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Among the many network rewiring approaches, no model-free statistical methods can differentiate gene\u2013gene pattern changes not attributed to marginal changes. This may obscure fundamental rewiring from superficial changes.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>Here we introduce a model-free Sharma\u2013Song test to determine if patterns differ in the second order, meaning that the deviation of the joint distribution from the product of marginal distributions is unequal across conditions. We prove an asymptotic chi-squared null distribution for the test statistic. Simulation studies demonstrate its advantage over alternative methods in detecting second-order differential patterns. Applying the test on three independent mammalian developmental transcriptome datasets, we report a lower frequency of co-expression network rewiring between human and mouse for the same tissue group than the frequency of rewiring between tissue groups within the same species. We also find second-order differential patterns between microRNA promoters and genes contrasting cerebellum and liver development in mice. These patterns are enriched in the spliceosome pathway regulating tissue specificity. Complementary to previous mammalian comparative studies mostly driven by first-order effects, our findings contribute an understanding of system-wide second-order gene network rewiring within and across mammalian systems. Second-order differential patterns constitute evidence for fundamentally rewired biological circuitry due to evolution, environment or disease.<\/jats:p><\/jats:sec><jats:sec><jats:title>Availability and implementation<\/jats:title><jats:p>The generic Sharma\u2013Song test is available from the R package \u2018DiffXTables\u2019 at https:\/\/cran.r-project.org\/package=DiffXTables. Other code and data are described in Section 2.<\/jats:p><\/jats:sec><jats:sec><jats:title>Supplementary information<\/jats:title><jats:p>Supplementary data are available at Bioinformatics online.<\/jats:p><\/jats:sec>","DOI":"10.1093\/bioinformatics\/btab240","type":"journal-article","created":{"date-parts":[[2021,4,9]],"date-time":"2021-04-09T12:10:05Z","timestamp":1617970205000},"page":"3293-3301","source":"Crossref","is-referenced-by-count":6,"title":["Fundamental gene network rewiring at the second order within and across mammalian systems"],"prefix":"10.1093","volume":"37","author":[{"given":"Ruby","family":"Sharma","sequence":"first","affiliation":[{"name":"Department of Computer Science, New Mexico State University , Las Cruces, NM 88003, USA"}]},{"given":"Sajal","family":"Kumar","sequence":"additional","affiliation":[{"name":"Department of Computer Science, New Mexico State University , Las Cruces, NM 88003, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6883-6547","authenticated-orcid":false,"given":"Mingzhou","family":"Song","sequence":"additional","affiliation":[{"name":"Department of Computer Science, New Mexico State University , Las Cruces, NM 88003, USA"},{"name":"Molecular Biology and Interdisciplinary Life Sciences Graduate Program, New Mexico State University , Las Cruces, NM 88003, USA"}]}],"member":"286","published-online":{"date-parts":[[2021,5,5]]},"reference":[{"key":"2023051701222048100_btab240-B1","doi-asserted-by":"crossref","first-page":"2501","DOI":"10.1111\/j.1528-1167.2009.02189.x","article-title":"Array-CGH detection of a de novo 0.7-Mb deletion in 19p13.13 including CACNA1A associated with mental retardation and epilepsy with infantile spasms","volume":"50","author":"Auvin","year":"2009","journal-title":"Epilepsia"},{"key":"2023051701222048100_btab240-B2","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1111\/j.2517-6161.1995.tb02031.x","article-title":"Controlling the false discovery rate: a practical and powerful approach to multiple testing","volume":"57","author":"Benjamini","year":"1995","journal-title":"J. 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