## 1 Introduction  
Study of populations via simulations is an important problem, with applications ranging from tracking population history to modeling heritable diseases. Numerous population simulation methods exist in the literature that are geared towards handling human data [1; 2; 3]. In comparison, only a small number of systems cater to plant and animal breeding populations [4,5]. The former is dominated by the backward simulation approaches, but the latter usually uses forward simulations. Although the backward simulation is a mathematically clever scheme of avoiding redundant computations, as well as redundant ancestors in the simulation, the approach is cumbersome when the requirement is to track multiple segments (chromosomes) for breeding simulations. The whole genome, spread across multiple chromosomes, is required to obtain a realistic genetic or breeding value. Thus, a time and space efficient representation and computation is necessary for realistic simulations. This also enables comparative simulations where thousands of simulations can be carried out based on varying breeding processes to detect the few favorable ones that can be implemented in practice. Classical plant breeding is performed by crossing closely or distantly related individuals to produce new crop varieties with desirable properties. Breeding aims to generate individuals with new and enhanced genetic material by combining genes encoding favorable traits (e.g., disease resistance, drought tolerance, high yield). The quality of the new genetic material is often measured by a phenotype value computed via some mathematical model based on quantitative genetics theory [6,7]. The general problem setting of crossing genetic material and computing phenotype values of the progeny is illustrated in Figure 1. The interested reader is referred to [8] for more details capturing the meiotic crossovers. Ideally, one would be able to predict, via inexpensive and fast computer simulations, the actual phenotypes of progeny resulting from crosses between existing genotyped individuals. This could potentially yield great improvement in time and cost required for developing new and successful  
Figure 1: Illustration of the general problem setting. Crossing the diploid founder genomes, \(A\) and \(B\), produces three progeny, \(P_{1},P_{2},P_{3}\), and each progeny haploid has a single crossover introduced in the meiosis, illustrated by the two different colors per haploid. The genotype matrix for five markers, \(m_{1},...,m_{5}\), represents the aggregate of haploid information per progeny, at specific genomic locations. Each progeny is assigned a phenotype value based on their genotype and a phenotype model. varieties. Due to the advent of high-throughput genomic measurement technologies, there is a continuing substantial increase in the amount of genotype data that the simulation process should be able to utilize. The interested reader is referred to [9] for the relevance of data representation in bioinformatics in general. In order to address the important issue of genotype data representation, in this paper, we propose an efficient data structure that is especially designed for plant population simulations, while also applicable for animal breeding or other related applications. We describe a time- and space-efficient (i) genome representation as segments from founder genomes and (ii) computation of phenotype values (when the underlying phenotype model is additive). Our segment-based representation takes less time and space than a traditional representation of individuals as vectors of genotype values at specific markers. The segment approach is also more general, since it may be used with any selection of markers along the genome. Furthermore, the segment representation allows precise tracking of the parental origin of each location in the genome. This will make any task related to breeding simulations more efficient, including simulating a particular breeding process and optimizing the choice of breeding processes.