2 Notation and conventions
2.1 Genotype orientation
The standard numeric input uses -1 and 1 for the two homozygotes and 0 for the heterozygote. The allele represented by 1 depends on the input and its orientation metadata. Do not infer a biological reference allele from the sign alone. The first chapter uses an already coded maize dataset and shows the entry point for importing your own files. The genotype input chapter examines format-specific conversion and orientation checks in detail.
Markers occupy rows in the numeric input table, whereas outputs such as genetic_values() use individuals in rows. Align identifiers whenever combining outputs instead of assuming that two objects share their row order.
2.2 Symbols used in the first chapter
| Symbol | Meaning | Scale |
|---|---|---|
| \(x_{ij}\) | Coded genotype | -1, 0, 1 |
| \(b_j\) | Raw additive effect series | Before component normalization |
| \(c_i\) | Unscaled marker score | Sum of marker contributions |
| \(\pi\) | Requested layer variance allocation | Package simulation scale |
| \(g_i\) | Realized genetic value | After component normalization |
| \(e_i\) | Realized residual | After residual normalization |
| \(y_i\) | Realized phenotype | Genetic value plus residual in this example |
| \(s_g^2\), \(s_e^2\), \(s_y^2\) | Sample variances | Denominator \(n-1\) |
| \(s_{ge}\) | Sample covariance | Denominator \(n-1\) |
| \(R_G\) | Realized genetic-to-phenotypic variance ratio | Diagnostic, not an estimated parameter |
The derivation in Section A.2 defines these sample quantities explicitly. Later methods chapters will distinguish additive breeding values, total genetic values, estimated breeding values, and genotypic effects in their own model contexts.
2.3 Two kinds of replication
n_reps requests simulation replications, represented by rep in phenotype tables. The separate reps argument concerns entry-mean records and residual scaling. They answer different experimental questions. The trait values chapter demonstrates both rather than treating them as interchangeable ways to increase the number of observations.
2.4 A function is not a method
select_ind() exposes several selection methods; predict_ebv() has different relationship and trait configurations. Conversely, a single scientific method can involve many internal functions. The coverage register therefore tracks public functions and method options separately.