In multiple regression Y ~ β₀ + β₁X₁ + β₂X₂ + β₃X₁ X₂ + ɛ., the interaction term is quantified as the product of X₁ and X₂. We developed fractional-power interaction regression (FPIR), using βX₁ ^M X₂ ^N as the interaction term. The rationale of FPIR is that the slopes of Y-X₁ regression along the X₂ gradient are modeled using the nonlinear function (Slope = β₁ + β₃MX₁ ^M-1 X₂ ^N), instead of the linear function (Slope = β₁ + β₃X₂) that regular regressions normally implement. The ranges of M and N are from -56 to 56 with 550 candidate values, respectively. We applied FPIR using a well-studied dataset, nest sites of the crested ibis (Nipponia nippon).We further tested FPIR by other 4692 regression models. FPIRs have lower AIC values (-302 ± 5003.5) than regular regressions (-168.4 ± 4561.6), and the effect size of AIC values between FPIR and regular regression is 0.07 (95% CI: 0.04-0.10). We also compared FPIR with complex models such as polynomial regression, generalized additive model, and random forest. FPIR is flexible and interpretable, using a minimum number of degrees of freedom to maximize variance explained. We have provided a new R package, interactionFPIR, to estimate the values of M and N, and suggest using FPIR whenever the interaction term is likely to be significant. • Introduced fractional-power interaction regression (FPIR) as Y ~ β₀ + β₁X₁ + β₂X₂ + β₃X₁ ^M X₂ ^N + ɛ to replace the current regression model Y ~ β₀ + β₁X₁ + β₂X₂ + β₃X₁ X₂ + ɛ; • Clarified the rationale of FPIR, and compared it with regular regression model, polynomial regression, generalized additive model, and random forest using regression models for 4692 species; • Provided an R package, interactionFPIR, to calculate the values of M and N, and other model parameters.

Myelination in the central nervous system takes place predominantly during the postnatal development of humans and rodents by myelinating oligodendrocytes (OLs), which are differentiated from oligodendrocyte progenitor cells (OPCs). We recently reported that Sox2 is essential for developmental myelination in the murine brain and spinal cord. It is still controversial regarding the role of Sox2 in oligodendroglial lineage progression in the postnatal murine spinal cord. Analyses of a series of cell- and stage-specific Sox2 mutants reveal that Sox2 plays a biphasic role in regulating oligodendroglial lineage progression in the postnatal murine spinal cord. Sox2 controls the number of OPCs for subsequent differentiation through regulating their proliferation. In addition, Sox2 regulates the timing of OL differentiation and modulates the rate of oligodendrogenesis. Our experimental data prove that Sox2 is an intrinsic positive timer of oligodendroglial lineage progression and suggest that interventions affecting oligodendroglial Sox2 expression may be therapeutic for overcoming OPC differentiation arrest in dysmyelinating and demyelinating disorders.

To better determine the history of modern birds, we performed a genome-scale phylogenetic analysis of 48 species representing all orders of Neoaves using phylogenomic methods created to handle genome-scale data. We recovered a highly resolved tree that confirms previously controversial sister or close relationships. We identified the first divergence in Neoaves, two groups we named Passerea and Columbea, representing independent lineages of diverse and convergently evolved land and water bird species. Among Passerea, we infer the common ancestor of core landbirds to have been an apex predator and confirm independent gains of vocal learning. Among Columbea, we identify pigeons and flamingoes as belonging to sister clades. Even with whole genomes, some of the earliest branches in Neoaves proved challenging to resolve, which was best explained by massive protein-coding sequence convergence and high levels of incomplete lineage sorting that occurred during a rapid radiation after the Cretaceous-Paleogene mass extinction event about 66 million years ago.

Birds are the most species-rich class of tetrapod vertebrates and have wide relevance across many research fields. We explored bird macroevolution using full genomes from 48 avian species representing all major extant clades. The avian genome is principally characterized by its constrained size, which predominantly arose because of lineage-specific erosion of repetitive elements, large segmental deletions, and gene loss. Avian genomes furthermore show a remarkably high degree of evolutionary stasis at the levels of nucleotide sequence, gene synteny, and chromosomal structure. Despite this pattern of conservation, we detected many non-neutral evolutionary changes in protein-coding genes and noncoding regions. These analyses reveal that pan-avian genomic diversity covaries with adaptations to different lifestyles and convergent evolution of traits.