1. Genomics in Tree Breeding and Forest Ecosystem Management
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Module 10 – Linkage Disequilibrium
In previous modules we have only briefly mentioned the term linkage disequilibrium or LD. In Module 10 it will be our focus, and will pave the way for the introduction of association genetics and genomic selection. LD is at the root of virtually all marker informed breeding applications. Most outcrossing plants, including the vast majority of coniferous and flowering trees, have genomes that are largely in linkage equilibrium at the population level. QTL mapping works because specific crosses create short-lived LD as a function of genetic linkage unspoiled by generations of recombination (crossing over). Strong LD is largely a function of tight linkage, though as we shall see, there are other factors at play – indeed, alleles in different genes at great distances from one another on a linkage group, or even on different LGs, may persist in LD for some time. The study of LD has revealed a great deal about genome organization and evolution.
Nicholas Wheeler & David Harry – Oregon State University

2. Moving from family-based to population-based QTL discovery
Linkage and QTL mapping using pedigreed families
QTL, when located, are on large chromosomal blocks
With only a few generations, the amount of recombination is limited
Association genetics: Identifying QTL using populations comprising unrelated individuals or mixed relationships
QTL are located on small chromosomal blocks. These locations are mapped with great precision relative to closely linked markers
Linkage blocks are shaped by historical recombination
Population histories reflect 10’s – 1000’s of generations
The previous module introduced the concept of QTL mapping in controlled crosses or pedigrees and described it’s utility for characterizing the genetic basis of quantitatively inherited traits. In this module, we briefly introduce an alternative approach to complex trait dissection, called association genetics, but spend most of the module discussing linkage disequilibrium, the genetic basis or foundation upon which association is built. Just to make sure you start off thoroughly versed, association genetics has also been called association mapping or linkage disequilibrium mapping. Sadly, the term linkage disequilibrium itself is a bit confusing, but has solidly found it’s way into the vernacular. Most geneticists would prefer the term “gametic phase disequilibrium”. In the subsequent module we provide a more thorough discussion of association mapping itself.

3. Chromosome blocks in families and populations
Family-based linkage mapping (a) involves tracking a QTL, here denoted as “m”, over a few generations in larger chromosomal blocks
Population-based association mapping (b) tracks “m” on smaller chromosomal segments, taking advantage of historical recombination
It is often said that QTL mapping is based on linkage, while association genetics is based on linkage disequilibrium. The distinction is perhaps not fully warranted and certainly needs explaining. LD measures non-random association among alleles—describing the extent to which the presence of an allele at one locus predicts the presence of a specific allele at a second locus. This sounds a great deal like QTL mapping: we seek to find a marker allele that predicts a QTL allele. How is that different from LD. In large part, the distinction is one of degree. With families, which are the product of only 1 or 2 generations of recombination, LD extends over rather large chromosomal blocks. This is called high or large LD. Now consider simply sampling an array of unrelated individuals, each the product of 10s to 100s of generations of cross-overs. Chromosomal blocks in these individuals are much smaller, and markers even a few cM away from a QTL may not be predictive of the QTL allele desired. Association genetics seeks to find markers that remain in disequilibrium with the QTL, even after all this recombining. To be fair, LD is a bit more complicated. Two loci may be in strong LD even though they are not tightly linked!
Use as one of several introductory slides. Linkage is family-based, whereas association mapping need not be. Linkage studies are typically constrained in the number of generations included, so chromosomal segments tend to be large. In association studies, however, many more generations can be included (20 are shown here, but it could be 100’s-1000’s), so chromosomal segments are much smaller.
Cardon & Bell Nat Rev Genet 2: 91-99

4. It is a question of resolution
Again, we call upon this cartoon to illustrate the distinction between the approaches to complex trait dissection. In the figure, the grey rectangle represents a gene, situated along a chromosome and the little symbols are markers or mutations. For family based QTL mapping, flanking markers within some reasonable proximity of the QTL will suffice for prediction. Association genetics seeks to find markers that are in much greater LD with the QTL, preferably within the gene responsible, and near the causal polymorphism, or the actual causal polymorphism itself.
Modified from: Grattapaglia. 2007

5. From families to populations: Linkage to linkage disequilibrium
So it should be apparent from diagrams, such as these, that there are some significantly different requirements for association genetics, relative to family based QTL mapping. One obvious distinction is the number of markers required to locate the associations. Lets take a quick look at the key differences between the two approaches before lunging on with our discussion of LD.
Modified from Rafalski COPB 5:

6. Comparing approaches
This table provides a concise comparison of pedigreed QTL mapping and association genetic mapping. QTL mapping requires but a modest set of framework markers to locate QTL. Depending on what approach is taken for AG, 100s to many thousands of markers may be required. Human association studies based on “whole genome” scans, can use over 200,000 markers. Family-based QTL mapping looks at one family at a time, with many progeny per family. AG requires many families, with only 1 or a few individuals per family. Analytical approaches for the two methods may share similarities (for instance, ANOVA or regression), but vary greatly in some protocols required to reduce risk of falsely identifying QTL. AG is vastly superior in pinpointing the location of causal polymorphisms, in finding all the genes affecting the trait of interest, and in providing a predictive tool that is functional within and among populations. In short, AG is a preferred approach for marker informed breeding and resource management.

7. Linkage disequilibrium (LD): The foundation of association genetics
LD measures non-random associations among alleles at different loci (or non-random associations among SNPs)
LD is the basis for associating markers with traits. It is the “glue” that binds them
LD also provides insights into population history, which helps in selecting experimental populations for marker-trait associations
Estimating LD, and understanding how it is organized in populations, is crucial for deciding how to sample marker genotypes
Knowing how population history can affect LD is essential for avoiding pitfalls and spurious false-positives
So lets begin our LD discussion by reviewing a few simple tenets, some of which you have already seen. LD is a measure of non-random association among alleles at different loci. One would expect population level LD to be zero for most two locus comparisons since most loci segregate totally independently of each other. Of course, without LD, associating markers with QTL would not be feasible. LD can provide information on a populations history. For instance, if LD appears to be high in a population, one can deduce that recent bottleneck or admixture events likely took place. For those entertaining the use of AG for practical purposes, characterizing the patterns of LD in their species and populations can guide the number and distribution of markers required, as we shall review shortly. The last bullet here refers especially to the issue of population subdivision which can lead to the detection of false positive associations. This too will be discussed further.

8. A conceptual view of LD
By now you should have a pretty good conceptual idea of what constitutes LD, but if not, this picture should help. These two cartoons demonstrate the two ends of the range of LD in a population. Notice that on the left (a), only two types of haplotypes are observed, with the orange allele at locus 1 completely associated with the blue allele at locus 2, and the aqua allele of locus 1 associated with the yellow allele of locus 2. This population shows maximum LD, denoted by D’ = 1 (we’ll define D’ in a moment). On the right (b), all four gamete classes are equally frequent, such that an orange allele at locus one is just as likely to be associated with a blue or yellow allele at the second locus. In this instance, there is no LD at all. Loci are behaving independently of each other.
Rafalski COPB 5: 8

9. Calculating LD (for biallelic loci)
Pairwise single-locus allele frequencies predict frequencies for each of four gamete types (left)
D = 0 (center) implies that predicted = observed gamete frequencies
D measures the degree to which observed and predicted gamete frequencies differ (right)
At first blush, LD seems relatively straightforward, but much like quantifying molecular diversity, there are multiple measures of the strength of two-locus association. The first measure of LD was proposed in 1960 by Lewontin and Kojima. It was simply termed D. The frequency expectation for a multi-locus genotype is simply the product of the single locus allele frequencies. The difference between the observed and expected multi-locus genotype was D.

10. LD can be positive (+) or negative (-)
The sign of D can be either positive or negative, depending on allelic designation. It is strictly arbitrary, and has no biological or genetic relevance.

11. Standardized measures for LD
Our definition of LD means that its magnitude depends on allele frequencies
D values of 0.01 in one population may be small, and yet in another, may be large — depending on allele frequencies
From our previous example
D =
D = 0.40 – 0.5*0.5 = 0.15
How large is D = 0.15?
Consequently, two standardized measures of LD were created
PAB – pA pB
The problem with D, as you might intuit by playing with various combinations of allele frequencies, is that the range of D is a function of allele frequencies. D had no relative, interpretive value. To address this weakness, Lewontin, in 1964, and later Hill and Roberson, in 1968, developed standardized measures of LD. We’ll briefly look at each of these measures of LD, denoted as D’ and r2. Both range from 0 to 1 (from no LD to complete LD) and both are common in the literature. They are sensitive to different things, and there is no universal agreement as to which should be used.
D' and r2 11

12. Standardized measures for LD: D’
Read “D prime”, D' ranges from 0 to 1
D' is maximized (D' = 1) whenever a gamete type is missing, as would happen for a recent mutation
However, D' is unstable when alleles are rare, as often happens for recent mutations
D' can be made more reliable by establishing a minimum threshold frequency for minor alleles, e.g., MAF ≥ 0.05; or MAF ≥ 0.10
We’ll introduce the measure D’ first because of historical precedence. The basic idea behind D’ is to use it as a relative measure of LD given the maximum theoretical value given observed allele frequencies. D’ ranges from 0 (no LD) to 1 (large LD). You might find it useful to think of D and D’ as the difference between counts and percentages: 10 sick students in a class of 300 isn’t too bad—it’s only ~3%; yet 10 sick students in a class of 15 (66%) is an epidemic!

13. Standardized measures for LD: r2
D is the covariance between alleles at different loci
Can consider r2 to be the square of the correlation coefficient
Note that r2 can only attain a value of 1 when allele frequencies at the two loci are the same
Like a correlation coefficient, r2 can be used to assess to what extent variation in one marker explains variation in a second
Both measures are often used, as D´ and r2 are sensitive to different factors (e.g., recombination, haplotype history, allele frequencies)
The second common measure we’ll introduce is r2. It shares similarities with D’ in that it also ranges from 0 to 1 (small to large). And yet it has different properties in some subtle and yet important ways. One distinction is that D’ will always be 1 if any gamete class (i.e., haplotype) is missing, whereas r2 will only equal 1 if allele frequencies for both loci are the same. The biological interpretation of this numerical fact takes some time to swallow. For those interested in comparing the approaches, we recommend the papers cited here.
Devlin and Risch.1995 13

14. LD in populations: Determining phase
LD metrics such as r2 or D' are based on counts or frequencies of gametes or haplotypes (e.g., PAB vs. PAb)
Diploid genotypes create challenges: When individuals are heterozygous for two loci, how do we know which alleles are associated?
In the following example, phase is unknown
Before we move on, we have to once again address a challenge that we have touched on before. The issue of linkage phase. It is necessary to know phase, or at least to be able to predict it with some confidence, in order to calculate LD. We can do this a few different ways. 14

15. Approaches for determining phase
Phase can be observed directly in haploids (best approach)
Single sperm
Conifer megagametophytes
Determine sequence (hence phase) using cloned DNA
Cloned fragments are copies of individual chromosomes
Larger clones yield more extensive information on phase
Statistically infer phase from population data
Determine haplotype frequencies from unambiguous genotypes, e.g., AB/AB; AB/Ab; Ab/Ab; aB/aB; etc
Use these estimates to infer haplotypes for ambiguous genotypes (AB/ab and Ab/aB)
Computer programs exist to make these calculations
For those of us that work with conifers, the simplest way to determine phase is to look at an array of seed megagametophytes. We have explained this unique biology enough by now that we need not pester you once again with it. Needless to say, it makes doing many things very easy. With the development of fast and inexpensive (relatively speaking) sequencing technology, it is certainly possible to determine phase from virtually any complex diploid organism. Finally, one can infer or predict phase based on existing frequency information as found in population data. 15

16. Statistical tests for LD
As with many such measures, statistical significance depends on sample sizes, allele frequencies, and strength of association. How can we assess the significance of LD?
LD between two loci with two alleles/locus
D Fisher’s exact test or
D' Likelihood ratio test
r 2
LD can also be calculated for loci with more than two alleles, for unknown linkage phase of double heterozygotes, and for samples of rare alleles, but that goes well beyond what we need to know here
Interestingly, the statistical significance of a given measure of LD is not determined by the measure itself but by relatively standard contingency tests, like Chi-square, or, in the case of small sample sizes, Fisher’s exact test. These are relatively straightforward and many programs exist to calculate them. A very nice, succinct review of statistical tests is provided in Gibson and Muse 2004 and later editions. 16

17. Biology of linkage disequilibrium
What does LD mean biologically?
What promotes LD
Linkage
Population admixture
Selection / epistasis
What affects LD
How is LD maintained?
How does LD change?
We have discussed LD conceptually and mathematically. Now let us give thought to the biological mechanisms that create, maintain or breakdown LD. LD must be viewed in a relative way, across time (generations) and genetic backgrounds (families or populations). Recall the figures in this slide and consider the two blue arrows. From a population perspective, the chromosome represented by the lower arrow appears to consist of many small chromosomal blocks, each with an array of genes in strong LD. Now take that same chromosome and imagine it representing one of a pair of chromosomes in a cross (as indicated by the upper arrow). Our perception of the chromosome in this world is that all genes are in LD. After one generation, and one cross over event, roughly half the chromosome is still in complete LD. At any one time LD exists at multiple levels, small blocks of which persist much longer than large ones. The distinction here is simply that between LD at the family level and LD at the population level. So, what factors promote LD? Certainly, proximity / linkage is the main cause. Population admixture will result in LD, even when two genes are far apart or on different chromosomes. Selection can both cause and maintain LD through epistasis, where certain allelic combinations are superior to others. Again, in such cases, the epistatic loci need not be tightly linked, or linked at all. Mating systems such as selfing or inbreeding will maintain LD. Consider that highly inbred lines exhibit virtually complete LD across the entire genome. And what leads to the breakdown of LD: again, this is primarily a function of crossing over events. Lets discuss some of these factors at greater length.
Modified from Cardon and Bell, 2001 17

18. LD and random mating
HWE and LD (or LE) both pertain to random (or non-random) associations of alleles and genotypes
HWE describes associations of alleles at the same locus
LD (or LE) measures associations of alleles at different loci
HW proportions are restored by one generation of random mating
However, once established, LD persists for some time, even in random mating populations
How quickly LD dissipates depends on several factors
Population geneticists like to view all evolutionary phenomena from a base case scenario that assumes certain conditions, one of them being random mating. It helps us explain and predict how things work. Take LD, or its alternative, linkage equilibrium, and the Hardy Weinberg Equilibrium. Both relate to the random associations of alleles at one or more loci. The HWE mathematicallydescribes the association of alleles at a single locus, or for that matter, at two or more loci, assuming they are independent of one another. LD actually measures that level of independence by gauging whether alleles at different loci are statistically associated. Assuming no evolutionary forces at play, HWE is reached in one generation of random mating, for loci that are not in LD. For those that are, many generations of random mating are necessary to approximate equilibrium. 18

19. Factors affecting the decay of LD
Recombination rate — describes how often linked loci tend to recombine
Closely linked loci rarely recombine
Selfing — decreases the frequency of double heterozygotes, which decreases the opportunity for creation of new recombinants
Small populations or population bottlenecks — mechanism is analogous to the reduction of heterozygosity in small populations, so double heterozygotes are also less common
Selection — can increase the frequency of certain haplotypes, counteracting LD decay from recombination
Selection favoring one or a few haplotypes (positive selection)
Selection favoring heterozygotes (or genotypic combinations in different environments, balancing selection)
These bullets should be self explanatory. When you are done, lets look at some graphical representation of these words. 19

20. Rate of LD decay driven by recombination (r)
The decay of linkage disequilibrium, as influenced by the recombination fraction (r), is described by the equation shown here. For unlinked loci, where r = 0.5, LD decays rapidly within a small number of generations. Though in some cases LD may never go completely to zero, it generally comes very close. For closely linked loci, such as shown for the other three cases here, the decay in LD is extremely slow. What about two loci that are located roughly 25 cM apart? Within 10 generation, D will be around 0.06.
Mackay & Powell TIPS 12: 57-63 20

21. Effect of mating system on LD decay
Bottlenecks or strong inbreeding will result in a significant loss of heterozygosity and consequently, the maintenance of very strong LD. If all the individuals in a population share almost all of the same alleles at every locus, then LD will virtually extend over the entire genome, or at the least linkage group. Individuals from another population of the same selfing species would likely have similarly high levels of LD, but the specific associations would more than likely be very different.
Jennifer Kling – Oregon State University

22. Average decay for LD in Pinus taeda
Conifers are primarily outcrossing and have large Ne
Therefore, LD decays rapidly
Figure shows average decay of LD over 19 candidate genes in loblolly pine (Pinus taeda)
LD decays to ~r2 = 0.2 within ~1500 bp
So what might we expect LD to actually be in a forest tree such as loblolly pine or Norway spruce? It has only been in the last few years (since or so) that we have had sufficient sequence information to really estimate the rate of LD decay. Our expectation was that LD would be relatively low for most of our outcrossing species that exist in large, nearly randomly mating populations. These expectations were largely met. Though considerable variation exists among loci, LD, as measured here by r2 , deteriorates rapidly over distances of hundreds to a few thousand base pairs. From a practical standpoint, markers needed to tag causal polymorphisms would have to be located within a very short distance of one another, say 100 bp.
Neale & Savolainen Tr Pl Sci 9: 22

23. Decay of LD in Eucalyptus
Rapid decay of intragenic linkage disequilibrium in the cinnamyl- alcoholdehydrogenase (cad) gene in two Eucalyptus species
In the largely outcrossing Eucalyptus hardwood species, E. grandis, and E. urophylla, LD appears to decay even faster than for loblolly pine. Of course, these data are for two loci only, and they may not reflect the situation of the genome as a whole. Why? One reason, as we shall see, is that the rate of recombination varies dramatically across the genome and within LGs. In fact, it appears that for many species, there are specific recombination hot spots and large areas where recombination is dramatically hindered. This was shown to be the case in poplar, the first tree to be fully sequenced, where large sections of 2 chromosomes exhibit virtually no recombination.
Grattapaglio FAO MAS, Chapt. 14 23

24. Extent of LD in various plants
The extent of LD, or the average size of LD blocks, varies widely among species. In general, LD decays more quickly for outcrossing species. In maize, LD varies widely among populations, being the most extensive in commercial inbreds. Note the extremely large ranges for significant level LD in most of the selfing species. Interestingly, LD range in humans is quite large. LD blocks of 60K to 250K bp are common, though differences in LD range exist among populations. For instance, LD block size is much lower in Nigerian populations than in populations from northern Europe. This latter point suggests relatively recent admixture events during the human diasporas.
Gupta et al Plant Mol Biol 57:

25. Tools for visualizing LD: Haploview
This cartoon illustrates a common tool for visually assessing LD among markers, often called an LD plot or an LD triangle plot. In this example, we zoom in on a small segment of a chromosome, which is a single gene characterized by SNPs in exons, introns, and other non-coding regions. The magnitude of LD can be assessed qualitatively by the intensity of the red color: bright red signifies high LD, pink less so, and white no LD. Estimates of pairwise LD are obtained by following diagonals to the their intersecting square. In some displays, the value of LD (r2, D’ etc) is shown within the boxes. Notice that two “blocks” are shown here, block 1 on the left and block 2 on the right. LD is high within blocks, but tends to break down between boxes, with some exceptions. How do we explain the continued LD between some of the block 1 and block 2 SNPs when LD seems to have broken down between SNP 5 and SNPs 1-4? Double crossover? In any event, the haploview tool is widely used and freely available on line at the URL noted here.
Christensen & Murray NEJM 356: 25

26. Recombination and demography shape haploblock structure
As suggested earlier, LD is shaped, in large part, by recombination, but other factors do play a role. In this figure, taken from Stumf and McVeen, haplotype blocks are illustrated as a function of recombination and demography.
In figure a Haplotype and/or linkage disequilibrium (LD) blocks are expected to depend on the sample populations. Generally, the larger the effective population size the smaller the blocks will be, because more recombination events will have occurred. It is well known that haplotype and/or LD blocks will arise by chance even if the recombination rate is uniform. However, if recombination hotspots such as shown in profile 1 of figure b are ubiquitous features of the genome, then some aspects of blocks will be transferable between populations, with details of the block pattern dependent on demography. If, however, recombination shows only mild levels of variation (profile 2) then blocks reflect past recombination events and only very old recombination events can result in block boundaries that are shared between populations. So, whether or not blocks offer a convincing description of genetic diversity depends on how the recombination rate varies along a stretch of DNA.
Stumpf & McVean Nat. Rev. Genet. 4:959

27. Recombination “hotspots” delineate haplotype boundaries in human populations
In the haploview slide shown previously, we viewed an LD plot at a rather restricted level. This diagram shows the extent of long-distance LD on chromosomes 2q (left) and 7q (right) for Chinese and Japanese populations from the human HapMap project. These diagrams make two important points
the distribution of LD is not uniform (which we saw earlier but on a larger scale). Red triangles show high LD within blocks (also called haplo-blocks) and low levels of LD among blocks.
Haploblocks are bounded by regions of higher rates of recombination, as indicated by peaks of recombination rates (shown below).
Such patterns tell us that recombination and LD are related, and that different portions of the human genome are more “blocky” than others.
Comparison of linkage disequilibrium and recombination for two ENCODE (Left: ENr131.2q37.1 and Right: ENm014.7q31.33). Shown here is the panel for the CHB+JPT populations (Asian; CHB are Han Chinese from Beijing, while JPT are Japanese from Tokyo). The LD triangle plots (upper) show LD qualitatively classified as strong (red), modest (pink), weak (blue) and little (white). Beneath the LD triangles, blue and green squares show specific recombination events. Recombination hotspots are depicted as red triangles. Peak heights corresponding to recombination rates correspond to locations of observed recombination.
Modified from HapMap Consortium Nature 437:

28. LD within and among nearby genes in P. taeda
Here we offer a slightly different haploview presentation for a relatively large section of a loblolly pine linkage group that contains three known genes. This view varies from the others in that LD is quantified above the diagonal by R squared and below the diagonal by a P value of significance. Though not shown, imagine that the basepair numbering shown on the Y axis also stretches across the X axis. The genes, shown here as c3h, 4cl and agpX, are characterized at the bottom of the figure by alternating pink and yellow bars reflecting introns and exons, with black lines denoting SNPs. Strength of LD is illustrated by color. A number of points are worth noting here. First, it appears that very little LD exists between genes, though the odd colored box is found indicating LD across many cM. Where do those odd-ball blocks come from? It could be an epistatic allelic interaction, or very possibly a very rare allele that gives a false impression of LD, merely by chance. The second point to make here is that even within genes LD can rapidly decline over short distances.
David Neale, U.C. Davis

29. Patterns of intra and interlocus LD for coastal Douglas-fir
Next we look at patterns of LD in another conifer, Douglas-fir. In the study reported here, 384 SNPs from 121 candidate genes for cold tolerance were studied. Figure A suggests, as we have seen before, that LD breaks down pretty quickly within loci, as indicated by this plot of LD decay across many genes. That is a picture of the average rate of decay. The lower figure (b) paints a different picture, however. This haploview of LD stretches across a rather large stretch (63.7 cM to be exact) of one linkage group. In this plot, solid lines delineate comparisons within and among candidate genes, with letters indicating placement of the candidate genes within the matrix. Clearly, interlocus LD is much higher here than observed in loblolly pine or Norway spruce. This may reflect a very low rate of recombination, though other factors such as selection, mutation rate variation, population structure and extreme bottlenecks can not be ruled out. The take home message here is simply that patterns of nucleotide diversity and LD are highly variable across the genome, within and among populations, and within and among species.
Eckert et al. 2009, Genetics 183:

30. Haplotype genealogy and LD
Colored circles are polymorphic sites (e.g., SNPs) located along haplotypes with evolutionary histories shown on the left
LD reflects mutational events bound by history
Areas of LD (circled) don't tell us about the presence or nature of selection
LD is reduced by recombination
Amount of reduction depends when recombination occurs relative to haplotype history
We conclude this module with a reference to gene genealogies, as introduced in module 7. We extend the concept to haplotype genealogies and use it to trace how history shapes LD. Mutational events near to one another share common evolutionary fates unless broken apart by recombination. The patterns of LD seen today reflect literally thousands of years of history, influenced by the rate of mutation and recombination, the strength and direction of selection, demographic events such as population admixture and bottlenecks, and so forth. As we garner more sequence for more species and more individuals within species, more of the evolutionary history of organisms will be revealed.
Modified from Bamshad & Wooding Nat Rev Gen 4:99-111

31. References cited in this module
Bamshad , M. and S. Wooding Signatures of natural selection in the human genome. Nature Reviews Genetics 4:99-111
Cardon, L. and J. Bell Association study designs for complex diseases Nature Reviews Genetics 2: 91-99
Christensen, K and J. Murray What genome-wide associaton studies can do for medicine. New England Journal of Medicine 356(11):
Devlin, B and N. Risch A comparison of linkage disequilibrium measures for fine scale mapping. Genomics 29:
Eckert A, J. Wegrzyn et al Multilocus Patterns of Nucleotide Diversity and Divergence Reveal Positive Selection at Candidate Genes Related to Cold Hardiness in Coastal Douglas Fir (Pseudotsuga menziesii var. menziesii) Genetics 183:

32. References cited in this module
Gibson, G and S. Muse A primer of genome science. Sinauer Associates, Sunderland, MA
Grattapaglia, D Marker – assisted selection in Eucalyptus. In. Marker assisted selection: current status and future perspectives in crops, livestock, forestry and fish. (Eds) Guimaraes, Ruane, Schert, Sonnino, and Dargie. FAO:
Gupta, P., R. Rustgi et al Linkage disequilibrium and association studies in higher plants: present status and future prospects. Plant Molecular Biology 57: (4):
HapMap Consortium Nature 437:
Mackay ,I. and W. Powell Methods for linkage disequilibrium mapping in crops. Trends In Plant Science 12: 57-63
Stumpf , M. and G. McVean Estimating recombination rates from populaltion- genetic data. Nature Reviews Genetics. 4:

33. Thank You. Conifer Translational Genomics Network
Coordinated Agricultural Project