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Abstract Quantifying the structure and dynamics of species interactions in ecological communities is fundamental to studying ecology and evolution. While there are numerous approaches to analysing ecological networks, there is not yet an approach that can (1) quantify dissimilarity in the global structure of ecological networks that range from identical species and interaction composition to zero shared species or interactions and (2) map species between such networks while incorporating additional ecological information, such as species traits or abundances.To address these challenges, we introduce the use of optimal transport distances to quantify ecological network dissimilarity and functionally equivalent species between networks. Specifically, we describe the Gromov–Wasserstein (GW) and Fused Gromov–Wasserstein (FGW) distances. We apply these optimal transport methods to synthetic and empirical data, using mammal food webs throughout sub‐Saharan Africa for illustration. We showcase the application of GW and FGW distances to identify the most functionally similar species between food webs, incorporate additional trait information into network comparisons and quantify food web dissimilarity among geographic regions.Our results demonstrate that GW and FGW distances can effectively differentiate ecological networks based on their topological structure while identifying functionally equivalent species, even when networks have different species. The FGW distance further improves node mapping for basal species by incorporating node‐level traits. We show that these methods allow for a more nuanced understanding of the topological similarities in food web networks among geographic regions compared to an alternative measure of network dissimilarity based on species identities.Optimal transport distances offer a new approach for quantifying functional equivalence between networks and a measure of network dissimilarity suitable for a broader range of uses than existing approaches. OT methods can be harnessed to analyse ecological networks at large spatial scales and compare networks among ecosystems, realms or taxa. Optimal transport‐based distances, therefore, provide a powerful tool for analysing ecological networks with great potential to advance our understanding of ecological community structure and dynamics in a changing world.
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Projection‐based techniques for high‐dimensional optimal transport problems
Abstract Optimal transport (OT) methods seek a transformation map (or plan) between two probability measures, such that the transformation has the minimum transportation cost. Such a minimum transport cost, with a certain power transform, is called the Wasserstein distance. Recently, OT methods have drawn great attention in statistics, machine learning, and computer science, especially in deep generative neural networks. Despite its broad applications, the estimation of high‐dimensional Wasserstein distances is a well‐known challenging problem owing to the curse‐of‐dimensionality. There are some cutting‐edge projection‐based techniques that tackle high‐dimensional OT problems. Three major approaches of such techniques are introduced, respectively, the slicing approach, the iterative projection approach, and the projection robust OT approach. Open challenges are discussed at the end of the review. This article is categorized under:Statistical and Graphical Methods of Data Analysis > Dimension ReductionStatistical Learning and Exploratory Methods of the Data Sciences > Manifold Learning
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- PAR ID:
- 10443887
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- WIREs Computational Statistics
- Volume:
- 15
- Issue:
- 2
- ISSN:
- 1939-5108
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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