Abstract
At meiosis, each member of a pair of homologous chromosomes replicates to form two sister chromosomes known as chromatids. The maternally and paternally derived sister pairs then perfectly align to form a bundle of four chromatids. Crossing-over occurs at points along the bundle known as chiasmata. At each chiasma, one sister chromatid from each pair is randomly selected and cut at the crossover point. The cell then rejoins the partial paternal chromatid above the cut to the partial maternal chromatid below the cut, and vice versa, to form two hybrid maternal-paternal chromatids. The preponderance of evidence suggests that the two chromatids participating in a chiasma are chosen nearly independently from chiasma to chiasma [30]. This independence property is termed lack of chromatid interference. After crossing-over has occurred, the recombined chromatids of a bundle are coordinately separated by two cell divisions so that each of the four resulting gametes receives exactly one chromatid.
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References
Bailey NTJ (1961) Introduction to the Mathematical Theory of Genetic Linkage. Oxford University Press, London
Baum L (1972) An inequality and associated maximization technique in statistical estimation for probabilistic functions of Markov processes. Inequalities 3:1–8
Carter TC, Falconer DS (1951) Stocks for detecting linkage in the mouse and the theory of their design. J Genet 50:307–323
Carter TC, Robertson A (1952) A mathematical treatment of genetical recombination using a four-strand model. ProcRSocLondB 139:410–426.
Cox DR, Isham V (1980) Point Processes, Chapman and Hall, New York
Devijver PA (1985) Baum’s forward-backward algorithm revisited. Pattern Recognition Letters 3:369–373
Feller W (1971) An Introduction to Probability Theory and its Applications, Vol 2,2nd ed. Wiley, New York
Felsenstein J (1979) A mathematically tractable family of genetic mapping functions with different amounts of interference. Genetics 91:769–775
Fisher, RA, Lyon MF, Owen ARG (1947) The sex chromosome in the house mouse. Heredity 1:335–365.
Haidane JBS (1919) The combination of linkage values, and the calculation of distance between the loci of linked factors. J Genet 8:299–309
Karlin S (1984) Theoretical aspects of genetic map functions in recombination processes. In Human Population Genetics: The Pittsburgh Symposium, Chakravarti A, editor, Van Nostrand Reinhold, New York, pp 209–228
Karlin S, Liberman U (1979) A natural class of multilocus recombination processes and related measures of crossover interference. Adv Appl Prob 11:479–501
Karlin S, Liberman U (1983) Measuring interference in the chiasma renewal formation process. Adv Appl Prob 15:471–487
Karlin S, Taylor HM (1975) A First Course in Stochastic Processes, 2nd ed. Academic Press, New York
Kosambi DD (1944) The estimation of map distance from recombination values. Ann Eugen 12:172–175
Lange K, Risch N (1977) Comments on lack of interference in the four-strand model of crossingover. J Math Biol 5:55–59
Lange K, Zhao H, Speed TP (1997) The Poisson-skip model of crossingover. Ann Appl Prob (in press)
Mather K (1938) Crossing-over. Biol Reviews Camb Phil Soc 13:252–292
Morgan TH, Bridges CB, Schultz J (1935) Constitution of the germinal material in relation to heredity. Carnegie Inst Washington Yearbook 34:284–291
Owen ARG (1950) The theory of genetical recombination. Adv Genet 3:117–157
Payne LC (1956) The theory of genetical recombination: A general formulation for a certain class of intercept length distributions appropriate to the discussion of multiple linkage. Proc Roy Soc B 144:528–544.
Risch N, Lange K (1979) An alternative model of recombination and interference. Ann Hum Genet 43:61–70
Risch N, Lange K (1983) Statistical analysis of multilocus recombination. Biometrics 39:949–963
Ross SM (1983) Stochastic Processes. Wiley, New York
Schnell FW (1961) Some general formulations of linkage effects in inbreeding. Genetics 46:947–957
Speed TP (1996) What is a genetic map function? In Genetic Mapping and DNA Sequencing, IMA Vol 81 In Mathematics and its Applications. Speed TP, Waterman MS, editors, Springer-Verlag, New York, pp 65–88
Stahl FW (1979) Genetic Recombination: Thinking about it in Phage and Fungi. WH Freeman, San Francisco
Sturt E (1976) A mapping function for human chromosomes. Ann Hum Genet 40:147–163
Whitehouse HLK (1982) Genetic Recombination: Understanding the Mechanisms. St. Martin’s Press, New York
Zhao H, McPeek MS, Speed TP (1995) Statistical analysis of chromatid interference. Genetics 139:1057–1065
Zhao H, Speed TP (1996) On genetic map functions. Genetics 142:1369–1377
Zhao H, Speed TP, McPeek MS (1995) Statistical analysis of crossover interference using the chi-square model. Genetics 139:1045–1056.
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Lange, K. (1997). Models of Recombination. In: Mathematical and Statistical Methods for Genetic Analysis. Statistics for Biology and Health. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2739-5_12
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