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Abstract Latent space models are often used to model network data by embedding a network’s nodes into a low-dimensional latent space; however, choosing the dimension of this space remains a challenge. To this end, we begin by formalizing a class of latent space models we call generalized linear network eigenmodels that can model various edge types (binary, ordinal, nonnegative continuous) found in scientific applications. This model class subsumes the traditional eigenmodel by embedding it in a generalized linear model with an exponential dispersion family random component and fixes identifiability issues that hindered interpretability. We propose a Bayesian approach to dimension selection for generalized linear network eigenmodels based on an ordered spike-and-slab prior that provides improved dimension estimation and satisfies several appealing theoretical properties. We show that the model’s posterior is consistent and concentrates on low-dimensional models near the truth. We demonstrate our approach’s consistent dimension selection on simulated networks, and we use generalized linear network eigenmodels to study the effect of covariates on the formation of networks from biology, ecology, and economics and the existence of residual latent structure. 

Reciprocity, or the stochastic tendency for actors to form mutual relationships, is an essential characteristic of directed network data. Existing latent space approaches to modelling directed networks are severely limited by the assumption that reciprocity is homogeneous across the network. In this work, we introduce a new latent space model for directed networks that can model heterogeneous reciprocity patterns that arise from the actors' latent distances. Furthermore, existing conditionally edge‐independent latent space models are nested within the proposed model class, which allows for meaningful model comparisons. We introduce a Bayesian inference procedure to infer the model parameters using Hamiltonian Monte Carlo. Lastly, we use the proposed method to infer different reciprocity patterns in an advice network among lawyers, an information‐sharing network between employees at a manufacturing company and a friendship network between high school students. 

Abstract Intraspecific trait variation can influence plant performance in different environments and may thereby determine the ability of individual plants to respond to climate change. However, our understanding of its patterns and environmental drivers across different spatial scales is incomplete, especially in understudied regions like the Arctic.To fill this knowledge gap, we examined above‐ground and below‐ground traits from three shrub taxa expanding across the tundra biome and evaluated their relationships with multiple microenvironmental and macroclimatic factors. The traits reflected plant size and structure (plant height, leaf area and root to shoot ratio), leaf economics (specific leaf area, nitrogen content), and root economics and collaboration with mycorrhizal fungi (specific root length, root tissue density, nitrogen content, and ectomycorrhizal colonisation intensity). We also measured leaf and root δ¹⁵N and leaf δ¹³C to characterise nitrogen source and acquisition pathways and plant water stress. Traits were measured in replicated plots (N = 135) varying in soil microclimate, thaw depth and organic layer thickness established across five sites spanning a macroclimate gradient in northern Alaska. This hierarchical design allowed us to disentangle the independent and combined effects of fine‐scale and broad‐scale factors on intraspecific trait variation.We found substantial intraspecific variation at fine spatial scales for most traits and less variation along the macroclimate gradient and between shrub taxa. Consistent with these patterns, microenvironmental factors, mainly soil moisture and thaw depth, interacted with macroclimate, mainly climatic water deficit, to structure size‐structural and leaf trait variation. In contrast, most root traits responded additively to thaw depth and macroclimate.Synthesis. Our results demonstrate that above‐ground and below‐ground tundra shrub traits respond differently to microenvironmental and macroclimatic variation. These differing responses contribute to substantial trait variation at fine spatial scales and may decouple above‐ground and below‐ground trait responses to climate change.