Page 290 - Applied Probability

12. Models of Recombination
278
The only decreasing function fitting this description is ψ(x)= e
for some β> 0. Argue that this solution entails
n−1 −β
β
=
p n
µn!
1 − e e −β , n ≥ 1 −βx
1 − p 0 = .
βµ
12.9 References
[1] Bailey NTJ (1961) Introduction to the Mathematical Theory of Genetic
Linkage. Oxford University Press, London
[2] Baum L (1972) An inequality and associated maximization tech-
nique in statistical estimation for probabilistic functions of Markov
processes. Inequalities 3:1–8
[3] Browning S (2000) The relationship between count-location and sta-
tionary renewal models for the chiasma process. Genetics 155:1955–
1960

[4] Carter TC, Falconer DS (1951) Stocks for detecting linkage in the
mouse and the theory of their design. J Genet 50:307–323

[5] Carter TC, Robertson A (1952) A mathematical treatment of genetical
recombination using a four-strand model. Proc R Soc Lond B 139:410–
426.

[6] Cox DR, Isham V (1980) Point Processes. Chapman and Hall, New
York

[7] Devijver PA (1985) Baum’s forward-backward algorithm revisited.
Pattern Recognition Letters 3:369–373

[8] Feller W (1971) An Introduction to Probability Theory and its Appli-
cations, Vol 2, 2nd ed. Wiley, New York

[9] Felsenstein J (1979) A mathematically tractable family of genetic map-
ping functions with different amounts of interference. Genetics 91:769–
775

[10] Fisher, RA, Lyon MF, Owen ARG (1947) The sex chromosome in the
house mouse. Heredity 1:335–365.

[11] Haldane JBS (1919) The combination of linkage values, and the calcu-
lation of distance between the loci of linked factors. J Genet 8:299–309