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The extent to which evolution is repeatable remains debated. Here, we study changes over time in the frequency of cryptic color-pattern morphs in 10 replicate long-term field studies of a stick insect, each spanning at least a decade (across 30 years of total data). We find predictable "up-and-down" fluctuations in stripe frequency in all populations, representing repeatable evolutionary dynamics based on standing genetic variation. A field experiment demonstrates that these fluctuations involve negative frequency-dependent natural selection (NFDS). These fluctuations rely on demographic and selective variability that pushes populations away from equilibrium, such that they can reliably move back toward it via NFDS. Last, we show that the origin of new cryptic forms is associated with multiple structural genomic variants such that which mutations arise affects evolution at larger temporal scales. Thus, evolution from existing variation is predictable and repeatable, but mutation adds complexity even for traits evolving deterministically under natural selection. [ABSTRACT FROM AUTHOR]