SEARCH

SEARCH BY CITATION

Keywords:

  • antagonistic pleiotropy;
  • constraint;
  • genetic correlation;
  • linkage;
  • trade-off

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Predicting the genetic correlation from QTL effects
  5. Literature survey — methods
  6. Literature survey — results
  7. Antagonistic QTL and negative correlations
  8. Linkage disequilibrium and pleiotropy
  9. Discussion and summary
  10. Acknowledgements
  11. References

We review genetic correlations among quantitative traits in light of their underlying quantitative trait loci (QTL). We derive an expectation of genetic correlation from the effects of underlying loci and test whether published genetic correlations can be explained by the QTL underlying the traits. While genetically correlated traits shared more QTL (33%) on average than uncorrelated traits (11%), the actual number of shared QTL shared was small. QTL usually predicted the sign of the correlation with good accuracy, but the quantitative prediction was poor. Approximately 25% of trait pairs in the data set had at least one QTL with antagonistic effects. Yet a significant minority (20%) of such trait pairs have net positive genetic correlations due to such antagonistic QTL ‘hidden’ within positive genetic correlations. We review the evidence on whether shared QTL represent single pleiotropic loci or closely linked monotropic genes, and argue that strict pleiotropy can be viewed as one end of a continuum of recombination rates where r = 0. QTL studies of genetic correlation will likely be insufficient to predict evolutionary trajectories over long time spans in large panmictic populations, but will provide important insights into the trade-offs involved in population and species divergence.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Predicting the genetic correlation from QTL effects
  5. Literature survey — methods
  6. Literature survey — results
  7. Antagonistic QTL and negative correlations
  8. Linkage disequilibrium and pleiotropy
  9. Discussion and summary
  10. Acknowledgements
  11. References

The evolutionary change in response to selection depends on the additive genetic variance. Extending to multivariate phenotypes, response to selection depends on both the genetic variance of single traits, and the genetic correlations among them. Genetic correlations among traits have the effect of preventing the correlated traits from independently responding to natural selection. Selection on one trait will produce a response in all of the correlated traits (Lande & Arnold 1983; Arnold 1992; Schluter 1996; Jones et al. 2004), and selection acting in opposite directions on two correlated traits may tend to cancel out, such that with balanced selective forces, the net result is little or no change (Jones et al. 2004). Thus, by limiting the number of trait combinations which can occur, genetic correlations tend to constrain the evolution of multitrait phenotypes (Arnold 1992; Schluter 1996; McGuigan 2006).

Genetic variance has been well studied, and estimates of additive genetic variance (or its standardized version, heritability) have been made for a large number of domestic and wild species (see reviews in Mousseau & Roff 1987; Roff 1997). Over the last 15 years, it has become possible to identify the specific chromosomal regions [quantitative trait loci (QTL)] (see ), that contribute additive genetic variance in continuously varying traits (Tanksley 1993; Mackay 2001; Erickson et al. 2004). Several reviewers have compared the observed genetic variance of traits with the QTL results (Roff 1997; Lynch & Walsh 1998). The general observation is that a large portion of the genetic variance can be accounted for by detected QTL. For example, Lynch & Walsh (1998) showed that of 222 traits studied in inbred line crosses, detected QTL could explain 20% or more of the variance in 80% of the cases. Such observations must be treated cautiously, however, because there can be considerable bias which tends to overestimate the effect of detected QTL (Beavis 1998).

More recently, there has been an increasing number of studies which seek to measure genetic covariances (Shaw 1991; Roff 2000) and compare them among populations (Brodie 1992; Mitchell-Olds 1996; Service 2000), environments (Donohue & Schmitt 1999; Conner et al. 2003) and species (Steppan 1997; Begin & Roff 2003; see Steppan et al. 2002 for review). Genetic covariances can be notoriously difficult to measure accurately, and standard errors on the estimates are typically large (for a discussion of the issues involved in comparing G-matrices, see e.g. Shaw 1991; Houle et al. 2002; Roff 2002a). Nevertheless, a general agreement has emerged that while genetic correlations clearly influence evolutionary trajectories in the short term, G-matrices can themselves evolve. Focus has now turned to how that evolution occurs, and this will be strongly influenced by the underlying mechanism of the correlations.

To our knowledge, however, there has not been any attempt to trace the genetic covariance to its underlying QTL in the same manner as for genetic variances. It therefore seems useful to ask whether the same QTL tend to contribute variation to genetically correlated traits. The first goal of our review is thus primarily descriptive. We survey the QTL literature to ask how much of the genetic correlation between pairs of traits can be accounted for by common QTL. We develop a simple extension of the theory relating allelic variance to trait variance to predict the covariance, and hence correlation expected in a trait pair with a given set of underlying QTL. We then compare these predictions to empirical correlation estimates, assessing the outcome for qualitative fit (sign of the correlation), precision, accuracy, and bias.

Our second goal follows from the sign of the covariance, and the genetic underpinnings of constraint. Negative covariances are typically interpreted as a constraint on the response to selection, in that a negative covariance prevents both traits from increasing. However, it has been pointed out that such trade-offs can be masked within a positive covariance, if traits reflect a combination of genes affecting resource acquisition (positive pleiotropy) and allocation (negative pleiotropy) (Houle 1991; De Jong 1993; Fry 1996; Worley et al. 2003; Bjorklund 2004). This is an important caveat. It implies that constraints may occur through allocational trade-offs, even as positive correlations are generated by variation in the acquisition of resources. QTL results may have much to contribute to documenting this pattern of pleiotropy. We therefore examine the QTL results for cases where QTL contributing to negative correlation are masked by others contributing positive correlation.

We must explicitly recognize at the outset, however, that genetic correlation can result either from pleiotropy, where the same locus or loci have effects on two or more separate traits, or from linkage disequilibrium between separate loci, each of which affects a single trait (Falconer & MacKay 1996; Lynch & Walsh 1998). QTL studies cannot entirely distinguish linkage from pleiotropy, because of the relatively low resolution of QTL position (typically ≥ 10 cm, Mackay 2001). Thus a QTL affecting two traits may represent a single pleiotropic locus, or two single-trait loci in close linkage. This distinction has an important evolutionary implication, in that, to the extent that linkage disequilibrium decays with successive rounds of random mating, the correlation between traits will degrade, opening up new multitrait combinations on which selection can act. Linkage disequilibrium is thus seen as a weaker constraint on evolution than pleiotropy. We will review studies which have tried to distinguish between pleiotropy and linkage disequilibrium as they relate to the interpretation of QTL studies, and highlight those factors which affect the level of evolutionary constraint.

Predicting the genetic correlation from QTL effects

  1. Top of page
  2. Abstract
  3. Introduction
  4. Predicting the genetic correlation from QTL effects
  5. Literature survey — methods
  6. Literature survey — results
  7. Antagonistic QTL and negative correlations
  8. Linkage disequilibrium and pleiotropy
  9. Discussion and summary
  10. Acknowledgements
  11. References

To determine whether shared QTL are sufficient to explain the measured correlation between two traits, we need to predict how much correlation would be expected if the identified QTL were the only loci underlying the traits. Using allelic effects at a locus, a (defined as half the difference of trait value between the homozygotes), Falconer & MacKay (1996) showed that the additive genetic variance expected in a trait, Z, is found by summing the squared allelic effects (deviations) across all loci:

  • image((eqn 1))

where p and q are allele frequencies. By extension, we can calculate the expected additive covariance between traits Z1 and Z2 by taking the cross products of the allelic effects and summing across all loci:

  • image( (eqn 2))

where ai(Z1) is the additive effect of locus i on trait Z1. From here it is straightforward to calculate the genetic correlation expected if shared QTL fully account for the genetic correlation:

  • image( (eqn 3))

Two linked loci, each affecting a different trait, will contribute to the covariance of traits as:

  • image((eqn 4))

where the summation is over all pairs of loci affecting the traits separately, and Djk is the linkage disequilibrium and determines what fraction of the allelic covariance contributes to the overall trait covariance (note that Djk depends not only on the recombination distance between loci, but also on the crossing scheme imposed in the QTL study; see ). This allows more of the additive covariation in a trait to be explained, so that the total covariance expected through both linkage and pleiotropy is:

  • image( (eqn 5))

where the first term is the covariance due to pleiotropy following equation 2, and the second term is that due to linkage disequilibrium. While this equation permits a relatively simple inclusion of linked QTL in the calculation of rQ, many studies do not report the data necessary to calculate Djk. Therefore, we restrict our analysis here to the assumption of pleiotropic effects using equation 3.

In the above, we assume that all loci have purely additive effects on each trait, although dominance effects may also influence multiple traits. The dominance covariance can be included in the covariance calculation above by adding terms ∑(2piqidi)2 to equation 1 and ∑2piqidi(Z1) ⋅ 2piqidi(Z1) to equations 2 and 4. However, most of the studies we review below are based on doubled haploid or recombinant inbred line mapping populations, in which heterozygotes are absent, and thus dominance effects will be zero. While variance and covariance will be increased in inbred mapping populations (Lynch & Walsh 1998), the effects cancel in the numerator and denominator of equation 3.

Literature survey — methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Predicting the genetic correlation from QTL effects
  5. Literature survey — methods
  6. Literature survey — results
  7. Antagonistic QTL and negative correlations
  8. Linkage disequilibrium and pleiotropy
  9. Discussion and summary
  10. Acknowledgements
  11. References

To empirically assess the correspondence between shared QTL and genetic correlations requires studies that report both the QTL architecture of individual quantitative traits and genetic correlation between pairs of such traits. We searched for such studies in five genetics and applied genetics journals (Genetics, Theoretical and Applied Genetics, Crop Science, Genome, and Heredity) between 1994 and the spring of 2003. We included only those studies that reported QTL magnitude as the additive effect (a) of alleles. Numerous studies reported instead the proportion of variance explained by individual QTL, but these were excluded because they do not permit calculation of rQ.

Most studies meeting these criteria involved important agronomic crop species or model species, such as Arabidopsis, because organisms of this type are highly amenable to inbred line experimental designs, which are easier than other crossing designs (e.g. F2, backcross) to analyse for both QTL and genetic correlation estimates. However, a few studies involving model zoological systems, such as Drosophila, met the above criteria and were included. In a few studies, trait expression in different years or environments, were treated as separate correlated traits. In order to prevent bias in these cases, data for only one year/environment was included.

In total, 238 traits across 27 studies were included in the data set (Table 1), giving 1120 trait pairs which had rG and rQ values available for comparison. Studies, ranged from less than five trait pairs to 300 trait pairs (Table 1). Some studies did not report correlations for all pairs of traits. Within each study, we recorded the reported genetic correlation estimate (rG) (and the statistical significance of this estimate) for each pair of traits; and the position and effect of all QTL. While many studies reported point estimates of rG separately from significance tests, others simply reported ‘NS’ for nonsignificant rG. Although it is unlikely that all nonsignificant correlation estimates are indeed zero, we treated all nonsignificant rG as zero, to keep data analysis uniform across studies.

Table 1.  Studies reporting both genetic correlations and QTL architecture among traits. Studies are ordered by total number of traits examined. P values refer to the result of the Mantel test of association between rQ and rG. Cross design: RIL, recombinant inbred line. QTL method: IM, interval mapping; CIM, composite interval mapping; JCIM, joint trait composite interval mapping; MMIM, mixed model interval mapping. Correlation method: LM, correlation of line means; VC, variance component method of Lynch & Walsh (1998); SE, ‘subtract the environmental covariance’ method, in which environmental covariance is estimated in the F1 and subtracted from the phenotypic covariance in the F2 (e.g. Fishman et al. 2002)
 Cross designQTL methodCorrelation methodNo. of traitsPReferences
  • *

    two mapping populations in one study;

  • correlations of line means not explicitly stated as ‘correlation among lines’.

Capsicum annuumF3IMLM260.001Ben Chaim et al.(2001)
Lycopersicon spp.RILCIMLM260.001Saliba-Columbani et al. (2001)
Hordeum vulgareRILCIMLM140.001Mesfin et al.(2003)
Arabidopsis thalianaRILCIMVC140.001Ungerer et al. (2002)*
Arabidopsis thalianaRILCIMVC140.001Ungerer et al. (2002)*
Arabidopsis thalianaRILIMVC110.048Mitchell-Olds & Pedersen (1998)
Oryza sativaRILMMIMLM100.001Cui et al. (2002)
Drosophila melanogasterRILJCIMLM100.0002Vieira et al. (2000)
Arabidopsis thalianaRILCIMVC 80.001Juenger et al. (2000)
Zea maysF3IMLM 80.002Veldbloom & Lee (1996a)
Oryza sativaDHIMVC 80.002Yan et al. (1999)
Avena sativaRILCIMLM 80.005Zhu & Kaeppler (2003)
Mimulus guttatusF2JCIMSE 70.006Fishman et al. (2002)
Helianthus annuusRILCIMVC 70.005Herve et al. (2001)
Oryza sativaRILCIMLM 70.002Tan et al. (2001)
Hordeum vulgareDHCIMLM 70.001Tinker et al. (1996)
Lycopersicon pimpinellifoliumF2IMSE 60.181Georgiady et al. (2002)
Oryza sativaRILMMIMLM 60.154Zhuang et al. (2002)
Zea maysRILCIMLM 50.009Austin & Lee (1998)
Triticum aestivumRILCIMLM 50.445Kato et al. (2000)
Zea maysF3CIMVC 50.01Lubberstedt et al. (1997)
Zea maysF3IMLM 50.008Veldbloom & Lee (1996b)
Zea spp.F3CIMLM 40.153Bohn et al. (1996)
Avena sativaRILCIMLM 40.481Groh et al. (2001)
Triticum aestivumRILCIMLM 3naIgrejas et al. (2002)
Oryza spp.RILMMIMLM 3naKamoshita et al. (2002)
Oryza spp.DHJCIMLM 3naZhou et al. (2001)

For each trait pair, we determined the raw number of shared QTL, and total number of QTL (across both traits). Since there is no consensus that we are aware of as to the description of a shared QTL, we defined QTL that have overlapping 95% confidence intervals (on their chromosomal position) as mapping to the ‘same’ position. The 95% confidence intervals reported by the authors were used when given. Most studies reported confidence intervals estimated by bootstrapping or by either the one or two LOD support interval method (Doerge et al. 1997; Lynch & Walsh 1998). Both methods have been shown to give a similar result of a somewhat conservative (i.e. wide) confidence region (Doerge 1997). In instances where there were no confidence intervals given for the position of a QTL, we applied an arbitrary 10 centiMorgan (cM) confidence interval centred on the reported point estimate of QTL position. The average reported confidence interval around a QTL position estimate was 15.6 cm (based on > 200 identified QTL), making our choice of 10 cm somewhat conservative in the chance of confidence limits overlapping.

To measure the proportion of QTL shared between traits, while taking into account the total number of QTL detected for both traits, we modified a similarity index originally proposed to compare DNA sequences (Nei & Li 1979). The proportion of shared QTL (PSQ) is:

  • image

The resulting scale is standardized between zero (each trait influenced by a completely separate set of QTL) and one (all QTL affecting either of the traits affects both) and allows for straightforward comparisons across multiple trait pairs.

Qualitatively, we asked how often significantly correlated traits (rG ≠ 0) had shared QTL, and whether rG and rQ had the same sign. Quantitatively, we measured the correlation between rG and rQ as a measure of precision. In addition, we used major axis regression of rG on rQ (Sokal & Rohlf 1995) to determine the slope of the linear relationship between the correlation estimates. We also used the difference between rG and rQ as a measure of estimation accuracy to determine if there is any bias between the biometric and QTL observations, with rG – rQ = 0 the expectation under no bias.

We used Mantel tests to assess the significance of the correlation between rG and rQ matrices. A separate Mantel test was carried out for each study that reported complete rQ and rG correlation matrices. These were compared both using the raw correlation estimates as well as correlation values transformed via Fisher's Z transformation (Sokal & Rohlf 1995). Only the results from the use of the raw correlation are reported, as use of the transformed values did not change the outcome of any analyses. The sampling distributions of the Mantel test statistic (Z) for each study were derived from 9999 matrix randomizations using the program mantel (Liedloff 1999). The P values from each test were then combined across studies, following Sokal & Rohlf (1995), to give an overall level of significance to the test of association between rQ and rG.

Literature survey — results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Predicting the genetic correlation from QTL effects
  5. Literature survey — methods
  6. Literature survey — results
  7. Antagonistic QTL and negative correlations
  8. Linkage disequilibrium and pleiotropy
  9. Discussion and summary
  10. Acknowledgements
  11. References

Qualitative patterns

Across all significantly correlated trait pairs, the mean of the absolute values of rG was 0.46. This is comparable to the overall genetic correlation estimate across traits (~0.48) reported by Roff (1996) in a survey of approximately 1800 genetic correlation estimates. Seventy per cent of correlated trait pairs had identified shared QTL, in contrast with only 30% of uncorrelated pairs (Fig. 1), in spite of QTL being found for each of those traits individually (Table 2). The correlated trait pairs share significantly higher proportion of their QTL (higher PSQ) than uncorrelated traits (t-test, t = 13.7, d.f. = 1107, P < 0.0001) with 34% of QTL shared between correlated traits vs. 14% between uncorrelated traits (Table 2). However, the raw number of shared QTL is relatively low, with two QTL shared between the average correlated trait pair (median 1). While small, this number of QTL is larger than that for uncorrelated trait pairs which on average shared less than one (0.88) QTL (median 0). Likewise, correlated traits had significantly larger values of rQ (t-test, t = 16.0, d.f. = 1107, P < 0.0001) than uncorrelated traits (Table 2).

image

Figure 1. Distribution of genetic correlation estimates (rG and rQ), and shared QTL across trait pairs by significance of the biometrical genetic correlation, rG.

Download figure to PowerPoint

Table 2.  Comparison of the genetic basis of significantly correlated trait pairs versus uncorrelated trait pairs. Absolute values of rG and rQ are reported so that positive and negative values would not cancel to means of zero. PSQ, proportion of shared QTL.
 Correlated traits mean (SD)MedianUncorrelated traits mean (SD)Median
  • *

    All uncorrelated traits were assigned rG = 0 (see text).

|rG|0.46 (0.23)0.400.000.00*
|rQ|0.33 (0.30)0.310.10 (0.19)0.00
No. of shared QTL2.01 (4.05)1.000.86 (3.21)0.00
Total QTL8.69 (8.07)7.006.51 (6.29)5.00
PSQ0.34 (0.29)0.330.14 (0.23)0.00

There is good qualitative agreement between rG and rQ. Across all 1120 trait pairs, 67.6% (N = 757) had rG and rQ of the same sign (Table 3). This includes a large number of trait pairs (for which both rQ and rG were zero. The majority of the remaining trait pairs (30.3%) consisted of cases where a nonzero rG was paired with a zero rQ (N = 132); or a nonzero rQ with a zero rG (N = 207). These two results are likely attributable to lack of power to detect QTL, or to detect correlations. In only 24 cases (2.1%) were rG and rQ of opposite signs.

Table 3.  Number of trait pairs falling into each category grouped by the sign of rG and rQ. Mean number and proportion (PSQ) of shared QTL in each category is also given
 rQTotal
NegativeZeroPositive
rGPositiveN = 15 PSQ:0.44 Shared QTL:4.10N = 133 PSQ:0 Shared QTL:0N = 318 PSQ:0.51 Shared QTL:3.35 466
ZeroN = 60 PSQ:0.40 Shared QTL:2.67N = 272 PSQ:0 Shared QTL:0N = 72 PSQ:0.44 Shared QTL:2.55 404
NegativeN = 167 PSQ:0.41 Shared QTL:1.76N = 74 PSQ:0 Shared QTL:0N = 9 PSQ:0.61 Shared QTL:4.33 250
Total2424793991120

Quantitative patterns

There was a moderate linear correlation of 0.711 (Pearson product moment, N = 1120, P < 0.0001) between the rQ and rG estimates taken across all trait pairs (Fig. 2). The nonparametric Spearman rank correlation was 0.718 (N = 1120, P < 0.0001). For most studies, Mantel tests revealed significant associations between the rQ and rG estimates (Table 1). The only studies that failed to reject the null hypothesis, of no association, were those that had only a few (< 5) traits and thus only a small number of possible random permutations of the data in the Mantel test. The combined P values across all Mantel tests show a highly significant association (χ2 = 242.68, d.f. = 42, P < 0.00001) between the rG and rQ matrices. Of course, much of the overall correlation is driven by the qualitative agreement of sign of rG and rQ (Table 3).

image

Figure 2. Scatter plot of rG vs. rQ. Lines correspond to the slope of the major axis (type II regression slope) of variation in the quadrants where both rG and rQ are positive (b = 1.03) and where both rG and rQ are negative (b = 0.73). Each data point represents one trait pair.

Download figure to PowerPoint

Where rQ and rG are both positive, rQ explains approximately one-quarter of the variation in rG. Major axis regression (type II) of rG on rQ yielded a slope not different from 1.00, indicating a relatively even spread of points around the line of unity (Fig. 2). However, the mean difference between rG and rQ was positive, and significantly different from zero (rG – rQ = 0.062, P = 0.001) indicating there was a tendency for rQ to underestimate the magnitude of rG. Trait pairs that shared a greater proportion of their QTL were generally more strongly correlated (higher rG Fig. 3a); however, the bias between rG and rQ was not affected by the proportion of shared QTL (Fig. 3).

image

Figure 3. Observed rG and bias (rG – rQ) plotted against the proportion of QTL shared between traits. Plots are shown separately for positive (top two panes) and negative quadrants (lower two panes) (see Fig. 2).

Download figure to PowerPoint

A similar result was found in the negative quadrant (rG and rQ both negative) of Fig. 2, with variation in rQ estimates explaining approximately 19% of the variation in rG estimates (r2 = 0.189, N = 167). Interestingly the slope of the major axis regression for these data was significantly less than one (0.727). The mean, difference between rG and rQ was again positive, and significantly different from zero (mean difference rG – rQ = 0.034, P = 0.044). Note that when both rG and rQ are negative, a positive difference means rG is less negative than rQ, indicating a slight tendency for rQ to overestimate the strength of the genetic correlation for negatively correlated trait pairs, especially for high rQ (Fig. 2). Surprisingly, the bias between rG and rQ increased with a higher proportion of shared QTL (Fig. 3).

Limitations of the survey

The observed scatter around the regression line results from the input of error from several sources. The most obvious error stems from the fact that both rG and rQ will themselves be estimated with considerable error. Roff (1996) pointed out that genetic correlations have large confidence intervals at best. In addition, the large numbers of zero rG and rQ estimates are likewise candidates for error. Some of the time, these two situations actually reflect the genetic independence of the traits; however, in many cases they reflect the lack of statistical power to detect associations. In practice, most of the zero rG estimates would probably fall in the two gaps on either side of zero (Fig. 1) making the rG distribution approximately normal in shape. Similarly, a zero estimate of rQ may reflect either the absence of shared QTL or the inability to detect QTL. The sheer number of zero rQ estimates (N = 479) is perhaps a good indicator of the inherent difficulty in finding QTL for a single trait, let alone finding QTL for more than one trait that map to the same position.

Furthermore, estimation bias in the detection of QTL, and the estimation of their effects, is a key problem in QTL mapping (Beavis 1998). Bias in the detection of QTL arises due to limitations in statistical power to detect significant marker–trait associations and is essentially an issue of sample size (Orr 2001). In most cases, only the QTL of moderate-to-large effect are detected, leaving an unknown number of small-effect loci undetected and thus out of the analysis [see Otto & Jones (2000) for a method to infer the presence of such loci].

Our survey has of necessity been dominated by domesticated and model systems of plants, since these are the organisms in which it is easiest both to measure genetic correlations and to map QTL in the same cross. It is not immediately clear whether or not these will present a bias relative to wild populations of nonmodel systems. It has been noted that domestication tends to select for an increase in the recombination rate, as a by-product of selection for novel adaptations (Otto & LeNormand 2002), so we might expect linkage disequilibrium to be less pronounced in domestic species than in wild populations. That is, we might expect the degree of QTL overlap to be greater in wild species, and domestic species did exhibit lower PSQ on average than model or wild. However, domestic species tended to have higher rQ for the same value of rG than model or wild species (not shown), and this likely reflects the greater research effort (and therefore statistical power to detect QTL) that typically goes into domestic species.

Detailed study of patterns among different classes of traits (morphology, life history, etc.) is beyond the scope of this study. The number of categories of trait pair increases as the square of the number of trait categories, and consequently, the number of observations per category decreases. An approximate classification suggested that morphological traits had higher correlations than life history or physiological/biochemical traits (not shown), which is approximately concordant with the typically greater heritability of morphological traits. Correlations between traits in different classes tended (weakly) to be lower than between traits of the same category. This may reflect different genetic bases of different categories of trait, but this should be interpreted cautiously because many studies tended to focus on one category of trait. By the same reasoning, differences among studies using different mapping populations (F2, RIL, etc.) were small and may reflect differences among studies more than the differences among cross types.

Antagonistic QTL and negative correlations

  1. Top of page
  2. Abstract
  3. Introduction
  4. Predicting the genetic correlation from QTL effects
  5. Literature survey — methods
  6. Literature survey — results
  7. Antagonistic QTL and negative correlations
  8. Linkage disequilibrium and pleiotropy
  9. Discussion and summary
  10. Acknowledgements
  11. References

Trade-offs are an important form of constraint in which resources are allocated between competing demands, constraining the ability of selection to increase two traits when both are favoured individually. Trade-offs between fitness components are the most widely studied and form the basis of life-history theory (Roff 2002b). Trade-offs may be expected to manifest themselves in negative genetic correlations between traits, but documenting such negative genetic correlations has been difficult (Fry 1996). Indeed, some authors have questioned the relevance of negative genetic correlations to evolutionary constraint (Fry 1993), noting that theory of fitness trade-offs does not preclude the presence of genotypes with low values of both traits. The presence of such individuals would tend to induce positive correlations, at least until eliminated from the population by natural selection. Rather, theory posits that trade-offs will prevent the same genotype from having high values of both traits, and it is the absence of individuals with high values of both traits (Mackenzie 1996) that creates the constraint. Thus, trade-offs may be masked within trait pairs that are positively correlated.

Houle (1991) proposed a mechanism underlying this masking of negative genetic correlations by noting that an allocational trade-off involves two processes: the acquisition of resources, and the allocation of resources among the competing demands. Loci which affect the first process induce a positive correlation among traits, since alleles that increase resource acquisition will tend to increase all traits pleiotropically. Loci affecting the allocation of the resources among demands will be antagonistically pleiotropic, and induce negative correlations among the traits. If the effects of the former outweigh effects of the latter, trade-offs will be masked within positive genetic correlations. (Houle 1991; De Jong & Van Noordwijk 1992.)

Our literature review allows us to investigate this possibility empirically. Although we have made no effort here to predict or measure the direction of natural selection on the traits, we treat any locus with opposite effects on two traits as a proxy for trade-offs, since a trade-off must result from at least one antagonistic QTL. We therefore identified all instances where there was at least one shared QTL that had antagonistic effects on two traits (ignoring the question of whether the QTL is strictly pleiotropic; see below). Out of the 1120 trait pairs, there were 276 cases (~25%) where at least one antagonistic QTL was identified.

We divided these trait pairs into three groups based upon the reported value of rG (rG < 0, rG = 0 and rG > 0). The majority of the cases (177) led to a net negative biometrical genetic correlation (Table 4). In many fewer cases, there was no correlation (45) or a net positive correlation (54) between the traits. Thus, approximately one-third of the trait pairs exhibiting antagonistic QTL failed to show a negative genetic correlation. Surprisingly, these positively correlated trait pairs differed from the negatively correlated pairs not by having fewer antagonistic QTL, but rather in having more parallel-effect QTL in their genetic architecture. Most trait pairs with antagonistic QTL had only 1–2 such loci, regardless of the biometric correlation (Table 4). However, for the negatively correlated trait pairs, this represented nearly 90% of the total shared QTL (~1.5). Those trait pairs that were positively correlated in spite of having an antagonistic QTL have over twice as many total shared QTL (~3.5) as the negatively correlated traits, and thus the antagonistic QTL represent less than half of the shared QTL. Zero correlations were intermediate, typically resulting from a single antagonistic QTL, representing two-thirds of the total (Table 4).

Table 4.  Genetic architecture of the subset of trait pairs that have at least one antagonistic QTL. Trait pairs are grouped by the sign of the biometric estimate of genetic correlation, rG. Mean values (and standard deviations) are given for the genetic correlations, numbers of shared and antagonistic QTL and proportion of shared QTL (PSQ) in each category
Sign of correlationNo. of pairsrQrGNo. of antagonistic QTLNo of shared QTLTotal QTLPSQ
NegativeN = 177–0.405 (0.237)–0.361 (0.179)1.36 (0.634)1.51 (0.782) 8.23 (3.50)0.395 (0.168)
ZeroN = 45–0.197 (0.132) 01.02 (0.388)1.48 (0.661) 7.60 (3.16)0.413 (0.160)
PositiveN = 54 0.020 (0.395) 0.310 (0.222)1.48 (0.966)3.52 (3.78)12.55 (8.13)0.509 (0.190)

Therefore, antagonistic QTL seem to have been swamped by parallel-effect QTL in these cases as suggested by Houle (1991) and others. Indeed, it appears to be the number of positive QTL that determines the sign of the correlation rather than the number of antagonistic QTL. For example, in the study of QTL affecting tomato fruit characteristics, Saliba-Colombani et al. (2001) documented one QTL on chromosome 9 with parallel effects on the concentrations of two of the aromatic secondary compounds, 3-(Methylthio)-propanol and eugenol. A second QTL on chromosome 2 has antagonistic effects on the two chemicals. Such a pattern would be consistent with the locus on chromosome 9 affecting the total pool of carbon allocated to secondary chemistry, while the locus on chromosome 2 allocates that pool between competing synthetic pathways.

This pattern may shed some light on the source of bias between rG and rQ. The general tendency is for correlations to be more positive than expected from the underlying QTL (Fig. 2). Intriguingly, the bias decreased with detection of additional pleiotropic QTL for positive correlations (Fig. 3), but increased with additional pleiotropic QTL for negative correlations. In other words, as more loci are detected, it seems that these loci tend to create positive correlations. If we assume that detecting more QTL implies detecting QTL of smaller effect, then it appears that the smaller-effect loci tend to contribute positive correlation through parallel effects on pairs of traits. One important source of error in QTL studies is the inability to detect QTL of small effect, combined with a tendency to overestimate the effect of those QTL that are detected, and this is no doubt a source of the scatter in Fig. 2. If these undetected loci tend to contribute positive trait covariance, they may pull rG towards more positive values.

Linkage disequilibrium and pleiotropy

  1. Top of page
  2. Abstract
  3. Introduction
  4. Predicting the genetic correlation from QTL effects
  5. Literature survey — methods
  6. Literature survey — results
  7. Antagonistic QTL and negative correlations
  8. Linkage disequilibrium and pleiotropy
  9. Discussion and summary
  10. Acknowledgements
  11. References

The most serious criticism of QTL studies in the context of genetic correlations is that multiple, closely linked loci will appear as a single QTL (Lynch & Walsh 1998). Thus, we cannot distinguish between pleiotropic single loci, and separate, but linked loci. We have operationally treated QTL with overlapping confidence limits as a single pleiotropic gene, although this will undoubtedly include many pairs of loci which are closely linked but distinct. We justify this decision primarily because the data reported in the literature force this approach. Many studies do not report position estimates for the QTL position, presenting instead only the confidence limits. Position estimates are necessary to determine the distance between neighbouring QTL and so to incorporate Djk into the calculation of rQ (equation 5). On the other hand, the precision of QTL position estimates is inherently low, and Djk would inevitably be estimated with considerable error. The caution in displaying QTL position is well justified by the inherent limitations of the technique.

Whether shared QTL represent single pleiotropic loci, or separate linked loci, not surprisingly, seems to vary between traits, loci and study organisms. McKay et al. (2003) provided good evidence to suggest that shared QTL underlying flowering time and water-use efficiency in Arabidopsis, appear to represent truly pleiotropic genes. They demonstrated that candidate genes underlying the QTL for each trait showed allelic variation that affected both traits in the direction of the correlation. Moreover, they induced specific mutations in these loci and documented pleiotropic effects of those mutations on the two traits. Similarly, Camara & Pigliucci (1999) induced mutations broadly throughout the Arabidopsis genome. Several traits were ‘decoupled’ by the new mutations, which presumably occurred in loci with effects on only a single trait. However, certain trait pairs, notably flowering time and number of rosette leaves remained correlated despite the mutation treatment, indicating pleiotropic underlying loci (Camara et al. 2000).

On the other hand, fine-scale mapping in Drosophila, has resolved several QTL into separate loci, often into separate mutations within the same gene. For example, Stam & Laurie (1996) showed that ADH activity traced to three separate polymorphisms within ADH. De Luca et al. (2003) showed a similar dissection of Dopa-decarboxylase effects on longevity into multiple polymorphisms within the gene. In both of these cases, the polymorphisms interact epistatically within the gene to create the total effect on the trait (perhaps not surprisingly, since the gene must presumably function as an integrated unit). While most such examples dissect QTL effects on single traits, a few suggest separate polymorphisms for separate traits. Long et al. (2000) found that separate polymorphisms within the Delta gene of Drosophila affect abdominal vs. stenopleural bristle number separately. Similarly, Fanara et al. (2002) dissected a QTL for olfactory behaviour into separate loci affecting male vs. female behaviour, which can be viewed as separate traits. Thus, a shared QTL can clearly contain separate linked loci.

The question of interest in many applications is the strength of the constraint imposed by such loci. A conceptual way forward is suggested by recognizing that a pleiotropic locus can be treated theoretically as two loci with zero recombination. Using this formulation, the first term of equation 5 is absorbed into the second, and equation 5 reduces to equation 4. In this view, pleiotropy is not fundamentally different from linkage disequilibrium as a source of genetic correlation, but is instead one extreme of a continuum. Moderately linked loci (say, r < 0.05) may present a substantial constraint on short-term evolution in small subdivided populations. By contrast, very tight (intragenic) linkage will decay to linkage equilibrium given enough time in a large, panmictic population (see §).

QTL mapping imposes a specific linkage disequilibrium structure on the genome, where strong linkage disequilibrium is induced between linked loci, while unlinked loci are randomized into linkage equilibrium (see ). It is this imposed pattern of linkage disequilibrium that limits the resolution of tightly linked loci. Whether this level of resolution is relevant to the ability of recombination to break down the genetic correlation between traits depends on the level of evolutionary constraint being studied. When a cross is performed between populations, strains, ecotypes or sister species (e.g. Kim & Rieseberg 1999; Hawthorne & Via 2001; Verhoeven et al. 2004; Gardner & Latta 2006), there is considerable association (linkage disequilibrium) between unlinked loci in the parental strains, caused by the population subdivision that created the separate strains in the first place. Recombination between unlinked loci following the cross, leaves linkage disequilibrium only among those loci that are linked closely enough to restrain the production of novel trait combinations. In one prominent example, Hawthorne & Via (2002) showed that fitness of pea aphids (Acyrthosiphon pisum) is negatively correlated across two host plants, and this correlation traces to antagonistic QTL underlying fitness in the two environments. Since the populations are highly structured, recombination is reduced, and the antagonistic QTL will present a strong barrier to the evolution of a generalist genotype even if further study resolves the QTL into separate linked loci, each with fitness effects on only one host.

On the other hand, questions of the evolutionary trajectory in panmictic populations are much more difficult to address at the QTL level. Tightly linked loci (even separate mutations within a single gene) will likely be in linkage equilibrium for large populations of outcrossers (Nordborg & Tavare 2002), and QTLs that comprise multiple loci will quickly be recombined. In this case, either detailed molecular analysis (Long et al. 2000; Fanara et al. 2002) or experimental approaches are likely to be necessary. In a direct experimental test of the degree of constraint, Conner (2002) showed that genetic correlations persist under repeated rounds of enforced random mating in Raphanus sativa. Similarly, Mitchell-Olds (1996) showed that patterns of correlation were similar within multiple populations of Brassica, and mirrored in between population correlations. Neither of these results is expected under linkage disequilibrium unless linkage is far too tight to be resolved by QTL analysis. By contrast, Beldade et al. (2002a) argued from selection experiments that correlation of anterior and posterior spot diameter on the forewing of butterflies does not constrain the ability of the spots to respond independently to selection on size. This experiment perhaps best highlights the different perspectives on constraint derived from long-term vs. short-term evolutionary perspectives. While Beldade's results showed that evolution is possibly perpendicular to the direction of the correlation, the response is less than that along the main axis of the correlation. This suggests a true ‘genetic line of least resistance’ (Schluter 1996) formed by the correlation, and prompted Beldade et al. (2002b) to conclude ‘among-eyespot correlations are unlikely to have constrained the evolutionary diversification of butterfly wing patterns but might be important when only limited time is available for adaptive evolution to occur.’

Discussion and summary

  1. Top of page
  2. Abstract
  3. Introduction
  4. Predicting the genetic correlation from QTL effects
  5. Literature survey — methods
  6. Literature survey — results
  7. Antagonistic QTL and negative correlations
  8. Linkage disequilibrium and pleiotropy
  9. Discussion and summary
  10. Acknowledgements
  11. References

Genetically correlated traits are usually interpreted to have some common genetic basis, in the form of either pleiotropic loci, or nonpleiotropic loci located in tightly linked parts of the genome. We found that correlated traits (rG significantly different from zero) share a greater proportion (34%) of their QTL than uncorrelated traits (14%), and that traits which shared more QTL tended to be more tightly correlated (Table 2, Figs 2 and 3). However, the actual number of pleiotropic QTL was generally small — correlated traits typically share only one or two pleiotropic loci (Table 1). This seems to imply that a greater number of QTL in common will lead to larger values of genetic correlation, but sharing a few loci, most likely of moderate-to-large effect, can generate enough genetic covariance to lead to a significant genetic correlation.

Using the additive effects of these shared QTL, we can estimate the strength of the genetic correlation expected if shared QTL perfectly account for the correlation (3). This estimate was well matched qualitatively by the observed genetic correlations. There are very few cases of rQ predicting a value of opposite sign to rG (Fig. 2, Table 3). The quantitative match of rG and rQ is much weaker, however. Variation in rQ explains 19–25% of the variation in rG once the sign of the correlation is accounted for. Thus, the disagreement between QTL results and biometric genetic correlation is mainly in correlation magnitude rather than correlation sign. Given the limited resolution of QTL mapping and the wide error typical in estimates of genetic correlation, this weakness is perhaps inevitable.

Nevertheless, the comparison of biometric correlations with QTL results does allow some insights into the nature of genetic correlation and evolutionary constraint. Several authors (e.g. Houle 1991; De Jong 1993) have presented models in which trade-offs can be masked within positive genetic correlations when the antagonistic QTL are outweighed by QTL with parallel effects. Our results provide direct evidence that this mechanism does indeed occur in real species. Antagonistic QTL were reported in about 25% of trait pairs. However, in 54 of these trait pairs (19%), significant positive correlations were reported despite the antagonistic effects of one or more QTL (Table 4).

Clearly, we cannot distinguish between linkage and pleiotropy using QTL results. Rigorous determination between strict pleiotropy and tight linkage (e.g. Long et al. 2000; Mackay 2001) is extremely difficult. Such careful scrutiny of candidate genes is likely to be possible for only a handful of intensively studied model organisms. However, we argue that the level of resolution afforded by QTL studies remains useful for many purposes. If strict pleiotropy is interpreted as extreme linkage (r = 0), the dichotomy is removed. Researchers can then focus directly on the level of evolutionary constraint imposed by the genetic correlation, which is of greater interest in many ecological/evolutionary studies. The level of resolution afforded by QTL mapping is unlikely to reveal long-term evolutionary constraints. However, it may give valuable insights into the constraints shaping divergence between lineages, and the evolution of ecological specialization.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Introduction
  4. Predicting the genetic correlation from QTL effects
  5. Literature survey — methods
  6. Literature survey — results
  7. Antagonistic QTL and negative correlations
  8. Linkage disequilibrium and pleiotropy
  9. Discussion and summary
  10. Acknowledgements
  11. References

We are grateful to Christophe Herbinger, Mark Johnston, John Willis and two anonymous reviewers for valuable comments and insight into this work. The suggestion that pleiotropy be viewed as a special case of extreme linkage was suggested by an anonymous reviewer to whom we are very grateful. Funding was provided by an NSERC Discovery Grant to R.G.L. and by an NSERC Postgraduate Scholarship to K.M.G.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Predicting the genetic correlation from QTL effects
  5. Literature survey — methods
  6. Literature survey — results
  7. Antagonistic QTL and negative correlations
  8. Linkage disequilibrium and pleiotropy
  9. Discussion and summary
  10. Acknowledgements
  11. References
  • Arnold SJ (1992) Constraints on phenotypic evolution. American Naturalist, 140, S85S107.
  • Austin DF, Lee M (1998) Detection of quantitative trait loci for grain yield and yield components in maize across generations in stress and nonstress environments. Crop Science, 38 (5), 12961308.
  • Beavis WD (1998) QTL analyses: power, precision, and accuracy. In: Molecular Dissection of Complex Traits (ed. PattersonAH), pp. 145162. CRC Press, London.
  • Begin M, Roff DA (2003) The constancy of the G matrix through species divergence and the effects of quantitative genetic constraints on phenotypic evolution: a case study in crickets. Evolution, 57 (5), 11071120.
  • Beldade P, Koops K, Brakefield PM (2002a) Developmental constraints versus flexibility in morphological evolution. Nature, 416 (6883), 844847.
  • Beldade P, Koops K, Brakefield PM (2002b) Modularity, individuality, and evo-devo in butterfly wings. Proceedings of the National Academy of Sciences, USA, 99 (22), 1426214267.
  • Ben Chaim A, Paran I, Grube RC, Jahn M, Van Wijk R, Peleman J (2001) QTL mapping of fruit-related traits in pepper (Capsicum annuum). Theoretical and Applied Genetics, 102 (6–7), 10161028.
  • Bjorklund M (2004) Constancy of the G matrix in ecological time. Evolution, 58 (6), 11571164.
  • Bohn M, Khairallah MM, GonzalezdeLeon D et al . (1996) QTL mapping in tropical maize.1. Genomic regions affecting leaf feeding resistance to sugarcane borer and other traits. Crop Science, 36 (5), 13521361.
  • Brodie ED (1992) Correlational selection for color pattern and antipredator behavior in the garter snake Thamnophis ordinoides. Evolution, 46 (5), 12841298.
  • Camara MD, Ancell CA, Pigliucci M (2000) Induced mutations: a novel tool to study phenotypic integration and evolutionary constraints in Arabidopsis thaliana. Evolutionary Ecology Research, 2 (8), 10091029.
  • Camara MD, Pigliucci M (1999) Mutational contributions to genetic variance-covariance matrices: an experimental approach using induced mutations in Arabidopsis thaliana. Evolution, 53 (6), 16921703.
  • Conner JK (2002) Genetic mechanisms of floral trait correlations in a natural population. Nature, 420 (6914), 407410.
  • Conner JK, Franks R, Stewart C (2003) Expression of additive genetic variances and covariances for wild radish floral traits: comparison between field and greenhouse environments. Evolution, 57 (3), 487495.
  • Cui KH, Peng SB, Xing YZ, Xu CG, Yu SB, Zhang Q (2002) Molecular dissection of seedling-vigor and associated physiological traits in rice. Theoretical and Applied Genetics, 105 (5), 745753.
  • De Jong G (1993) Covariances between traits deriving from successive allocations of a resource. Functional Ecology, 7 (1), 7583.
  • De Jong G, Van Noordwijk AJ (1992) Acquisition and allocation of resources — genetic (co) variances, selection, and life histories. American Naturalist, 139 (4), 749770.
  • De Luca M, Roshina NV, Geiger-Thornsberry GL, Lyman RF, Pasyukova EG, Mackay TFC (2003) Dopa decarboxylase (Ddc) affects variation in Drosophila longevity. Nature Genetics, 34 (4), 429433.
  • Doerge RW, Zeng ZB, Weir BS (1997) Statistical issues in the search for genes affecting quantitative traits in experimental populations. Statistical Science, 12 (3), 195219.
  • Donohue K, Schmitt J (1999) The genetic architecture of plasticity to density in Impatiens capensis. Evolution, 53 (5), 13771386.
  • Erickson DL, Fenster CB, Stenøien HK, Price D (2004) Quantitative trait locus analyses and the study of evolutionary process. Molecular Ecology, 13, 25052522.
  • Falconer DS, MacKay TFC (1996) Introduction to Quantitative Genetics. Longman, Essex, UK.
  • Fanara JJ, Robinson KO, Rollmann SM, Anholt RRH, Mackay TFC (2002) Vanaso is a candidate quantitative trait gene for Drosophila olfactory behavior. Genetics, 162 (3), 13211328.
  • Fishman L, Kelly AJ, Willis JH (2002) Minor quantitative trait loci underlie floral traits associated with mating system divergence in Mimulus. Evolution, 56 (11), 21382155.
  • Fry JD (1993) The general vigor problem — can antagonistic pleiotropy be detected when genetic covariances are positive. Evolution, 47 (1), 327333.
  • Fry JD (1996) The evolution of host specialization: are trade-offs overrated? American Naturalist, 148, S84S107.
  • Gardner KM, Latta RG (2006) Identifying the targets of selection across contrasting environments in Avena barbata using quantitative trait locus mapping. Molecular Ecology, 15, 13211333.
  • Georgiady MS, Whitkus RW, Lord EM (2002) Genetic analysis of traits distinguishing outcrossing and self-pollinating forms of currant tomato, Lycopersicon pimpinellifolium (Jusl.) Mill. Genetics, 161 (1), 333344.
  • Groh S, Kianian SF, Phillips RL et al . (2001) Analysis of factors influencing milling yield and their association to other traits by QTL analysis in two hexaploid oat populations. Theoretical and Applied Genetics, 103 (1), 918.
  • Hawthorne DJ, Via S (2001) Genetic linkage of ecological specialization and reproductive isolation in pea aphids. Nature, 412 (6850), 904907.
  • Herve D, Fabre F, Berrios E et al . (2001) QTL analysis of photosynthesis and water statue traits in sunflower (Helianthus annuus) under greenhouse conditions. Journal of Experimental Botany, 52, 18571864.
  • Houle D (1991) Genetic covariance of fitness correlates — what genetic correlations are made of and why it matters. Evolution, 45 (3), 630648.
  • Houle D, Mezey J, Galpern P (2002) Interpretation of the results of common principal components analyses. Evolution, 56 (3), 433440.
  • Igrejas G, Leroy P, Charmet G, Gaborit T, Marion D, Branlard G (2002) Mapping QTLs for grain hardness and puroindoline content in wheat (Triticum aestivum L.). Theoretical and Applied Genetics, 106 (1), 1927.
  • Jones AG, Arnold SJ, Burger R (2004) Evolution and stability of the G-matrix on a landscape with a moving optimum. Evolution, 58 (8), 16391654.
  • Juenger T, Purugganan M, Mackay TFC (2000) Quantitative trait loci for floral morphology in Arabidopsis thaliana. Genetics, 156 (3), 13791392.
  • Kamoshita A, Wade LJ, Ali ML et al . (2002) Mapping QTLs for root morphology of a rice population adapted to rainfed lowland conditions. Theoretical and Applied Genetics, 104 (5), 880893.
  • Kato K, Miura H, Sawada S (2000) Mapping QTLs controlling grain yield and its components on chromosome 5A of wheat. Theoretical and Applied Genetics, 101 (7), 11141121.
  • Kim SC, Rieseberg LH (1999) Genetic architecture of species differences in annual sunflowers: implications for adaptive trait introgression. Genetics, 153 (2), 965977.
  • Lande R (1975) Maintenance of genetic-variability by mutation in a polygenic character with linked loci. Genetical Research, 26 (3), 221235.
  • Lande R, Arnold SJ (1983) The measurement of selection on correlated characters. Evolution, 37 (6), 12101226.
  • Liedloff A (1999) mantel, Version 2.0: a nonparametric test calculator. School of Natural Resource Sciences, Queensland University of Technology, Brisbane, Australia.
  • Long AD, Lyman RF, Morgan AH, Langley CH, Mackay TFC (2000) Both naturally occurring insertions of transposable elements and intermediate frequency polymorphisms at the achaete-scute complex are associated with variation in bristle number in Drosophila melanogaster. Genetics, 154 (3), 12551269.
  • Lubberstedt T, Melchinger AE, Schon CC, Utz HF, Klein D (1997) QTL mapping in testcrosses of European flint lines of maize. 1. Comparison of different testers for forage yield traits. Crop Science, 37 (3), 921931.
  • Lynch M, Walsh B (1998) Genetics and Analysis of Quantitative Traits. Sinauer Associates, Sunderland, Massachusetts.
  • Mackay TFC (2001) The genetic architecture of quantitative traits. Annual Review of Genetics, 35, 303339.
  • Mackenzie A (1996) A trade-off for host plant utilization in the black bean aphid, Aphis fabae. Evolution, 50 (1), 155162.
  • McGuigan K (2006) Studying phenotypic evolution using multivariate quantitative genetics. Molecular Ecology, 15, 883896.
  • McKay JK, Richards JH, Mitchell-Olds T (2003) Genetics of drought adaptation in Arabidopsis thaliana. I. Pleiotropy contributes to genetic correlations among ecological traits. Molecular Ecology, 12 (5), 11371151.
  • Mesfin A, Smith KP, Dill-Macky R et al . (2003) Quantitative trait loci for fusarium head blight resistance in barley detected in a two-rowed by six-rowed population. Crop Science, 43 (1), 307318.
  • Mitchell-Olds T (1996) Genetic constraints on life history evolution: quantitative trait loci influencing growth and flowering in Arabidopsis thaliana. Evolution, 50, 140145.
  • Mitchell-Olds T, Pedersen D (1998) The molecular basis of quantitative genetic variation in central and secondary metabolism in Arabidopsis. Genetics, 149 (2), 739747.
  • Mousseau TA, Roff DA (1987) Natural selection and the heritability of fitness components. Heredity, 59, 181197.
  • Nei M, Li WH (1979) Mathematical model for studying genetic-variation in terms of restriction endonucleases. Proceedings of the National Academy of Sciences, USA, 76 (10), 52695273.
  • Nordborg M, Tavare S (2002) Linkage disequilibrium: What history has to tell us. Trends in Genetics, 18, 8390.
  • Orr HA (2001) The genetics of species differences. Trends in Ecology & Evolution, 16 (7), 343350.
  • Otto SP, Jones CD (2000) Detecting the undetected: estimating the total number of loci underlying a quantitative trait. Genetics, 156 (4), 20932107.
  • Otto SP, LeNormand T (2002) Resolving the paradox of sex and recombination. Nature Reviews Genetics, 3, 252261.
  • Roff DA (1996) The evolution of genetic correlations: an analysis of patterns. Evolution, 50 (4), 13921403.
  • Roff DA (1997) Evolutionary Quantitative Genetics. Chapman & Hall, London.
  • Roff DA (2000) The evolution of the G matrix: selection or drift? Heredity, 84 (2), 135142.
  • Roff DA (2002a) Comparing G matrices: a manova approach. Evolution, 56 (6), 12861291.
  • Roff DA (2002b) Life History Evolution. Sinauer Associates, Sunderland, Massachusetts.
  • Saliba-Colombani V, Causse M, Langlois D, Philouze J, Buret M (2001) Genetic analysis of organoleptic quality in fresh market tomato. 1. Mapping QTLs for physical and chemical traits. Theoretical and Applied Genetics, 102 (2–3), 259272.
  • Schluter D (1996) Adaptive radiation along genetic lines of least resistance. Evolution, 50 (5), 17661774.
  • Service PM (2000) The genetic structure of female life history in D. melanogaster: comparisons among populations. Genetical Research, 75 (2), 153166.
  • Shaw RG (1991) The comparison of quantitative genetic-parameters between populations. Evolution, 45 (1), 143151.
  • Sokal RR, Rohlf FJ (1995) Biometry, 3rd edn. W.H. Freeman, New York.
  • Stam LF, Laurie CC (1996) Molecular dissection of a major gene effect on a quantitative trait: the level of alcohol dehydrogenase expression in Drosophila melanogaster. Genetics, 144 (4), 15591564.
  • Steppan SJ (1997) Phylogenetic analysis of phenotypic covariance structure. 2. Reconstructing matrix evolution. Evolution, 51 (2), 587594.
  • Steppan SJ, Phillips PC, Houle D (2002) Comparative quantitative genetics: evolution of the G matrix. Trends in Ecology & Evolution, 17 (7), 320327.
  • Tan YF, Sun M, Xing YZ et al . (2001) Mapping quantitative trait loci for milling quality, protein content and color characteristics of rice using a recombinant inbred line population derived from an elite rice hybrid. Theoretical and Applied Genetics, 103 (6–7), 10371045.
  • Tanksley SD (1993) Mapping polygenes. Annual Review of Genetics, 27, 205233.
  • Tinker NA, Mather DE, Rossnagel BG et al . (1996) Regions of the genome that affect agronomic performance in two-row barley. Crop Science, 36 (4), 10531062.
  • Ungerer MC, Halldorsdottir SS, Modliszewski JL, Mackay TFC, Purugganan MD (2002) Quantitative trait loci for inflorescence development in Arabidopsis thaliana. Genetics, 160 (3), 11331151.
  • Veldboom LR, Lee M (1996a) Genetic mapping of quantitative trait loci in maize in stress and nonstress environments. 1. Grain yield and yield components. Crop Science, 36 (5), 13101319.
  • Veldboom LR, Lee M (1996b) Genetic mapping of quantitative trait loci in maize in stress and nonstress environments. 2. Plant height and flowering. Crop Science, 36 (5), 13201327.
  • Verhoeven KJF, Vanhala TK, Biere A, Nevo E, Van Damme JMM (2004) The genetic basis of adaptive population differentiation: a quantitative trait locus analysis of fitness traits in two wild barley populations from contrasting habitats. Evolution, 58 (2), 270283.
  • Vieira C, Pasyukova EG, Zeng ZB, Hackett JB, Lyman RF, Mackay TFC (2000) Genotype–environment interaction for quantitative trait loci affecting life span in Drosophila melanogaster. Genetics, 154 (1), 213227.
  • Whitlock MC, Phillips PC, Moore FBG, Tonsor SJ (1995) Multiple fitness peaks and epistasis. Annual Review of Ecology and Systematics, 26, 601629.
  • Worley AC, Houle D, Barrett SCH (2003) Consequences of hierarchical allocation for the evolution of life-history traits. American Naturalist, 161 (1), 153167.
  • Yan JQ, Zhu J, He CX, Benmoussa M, Wu P (1999) Molecular marker-assisted dissection of genotype–environment interaction for plant type traits in rice (Oryza sativa L.). Crop Science, 39 (2), 538544.
  • Zhou Y, Li W, Wu W, Chen Q, Mao D, Worland AJ (2001) Genetic dissection of heading time and its components in rice. Theoretical and Applied Genetics, 102 (8), 12361242.
  • Zhu S, Kaeppler HF (2003) A genetic linkage map for hexaploid, cultivated oat (Avena sativa L.) based on an intraspecific cross ‘Ogle/MAM17–5′. Theoretical and Applied Genetics, 107 (1), 2635.
  • Zhuang JY, Fan YY, Rao ZM, Wu JL, Xia YW, Zheng KL (2002) Analysis on additive effects and additive-by-additive epistatic effects of QTLs for yield traits in a recombinant inbred line population of rice. Theoretical and Applied Genetics, 105 (8), 11371145.

Robert Latta and Kyle Gardner are both interested in the relationship between genetic variation at the single gene level and heritable variation in ecologically relevant characters or traits. Research into this process involves a combination of molecular, QTL mapping, field and theoretical studies, focusing primarily on the annual grass, Avena barbata. The present review was undertaken to understand the relationship between single gene variation and genetic correlation in the context of constraints on niche breadth.