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Spatially resolved transcriptomics offers unprecedented insight by enabling the profiling of gene expression within the intact spatial context of cells, effectively adding a new and essential dimension to data interpretation. To efficiently detect spatial structure of interest, an essential step in analyzing such data involves identifying spatially variable genes. Despite researchers having developed several computational methods to accomplish this task, the lack of a comprehensive benchmark evaluating their performance remains a considerable gap in the field. Here, we present a systematic evaluation of 14 methods using 60 simulated datasets generated by four different simulation strategies, 12 real-world transcriptomics, and three spatial ATAC-seq datasets. We find that spatialDE2 consistently outperforms the other benchmarked methods, and Moran's I achieves competitive performance in different experimental settings. Moreover, our results reveal that more specialized algorithms are needed to identify spatially variable peaks.