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.


Renewal Process Recombination Fraction Renewal Function Positive Interference Chiasma Interference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Bailey NTJ (1961) Introduction to the Mathematical Theory of Genetic Linkage. Oxford University Press, LondonzbMATHGoogle Scholar
  2. [2]
    Baum L (1972) An inequality and associated maximization technique in statistical estimation for probabilistic functions of Markov processes. Inequalities 3:1–8Google Scholar
  3. [3]
    Carter TC, Falconer DS (1951) Stocks for detecting linkage in the mouse and the theory of their design. J Genet 50:307–323CrossRefGoogle Scholar
  4. [4]
    Carter TC, Robertson A (1952) A mathematical treatment of genetical recombination using a four-strand model. ProcRSocLondB 139:410–426.Google Scholar
  5. [5]
    Cox DR, Isham V (1980) Point Processes, Chapman and Hall, New YorkzbMATHGoogle Scholar
  6. [6]
    Devijver PA (1985) Baum’s forward-backward algorithm revisited. Pattern Recognition Letters 3:369–373zbMATHCrossRefGoogle Scholar
  7. [7]
    Feller W (1971) An Introduction to Probability Theory and its Applications, Vol 2,2nd ed. Wiley, New YorkGoogle Scholar
  8. [8]
    Felsenstein J (1979) A mathematically tractable family of genetic mapping functions with different amounts of interference. Genetics 91:769–775MathSciNetGoogle Scholar
  9. [9]
    Fisher, RA, Lyon MF, Owen ARG (1947) The sex chromosome in the house mouse. Heredity 1:335–365.Google Scholar
  10. [10]
    Haidane JBS (1919) The combination of linkage values, and the calculation of distance between the loci of linked factors. J Genet 8:299–309Google Scholar
  11. [11]
    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 209–228Google Scholar
  12. [12]
    Karlin S, Liberman U (1979) A natural class of multilocus recombination processes and related measures of crossover interference. Adv Appl Prob 11:479–501zbMATHCrossRefMathSciNetGoogle Scholar
  13. [13]
    Karlin S, Liberman U (1983) Measuring interference in the chiasma renewal formation process. Adv Appl Prob 15:471–487zbMATHCrossRefGoogle Scholar
  14. [14]
    Karlin S, Taylor HM (1975) A First Course in Stochastic Processes, 2nd ed. Academic Press, New YorkzbMATHGoogle Scholar
  15. [15]
    Kosambi DD (1944) The estimation of map distance from recombination values. Ann Eugen 12:172–175Google Scholar
  16. [16]
    Lange K, Risch N (1977) Comments on lack of interference in the four-strand model of crossingover. J Math Biol 5:55–59CrossRefMathSciNetGoogle Scholar
  17. [17]
    Lange K, Zhao H, Speed TP (1997) The Poisson-skip model of crossingover. Ann Appl Prob (in press)Google Scholar
  18. [18]
    Mather K (1938) Crossing-over. Biol Reviews Camb Phil Soc 13:252–292CrossRefGoogle Scholar
  19. [19]
    Morgan TH, Bridges CB, Schultz J (1935) Constitution of the germinal material in relation to heredity. Carnegie Inst Washington Yearbook 34:284–291Google Scholar
  20. [20]
    Owen ARG (1950) The theory of genetical recombination. Adv Genet 3:117–157CrossRefGoogle Scholar
  21. [21]
    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.CrossRefGoogle Scholar
  22. [22]
    Risch N, Lange K (1979) An alternative model of recombination and interference. Ann Hum Genet 43:61–70zbMATHCrossRefGoogle Scholar
  23. [23]
    Risch N, Lange K (1983) Statistical analysis of multilocus recombination. Biometrics 39:949–963zbMATHCrossRefMathSciNetGoogle Scholar
  24. [24]
    Ross SM (1983) Stochastic Processes. Wiley, New YorkzbMATHGoogle Scholar
  25. [25]
    Schnell FW (1961) Some general formulations of linkage effects in inbreeding. Genetics 46:947–957Google Scholar
  26. [26]
    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 65–88CrossRefGoogle Scholar
  27. [27]
    Stahl FW (1979) Genetic Recombination: Thinking about it in Phage and Fungi. WH Freeman, San FranciscoGoogle Scholar
  28. [28]
    Sturt E (1976) A mapping function for human chromosomes. Ann Hum Genet 40:147–163CrossRefGoogle Scholar
  29. [29]
    Whitehouse HLK (1982) Genetic Recombination: Understanding the Mechanisms. St. Martin’s Press, New YorkGoogle Scholar
  30. [30]
    Zhao H, McPeek MS, Speed TP (1995) Statistical analysis of chromatid interference. Genetics 139:1057–1065Google Scholar
  31. [31]
    Zhao H, Speed TP (1996) On genetic map functions. Genetics 142:1369–1377Google Scholar
  32. [32]
    Zhao H, Speed TP, McPeek MS (1995) Statistical analysis of crossover interference using the chi-square model. Genetics 139:1045–1056.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Kenneth Lange
    • 1
  1. 1.Department of Biostatistics and MathematicsUniversity of MichiganAnn ArborUSA

Personalised recommendations