E-Index for Differentiating Complex Dynamic Traits

Abstract

While it is a daunting challenge in current biology to understand how the underlying network of genes regulates complex dynamic traits, functional mapping, a tool for mapping quantitative trait loci (QTLs) and single nucleotide polymorphisms (SNPs), has been applied in a variety of cases to tackle this challenge. Though useful and powerful, functional mapping performs well only when one or more model parameters are clearly responsible for the developmental trajectory, typically being a logistic curve. Moreover, it does not work when the curves are more complex than that, especially when they are not monotonic. To overcome this inadaptability, we therefore propose a mathematical-biological concept and measurement, E-index (earliness-index), which cumulatively measures the earliness degree to which a variable (or a dynamic trait) increases or decreases its value. Theoretical proofs and simulation studies show that E-index is more general than functional mapping and can be applied to any complex dynamic traits, including those with logistic curves and those with nonmonotonic curves. Meanwhile, E-index vector is proposed as well to capture more subtle differences of developmental patterns.

E-index Method for Identifying Dynamic Growth Traits of Poplar

“…To calculate the E-index value about the plant, the spline interpolation can be used to fit the phenotypic data of poplar growth because the interpolation error can be made small even when using low-degree polynomials for the spline. Meanwhile, it has been verified that a typical kind of spline interpolation, the cubic spline interpolation function, fits the growth data well under the condition of unknown growth curve [16]. Here, we took one of the parents of poplar plant I-69 for example to describe the calculation process.…”

“…The concept of E-index was proposed by Wang et al to measure the earliness degree of growth, which is a powerful tool to quantitatively depict the development features such as the faster or slower, earlier or later growth [16]. This method could successfully identify the specific SNP which govern the growth process for the same biomass at the final time point.…”

“…But the functional mapping method does not work well to find the significant gene loci related to traits when the growth curve or function of its growth process is not monotonic or even worse there does not exist uniform function with parameters to fit the successively collected measurement values. To overcome the inherent inadaptability of functional mapping, we proposed E-index method to cumulatively measure earliness degree of development in the overall process which was verified in simulation data and showed very good effect [16].…”