*2.3.1. DNA quality inspection*

The degree of degradation of the DNA was analyzed by agarose gel electrophoresis and imaged with an ultraviolet gel imager. The DNA sample was determined to be without degradation if

**Figure 2.** *Arabidopsis* growth conditions at 1 week (a), 3 weeks (b), and 6 weeks (c).

the sample did exhibit dispersion phenomena. All of the samples were determined not to be degraded and were sequenced.

**3. Functional mapping**

(1), <sup>⋯</sup> ,*yi*

(T)

*<sup>L</sup>*(Φ|y) <sup>=</sup> <sup>∏</sup>*<sup>i</sup>*=<sup>1</sup>

) denote the vector of trait values for RIL, *i* measured at *T* time-points.

RILs. In this study, the likelihood for height growth data of *A. thaliana* is

RILs

81

<sup>1</sup>(yi )

2(yi) (1)

Functional Mapping of Plant Growth in *Arabidopsis thaliana*

http://dx.doi.org/10.5772/intechopen.74424

(T))*for qq*. (2)

<sup>1</sup> <sup>+</sup> *be*<sup>−</sup>*rt*, (3)

Consider a SNP with two alleles *Q* and *q*, generating two genotypes: *QQ* with *n*<sup>1</sup>

*n*1 *f* <sup>1</sup>(yi) <sup>∏</sup>*<sup>i</sup>*=<sup>1</sup> *n*2 *f*

where Φ indicates the unknown parameters including the time-dependent effects of different QTL genotypes and the time-dependent residual variance and correlations. *f*

(1),.…*μ*<sup>1</sup>

(T × T)-dimensional longitudinal covariance matrix is expressed as Σ, which can be modeled by using a statistical approach such as the first-order autoregressive [AR(1)] model or an autoregressive moving-average process (ARMA). The maximum-likelihood estimates (MLEs) of the unknown parameters are implemented with the simplex algorithm in R software [48].

One of the most important equations for capturing time-specific change in growth is the logistic curve [49, 50], which we used to describe height growth of the QTL genotype according to

where *g*(*t*) represents the trait value at time point t, *a* indicates the asymptotic value of g when *t* → ∞, *b* is a parameter to position the curve on the time axis, and *r* indicates the relative growth rate. Consequently, any specific growth characteristics described by the logistic growth equation can be captured by parameter *a*, *b*, and *r,* and these can be used to determine the coordinates of biologically important benchmarks along the growth trajectory. The mean vector for the QTL genotypes *QQ* and *qq* from time *1* to *T* in the multivariate normal density function is

(1),.…*μ*<sup>2</sup>

*<sup>μ</sup>*<sup>2</sup> <sup>=</sup> (*μ*<sup>2</sup>

*μ*<sup>1</sup> = (*μ*<sup>1</sup>

) are a multivariate normal distribution with a time-dependent mean vector for

(T))*for QQ*,

**3.1. Statistical model**

genotype *QQ* and *qq*,

{

**3.2. Modeling the mean vector**

*g*(t) = \_\_\_\_\_\_ *<sup>a</sup>*

the following expression:

expressed as:

Let *yi* <sup>=</sup> *<sup>c</sup>*(yi

and *qq* with *n*<sup>2</sup>

expressed as

and *f* 2(yi

We measured the absorbance of the DNA samples at wavelengths of 260 and 280 nm and calculated the value of the optical density (OD) 260/OD280. Samples were determined to be of sufficient quality if this value was greater than 1.8 and less than 2.2. After testing, all samples were found to meet the requirements for sequencing.
