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Developmental hourglasses have attracted increased attention as candidates for such laws, but the necessity of their emergence remains elusive. We conducted evolutionary simulations of developmental processes to confirm the emergence of the developmental hourglass and unveiled its establishment. We considered organisms consisting of cells containing identical gene networks that control morphogenesis and evolved them under selection pressure to induce more cell types. By computing the similarity between the spatial patterns of gene expression of two species that evolved from a common ancestor, a developmental hourglass was observed, that is, there was a correlation peak in the intermediate stage of development. The fraction of pleiotropic genes increased, whereas the variance in individuals decreased, consistent with previous experimental reports. Reduction of the unavoidable variance by initial or developmental noise, essential for survival, was achieved up to the hourglass bottleneck stage, followed by diversification in developmental processes, whose timing is controlled by the slow expression dynamics conserved among organisms sharing the hourglass. This study suggests why developmental hourglasses are observed within a certain phylogenetic range of species.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1011867","type":"journal-article","created":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T13:52:11Z","timestamp":1709214731000},"page":"e1011867","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":5,"title":["Developmental hourglass: Verification by numerical evolution and elucidation by dynamical-systems theory"],"prefix":"10.1371","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9005-3805","authenticated-orcid":true,"given":"Takahiro","family":"Kohsokabe","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shigeru","family":"Kuratanai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6400-8587","authenticated-orcid":true,"given":"Kunihiko","family":"Kaneko","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2024,2,29]]},"reference":[{"key":"pcbi.1011867.ref001","volume-title":"\u00dcber entwickelungsgeschichte der thiere. 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