# Genetic Parameters for Selected Traits of Inbred Lines of Maize (_Zea mays_ L.)
## 1 Introduction  
Currently, maize, along with wheat and rice, are among the economically most essential grain species [1]. Maize is one of the most important crops that allow for the continuous growth of the world's population. The importance of maize is greatly influenced by its high production potential and the possibility of extensive use of crops (food source, industrial raw material, various types of animal feed). In recent years, the area of maize cultivation in the world ranges from 140 to 145 million hectares, while its production exceeds 600 million tons of grain. The continuous increase in the range of maize cultivation is related to the breeding progress, which includes the use of heterosis and the creation of hybrids with fewer climate requirements [2; 3; 4]. It is also crucial to have access to more and more modern breeding methods and cultivation technologies. The demand for new varieties of maize is constantly growing, which makes it the subject of intensive genetic and breeding research.  
From the breeding point of view, in the case of quantitative traits, the interaction of genes in the creation of a given trait is critical. It is known that each of the genes that determine a polygenic trait is inherited according to Mendel's laws. Three independent genes and two alleles at the locus are enough for the frequency distribution of the genotypes to approach the normal distribution. However, such a situation occurs in a very simplified case, i.e., when two-allelic loci with an identical, linear phenotypic effect interact additively [5].  
In fact, the phenotypic effect of different loci may be different. Loci can be multiallelic. There can be partial or full dominance. We can also deal with overdomination, couplings, and the effect of interallelic interaction. Modifier genes may also appear, modifying the functions of other genes [6; 7].  
The traits with minor polygenic effects of each genotype overlap with environmental effects, i.e., the variability of the polygenic feature is influenced by the environment. Consequently, it is impossible to identify the genotype based on the phenotype [8].  
Therefore, one of the primary tasks of applied genetics is to explain the relationship between genotype and phenotype. Thus, the phenotypic observation of a quantitative trait includes the environmental, genetic, as well as genotype by environment interaction [9; 10].  
Genetic analyses of various maize genotypes conducted for years have shown that gene interactions--dominance, epistasis, and pleiotropy--play an essential role in the evolution of the maize phenotype. It has long been noticed that many of the loci that differentiate maize and tosinte are pleiotropic. The latest examination of the regulatory architecture of tb1 provides a detailed understanding of pleiotropy for a single domestication gene. The tb1 is pleiotropic across many traits such as apical dominance, length of lateral branches, growth of leaves on the lateral branches, pedicellate spikelet development, and root architecture [11; 12].  
Genetic analyses are of the most importance for understanding the variability of phenotypic traits. The influence on those traits by genes and their pairwise interactions are well known [1; 13; 14], but considering higher-order interactions is still a novelty in this kind of studies [15].  
The aim of this paper was an estimation of the three parameters connected with gene effects: additive (_a_), additive by additive (_aa_) epistatic, and additive by additive by additive (_aaa_) interaction for nine quantitative traits of maize inbred lines. Acquiring this new insight, especially on the effect of the higher-order interaction, was considered for the potential homozygous line crossing. On the basis of available literature, this is the first report concerning the presence of estimation of the additive \(\times\) additive \(\times\) additive interaction gene effect of maize inbred lines.