Lecture 13: Genetic maps and mapping functions

(version 20 July 1999)

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Problems with maps based solely on the recombination frequency c

If gene order on the map is 1 2 3, additivity would imply c₁₃ = c₁₂ + c₂₃

In reality, c₁₃ < c₁₂ + c₂₃

Require some gene distance measure that is additive

Obvious one: the expected number of crossovers, m, between two loci.

Mapping functions provide the connection between

c = observed recombination frequency

m= map distance (number of recombination events)

We observe c and wish to estimate m.

Based on assumptions about interference, a mapping function , c = F(m) that relates c and m is obtained.

Hence, m = F^-1(c)

Works over very short distances

Fails (i.e., highly non-additive) if c is moderate to large (c > .2)

c = (1 - e^-2m) /2. Solving gives m = -(1/2) ln(1-2c)

Assumes no interference between loci --- Derivation

Warning: book (pg 158-159) uses m in place of 2m

For very small map distances, m = c

For large distances c = 1/2

Consider the three linked genes A-B- D, where c(A-D) = .20, c(A-B) = .13, C(B-D) = .09

The Haldane distance between A and D is m(A-D) = -(1/2) ln(1-2*.20) = 0.26

Hence, on average expect 0.26 crossovers between A and D

Likewise m(A-B) = 0.15, m(B-D) = 0.10

How much is additivity improved?

For recombination frequency c(A-D) - [ c(A-B) + c(B-D) ] = -0.02

Haldane's distance: m(A-D) - [ m(A-B) + m(B-D) ] = 0.01

Make different assumptions about how recombination events between one pair of loci influences an adjacent pair of loci

For example, Kosambi's mapping function allows for interference

If recombination suppressed

Genetic distance decreases

shrinkage of genetic map relative to physical map

If recombination enhanced

Genetic distance increases

expansion of genetic map relative to physical map