Phylogenetic mixtures and linear invariants for equal input models
The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely...
Saved in:
| Published in: | Journal of mathematical biology Vol. 74; no. 5; pp. 1107 - 1138 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article Publication |
| Language: | English |
| Published: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.04.2017
Springer Nature B.V |
| Subjects: | |
| ISSN: | 0303-6812, 1432-1416, 1432-1416 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the ‘equal input model’. This model generalizes the ‘Felsenstein 1981’ model (and thereby the Jukes–Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a ‘random cluster’ process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees—the so called ‘model invariants’), on any number
n
of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of
n
=
4
leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167–191,
1987
). |
|---|---|
| AbstractList | The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987).The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987). (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees--the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of ... leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987 ). The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of n = 4 leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987). The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the ‘equal input model’. This model generalizes the ‘Felsenstein 1981’ model (and thereby the Jukes–Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a ‘random cluster’ process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees—the so called ‘model invariants’), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of n = 4 leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167–191, 1987 ). The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987). The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the ‘equal input model’. This model generalizes the ‘Felsenstein 1981’ model (and thereby the Jukes–Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a ‘random cluster’ process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees—the so called ‘model invariants’), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of n=4 leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167–191, 1987). Peer Reviewed |
| Author | Steel, Mike Casanellas, Marta |
| Author_xml | – sequence: 1 givenname: Marta surname: Casanellas fullname: Casanellas, Marta organization: Department of Mathematics, Universitat Politècnica de Catalunya – sequence: 2 givenname: Mike surname: Steel fullname: Steel, Mike email: mike.steel@canterbury.ac.nz organization: Biomathematics Research Centre, University of Canterbury |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/27604275$$D View this record in MEDLINE/PubMed |
| BookMark | eNqNkU1r3DAQhkVJaTZpf0AvxdBLL25HkvXhYxv6EQgkh_QsZHmcKtjSRpJD8-9js7s0FFpyEELieYaZeU_IUYgBCXlL4SMFUJ8yANOiBiprCkLU-gXZ0IazmjZUHpENcOC11JQdk5OcbwGoEi19RY6ZktAwJTbky9WvhzHeYMDiXTX532VOmCsb-mr0AW2qfLi3ydtQcjXEVOHdbMflczuXaoo9jvk1eTnYMeOb_X1Kfn77en32o764_H5-9vmidk0LpUYHTGiJGnvshsEt3XCJwuqmQ0TZqNZxybsBnIJBKyYdMgmS9j0VHbacnxK6q-vy7ExCh8nZYqL1fx7rYaCYYS3jYnU-7Jxtincz5mImnx2Oow0Y52yobhXXrZDqGahYWNCcLej7v9DbOKewDL9QWgotmFipd3tq7ibszTb5yaYHc1j-Aqj9QCnmnHAwzhdbfAwlWT8aCmaN2exiNkvMZo3Z6CerOJiH4v9z2M7JCxtuMD1p-p_SIzEkt7w |
| CitedBy_id | crossref_primary_10_1093_sysbio_syz054 crossref_primary_10_1089_cmb_2020_0315 crossref_primary_10_1137_23M1605302 |
| Cites_doi | 10.1089/cmb.1995.2.39 10.1016/j.mbs.2003.10.004 10.1089/cmb.1994.1.153 10.1093/sysbio/syv086 10.1007/s11538-007-9293-y 10.1016/0025-5564(91)90083-U 10.1093/molbev/msr259 10.1186/1748-7188-7-33 10.1089/cmb.2005.12.204 10.1006/jtbi.1995.0067 10.1016/S0025-5564(96)00075-2 10.1093/sysbio/syq069 10.1016/j.matpur.2010.11.002 10.1089/cmb.2006.0126 10.1093/sysbio/sys064 10.1093/oso/9780198509424.001.0001 |
| ContentType | Journal Article Publication |
| Contributor | Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions Universitat Politècnica de Catalunya. Departament de Matemàtiques |
| Contributor_xml | – sequence: 1 fullname: Universitat Politècnica de Catalunya. Departament de Matemàtiques – sequence: 2 fullname: Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions |
| Copyright | Springer-Verlag Berlin Heidelberg 2016 Journal of Mathematical Biology is a copyright of Springer, 2017. info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/3.0/es |
| Copyright_xml | – notice: Springer-Verlag Berlin Heidelberg 2016 – notice: Journal of Mathematical Biology is a copyright of Springer, 2017. – notice: info:eu-repo/semantics/openAccess <a href="http://creativecommons.org/licenses/by-nc-nd/3.0/es/">http://creativecommons.org/licenses/by-nc-nd/3.0/es/</a> |
| DBID | AAYXX CITATION CGR CUY CVF ECM EIF NPM 3V. 7TK 7TM 7U9 7X7 7XB 88A 88E 8AO 8FD 8FE 8FG 8FH 8FI 8FJ 8FK ABJCF ABUWG AFKRA ARAPS AZQEC BBNVY BENPR BGLVJ BHPHI CCPQU DWQXO FR3 FYUFA GHDGH GNUQQ H94 HCIFZ JQ2 K7- K9. L6V LK8 M0S M1P M7N M7P M7S M7Z P5Z P62 P64 PHGZM PHGZT PJZUB PKEHL PPXIY PQEST PQGLB PQQKQ PQUKI PRINS PTHSS 7X8 RC3 XX2 |
| DOI | 10.1007/s00285-016-1055-8 |
| DatabaseName | CrossRef Medline MEDLINE MEDLINE (Ovid) MEDLINE MEDLINE PubMed ProQuest Central (Corporate) Neurosciences Abstracts Nucleic Acids Abstracts Virology and AIDS Abstracts Health & Medical Collection ProQuest Central (purchase pre-March 2016) Biology Database (Alumni Edition) Medical Database (Alumni Edition) ProQuest Pharma Collection Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Natural Science Collection Hospital Premium Collection Hospital Premium Collection (Alumni Edition) ProQuest Central (Alumni) (purchase pre-March 2016) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials Biological Science Collection ProQuest Central ProQuest Technology Collection Natural Science Collection ProQuest One ProQuest Central Korea Engineering Research Database Health Research Premium Collection Health Research Premium Collection (Alumni) ProQuest Central Student AIDS and Cancer Research Abstracts SciTech Collection (ProQuest) ProQuest Computer Science Collection Computer Science Database ProQuest Health & Medical Complete (Alumni) ProQuest Engineering Collection ProQuest Biological Science Collection Health & Medical Collection (Alumni) Medical Database Algology Mycology and Protozoology Abstracts (Microbiology C) Biological Science Database Engineering Database Biochemistry Abstracts 1 Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Biotechnology and BioEngineering Abstracts ProQuest Central Premium ProQuest One Academic (New) ProQuest Health & Medical Research Collection ProQuest One Academic Middle East (New) ProQuest One Health & Nursing ProQuest One Academic Eastern Edition (DO NOT USE) One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection MEDLINE - Academic Genetics Abstracts Recercat |
| DatabaseTitle | CrossRef MEDLINE Medline Complete MEDLINE with Full Text PubMed MEDLINE (Ovid) Computer Science Database ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Nucleic Acids Abstracts SciTech Premium Collection ProQuest Central China ProQuest One Applied & Life Sciences Health Research Premium Collection Natural Science Collection Health & Medical Research Collection Biological Science Collection ProQuest Central (New) ProQuest Medical Library (Alumni) Engineering Collection Advanced Technologies & Aerospace Collection Engineering Database Virology and AIDS Abstracts ProQuest Biological Science Collection ProQuest One Academic Eastern Edition ProQuest Hospital Collection ProQuest Technology Collection Health Research Premium Collection (Alumni) Biological Science Database Neurosciences Abstracts ProQuest Hospital Collection (Alumni) Biotechnology and BioEngineering Abstracts ProQuest Health & Medical Complete ProQuest One Academic UKI Edition Engineering Research Database ProQuest One Academic ProQuest One Academic (New) Technology Collection Technology Research Database ProQuest One Academic Middle East (New) ProQuest Health & Medical Complete (Alumni) ProQuest Central (Alumni Edition) ProQuest One Community College ProQuest One Health & Nursing ProQuest Natural Science Collection ProQuest Pharma Collection ProQuest Biology Journals (Alumni Edition) ProQuest Central ProQuest Health & Medical Research Collection ProQuest Engineering Collection Health and Medicine Complete (Alumni Edition) ProQuest Central Korea Algology Mycology and Protozoology Abstracts (Microbiology C) AIDS and Cancer Research Abstracts ProQuest SciTech Collection Advanced Technologies & Aerospace Database ProQuest Medical Library Materials Science & Engineering Collection Biochemistry Abstracts 1 ProQuest Central (Alumni) MEDLINE - Academic Genetics Abstracts |
| DatabaseTitleList | MEDLINE - Academic Computer Science Database Genetics Abstracts MEDLINE |
| Database_xml | – sequence: 1 dbid: NPM name: PubMed url: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database – sequence: 2 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Biology Mathematics |
| EISSN | 1432-1416 |
| EndPage | 1138 |
| ExternalDocumentID | oai_recercat_cat_2072_292353 4321630437 27604275 10_1007_s00285_016_1055_8 |
| Genre | Research Support, Non-U.S. Gov't Journal Article |
| GroupedDBID | --- -52 -5D -5G -BR -EM -Y2 -~C -~X .86 06D 0R~ 0VY 186 199 1N0 1SB 2.D 203 28- 29L 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 3-Y 30V 3SX 3V. 4.4 406 408 409 40D 40E 53G 5GY 5QI 5VS 67Z 6NX 78A 7X7 88A 88E 8AO 8FE 8FG 8FH 8FI 8FJ 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAGAY AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDPE ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACPRK ACZOJ ADBBV ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFFNX AFGCZ AFKRA AFLOW AFQWF AFRAH AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHMBA AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALIPV ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BBNVY BBWZM BDATZ BENPR BGLVJ BGNMA BHPHI BPHCQ BSONS BVXVI CAG CCPQU COF CS3 CSCUP D0L DDRTE DL5 DNIVK DPUIP DU5 EBD EBLON EBS EIOEI EJD EMB EMOBN EPAXT ESBYG F5P FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC FYUFA GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HCIFZ HF~ HG5 HG6 HMCUK HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K6V K7- KDC KOV KOW L6V LAS LK8 LLZTM M0L M1P M4Y M7P M7S MA- MQGED MVM N2Q NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P2P P62 P9R PF0 PQQKQ PROAC PSQYO PT4 PT5 PTHSS Q2X QOK QOS R4E R89 R9I RHV RIG RNI RNS ROL RPX RRX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SV3 SZN T13 T16 TN5 TSG TSK TSV TUC U2A U9L UG4 UKHRP UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WH7 WIP WJK WK6 WK8 YLTOR YQT Z45 Z7U ZMTXR ZWQNP ZXP ~EX ~KM AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT PJZUB PPXIY PQGLB CGR CUY CVF ECM EIF NPM 7TK 7TM 7U9 7XB 8FD 8FK AZQEC DWQXO FR3 GNUQQ H94 JQ2 K9. M7N M7Z P64 PKEHL PQEST PQUKI PRINS 7X8 PUEGO RC3 XX2 |
| ID | FETCH-LOGICAL-c490t-ec02586e8edebffc00136e5a84beee6479c363bf0c70f8726ce26061dd15be933 |
| IEDL.DBID | M7P |
| ISICitedReferencesCount | 3 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000399219000004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0303-6812 1432-1416 |
| IngestDate | Fri Nov 07 13:40:14 EST 2025 Sun Nov 09 10:26:50 EST 2025 Thu Oct 02 06:41:45 EDT 2025 Tue Nov 04 22:10:14 EST 2025 Wed Feb 19 02:43:30 EST 2025 Sat Nov 29 03:20:17 EST 2025 Tue Nov 18 20:12:33 EST 2025 Fri Feb 21 02:36:08 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Keywords | Markov processes 60J28 Linear invariants 92D15 Phylogenetic tree 05C05 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c490t-ec02586e8edebffc00136e5a84beee6479c363bf0c70f8726ce26061dd15be933 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 |
| OpenAccessLink | https://recercat.cat/handle/2072/292353 |
| PMID | 27604275 |
| PQID | 1886585252 |
| PQPubID | 54026 |
| PageCount | 32 |
| ParticipantIDs | csuc_recercat_oai_recercat_cat_2072_292353 proquest_miscellaneous_1897389567 proquest_miscellaneous_1859730832 proquest_journals_1886585252 pubmed_primary_27604275 crossref_citationtrail_10_1007_s00285_016_1055_8 crossref_primary_10_1007_s00285_016_1055_8 springer_journals_10_1007_s00285_016_1055_8 |
| PublicationCentury | 2000 |
| PublicationDate | 2017-04-01 |
| PublicationDateYYYYMMDD | 2017-04-01 |
| PublicationDate_xml | – month: 04 year: 2017 text: 2017-04-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Berlin/Heidelberg |
| PublicationPlace_xml | – name: Berlin/Heidelberg – name: Germany – name: Heidelberg |
| PublicationTitle | Journal of mathematical biology |
| PublicationTitleAbbrev | J. Math. Biol |
| PublicationTitleAlternate | J Math Biol |
| PublicationYear | 2017 |
| Publisher | Springer Berlin Heidelberg Springer Nature B.V |
| Publisher_xml | – name: Springer Berlin Heidelberg – name: Springer Nature B.V |
| References | Fernández-Sánchez, Casanellas (CR6) 2016; 65 Allman, Rhodes, Sullivant (CR1) 2012; 61 Sturmfels, Sullivant (CR19) 2005; 12 Steel, Fu (CR17) 1995; 2 Lake (CR11) 1987; 4 Semple, Steel (CR14) 2003 Fu, Li (CR8) 1991; 105 Štefakovič, Vigoda (CR18) 2007; 14 Chang (CR4) 1996; 137 Casanellas, Fernández-Sánchez, Kedzierska (CR2) 2012; 7 Matsen, Mossel, Steel (CR12) 2008; 70 Casanellas, Fernández-Sánchez (CR3) 2011; 96 Steel, Székely, Hendy (CR15) 1994; 1 Mossel, Steel (CR13) 2004; 187 Kemeny, Snell (CR10) 1976 Fu (CR7) 1995; 173 Kedzierska, Drton, Guigó, Casanellas (CR9) 2012; 29 Felsenstein (CR5) 2004 Steel (CR16) 2011; 60 J Lake (1055_CR11) 1987; 4 FA Matsen (1055_CR12) 2008; 70 M Casanellas (1055_CR3) 2011; 96 JT Chang (1055_CR4) 1996; 137 YX Fu (1055_CR7) 1995; 173 B Sturmfels (1055_CR19) 2005; 12 C Semple (1055_CR14) 2003 M Casanellas (1055_CR2) 2012; 7 J Felsenstein (1055_CR5) 2004 M Steel (1055_CR16) 2011; 60 ES Allman (1055_CR1) 2012; 61 A Kedzierska (1055_CR9) 2012; 29 E Mossel (1055_CR13) 2004; 187 D Štefakovič (1055_CR18) 2007; 14 YX Fu (1055_CR8) 1991; 105 JG Kemeny (1055_CR10) 1976 MA Steel (1055_CR17) 1995; 2 MA Steel (1055_CR15) 1994; 1 J Fernández-Sánchez (1055_CR6) 2016; 65 1806100 - Math Biosci. 1991 Jul;105(2):229-38 17456014 - J Comput Biol. 2007 Mar;14(2):156-89 21084501 - Syst Biol. 2011 Jan;60(1):96-109 26559009 - Syst Biol. 2016 Mar;65(2):280-91 7497119 - J Comput Biol. 1995 Spring;2(1):39-47 7783448 - J Theor Biol. 1995 Apr 21;173(4):339-52 23190710 - Algorithms Mol Biol. 2012 Nov 28;7(1):33 14739084 - Math Biosci. 2004 Feb;187(2):189-203 18175189 - Bull Math Biol. 2008 May;70(4):1115-39 8854662 - Math Biosci. 1996 Oct 1;137(1):51-73 3447007 - Mol Biol Evol. 1987 Mar;4(2):167-91 8790461 - J Comput Biol. 1994 Summer;1(2):153-63 15767777 - J Comput Biol. 2005 Mar;12(2):204-28 22798332 - Syst Biol. 2012 Dec 1;61(6):1049-59 22009060 - Mol Biol Evol. 2012 Mar;29(3):929-37 |
| References_xml | – volume: 2 start-page: 39 year: 1995 end-page: 47 ident: CR17 article-title: Classifying and counting linear phylogenetic invariants for the Jukes–Cantor model publication-title: J Comput Biol doi: 10.1089/cmb.1995.2.39 – volume: 4 start-page: 167 year: 1987 end-page: 191 ident: CR11 article-title: A rate-independent technique for analysis of nucleic acid sequences: evolutionary parsimony publication-title: Mol Biol Evol – volume: 187 start-page: 189 year: 2004 end-page: 203 ident: CR13 article-title: A phase transition for a random cluster model on phylogenetic trees publication-title: Math Biosci doi: 10.1016/j.mbs.2003.10.004 – volume: 1 start-page: 153 year: 1994 end-page: 163 ident: CR15 article-title: Reconstructing trees when sequence sites evolve at variable rates publication-title: J Comput Biol doi: 10.1089/cmb.1994.1.153 – volume: 65 start-page: 280 year: 2016 end-page: 291 ident: CR6 article-title: Invariant versus classical quartet inference when evolution is heterogeneous across sites and lineages publication-title: Syst Biol doi: 10.1093/sysbio/syv086 – volume: 70 start-page: 1115 year: 2008 end-page: 1139 ident: CR12 article-title: Mixed-up trees: the structure of phylogenetic mixtures publication-title: Bull Math Biol doi: 10.1007/s11538-007-9293-y – year: 2004 ident: CR5 publication-title: Inferring Phylogenies – volume: 105 start-page: 229 year: 1991 end-page: 238 ident: CR8 article-title: Necessary and sufficient conditions for the existence of certain quadratic invariants under a phylogenetic tree publication-title: Math Biosci doi: 10.1016/0025-5564(91)90083-U – volume: 29 start-page: 929 year: 2012 end-page: 937 ident: CR9 article-title: SPIn: model selection for phylogenetic mixtures via linear invariants publication-title: Mol Biol Evol doi: 10.1093/molbev/msr259 – volume: 7 start-page: 33 year: 2012 ident: CR2 article-title: The space of phylogenetic mixtures for equivariant models publication-title: Algorithms Mol Biol doi: 10.1186/1748-7188-7-33 – volume: 12 start-page: 204 year: 2005 end-page: 228 ident: CR19 article-title: Toric ideals of phylogenetic invariants publication-title: J Comput Biol doi: 10.1089/cmb.2005.12.204 – volume: 173 start-page: 339 year: 1995 end-page: 352 ident: CR7 article-title: Linear invariants under Jukes’ and Cantor’s one-parameter model publication-title: J Theor Biol doi: 10.1006/jtbi.1995.0067 – volume: 137 start-page: 51 year: 1996 end-page: 73 ident: CR4 article-title: Full reconstruction of Markov models on evolutionary trees: identifiability and consistency publication-title: Math Biosci doi: 10.1016/S0025-5564(96)00075-2 – volume: 60 start-page: 96 year: 2011 end-page: 109 ident: CR16 article-title: Can we avoid ‘SIN’ in the house of ‘no common mechanism’? publication-title: Syst Biol doi: 10.1093/sysbio/syq069 – year: 2003 ident: CR14 publication-title: Phylogenetics – volume: 96 start-page: 207 year: 2011 end-page: 229 ident: CR3 article-title: Relevant phylogenetic invariants of evolutionary models publication-title: J Math Pures Appl doi: 10.1016/j.matpur.2010.11.002 – year: 1976 ident: CR10 publication-title: Finite Markov chains – volume: 14 start-page: 156 year: 2007 end-page: 189 ident: CR18 article-title: Phylogeny of mixture models: robustness of maximum likelihood and non-identifiable distributions publication-title: J Comput Biol doi: 10.1089/cmb.2006.0126 – volume: 61 start-page: 1049 year: 2012 end-page: 1059 ident: CR1 article-title: When do phylogenetic mixture models mimic other phylogenetic models? publication-title: Syst Biol doi: 10.1093/sysbio/sys064 – volume: 1 start-page: 153 year: 1994 ident: 1055_CR15 publication-title: J Comput Biol doi: 10.1089/cmb.1994.1.153 – volume: 60 start-page: 96 year: 2011 ident: 1055_CR16 publication-title: Syst Biol doi: 10.1093/sysbio/syq069 – volume: 173 start-page: 339 year: 1995 ident: 1055_CR7 publication-title: J Theor Biol doi: 10.1006/jtbi.1995.0067 – volume-title: Phylogenetics year: 2003 ident: 1055_CR14 doi: 10.1093/oso/9780198509424.001.0001 – volume: 137 start-page: 51 year: 1996 ident: 1055_CR4 publication-title: Math Biosci doi: 10.1016/S0025-5564(96)00075-2 – volume: 105 start-page: 229 year: 1991 ident: 1055_CR8 publication-title: Math Biosci doi: 10.1016/0025-5564(91)90083-U – volume: 2 start-page: 39 year: 1995 ident: 1055_CR17 publication-title: J Comput Biol doi: 10.1089/cmb.1995.2.39 – volume-title: Finite Markov chains year: 1976 ident: 1055_CR10 – volume: 14 start-page: 156 year: 2007 ident: 1055_CR18 publication-title: J Comput Biol doi: 10.1089/cmb.2006.0126 – volume: 65 start-page: 280 year: 2016 ident: 1055_CR6 publication-title: Syst Biol doi: 10.1093/sysbio/syv086 – volume: 12 start-page: 204 year: 2005 ident: 1055_CR19 publication-title: J Comput Biol doi: 10.1089/cmb.2005.12.204 – volume: 4 start-page: 167 year: 1987 ident: 1055_CR11 publication-title: Mol Biol Evol – volume-title: Inferring Phylogenies year: 2004 ident: 1055_CR5 – volume: 61 start-page: 1049 year: 2012 ident: 1055_CR1 publication-title: Syst Biol doi: 10.1093/sysbio/sys064 – volume: 7 start-page: 33 year: 2012 ident: 1055_CR2 publication-title: Algorithms Mol Biol doi: 10.1186/1748-7188-7-33 – volume: 187 start-page: 189 year: 2004 ident: 1055_CR13 publication-title: Math Biosci doi: 10.1016/j.mbs.2003.10.004 – volume: 96 start-page: 207 year: 2011 ident: 1055_CR3 publication-title: J Math Pures Appl doi: 10.1016/j.matpur.2010.11.002 – volume: 29 start-page: 929 year: 2012 ident: 1055_CR9 publication-title: Mol Biol Evol doi: 10.1093/molbev/msr259 – volume: 70 start-page: 1115 year: 2008 ident: 1055_CR12 publication-title: Bull Math Biol doi: 10.1007/s11538-007-9293-y – reference: 3447007 - Mol Biol Evol. 1987 Mar;4(2):167-91 – reference: 8854662 - Math Biosci. 1996 Oct 1;137(1):51-73 – reference: 1806100 - Math Biosci. 1991 Jul;105(2):229-38 – reference: 18175189 - Bull Math Biol. 2008 May;70(4):1115-39 – reference: 23190710 - Algorithms Mol Biol. 2012 Nov 28;7(1):33 – reference: 7497119 - J Comput Biol. 1995 Spring;2(1):39-47 – reference: 22798332 - Syst Biol. 2012 Dec 1;61(6):1049-59 – reference: 8790461 - J Comput Biol. 1994 Summer;1(2):153-63 – reference: 17456014 - J Comput Biol. 2007 Mar;14(2):156-89 – reference: 21084501 - Syst Biol. 2011 Jan;60(1):96-109 – reference: 7783448 - J Theor Biol. 1995 Apr 21;173(4):339-52 – reference: 22009060 - Mol Biol Evol. 2012 Mar;29(3):929-37 – reference: 14739084 - Math Biosci. 2004 Feb;187(2):189-203 – reference: 15767777 - J Comput Biol. 2005 Mar;12(2):204-28 – reference: 26559009 - Syst Biol. 2016 Mar;65(2):280-91 |
| SSID | ssj0017591 |
| Score | 2.1799247 |
| Snippet | The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such... (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) The reconstruction of phylogenetic trees from molecular sequence data relies on... |
| SourceID | csuc proquest pubmed crossref springer |
| SourceType | Open Access Repository Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 1107 |
| SubjectTerms | 05 Combinatorics 05C Graph theory 60 Probability theory and stochastic processes 60J Markov processes 92 Biology and other natural sciences 92D Genetics and population dynamics Applications of Mathematics Biomatemàtica Biomathematics Classificació AMS linear invariants Markov Chains Markov processes Markov, Processos de Matemàtiques i estadística Mathematical and Computational Biology Mathematics Mathematics and Statistics Models, Biological Molecular Sequence Data Phylogenetic tree Phylogeny Àrees temàtiques de la UPC |
| SummonAdditionalLinks | – databaseName: SpringerLINK Contemporary 1997-Present dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Lb9QwEB7BAlJ74FGghBZkJE6gSFk7ju1jQa24UFW81JuVOGN1JUirTbaCf89MXgJRKsFhD9lMIscee77RPD6Al4XBYMg0pDG6yGFGlVYqYKqjDHXpZIZZ7MkmzPGxPT11J2Mddztlu08hyf6knovd2D3gRLMiZVLH1N6EW2TtLPM1fPj4ZQ4dGD3Q5NHZnHJzrSmUedUrfjNGi9BuwlVA848gaW97ju7916jvw90RaoqDQTcewA1sduDOQD75Ywe2388dW9uH8ObkjFx30iYuahTfVt85stCKsqkFA9FyLVbNJfnVnDYjCOgK5HJM-vNi04meTqd9BJ-PDj-9fZeO_AppyF3WpRgI8NgCLdZYxRj6_m2oS5tXiFjkxgVVqCpmwWTRGsnkYeTvLOt6qSt0Sj2GRXPe4BMQyuZ1rpXD6CwdCdJV1ZIWOycAUFYEEhPIpon2YWw-zhwYX_3cNrmfKM8JZzxR3ibwan7kYui8cb0wrZ4nK4HrUHaeu2bPF_yTmZFeEpzVKoH9aY39uGNbv7SWwJiWWibwYr5Ne40DKGWD5xuWIfdLEWi9VoZELHmdJoHdQX_m4UtTMLWJTuD1pCy_DOBv3_b0n6T3YEsy8uiTi_Zh0a03-Axuh8tu1a6f91vlJ0_fC0E priority: 102 providerName: Springer Nature |
| Title | Phylogenetic mixtures and linear invariants for equal input models |
| URI | https://link.springer.com/article/10.1007/s00285-016-1055-8 https://www.ncbi.nlm.nih.gov/pubmed/27604275 https://www.proquest.com/docview/1886585252 https://www.proquest.com/docview/1859730832 https://www.proquest.com/docview/1897389567 https://recercat.cat/handle/2072/292353 |
| Volume | 74 |
| WOSCitedRecordID | wos000399219000004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1432-1416 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0017591 issn: 0303-6812 databaseCode: P5Z dateStart: 19971101 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Biological Science Database customDbUrl: eissn: 1432-1416 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0017591 issn: 0303-6812 databaseCode: M7P dateStart: 19971101 isFulltext: true titleUrlDefault: http://search.proquest.com/biologicalscijournals providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1432-1416 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0017591 issn: 0303-6812 databaseCode: K7- dateStart: 19971101 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1432-1416 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0017591 issn: 0303-6812 databaseCode: M7S dateStart: 19971101 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: Health & Medical Collection customDbUrl: eissn: 1432-1416 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0017591 issn: 0303-6812 databaseCode: 7X7 dateStart: 19971101 isFulltext: true titleUrlDefault: https://search.proquest.com/healthcomplete providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1432-1416 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0017591 issn: 0303-6812 databaseCode: BENPR dateStart: 19971101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1432-1416 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0017591 issn: 0303-6812 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3di9QwEB-8PQVf7vy23rlU8EkJdpOmSZ_EkzsEYSl3KosvpU0TbkG767Z7eP-9M-mHirovPjTQNoWkk2R-k5nMD-B5oqxRqBqYc6kjN6NgpTCWScdNVaQ8spHzZBNqPteLRZr1G25NH1Y5rIl-oa5WhvbIX820RmUpueSv198YsUaRd7Wn0NiDfcqSwH3oXjZ6EZTsGPNwmWaUZ2vwakY-iSjXFLaWMKKIZPo3vTQxzdb8DXP-4S_1aujs8H87cAcOegAavulGzF24Yet7cKujpLy-DyfZJZrwOKrocGP4dfmdPAxNWNRVSIC02ITL-grtawqfCRHwhpaOZeLD9bYNPa1O8wA-np1-ePuO9TwLzMRp1DJrEPjoxGpb2dI54_O4WVnouLTWJrFKjUhE6SKjIqcVJxIxtHtmVTWTpU2FeAiTelXbxxAKHVexFKl1qcalgadlOUOhxwgEihLBYgDR8Jdz0ychJy6ML_mYPtkLJqfAMxJMrgN4MX6y7jJw7K6MostRW9iNKdqcsmePN3TxSPGcI6yVIoDjQVJ5P3Ob_KeYAng2vsY5R46UorarLdVBM0wgeN1ZB6totD5VAI-6wTM2n6uEKE5kAC-H0fRLA_7Vtye7m3sEtzlBDh9VdAyTdrO1T-GmuWqXzWYKe2qhfKmnsH9yOs_O8e69YlM_ZXx5gWUmP2N5fvHpB5FVGLk |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9QwEB5VBQQX3o9AASPBBWQ16zzsHBDiVbXasuqhSL2ZxBmLlSC7bLKF_VP8RmaSTQABe-uBQ6Q8HMmJP8989tjzATxONTpNrkF6n3kOM0ayiBzKxCtX5pkKMfSt2ISeTMzJSXa0Bd_7vTC8rLK3ia2hLmeO58h3R8aQs0xUol7Mv0hWjeLoai-h0cFijKuvNGSrnx-8ofZ9otTe2-PX-3KtKiBdnIWNREdu3qRosMTCe9dmLcMkN3GBiGmsMxelUeFDp0NvtGLJLGL5o7IcJQVmPAFKJv9cHBnN_Wqs5RC10Emn0EduQXJerz6KGrZJS5XhZXKpZElKaX7zg9uuXrq_cdw_4rOt29u78r_9sKtweU2wxcuuR1yDLayuw4VOcnN1A14dfVzRGVl4ei4-T79xBKUWeVUKJtz5Qkyr05x6ZdXUggi9QN52Sjfny0a0skH1TXh_Jh9wC7arWYV3QEQmLuMkytBnhkyfyopiRKCOiejkBZHhAMK-Va1bJ1lnrY9PdkgP3QLB8sI6BoI1ATwdXpl3GUY2FyaoWPKGuHB5Yzk7-HDBhwq1sopoexIFsNMjw64tU21_wiKAR8NjsikcKMornC25DA0zIyLnG8tQEUOjax3A7Q6sQ_WVTlnCJQngWY_eXyrwr2-7u7m6D-Hi_vG7Q3t4MBnfg0uK6VW7gmoHtpvFEu_DeXfaTOvFg7ZTCvhw1qD-Acsub44 |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lj9MwEB6tykNceD8CCxgJLiBrUyeOnQNCwFKxWlT1ANKKi0kcW1TaTUuTLvSv8euYyQsQ0NseOETKw5Gc5PPMZ89kPoDHiXJWoWvg3qeewowRzyPruPTCFlkqQhf6RmxCTaf66Cid7cD3_l8YSqvsbWJjqIuFpTXyvbHW6CylkGLPd2kRs_3Ji-UXTgpSFGnt5TRaiBy6zVecvlXPD_bxWz8RYvLm_eu3vFMY4DZOw5o7iy5fJ067wuXe26aCmZOZjnPnXBKr1EZJlPvQqtBrJUg-Cxn_uCjGMncpLYai-T-ncI5J6YQz-XGIYCjZqvWhi-BU46uPqIZNAVOhKWUu4SRPyfVvPnFkq7X9G9_9I1bbuMDJlf_55V2Fyx3xZi_bkXINdlx5HS60UpybG_Bq9nmDe2j58To7mX-jyErFsrJgRMSzFZuXpxmO1rKuGBJ95uh3VDy5XNeskROqbsKHM3mAWzAqF6W7AyzScRHLKHU-1WgSRZrnYwR7jAQoy5EkBxD2X9jYrvg6aYAcm6FsdAMKQwl3BAqjA3g63LJsK49sb4ywMegl3cpmtaGq4cMBbSJUwgik8zIKYLdHieksVmV-QiSAR8NltDUUQMpKt1hTG5x-Rkjat7bBJhpn3SqA2y1wh-4LlZC0iwzgWY_kXzrwr2e7u727D-EiYtm8O5ge3oNLglhXk1i1C6N6tXb34bw9refV6kEzPhl8OmtM_wAIZHiy |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Phylogenetic+mixtures+and+linear+invariants+for+equal+input+models&rft.jtitle=Journal+of+mathematical+biology&rft.au=Casanellas%2C+Marta&rft.au=Steel%2C+Mike&rft.date=2017-04-01&rft.issn=0303-6812&rft.eissn=1432-1416&rft.volume=74&rft.issue=5&rft.spage=1107&rft.epage=1138&rft_id=info:doi/10.1007%2Fs00285-016-1055-8&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s00285_016_1055_8 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0303-6812&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0303-6812&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0303-6812&client=summon |