The field of landscape genomics aims to infer how landscape features affect gene flow throughout a population. Most landscape genomic frameworks assume the isolation-by-distance and isolation-by-resistance hypotheses, which propose that genetic dissimilarities between individuals increase as a function of distance and as a function of cumulative landscape resistance, respectively. While these hypotheses are valid in certain settings, other mechanisms may affect gene flow. For example, the gene flow of invasive species may depend on founder effects and multiple introductions. Such mechanisms are not considered in modern landscape genomic models. We extend dyadic models to allow for mechanisms that range-shifting and/or invasive species may experience by introducing dyadic spatially-varying coefficients (DSVCs) defined on pairs of sampled locations. The DSVCs allow the effects of landscape on gene flow to vary across space, capturing nonstationary and asymmetric connectivity. Additionally, we incorporate explicit landscape features as connectivity covariates, which are localized to specific regions of the spatial domain and may function as barriers or corridors to gene flow. Such covariates are central to colonization and invasion, where spread accelerates along corridors and slows across landscape barriers. The proposed framework accommodates colonization-specific processes while retaining the ability to assess landscape influences on gene flow. Our case study of the highly invasive cheatgrass (Bromus tectorum) demonstrates the necessity of accounting for nonstationary gene flow in range-shifting species.

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