02 Phenotyping For Qtl Mapping

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Phenotyping for QTL Mapping Article · January 2002

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5.2 Phenotyping for QTL Mapping S Chandra1 and F R Bidinger2 Abstract The reliability of QTL mapping results depends in a major way on the achieved level of accuracy and precision of field phenotyping of mapping population individuals. The accuracy of phenotyping determines how realistic the QTL mapping results are. Increased precision of phenotyping increases heritability which, in turn, increases the statistical power of QTL detection. Using appropriate incomplete block designs and biometric analysis techniques that effectively account for extraneous variation in the field can increase the accuracy and precision of field phenotyping. Randomization of mapping population individuals to field plots, although it should be faithfully followed, may not alone guarantee bias-free phenotyping. This is due to the use of typically closely laid out small plot sizes in field phenotyping, which induces spatial correlation among observations from nearby plots, introducing bias in phenotyping. Based on our experience, we strongly recommend using spatial statistical methods to account for this spatial correlation in order to achieve bias-free and precise phenotyping.

Introduction Mapping of quantitative trait loci (QTL) is predicated on detecting a significant statistical association between the phenotypes and the markergenotypes of individuals of a mapping population. Data on both phenotypic value or performance and marker-genotyping of mapping population individuals are therefore required. Phenotyping data contain information on segregation and genetic effects of QTL. Marker-genotyping data provide information on site-specific segregation of putative QTL on the genome. The level of accuracy and precision of both the phenotyping and the marker-

1. Senior Scientist (Statistics), International Crops Research Institute for the Semi-Arid Tropics, Patancheru 502 324, AP, India. 2. Principal Scientist (Physiology), International Crops Research Institute for the Semi-Arid Tropics, Patancheru 502 324, AP, India.

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genotyping data determines the level of reliability of results from QTL mapping. It is therefore important, to achieve a high level of reliability of QTL mapping results, so that highly accurate and precise phenotyping and markergenotyping data are generated using efficient phenotyping and genotyping protocols. This chapter presents a discussion of phenotyping protocols to enhance the reliability and relevance of QTL mapping results. An efficient suite of phenotyping protocols is one that, for the targeted environmental conditions, delivers highly accurate and precise assessment of phenotypic value or performance of mapping population individuals for the agroeconomic traits of interest. Given a random/representative sample of ng mapping population individuals to be phenotyped, with ng chosen to be large enough (≈500) to achieve high statistical power for QTL detection, the required components of the suite of phenotyping protocols are: A representative sample of ne environments and their optimal location; Number of replications nr per individual in each environment; An experimental field with np=ngnr plots in each environment; An experimental design to effectively account for extraneous variation in experimental field; and • Appropriate biometric techniques for efficient analysis of data.

• • • •

Before any discussion on these issues, it is useful to first clarify the meaning of the key concepts of precision and accuracy of estimates.

Accuracy and Precision The basic phenotypic data required for QTL analyses are the estimates of phenotypic performance of individuals in single environments and/or across environments. The total uncertainty/error in the estimated phenotypic performance m of any individual, with m being its corresponding true, unknown phenotypic performance, is quantified by its mean square error MSE(m) = E(m-m)2 = E{m-E(m)}2+{E(m)-m}2 where E is the average value. The term E{m-E(m)}2 is the error variance of m, the square root of which is the standard error (SE). The second term represents the square of the bias in m. There are thus two component errors that make up the total error in m – the SE that measures the imprecision in m, and the bias that measures the inaccuracy in m. The smaller the SE, the higher the precision of m. The smaller the bias, the more accurate m is as an estimate of m. It is the accuracy

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of m that is the more critical factor for realistic QTL mapping results. In contrast, a smaller SE increases the heritability of the trait, which in turn enhances the power of QTL detection. The suite of phenotyping protocols to be used should be designed so as to minimize both SE and bias in m. It is often taken for granted that the physical act of randomization of individuals to field plots will provide unbiased/ accurate estimates of m. While this argument is mathematically valid, it provides no guarantee of achieving bias-free estimates. The randomization argument only allows us to proceed with data analysis as if the phenotypic expression of an individual in a given field plot is independent of the phenotypic expression of other individuals falling on other field plots in the experimental area. This is highly unlikely to be the case for typical small plot phenotyping trials for QTL mapping, however refined the randomization scheme may be. Due to the small size of closely laid out plots, there is a distinct possibility, despite randomization, of the phenotypic expressions of individuals in nearby plots affecting each other and hence being biased. Nevertheless, randomization should still be followed to avoid personal bias, but data analysis, where appropriate, should consider accounting for the possibility of correlated phenotypic expression of individuals in nearby plots in order to obtain maximally bias-free estimates of m.

Number of Environments and Replications With ng individuals, each phenotyped with nr replications in each of the ne environments, the error variance of the observed average phenotypic performance m of an individual is given by sm2= (sGE2/ne)+{se2/(nenr)}

(1);

where sGE2 and se2 are, respectively, the genotype-environment interaction variance and the pooled error variance. Increasing nr only reduces the second term, while increasing ne affects a reduction in both terms on the right-hand side of (1). For a fixed manageable number of plots, the maximal reduction in sm2 is theoretically achieved with nr=1, with a corresponding increase in ne. At least ne=3 environments should be considered, selected in a manner so as to represent one intermediate and two extreme points on the scale of expected variation in the targeted set of environmental conditions. Though nr=1 is optimal, it is advisable to take nr=2 so as to get an internal estimate of error

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variance in each environment and to enable estimation of sGE2, which is important in obtaining a more realistic multienvironment estimate of trait heritability h2 = sG2/(sG2+sm2).

Experimental Design A statistically sound design for an experiment requires three basic ingredients – replication and randomization of individuals, and local control of error arising from interplot variation. These ingredients, when properly used, have three benefits: they allow separation of signal from noise, needed to obtain unbiased estimates of differences in phenotypic performance m of individuals; they maximize the signal-to-noise ratio; and they deliver a valid and unbiased estimation of level of noise/uncertainty in results. The signal is the true differences among individuals and the noise/error is due to interplot variation. Replication is necessary to obtain an internal estimate of experimental error variance and to permit separation of sGE2 from error variance. Multiple observations from within a plot do not constitute replication. Randomization provides statistical validity to results and protection from bias. Local control of error can be physically achieved by proper blocking of plots in a manner that maximizes interblock and minimizes intrablock variation. It is the physical device of blocking that, if properly carried out, helps reduce experimental error. However, no matter how effective the blocking is, there is always some variation left uncontrolled within blocks. As the experiment progresses with time, it is also possible that the continuously changing nature of extraneous environmental factors will induce additional intrablock variations in field phenotyping experiments, if the block size is large. It is therefore safer to use blocks of not more than 8–10 plots. Orientation of the blocks, as far as possible, should be perpendicular to the expected gradient in the experimental field, glasshouse bench, etc.

Replication versus Blocking Replication simply indicates the number of plots (nr) assigned to an individual. The basic function of replication is to deliver an estimate of error mean square se2; it is not a device to reduce se2. Increased nr only helps in obtaining a better estimate of se2. In attempting to reduce SE of a mean SEm=√(se2/nr), the first thought that comes to mind is to increase nr. This increases the cost of experimentation. In contrast, blocking is a physical method to reduce se2.

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Rarely is enough thought given to reducing SEm by reducing se2, by attempting effective physical blocking of plots in terms of proper orientation and size. Attempts should be made, where appropriate, to use covariance/spatial analysis techniques for a possible additional reduction in se2. Generalized lattice (also known as alpha) designs are suitable for phenotyping large numbers of individuals. They are more flexible than lattice designs that need ng to be necessarily a perfect square of some integral number. Alpha designs also offer greater convenience for management of the experiment and better choices to conform to expected interplot variation in the field. For ng=300 individuals, some possible design choices are: 3 × 100, 5 × 60, 6 × 50, 10 × 30, and 15 × 20, where the first number is the block size and the second number is the number of (incomplete) blocks per replication. Alpha designs may also allow better use of available experimental area, as small blocks allow much more flexibility in the layout of an experiment than do larger blocks or classical replications.

Biometric Analysis of Data Having generated and entered the data, we are often eager to quickly get our results. While this is natural, haste may result in the waste of time and effort, because a sequential plan for data analysis has not been properly thought out. A plan for data analysis, made before undertaking actual data analysis, should consist of the following six steps: • First , screen and validate the data for correctness. • Second , bring the data into a format required by the software to be used for analysis. • Third , understand the treatment and block-structure of the data. • Fourth , understand the nature of the data (discrete, continuous, percentages, etc.). • Fifth , determine the nature of experimental and environmental factors – fixed or random. • Sixth , build an analysis model according to the structure and nature of data and the nature of experimental and environmental factors. It is only at the end of the sixth step that the actual data analysis can be effectively and confidently begun. In the context of phenotyping for QTL mapping, the effects of mapping population individuals should be considered as random, with their average

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phenotypic values derived as best linear unbiased predictions (BLUPs) using restricted maximum likelihood (ReML). The BLUPs differ from the usual (generalized) least square means in that the former show a smaller range among the phenotypic values of the individuals than the latter. BLUPs are expected to represent more realistic differences among individuals’ phenotypic values as extreme phenotypic values, which might arise by chance from a fortuitous interplay of external factors, are forced to shrink towards the general mean. Treating individuals’ effects as random is also consistent with the fact that the mapping population individuals constitute a representative sample from the underlying mapping population. Considering the effects of individuals as random is anyway necessary for a valid estimation of genetic variance and heritability, which is required to assess the prospects for markerassisted selection. The effects of (incomplete) blocks should be treated as random. The effects of environments should be considered as random if more than eight environments are used for phenotyping, and fixed if less than eight environments are used. As a result of genotype effects being random and environment effects being fixed/random, the effects of genotype-environment interactions (GEI) will be random. Analysis can be done for each environment separately, or jointly across-environments, depending on the approach to be used for QTL analyses. The ReML BLUPs of individuals and of GEI from an across-environments analysis, however, may be more appropriate to use for QTL mapping, as this will more objectively allow detecting QTL for GEI also (Yan et al. 1998). This is because an across-environments analysis will properly separate the effects of individuals from those of GEI.

Effect of Alpha Blocking and Spatial Analysis on Heritability and QTL Mapping As a result of effective blocking a decrease in error variance, and therefore an increase in heritability of a trait, can be expected. An increase in heritability, as noted earlier, effects an increase in the power of QTL mapping. Table 5.2.1 presents results of two analyses, one based on excluding and other on including the effects of blocks in a 9x18 alpha design trial on pearl millet at Patancheru conducted in 2000. Accounting for block effects (a) consistently resulted in an increase in heritability, (b) the number of detected QTL either remained the same or increased, and (c) LOD scores and R2 values of detected QTL generally increased.

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Table 5.2.1. Effect of Alpha-blocking (9 plots/block × 18 blocks/replication) on phenotyping of 160 testcrossed pearl millet mapping populations in irrigated control and early-onset terminal drought stress environments, Patancheru dry season, 2000. REML analyses were done with and without the block effect (+ and – block) in the model. Numbers of QTL detected are those with LOD scores > 2.0, from a combined model to obtain cumulative LOD score and R2 values using interval mapping in MAPMAKER. Plot mean heritability (%) Variable

Number of QTL detected

Cumulative LOD (R2) scores of detected putative QTL

–block

+ block

–block

+ block

–block

+ block

Irrigated control Days to flowering Stover yield m-2 Grain yield m-2 Biomass yield m-2 Harvest index

72.9 56.2 31.4 44.2 63.9

75.9 57.3 37.5 46.9 67.6

4 2 1 2 3

4 4 1 2 5

15.8 7.9 4.3 8.1 17.7

(41.1) (24.7) (13.8) (26.4) (45.2)

21.7 13.1 4.7 8.3 26.2

(51.2) (36.3) (15.2) (26.8) (57.7)

Early-onset stress Days to flowering Stover yield m-2 Grain yield m-2 Biomass yield m-2 Harvest index

72.0 54.7 53.4 39.7 68.6

79.3 57.3 58.9 43.8 71.2

3 3 4 2 5

4 4 4 4 5

17.7 11.6 17.2 6.0 27.2

(45.2) (33.7) (46.7) (19.0) (59.3)

22.2 12.2 17.3 9.3 26.2

(53.5) (36.0) (48.7) (29.1) (57.7)

In another detailed study of the effects of spatial analysis on QTL mapping results in pearl millet with 149 F2 intercross mapping population individuals laid out in an alpha design, it was found that strong spatial variability existed along rows and/or columns of the trial fields. Spatial adjustment substantially decreased the error variance and bias, and increased heritability, the latter up to 100% for days to flowering at Nagaur in Rajasthan. Relative ranking of spatially adjusted means for all traits analyzed was substantially different from unadjusted alpha-design-based means. Use of spatially adjusted means substantially increased LOD scores of detected QTL, the increase being as much as 100% for days to flowering QTL at Nagaur. This was accompanied by a correspondingly proportionate increase in R2 values of detected QTL. A number of additional QTL of large effects, not detectable in analysis based on unadjusted alpha means, were also detected. Spatial analysis, compared to alpha blocking, provided more realistic and powerful QTL

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mapping resulted, from use of bias-free and more precise estimates of phenotypic values.

Bibliography Kearsey, M. J. and Farquhar, A. G. L. 1998. QTL analysis in plants; where are we now? Heredity 80:137–142. Moreau, L., Monod, H., Charcosset, A., and Gallais, A. (1999). Marker-assisted selection with spatial analysis of unreplicated field trials. TAG 98:234-242. Yan, J., Zhu, J., He, C., Benmoussa, M., and Wu, P. (1998). Molecular dissection of developmental behavior of plant height in rice (Oryza sativa L.). Genetics 150:1257– 1265.

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