Fig. 1

Method schematic of SPARK-X and simulation results. A Schematic of the SPARK-X method. B Computational time of different methods for analyzing data with different sample sizes in the simulations. Plot shows computational time in minutes (y-axis) for analyzing 10,000 genes with different sample sizes (x-axis) for different methods. Compared methods include SPARK-X (red), SPARK (sky blue), SPARK-G (green) and SpatialDE (steel blue). C Random access memory (RAM) of different methods for analyzing data with different sample sizes in the simulations. Plot shows computational memory in gigabytes (y-axis) for analyzing 10,000 genes with different sample sizes (x-axis) for different methods. Computations are carried out using a single thread of an Intel Xeon E5-2683 2.00 GHz processor. SPARK-X is much more computationally efficient than SPARK, SPARK-G, and SpatialDE. For ease of computation, we did not apply SPARK to the data with sample size greater than 3000 and did not apply SPARK-G and SpatialDE to the data with sample size greater than 30,000. D Representative genes displaying random pattern and other three spatial expression patterns. E Quantile–quantile plot of the observed −log₁₀(P) from different methods against the expected −log₁₀(P) under the null simulations with high sparsity (μ = 0.005). P values were combined across ten simulation replicates. Simulations were performed under moderate sample size (n = 10,000) and moderate dispersion (2.5). F Power plots show the proportion of true positives (y-axis) detected by different methods at a range of sample sizes (x-axis) for the alternative simulations with high sparsity at an FDR cutoff of 0.05. Simulations were performed under a moderate fraction of marked cells (20%) and moderate SE strength (threefold) for the hotspot and streak patterns or under moderate SE strength (30% cells displaying expression gradient) for the gradient pattern