A recursive algorithm for the calculation of identity coefficients
SUMMARY
Based on a theory of generalized kinship coefficients a recursive algorithm for the calculation of the coefficient of kinship and all nine condensed identity coefficients for any two individuals with given pedigree is described. Furthermore, the algorithm also permits the calculation of all fifteen detailed coefficients for two individuals neither of whom is an ancestor of the other one. Results for standard as well as highly inbred relationships are given.
Citing Literature
Number of times cited according to CrossRef: 62
- Magnus Dehli Vigeland, Relatedness coefficients in pedigrees with inbred founders, Journal of Mathematical Biology, 10.1007/s00285-020-01505-x, (2020).
- Brent Kirkpatrick, Shufei Ge, Liangliang Wang, Efficient computation of the kinship coefficients, Bioinformatics, 10.1093/bioinformatics/bty725, 35, 6, (1002-1008), (2018).
- Chaozhi Zheng, Martin P. Boer, Fred A. van Eeuwijk, Recursive Algorithms for Modeling Genomic Ancestral Origins in a Fixed Pedigree, G3: Genes|Genomes|Genetics, 10.1534/g3.118.200340, 8, 10, (3231-3245), (2018).
- Anthony F. Herzig, Teresa Nutile, Daniela Ruggiero, Marina Ciullo, Hervé Perdry, Anne-Louise Leutenegger, Detecting the dominance component of heritability in isolated and outbred human populations, Scientific Reports, 10.1038/s41598-018-36050-7, 8, 1, (2018).
- E.N. Fernández, A. Legarra, R. Martínez, J.P. Sánchez, M. Baselga, Pedigree‐based estimation of covariance between dominance deviations and additive genetic effects in closed rabbit lines considering inbreeding and using a computationally simpler equivalent model, Journal of Animal Breeding and Genetics, 10.1111/jbg.12267, 134, 3, (184-195), (2017).
- Celia M.T. Greenwood, Alexandre Bureau, J Concepción Loredo-Osti, Nicole M. Roslin, M. Joyce Crumley, Carl G. Brewer, T. Mary Fujiwara, Darlene R. Goldstein, Kenneth Morgan, Pedigree Selection and Tests of Linkage in a Hutterite Asthma Pedigree, Genetic Epidemiology, 10.1002/gepi.2001.21.s1.s244, 21, S1, (S244-S251), (2017).
- Jennifer Lin, Anthony Hinrichs, Brian K. Suarez, A Kinship Analysis of Asthma Among the Hutterites, Genetic Epidemiology, 10.1002/gepi.2001.21.s1.s252, 21, S1, (S252-S257), (2017).
- Jinliang Wang, Pedigrees or markers: Which are better in estimating relatedness and inbreeding coefficient?, Theoretical Population Biology, 10.1016/j.tpb.2015.08.006, 107, (4-13), (2016).
- Kang Huang, Kermit Ritland, Derek W. Dunn, Xiaoguang Qi, Songtao Guo, Baoguo Li, Estimating Relatedness in the Presence of Null Alleles, Genetics, 10.1534/genetics.114.163956, 202, 1, (247-260), (2015).
- Héloïse Gauvin, Jean-François Lefebvre, Claudia Moreau, Eve-Marie Lavoie, Damian Labuda, Hélène Vézina, Marie-Hélène Roy-Gagnon, GENLIB: an R package for the analysis of genealogical data, BMC Bioinformatics, 10.1186/s12859-015-0581-5, 16, 1, (2015).
- Luis Alberto García-Cortés, A novel recursive algorithm for the calculation of the detailed identity coefficients, Genetics Selection Evolution, 10.1186/s12711-015-0108-6, 47, 1, (2015).
- Andres Legarra, Ole F. Christensen, Zulma G. Vitezica, Ignacio Aguilar, Ignacy Misztal, Ancestral Relationships Using Metafounders: Finite Ancestral Populations and Across Population Relationships, Genetics, 10.1534/genetics.115.177014, 200, 2, (455-468), (2015).
- Alejandro Q. Nato, Nicola H. Chapman, Harkirat K. Sohi, Hiep D. Nguyen, Zoran Brkanac, Ellen M. Wijsman, PBAP: a pipeline for file processing and quality control of pedigree data with dense genetic markers, Bioinformatics, 10.1093/bioinformatics/btv444, (btv444), (2015).
- P. W. Hedrick, R. C. Lacy, Measuring Relatedness between Inbred Individuals, Journal of Heredity, 10.1093/jhered/esu072, 106, 1, (20-25), (2014).
- K Huang, S T Guo, M R Shattuck, S T Chen, X G Qi, P Zhang, B G Li, A maximum-likelihood estimation of pairwise relatedness for autopolyploids, Heredity, 10.1038/hdy.2014.88, 114, 2, (133-142), (2014).
- H. Wang, I. Misztal, A. Legarra, Differences between genomic‐based and pedigree‐based relationships in a chicken population, as a function of quality control and pedigree links among individuals, Journal of Animal Breeding and Genetics, 10.1111/jbg.12109, 131, 6, (445-451), (2014).
- En Cheng, Z. Meral Ozsoyoglu, Path-Counting Formulas for Generalized Kinship Coefficients and Condensed Identity Coefficients, Computational and Mathematical Methods in Medicine, 10.1155/2014/898424, 2014, (1-20), (2014).
- C Laprise, The Saguenay-Lac-Saint-Jean asthma familial collection: the genetics of asthma in a young founder population, Genes & Immunity, 10.1038/gene.2014.12, 15, 4, (247-255), (2014).
- Clarissa C. Parker, Peter Carbonetto, Greta Sokoloff, Yeonhee J. Park, Mark Abney, Abraham A. Palmer, High-Resolution Genetic Mapping of Complex Traits from a Combined Analysis of F 2 and Advanced Intercross Mice , Genetics, 10.1534/genetics.114.167056, 198, 1, (103-116), (2014).
- Héloïse Gauvin, Claudia Moreau, Jean-François Lefebvre, Catherine Laprise, Hélène Vézina, Damian Labuda, Marie-Hélène Roy-Gagnon, Genome-wide patterns of identity-by-descent sharing in the French Canadian founder population, European Journal of Human Genetics, 10.1038/ejhg.2013.227, 22, 6, (814-821), (2013).
- Riyan Cheng, Clarissa C. Parker, Mark Abney, Abraham A. Palmer, Practical Considerations Regarding the Use of Genotype and Pedigree Data to Model Relatedness in the Context of Genome-Wide Association Studies, G3: Genes|Genomes|Genetics, 10.1534/g3.113.007948, 3, 10, (1861-1867), (2013).
- Elizabeth A. Thompson, Identity by Descent: Variation in Meiosis, Across Genomes, and in Populations, Genetics, 10.1534/genetics.112.148825, 194, 2, (301-326), (2013).
- Luis Alberto Garcia-Cortes, Andres Legarra, Claude Chevalet, Miguel Angel Toro, Variance and Covariance of Actual Relationships between Relatives at One Locus, PLoS ONE, 10.1371/journal.pone.0057003, 8, 2, (e57003), (2013).
- Lei Yang, En Cheng, Z Meral Özsoyoğlu, Efficient path-based computations on pedigree graphs with compact encodings, BMC Bioinformatics, 10.1186/1471-2105-13-S3-S14, 13, S3, (2012).
- M.P. Zalucki, J.P. Cunningham, S. Downes, P. Ward, C. Lange, M. Meissle, N.A. Schellhorn, J.M. Zalucki, No evidence for change in oviposition behaviour of Helicoverpa armigera (Hübner) (Lepidoptera: Noctuidae) after widespread adoption of transgenic insecticidal cotton , Bulletin of Entomological Research, 10.1017/S0007485311000848, 102, 4, (468-476), (2012).
- Lide Han, Mark Abney, Identity by descent estimation with dense genome‐wide genotype data, Genetic Epidemiology, 10.1002/gepi.20606, 35, 6, (557-567), (2011).
- Cary A Salzmann, Thierry JM Olivry, Dahlia M Nielsen, Judith S Paps, Tonya L Harris, Natasha J Olby, Genome-wide linkage study of atopic dermatitis in West Highland White Terriers, BMC Genetics, 10.1186/1471-2156-12-37, 12, 1, (37), (2011).
- Marie-Hélène Roy-Gagnon, Claudia Moreau, Claude Bherer, Pascal St-Onge, Daniel Sinnett, Catherine Laprise, Hélène Vézina, Damian Labuda, Genomic and genealogical investigation of the French Canadian founder population structure, Human Genetics, 10.1007/s00439-010-0945-x, 129, 5, (521-531), (2011).
- Riyan Cheng, Mark Abney, Abraham A Palmer, Andrew D Skol, QTLRel: an R Package for Genome-wide Association Studies in which Relatedness is a Concern, BMC Genetics, 10.1186/1471-2156-12-66, 12, 1, (66), (2011).
- EN CHENG, BRENDAN ELLIOTT, Z. MERAL ÖZSOYOǦLU, EFFICIENT COMPUTATION OF KINSHIP AND IDENTITY COEFFICIENTS ON LARGE PEDIGREES, Journal of Bioinformatics and Computational Biology, 10.1142/S0219720009004175, 07, 03, (429-453), (2011).
- Claude Bherer, Damian Labuda, Marie‐Hélène Roy‐Gagnon, Louis Houde, Marc Tremblay, Hélène Vézina, Admixed ancestry and stratification of Quebec regional populations, American Journal of Physical Anthropology, 10.1002/ajpa.21424, 144, 3, (432-441), (2010).
- Xin Li, Xiaolin Yin, Jing Li, Efficient identification of identical-by-descent status in pedigrees with many untyped individuals, Bioinformatics, 10.1093/bioinformatics/btq222, 26, 12, (i191-i198), (2010).
- Riyan Cheng, Jackie E. Lim, Kaitlin E. Samocha, Greta Sokoloff, Mark Abney, Andrew D. Skol, Abraham A. Palmer, Genome-Wide Association Studies and the Problem of Relatedness Among Advanced Intercross Lines and Other Highly Recombinant Populations, Genetics, 10.1534/genetics.110.116863, 185, 3, (1033-1044), (2010).
- Mark Abney, A graphical algorithm for fast computation of identity coefficients and generalized kinship coefficients, Bioinformatics, 10.1093/bioinformatics/btp185, 25, 12, (1561-1563), (2009).
- Vincenza Colonna, Teresa Nutile, Ronald R Ferrucci, Giulio Fardella, Mario Aversano, Guido Barbujani, Marina Ciullo, Comparing population structure as inferred from genealogical versus genetic information, European Journal of Human Genetics, 10.1038/ejhg.2009.97, 17, 12, (1635-1641), (2009).
- W. G. Pearce, J. A. Mackay, T. M. Holmes, K. Morgan, S. B. Fowlow, M. H. K. Shokeir, R. B. Lowry, Autosomal recessive juvenile cataract in Hutterites, Ophthalmic Paediatrics and Genetics, 10.3109/13816818709028527, 8, 2, (119-124), (2009).
- Maria G. Motlagh, Arshia Seddigh, Behnoosh Dashti, James F. Leckman, Javad Alaghband‐Rad, Consanguineous Iranian kindreds with severe Tourette syndrome, Movement Disorders, 10.1002/mds.22261, 23, 14, (2079-2083), (2008).
- Vincenza Colonna, Teresa Nutile, Maria Astore, Ombretta Guardiola, Giuliano Antoniol, Marina Ciullo, M.Graziella Persico, Campora: A Young Genetic Isolate in South Italy, Human Heredity, 10.1159/000101964, 64, 2, (123-135), (2007).
- Elizabeth Thompson, Inferring Gene Ancestry: Estimating Gene Descent, International Statistical Review, 10.1111/j.1751-5823.1998.tb00404.x, 66, 1, (29-40), (2007).
- K. LANGE, J. S. SINSHEIMER, Calculation of genetic identity coefficients, Annals of Human Genetics, 10.1111/j.1469-1809.1992.tb01162.x, 56, 4, (339-346), (2007).
- G. Karigl, Admissible Regions in a Simplex of Identity Coefficients, Biometrical Journal, 10.1002/bimj.4710260119, 26, 1, (101-109), (2007).
- E. A. THOMPSON, A recursive algorithm for inferring gene origins, Annals of Human Genetics, 10.1111/j.1469-1809.1983.tb00981.x, 47, 2, (143-152), (2007).
- G. Karigl, Multiple genetic relationships: joint and conditional genotype probabilities, Annals of Human Genetics, 10.1111/j.1469-1809.1982.tb00696.x, 46, 1, (83-92), (2007).
- Anne-Louise Leutenegger, Audrey Labalme, Emmanuelle Génin, Annick Toutain, Elisabeth Steichen, Françoise Clerget-Darpoux, Patrick Edery, Using Genomic Inbreeding Coefficient Estimates for Homozygosity Mapping of Rare Recessive Traits: Application to Taybi-Linder Syndrome, The American Journal of Human Genetics, 10.1086/504640, 79, 1, (62-66), (2006).
- Wenlei Liu, B.S Weir, Genotypic probabilities for pairs of inbred relatives, Philosophical Transactions of the Royal Society B: Biological Sciences, 10.1098/rstb.2005.1677, 360, 1459, (1379-1385), (2005).
- Paul Van Eerdewegh, Linkage analysis with inbreeding, Genetic Epidemiology, 10.1002/gepi.1370060148, 6, 1, (277-279), (2005).
- E. A. Thompson, Ancestry of alleles and extinction of genes in populations with defined pedigrees, Zoo Biology, 10.1002/zoo.1430050210, 5, 2, (161-170), (2005).
- R. B. Lowry, F. F. Snyder, R. L. Wesenberg, G. A. Machin, D. A. Applegarth, K. Morgan, R. J. Carter, J. R. Toone, T. M. Holmes, R. D. Dewar, John M. Opitz, James F. Reynolds, Morquio syndrome (MPS IVA) and hypophosphatasia in a Hutterite kindred, American Journal of Medical Genetics, 10.1002/ajmg.1320220304, 22, 3, (463-475), (2005).
- S. Beatrice Fowlow, Floyd F. Snyder, T. Mary Holmes, Kenneth Morgan, John M. Opitz, James F. Reynolds, Screening for methylmalonic aciduria in alberta: A voluntary program with particular significance for the Hutterite Brethren, American Journal of Medical Genetics, 10.1002/ajmg.1320220309, 22, 3, (513-519), (2005).
- R. B. Lowry, G. A. Machin, K. Morgan, D. Mayock, L. Marx, John M. Opitz, James F. Reynolds, Congenital contractures, edema, hyperkeratosis, and intrauterine growth retardation: A fatal syndrome in hutterite and mennonite kindreds, American Journal of Medical Genetics, 10.1002/ajmg.1320220311, 22, 3, (531-543), (2005).
- R. B. Lowry, K. Morgan, T. M. Holmes, S. W. M. Gilroy, John M. Opitz, James F. Reynolds, Congenital anomalies in the Hutterite population: A preliminary survey and hypothesis, American Journal of Medical Genetics, 10.1002/ajmg.1320220312, 22, 3, (545-552), (2005).
- Anthony Almudevar, Most Powerful Permutation Invariant Tests for Relatedness Hypotheses Using Genotypic Data, Biometrics, 10.1111/j.0006-341X.2001.01080.x, 57, 4, (1080-1088), (2004).
- Genetic Identity Coefficients, Applied Probability, 10.1007/b98849, (81-96), (2003).
- R.B. Lowry, A.M. Innes, F.P. Bernier, D.R. McLeod, C.R. Greenberg, A.E. Chudley, B. Chodirker, S.L. Marles, M.J. Crumley, J.C. Loredo‐Osti, K. Morgan, T.M. Fujiwara, Bowen–Conradi syndrome: A clinical and genetic study, American Journal of Medical Genetics Part A, 10.1002/ajmg.a.20059, 120A, 3, (423-428), (2003).
- Kenneth Lange, Kenneth Lange, Genetic Identity Coefficients, Mathematical and Statistical Methods for Genetic Analysis, 10.1007/978-0-387-21750-5_5, (81-96), (2002).
- Emmanuelle Génin, Alexandre A. Todorov, Françoise Clerget‐Darpoux, Properties of the transmission‐disequilibrium test in the presence of inbreeding, Genetic Epidemiology, 10.1002/gepi.0174, 22, 2, (116-127), (2002).
- Mark Abney, Mary Sara McPeek, Carole Ober, Estimation of Variance Components of Quantitative Traits in Inbred Populations, The American Journal of Human Genetics, 10.1086/302759, 66, 2, (629-650), (2000).
- Daniel E. Weeks, Janet S. Sinsheimer, Consanguinity and Relative-Pair Methods for Linkage Analysis, The American Journal of Human Genetics, 10.1086/301742, 62, 3, (730-733), (1998).
- Veronica J. Vieland, Susan E. Hodge, Reply to Karunaratne and Elston, The American Journal of Human Genetics, 10.1086/512146, 62, 3, (739-740), (1998).
- Emmanuelle Génin, Françoise Clerget-Darpoux, Reply to Weeks and Sinsheimer, The American Journal of Human Genetics, 10.1086/301744, 62, 3, (731-736), (1998).
- Kenneth Lange, Kenneth Lange, Genetic Identity Coefficients, Mathematical and Statistical Methods for Genetic Analysis, 10.1007/978-1-4757-2739-5_5, (70-84), (1997).
- Stephen P. Bryant, Software for genetic linkage analysis, Molecular Biotechnology, 10.1007/BF02762412, 5, 1, (49-61), (1996).
