haldane_mapping: Haldane's Mapping Function

In selection.index: Analysis of Selection Index in Plant Breeding

Haldane's Mapping Function

Description

Converts genetic distance (in Morgans) to recombination fraction using Haldane's mapping function. This function models the relationship between genetic distance and the probability of recombination between loci.

Usage

haldane_mapping(distance)

Arguments

distance

Genetic distance in Morgans (scalar or vector). One Morgan corresponds to a 50% recombination frequency.

Details

Mathematical Formula (Chapter 10, Section 10.1):

The relationship between recombination fraction (r) and genetic distance (d):

r = \frac{1}{2}(1 - e^{-2d})

Where: - d = Genetic distance in Morgans - r = Recombination fraction (probability of recombination per meiosis)

This function assumes no crossover interference beyond that implied by the mapping function itself.

Value

Recombination fraction (r) ranging from 0 to 0.5. - r = 0 indicates complete linkage (no recombination) - r = 0.5 indicates independent assortment (unlinked loci)

Examples

# Zero distance means complete linkage (no recombination)
haldane_mapping(0) # Returns 0

# 1 Morgan distance
haldane_mapping(1) # Returns ~0.43

# Large distance approaches 0.5 (independent assortment)
haldane_mapping(10) # Returns ~0.5

# Vector of distances
distances <- c(0, 0.1, 0.5, 1.0, 2.0)
haldane_mapping(distances)

selection.index documentation built on March 9, 2026, 1:06 a.m.