Dyadic Flow Models for Nonstationary Gene Flow in Landscape Genomics
Abstract
The field of landscape genomics aims to infer how landscape features affect gene flow across space. Most landscape genomic frameworks assume the isolation-by-distance and isolation-by-resistance hypotheses, which propose that genetic dissimilarity increases 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 source-destination pairs. 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 nonstationarity gene flow in range-shifting species.
Summary
This paper addresses the limitations of existing landscape genomic models, which primarily focus on isolation-by-distance (IBD) and isolation-by-resistance (IBR) hypotheses, particularly when applied to invasive species. The authors argue that invasion dynamics, such as founder effects, multiple introductions, and human-assisted transport, lead to nonstationary gene flow that traditional models fail to capture. To overcome this, they introduce dyadic spatially-varying coefficients (DSVCs) within a dyadic modeling framework. DSVCs allow the effects of landscape features on gene flow to vary across space, capturing nonstationary and asymmetric connectivity. Additionally, they incorporate connectivity covariates, representing localized landscape features like rivers or roads that act as corridors or barriers to gene flow. The methodology involves extending dyadic regression models to include DSVCs and connectivity covariates. A latent spatial factor model is used to address the high dimensionality of DSVCs, reducing the number of parameters needed. The model uses a separable Kronecker structure to define a dyadic covariance matrix, making computation feasible. Global-local shrinkage priors are applied to the covariate loading matrix to encourage parsimony and interpretability. The model is implemented within a Bayesian hierarchical framework and fit using a blocked Gibbs-Metropolis sampler. The authors demonstrate the utility of their approach through a simulation study and a case study analyzing cheatgrass (Bromus tectorum) gene flow in its native and invaded ranges. The key finding is that accounting for nonstationarity in gene flow, particularly through DSVCs and connectivity covariates, is crucial for accurately modeling the spread of invasive species. This research contributes to the field of landscape genomics by providing a more flexible and comprehensive framework for analyzing gene flow in invasive species. The introduction of DSVCs and connectivity covariates allows for the capture of complex, nonstationary, and directional processes that are often overlooked by traditional models. By explicitly modeling these dynamics, the framework provides a more accurate understanding of invasion processes and can be used to identify key environmental factors and pathways that influence the spread of invasive species. This has important implications for conservation efforts and management strategies aimed at controlling invasive species.
Key Insights
- •Novel Method: The paper introduces dyadic spatially-varying coefficients (DSVCs) and connectivity covariates within a dyadic regression framework for landscape genomics, enabling the modeling of nonstationary gene flow.
- •Dimensionality Reduction: A latent spatial factor model is used to reduce the dimensionality of DSVCs, making computation feasible by learning a low-rank structure with (N x Q) + (p x Q) parameters instead of N x p parameters, where Q << min(N,p).
- •Kronecker Structure: A separable Kronecker covariance structure is employed to efficiently compute the dyadic covariance matrix, avoiding the need to construct or factorize a dense N x N covariance matrix directly on the dyadic space.
- •Simulation Results: In the simulation study, models including DSVCs and connectivity covariates achieved significantly better performance based on Continuous Ranked Probability Score (CRPS). Specifically, the mean CRPS improved from 5.575 (standard model) to 1.236 (full model).
- •Cheatgrass Analysis: The cheatgrass case study demonstrates the necessity of accounting for nonstationary gene flow in range-shifting species, providing a novel way to investigate the genomic mechanisms of invasion.
- •Shrinkage Priors: Global-local shrinkage priors on the covariate loading matrix (C) adaptively enforce sparsity, highlighting influential environmental effects while maintaining computational tractability and ecological interpretability. This is crucial when the number of covariates (p) is large relative to the information in the dyads.
- •Computational Performance: The sampling rates of models varied significantly, with the standard dyadic model achieving 51 iterations per second (it/s) while the full model with DSVCs and connectivity covariates achieved 1 it/s on a 3.2 GHz processor with 64 GB of RAM, highlighting the computational cost of the extended model.
Practical Implications
- •Invasive Species Management: The framework provides a tool for identifying key environmental factors and pathways that influence the spread of invasive species, informing targeted management strategies.
- •Conservation Planning: The model can be used to predict the spread of populations across heterogeneous landscapes, aiding in conservation planning for both native and invasive species.
- •Risk Assessment: The framework can be applied to assess the risk of invasion by identifying potential corridors and barriers to gene flow, allowing for proactive measures to prevent or mitigate invasions.
- •Model Comparison & Selection: The paper highlights the importance of model selection based on the underlying data generating process. When non-stationary gene flow is present, models incorporating DSVCs and connectivity covariates should be preferred over simpler IBD/IBR models, even at the cost of increased computational complexity.
- •Future Research: The framework opens up avenues for future research, including the development of more efficient computational methods for fitting complex dyadic models and the application of the framework to other invasive species and ecological systems.