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Patterns of two molecules across biological systems are often labeled as conserved or differential. We argue that this classification is insufficient. Here, we introduce three types of relationships across systems. Upon stimuli, a type-0 pattern arises from conserved circuitry with active conserved trajectory; a type-1 pattern is conserved circuitry with active differential trajectory; a type-2 pattern is rewired circuitry with active trajectory. We present a 1st-order marginal change test, prove its optimality, and establish its asymptotic chi-squared distribution under the null hypothesis of identical marginals across conditions. The test outperformed other methods in detecting 1st-order difference in simulation studies. We also introduce a zeroth-order strength test to assess association of two variables across systems. We compared gene co-expression networks of planktonic microbial communities in cold California coastal water against the warm water of North Pacific Subtropical Gyre. The frequency of type-1 patterns is much higher than those of type-2 and type-0 patterns, revealing that the microbial communities are mostly conserved in molecular circuitry but responded differentially to ocean habitats. Type-1 and 2 patterns are enriched with genes known to respond to environmental changes or stress; type-0 patterns involve genes having essential function such as photosynthesis and general transcription. Our work provides a deep understanding to effects of the environment on gene regulation in microbial communities. The method is generally applicable to other biological systems. All tests are provided in the R package 'DiffXTables' at https://cran.r-project.org/package=DiffXTables. Other source code and lists of significant gene patterns are available at https://www.cs.nmsu.edu/~joemsong/ACM-BCB-2020/Plankton