Darwin argued speciation occurs by many, slight adaptive changes. This view predicts gradual population divergence involving polygenic trait variation, subtle genome wide differentiation, and an interconnected speciation continuum. In contrast, modern theory predicts speciation can be a more punctuated process involving genome re-arrangements, heterogeneous genomic differentiation, and apparent discontinuities generated by ephemeral intermediate forms. Here we help unite these views using ecological genomics in stick insects. We show how speciation gradually unfolds under a balance between divergent selection and gene flow, but can reach a tipping point driving punctuated differentiation. We show this tipping point is facilitated by genome re-arrangements and spatial reductions in gene flow. Thus, a gradual but irregular process can explain discontinuities in extant populations and the fossil record.