To estimate gene regulatory networks, it is important that we know the number of connections, or sparseness of the networks. It can be expected that the robustness to perturbations is one of the factors determining the sparseness. We reconstruct a semi-quantitative model of gene networks from gene expression data in embryonic development and detect the optimal sparseness against perturbations. The dense networks are robust to connectionremoval perturbation, whereas the sparse networks are

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... to misexpression perturbation. We show that there is an optimal sparseness that serves as a trade-off between these perturbations, in agreement with the optimal result of validation for testing data. These results suggest that the robustness to the two types of perturbations determines the sparseness of gene networks. OPEN ACCESS Citation: Ichinose N, Yada T, Wada H (2017) Estimating optimal sparseness of developmental gene networks using a semi-quantitative model. PLoS ONE 12(4): e0176492. https://doi.org/ 10.