17Changes in gene regulation at multiple levels may comprise an important share of the molecular 18 changes underlying adaptive evolution in nature. However, few studies have assayed within-and 19 between-population variation in gene regulatory traits at a transcriptomic scale, and therefore 20 inferences about the characteristics of adaptive regulatory changes have been elusive. Here, we assess 21 quantitative trait differentiation in gene expression levels and alternative splicing (intron usage) 22 between three closely-related pairs of natural populations of Drosophila melanogaster from contrasting 23 thermal environments that reflect three separate instances of cold tolerance evolution. The cold-24 adapted populations were known to show population genetic evidence for parallel evolution at the 25 SNP level, and here we find significant although somewhat limited evidence for parallel expression 26 evolution between them, and less evidence for parallel splicing evolution. We find that genes with 27 mitochondrial functions are particularly enriched among candidates for adaptive expression 28 evolution. We also develop a method to estimate cis-versus trans-encoded contributions to 29 expression or splicing differences that does not rely on the presence of fixed differences between 30 parental strains. Applying this method, we infer important roles of both cis-and trans-regulation 31 among our putatively adaptive expression and splicing differences. The apparent contributions of cis-32 versus trans-regulation to adaptive evolution vary substantially among population pairs, with an 33 Ethiopian pair showing pervasive trans-effects, suggesting that basic characteristics of regulatory 34 evolution may depend on biological context. These findings expand our knowledge of adaptive gene 35 regulatory evolution and our ability to make inferences about this important and widespread process.36 37 50 The level of parallelism for gene expression abundance changes varies across study systems. In some 51 taxa and natural conditions, significantly more genes show parallel changes (repeatedly up-or down-52 regulated in one ecotype relative to the other among independent population pairs) than anti-53 directional changes (Zhao et al. 2015; Hart et al. 2018; Kitano et al. 2018; McGirr and Martin.54 2018). However, some other cases did not show significant parallel patterns, or they even show anti-55 parallel patterns (Derome et al. 2006; Lai et al. 2008; Hanson et al. 2017). The varying degree of 56 parallelism may partly be explained by the level of divergence among ancestors: more closely related 57 ancestors are expected to show a higher degree of parallel genetic evolution underlie similar 58 phenotypic evolution (Conte et al. 2012; Rosenblum et al. 2014). 59 60 Furthermore, gene expression evolution can be caused by the same or different molecular 61 underpinnings. Because of the difficulties of mapping expression QTL, a first step is to classify the 62 expression evolution into two regulatory classes. Cis-regulatory change...