Σ∪θ(A))−then we say thatΣ′is obtained fromΣvia a single application ofθ.Finally,if for every subset A∈Cθ(Σ)we have θ(A)− Σthen we call an application ofθtoΣtrivial and say thatΣis closed with respect toθ.We are now in the position to present the2closure rules we are mostly concerned with in this paper:the M-rule which is originally due to Meacham [18]and the novel Y-rule.We start with Meacham’s rule.2.1The M-ruleSuppose S1,S2∈Σ(X)are two distinct partial splits of X.Then the M-rule θM is as follows:(θM)If there exists some A i∈S i,i=1,2such thatA1∩A2=∅and A1∩ A2=∅(1)then replace A={S1,S2}by the setθ{A1,A2}M (A)which comprises ofA and,in addition,also the partial splitsS′1=(A1∩A2)|( A1∪ A2)and S′2=( A1∩ A2)|(A1∪A2).7In case the partial splits S1and S2are such that there is no ambiguity with regards to the identity of the sets A1and A2in the statement of the M-rule orthey are irrelevant to the discussion,we will simplifyθ{A1,A2}M (A)toθM(A).Clearly,such ambiguity cannot arise if S1and S2are compatible,that is, there exist subsets D i∈S i,i=1,2such that D1∩D2=∅.However if S1 and S2are incompatible,that is,not compatible then caution is required.Note that if A1and A2as in the statement of the M-rule are such that A2⊆A1and A1⊆ A2,then it is easy to verify thatθM applies trivially to A.Also note that for anyΣ∈P(X)and any two distinct partial splitsS1,S2∈Σ,we haveΣ (Σ∪θM({S1,S2}))−.Finally,note that any phylogenetic tree on X that displays the partial splitsin some setΣ∈P(X)also displays the partial splits in(Σ∪θM({S1,S2}))−,S1,S2∈Σ.2.2The Y-ruleSuppose S i∈Σ(X),i=1,2,3,are three distinct partial splits of X.Then the Y-ruleθY is as follows:(θY)If there exists some A i∈S i,i=1,2,3such that∅∈{A1∩A2∩A3, A1∩ A2∩A3, A1∩A2∩ A3}andA1∩ A2∩ A3=∅.(2) (see Fig.3(a)for a graphical interpretation),then replace A={S1,S2,S3}by the setθ{A1,A2,A3}Y(A)which comprises of the partial splitsS′1= A1∪( A2∩ A3)|A1,S′2=A2∪(A1∩ A3)| A2,andS′3=A3∪(A1∩ A2)| A3.Although the condition in(2)might look quite strange atfirst sight,the class of triplets of partial splits that satisfy it is very rich.For example,sup-pose that S i=A i| A i,i=1,2,3are splits of X that can be arranged in the plane as indicated in Fig.3(b)where each bold,straight line represents oneof S i,i=1,2,3and the dots represent non-empty triplewise intersectionsof the parts of S i,i=1,2,3,in which they lie.For example,the dot in the bottom wedge represents the intersection A1∩A2∩A3.The shaded regions correspond to the3non-empty intersections mentioned in the statement of the Y-rule.The partial splits S′i=A′i| A′i i=1,2,3obtained by restricting81111111101111A12∩A3=∅(a)A1∩A2∩ A3=∅A1∩ A2∩ A1∩A2∩ A3=∅A1(b)A2A3A3A1A2Figure3:(a)A graphical representation of Condition(2)in the form of a Y.(b)An example of three splits,depicted in bold lines,that satisfy Condition(2)–see text for details.S1,S2,and S3to different subsets of X so that the shaded regions remain non-empty form a triplet of partial splits that satisfy(2).As the example of set A comprising the three partial splits S1=145|2367, S2=1357|246,and S3=127|356shows different choices of the sets A i,i=1,2,3lead to different setsθ{A1,A2,A3}Y(A).For example,if A1:= {1,4,5},A2:={1,3,5,7},and A3:={1,2,7}then(2)is satisfied andθ{A1,A2,A3}Y(A)={S1,S2,1247|356}.If however A1and A2are as beforeand A3:={3,5,6},then(2)is also satisfied andθ{A1,A2,A3}Y(A)is the set{S1,S2,127|3456}.Following our practise for the M-rule,for A={S1,S2,S3}we simplifyθ{A1,A2,A3}Y(A)toθY(A)if the partial splits S i, i=1,2,3are such that there is no ambiguity with regards to the iden-tity of the sets A i,i=1,2,3,in the statement of the Y-rule or they are irrelevant to the discussion.Note that if A i,i=1,2,3as in the statement of the Y-rule are suchthat,in addition,∅=A1∩ A2⊆A3,∅=A1∩ A3⊆A2,∅= A3∩ A2⊆ A1, and A1∩A2∩A3=∅it is easy to see thatθY applies trivially to A.Also note that for anyΣ∈P(X)and any3partial splits S1,S2,S3∈Σof X,we haveΣ (Σ∪θY({S1,S2,S3})−.3First closure rule relationshipsIn this section wefirst restate the Z-(closure)rule which was used in[13]inthe context of a supernetwork construction approach and then investigatethe relationship between the Y-,M-,and Z-rule.Also originally due to Meacham[18],the Z-ruleθZ can be restated as9follows:Suppose S1,S2∈Σ(X)are two distinct partial splits of X.(θZ)If there exists some A i∈S i,i=1,2such that∅∈{A1∩A2,A2∩ A1, A1∩ A2}and A1∩ A2=∅(3) then replace A={S1,S2}by the setθY(A)which comprises of the partial splits( A1∪ A2)|A1and A2|(A1∪A2).Note that any two compatible partial splits of X satisfy the condition in(3).With this third closure rule at hand we are now in the position to present afirst easy to verify result.Suppose S1,S2,and S3are3distinct partial splits of X such that there exist parts A i∈S i,i=1,2,3as in the statement of the Y-rule.If,in addition, A1∩ A2∩ A3=∅and A1⊆A2∪A3,then the partial split A1| A1∪( A2∩ A3)generated byθY is also generated byfirst applyingθM to S2and S3(with regards to A2∩ A3=∅)and then applying θM to the resulting partial split A2∪A3| A2∩ A3and S1.In addition,we have the following result whose straight forward proof we leave to the reader.Proposition3.1Suppose S1is a full split of X.Then the following state-ments hold.(i)If S2is a partial X-split andθZ applies toΣ={S1,S2},thenθM(Σ)−=θZ(Σ).(ii)If S2and S3are partial X-splits so thatθY applies toΣ={S1,S2,S3} andθZ applies to{S1,S2}and{S1,S3}.ThenθZ(S1,S i))−.(θY(Σ)∪ j=2,3θM(S1,S j))−=(i∈{2,3}4Closure rules and weakly compatible collections of partial splitsIn this section we introduce the notion of a weakly compatible collection of partial splits and study properties of the Y-and M-rules regarding such collections.A particular focus lies on the study of circular collections of partial splits which we also introduce.As we will see,they form a very rich subclass of such collections of partial splits.104.1Weakly compatible collections of partial splitsWe start this section with a definition that generalizes the concept of weak compatibility for(full)splits of X[1]to partial splits of X.Suppose S i= A i| A i∈Σ(X),i=1,2,3,are three partial X-splits.Then we call S1,S2,S3 weakly compatible if at least one of the four intersectionsA1∩A2∩A3, A1∩ A2∩A3, A1∩A2∩ A3,A1∩ A2∩ A3(4) is empty1.Since the roles of A i and A i in S i,i=1,2,3,can be interchanged without changing S1,S2,S3we have that S1,S2,S3are weakly compatible if and only if at least one of the four intersectionsA1∩ A2∩ A3,A1∩A2∩ A3,A1∩ A2∩A3, A1∩A2∩A3is empty.More generally,we call a collectionΣ⊆Σ(X)of partial X-splits weakly compatible if every three partial splits inΣare weakly compatible.To give an example,the partial splits S1=123|4567,S2=124|3567,and S3= 235|146are weakly compatible whereas the partial splits S3,S4=24|135, and S5=21|346are not.Thus,{S1,...,S5}is not weakly compatible.Note that,like in the case of(full)splits,it is easy to see that any collection of pairwise compatible partial splits is also weakly compatible. Clearly any three partial splits S i=A i| A i∈Σ(X),i=1,2,3,for which precisely one of the four intersections in(4)is empty also satisfies Condition (2).ThusθY may be applied to S1,S2,S3.However,as the example of the set{127|3456,1234|567,235|146}shows,application ofθY to a weakly compatible collection of partial splits does not,in general,yield a weakly compatible collection of partial splits.Also it should be noted thatθM applied to a weakly compatible collection of partial splits does not always yield a weakly compatible collection of partial splits.However,the next result whose proof is straight forward holds.Lemma4.1SupposeΣ,Σ′⊆Σ(X).IfΣ′is weakly compatible andΣ Σ′, thenΣmust also be weakly compatible.4.2Circular collections of partial splitsWe now turn our attention to the study of a special class of weakly compati-ble collections of partial splits called circular collections of partial splits.Tobe able to state their definition,we require some more terminology whichwe introduce next.A cycle C is a connected graph with|V(C)|≥3and every vertex hasdegree2.We call C an X-cycle if the vertex set of C is X.For x i∈X (1≤i≤n:=|X|)and C an X-cycle,we call x1,x2,...,x n,x n+1=x1avertex ordering(of C)if the edge set of C coincides with the set of all2-sets{x i,x i+1}of X,i=1,...,n.For a graph G=(V,E)and some subset E′of E,we denote by G−E′thegraph obtained from G by deleting the edges in E′.We say that a partial X-split A| A is displayed by an X-cycle C if there exist two distinct edges e1and e2in C such that the vertex set of one of the two components of C−{e1,e2}contains A and the other one contains A.More generally,we say that a setΣ⊆Σ(X)of partial splits is displayed by an X-cycle C if every partial split inΣis displayed by C.Finally,we say that a collectionΣ⊆Σ(X) is circular if there exists some X-cycle C such that every partial split inΣis displayed by C.Note that every split collection inΣ(X)displayed by a circular phylogenetic network is circular.As is well-known,every circular split system is in particular weakly com-patible.The next result shows that an analogous result holds for collectionsof partial splits.Lemma4.2SupposeΣ⊆Σ(X).IfΣis circular thenΣis also weakly compatible.Proof:Suppose C is an X-cycle that displaysΣbut there exist three partialsplits S1,S2,S3∈Σsuch that with A i∈S i,i=1,2,3,playing the role of their namesakes in(4)none of the four intersections in(4)is empty.Then S1and S2are incompatible and,since S1and S2are displayed by C,there must exist edges e1,e′1,e2,e′2∈E(C)such that,for all i,j∈{1,2}distinct, the vertex set of one component of C−{e i,e′i}contains A i∪e j and the other contains A i∪e′j.Since S3is displayed by C and neither A1∩A2∩A3nor A1∩ A2∩A3,nor A1∩A2∩ A3is empty,it follows that A1∩ A2∩ A3=∅, which is impossible.Lemma4.3SupposeΣ,Σ′⊆Σ(X).IfΣ′is displayed by an X-cycle C and Σ Σ′,thenΣis also displayed by C.4.3Circularity and the M-and Y-ruleAs was noted earlier,neither the Y-rule nor the M-rule preserve weak com-patibility in general.As the next result shows,the situation is different for the special case of circular collections of partial splits.Proposition4.4SupposeΣ,Σ′∈P(X)and C is an X-cycle.IfΣ′is obtained fromΣby a single application of eitherθY orθM thenΣis displayed by C if and only ifΣ′is displayed by C.Proof:SupposeΣ,Σ′∈P(X)and C is an X-cycle.We start the proof with noting that,regardless of whetherΣ′is obtained from a single application of eitherθY orθM toΣ,Σis displayed by C wheneverΣ′is displayed by C in view of Lemma4.3.Conversely,suppose thatΣis displayed by C.Assumefirst thatΣ′is obtained fromΣby a single application ofθY.Let{S1,S2,S3}⊆Σbe the set to whichθY is applied.With A i∈S i,i=1,2,3,playing the role of their namesakes in the statement of(2),we may assume without loss of generality that none of the three intersections D1=A1∩A2∩A3,D2= A1∩ A2∩A3, and D3= A1∩A2∩ A3is empty but that A1∩ A2∩ A3=∅.It suffices to show that the partial split S=A3∪(A1∩ A2)| A3is displayed by C. Clearly,if A1∩ A2=∅then S=S3and,therefore,S is displayed by C.So assume A1∩ A2=∅.Then since by assumption D i=∅,i=1,2,3, and S1and S2are displayed by C,there must exist four distinct edges e1,e′1,e2,e′2∈E(C)such that,for all i,j∈{1,2}distinct,one component of C−{e i,e′i}contains A i in its vertex set and e j⊆A i and the other contains A i in its vertex set and e′j⊆ A i.Without loss of generality,we may assume that X={x1,...,x n},n≥3,that x1,x2,...,x n is a vertex ordering of C, and that e1={x n,x1}.Furthermore,we may also assume without loss of generality that the component of C−{e1,e′1}that contains x1in its vertex set also contains A1.Since D1=∅=D2,and S3is displayed by C there must exist distinct paths P and P′in C such that either A3⊆V(P)or A3⊆V(P′)(see Figure4).If A3⊆V(P)then∅= A1∩A2∩ A3=D3which is impossible.Thus A3⊆V(P′)must hold.Suppose y,z∈V(C)are such that when starting at x1and traversing C clockwise y is contained in13A 3and the next vertex y ′on C with y ′∈A 3∪ A 3is contained in A 3whereasz ∈ A 3and the next vertex z ′on C with z ′∈A 3∪ A 3is contained in A 3.1∩A 2∩ A 22e ′e A 1∩ A 1∩Figure 4:A schematic representation of the two alternative locations for A 3(cf proof of Proposition 4.4).The closed curve is the X -cycle C ,the four curves with the short dashes represent the four non-empty intersections A 1∩A 2,A 1∩ A 2, A 1∩ A 2and A 1∩A 2(note that each of them can consist of more than one part),the rectangles mark the intersections D 1and D 2,and the dotted and dashed curves represent the two paths P and P ′on C on which A 3can lie.Let P ′′denote the path from z ′to y (taken clockwise).Then e 2ande ′1are edges on P′′and so A 1∩ A 2⊆V (P ′′).The choice of y and z ′implies V (P ′′)∩ A 3=∅and A 3∪(A 1∩ A 2)⊆V (P ′′).Hence,the splitV (P ′′)|X −V (P ′′)which is displayed by C extends the partial split S .Thus C displays S .This concludes the proof in case the applied closure rule applied is θY .To conclude the proof of the proposition suppose Σ′is obtained from Σby a single application of θM .Let {S 1,S 2}⊆Σbe the set to which θM is applied.With A i ∈S i ,i =1,2,we may assume without loss of generalitythat A 1∩A 2=∅and A 1∩ A 2=∅.If θM applies trivially to Σthen Σ=Σ′and so Σ′must be displayed by C .If θM does not apply trivially to Σit suffices to show that C displays (A 1∩A 2)|( A 1∪ A 2).Since S 1and S 2are displayed by C there must exist edges e i ,e ′i ∈E (C )such that the vertex set of one of the two components P i ,P ′i of C −{e i ,e ′i }contains A i and the other contains A i ,i =1,2.Put k :=|{e 1,e ′1}∩{e 2,e ′2}|and note that 0≤k ≤2.Without loss of generality,we may assumeA i ⊆V (P i )and A i ⊆V (P ′i ),i =1,2.Then,∅=A 1∩A 2⊆V (P 1)∩V (P 2).Since V (P 1)∩V (P 2)is the vertex set of one of the 4−k components of C14with the edges e i,e′i,i=1,2removed,it follows that there must exist two distinct edges e3,e4among the edges e1,e′1,e2,e′2so that the vertex set of one of the two components of C−{e3,e4}is V(P1)∩V(P2).SinceX−(V(P1)∩V(P2))=(X−V(P1))∪(X−V(P2))=V(P′1)∪V(P′2) is the vertex set of the other component of C−{e3,e4}and A i⊆V(P′i), i=1,2,it follows that C displays(A1∩A2)|( A1∪ A2).This concludes the proof in caseΣ′is obtained fromΣby a single application ofθM and thus the proof of the proposition.and call n the length ofσ.In addition,we call the last element ofσa split closure ofΣ.Note that in caseΣn=ω,θapplies only trivially toΣn.The following combinations of(P)andθare of interest to us:(a)(P)is the property thatΣis weakly compatible andθis the Y-rule.(b)(P)is unspecified andθis the M-rule.(c)(P)is the property thatΣis weakly compatible andθis the M/Y-combination closure ruleθM/Y which appliesθM orθY toΣ.To elucidate the notion of a split closure sequence and a split closure associated to a set in P(X)we next present an example for the assignments of(P)andθspecified in(a).Consider the set X={1,2,3,4,5}together with the collectionΣcomprising of the partial X-splits S1=12|34,S2= 23|14,S3=15|24,and S4=45|13.Clearly,Σis displayed by an X-cycle C with vertex ordering1,2,3,4,5.ThusΣis circular and so,by Lemma4.2,Σis weakly compatible.NowθY applied to{S1,S2,S3}generates the split S′3=15|234,θY applied to{S1,S2,S4}generates the split S′4=45|123and θY applied to{S2,S′3,S′4}generates the split S′2=145|23.Since every subset ofΣ′={S1,S′2,S′3,S′4}of size three contains two pairwise compatible full splits,θY can only be applied trivially toΣ′.Hence,the sequence S0=Σ,Σ1={S1,S2,S′3,S4},Σ2={S1,S2,S′3,S′4},Σ′is a split closure sequence forΣof length3andΣ′is a split closure forΣ.Regarding(c),it should be noted that even if for someΣ∈P(X)two distinct split closure sequences have the same length and terminate in the same elementΣ′=ωone of them might utilise fewer applications ofθY (and thus more applications ofθM!)than the other.For the previous example,one way to construct two such sequences is to exploit the following relationship between the Y-rule and the M-rule for{S2,S′3,S′4}. Proposition5.1SupposeΣ={S i=A i| A i:i=1,2,3}∈P(X)is such that A1⊆A2and A2− A1⊆ A3⊆ A1∪ A2.If the Y-rule applies toΣthen θY(Σ)−={ A1∪ A2|A1,S2,S3}={S3}∪θM(S1,S2)−.Proof:Assume thatΣand S i and A i,i=1,2,3,are such that the assump-tions of the proposition are satisfied.Then A1∩ A2=∅.Combined with the assumption thatθY applies toΣ,it follows that either(2)is satisfied withA i,i=1,2,3playing the roles of their namesakes in the statement of(2)or(2)is satisfied with A3playing the role of A3and A i playing the role of A i,16。