Fig. 1.

Time complexity analogies with respect to existing and proposed methods. Heuristically, the novel algorithms (bottom right) are to the stochastic, iterative algorithm implemented in the BOLT-LMM software [7, 8] (bottom left) as the direct methods exploiting the shifted structure of the two component genomic variance component model (1) (e.g., FaST-LMM and GEMMA [3, 5]; top right) are to standard direct methods (top left). For simplicity, we assume here that the number of markers is equal to the number of observations and omit low-order terms related to the spectral conditioning of the covariance structure and the number of random vectors generated by the stochastic methods; further details are provided in Table 1. n_eval denotes the number of objective function evaluations needed to achieve convergence