Linkage analyses and map construction

1.4.2.1 Mapping population

Development of a segregating population is the basic requirement for linkage map development and for subsequent QTL mapping. Genetic diversity of both parents is crucial as it decides the polymorphism rate in the population, i.e. how many genetic markers will be polymorphic and useful for map construction. Outcrossing species usually give higher polymorphism rates in their populations than inbreeding species where both parents are homozygous. Back cross (or testcross), double haploid, near isogenic and F2 populations from self pollinated and half-sib, full-sib families and two-way pseudo-testcross populations derived from cross pollinated species have

been used for genetic mapping in plant species (Doerge, 2002). The choice of mapping population applicable to some plants with long breeding cycles such as fruit trees is limited, and most genetic studies in fruit trees are based on one-generation full-sib families and the pseudo test cross strategy for map construction and QTL analysis (Zhao et al., 2013; Gardner et al., 2014; Jensen et al., 2014).

Population size (N) and heritability (h2) of the trait influence the QTL effect, as the proportion of additive variance effect of QTL is inversely proportional to h2N. Hence the prediction power for QTL (especially with small effects) for moderate to low heritability for smaller population (e.g. less than 100 segregating individuals) is low (Bradbury et al., 2011; Liu et al., 2012). Moreover smaller populations might also affect the resolution and accuracy of the linkage maps (Mohan et al., 1997). Denser maps are required for smaller populations.

1.4.2.2 Linkage analysis

This step involves the coding of each individual marker for a whole population and running of the linkage analysis by an appropriate software packages are presently available and have been used in recent years for genetic linkage mapping, including JoinMap (Stam, 1993), LINKAGE (Suiter et al., 1983), MAPMAKER/EXP (Lander et al., 1987), GMENDEL (Echt et al., 1992) and Map Manager QTX (Manly et al., 2001). This step involves the coding of each individual marker for a whole population and running of the linkage analysis by an appropriate software programme. A number of software packages are presently available and have been used in recent years for genetic linkage mapping, including JoinMap (Stam, 1993), LINKAGE (Suiter et al., 1983), MAPMAKER/EXP (Lander et al., 1987), GMENDEL (Echt et al., 1992)

Linkages between the markers are calculated by odds ratios (i.e. probability of linkage of two loci versus no linkage of two loci). This ratio is expressed in terms of logarithm of ratio and also known as logarithm of odds (LOD) value or LOD scores (Risch, 1992; Stam, 1993). The significant LOD scores used to create linkage groups are called ‘linklod’ (Stam, 1993; Ortiz et al., 2001) and marker groups having LOD score higher than critical ‘linklod’ are considered to be linked and vice versa. LOD 31

values of >3 have been used by many researchers as a minimum threshold level for linklod to see if the loci are linked or not. A LOD value of 3 specifies that chances of linkage between two markers is 1000 times higher in comparison to no linkage (i.e. 1000:1). However, higher and lower LOD threshold values can be used according to the situation, a lower LOD score will give few linkage groups with more markers but higher LOD score gives smaller fragments of chromosomes with fewer markers. However, a lower LOD threshold will give more false positives than a higher threshold, for example by merging groups that do not belong to the same chromosome. Conversely a high LOD threshold will generate more fragmented linkage groups, where more than one linkage group may be obtained for each chromosome. Ideally the number of linkage groups produced by linkage mapping should be the same as the number of haploid chromosomes for that species. When a genetic map reaches this stage it is said to be “saturated”. Failure to saturate a map may be due to insufficient number of markers. If a linkage group has markers from different chromosomes that often indicates suspect linkages in the map.

1.4.2.3 Map distance and mapping function

Map distances are a measure of recombination frequency between markers. Distances are directly proportional to recombination frequency when the map distances are small (<10 cM; centimorgan), however it is not the case when map distances are higher than 10 cM. For recombination frequency of 10% or lower Haldane or Kosambi mapping functions give the same map distance, but at higher frequencies map distance will be higher for Haldane than the Kosambi function. The Kosambi mapping function is usually used to translate recombination frequency into map units (cM), as it takes into account the physical interference between chiasma and minimises double recombinants at short distances. One genetic map unit is equivalent to one percent of recombinant or 1 cM.

It is important to keep in mind that genetic map distance in cM and physical distance (in bp or kb) have no direct linear relationship. Relationship between genetic and physical distance are variable due to variable rates of recombination within a single chromosome (Ahn and Tanksley, 1993; Young, 1994; Künzel et al., 2000) as there are specific hot or cold spots on chromosomes according to recombination

frequencies (Faris et al., 2000; Ma et al., 2001; Yao et al., 2002). For example in rice 1 cM map distance on average equals to 258.5 kb (International rice genome sequencing project, 2005).

High quality genetic linkage maps serve many purposes such as a) QTL analysis and identification of genes responsible for economically important traits (Mohan et al., 1997; Doerge, 2002; Yim et al., 2002) b) introgression of favourable loci or genes (Cullingham et al., 2013); c) for comparative genome mapping (Ahn and Tanksley, 1993; Celton et al., 2009; Illa et al., 2011); d) for anchoring DNA sequence scaffolds (Chagné et al., 2014).