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Our planet hosts a variety of highly diverse ecosystems. The persistence of high diversity is generally attributed to factors such as the structure of interactions among species and the dispersal of species in metacommunities. Here, we show that large contiguous landscapes-that are characterized by high dispersal-facilitate high species richness due to the spatial heterogeneity in interspecies interactions. We base our analysis on metacommunities under high dispersal where species densities become equal across habitats (spatially coherent). We find that the spatially coherent metacommunity can be represented by an effective species interaction-web that has a significantly lower complexity than the constituent habitats. Our framework also explains how spatial heterogeneity eliminates differences in the effective interaction-web, providing a basis for deviations from the area-heterogeneity tradeoff. These results highlight the often-overlooked case of high dispersal where spatial coherence provides a novel mechanism for supporting high diversity in large heterogeneous landscapes.

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Understanding ecosystem stability and functioning is a long-standing goal in theoretical ecology, with one of the main tools being dynamical modelling of species abundances. With the help of spatially unresolved (well-mixed) population models and equilibrium dynamics, limits to stability and regions of various ecosystem robustness have been extensively mapped in terms of diversity (number of species), types of interactions, interaction strengths, varying interaction networks (for example plant-pollinator, food-web) and varying structures of these networks. Although many insights have been gained, the impact of spatial extension is not included in this body of knowledge. Recent studies of spatially explicit modelling on the other hand have shown that stability limits can be crossed and diversity increased for systems with spatial heterogeneity in species interactions and/or chaotic dynamics. Here we show that such crossing and diversity increase can appear under less strict conditions. We find that the mere possibility of varying species abundances at different spatial locations make possible the preservation or increase in diversity across previous boundaries thought to mark catastrophic transitions. In addition, we introduce and make explicit a multitude of different dynamics a spatially extended complex system can use to stabilise. This expanded stabilising repertoire of dynamics is largest at intermediate levels of dispersal. Thus we find that spatially extended systems with intermediate dispersal are more robust, in general have higher diversity and can stabilise beyond previous stability boundaries, in contrast to well-mixed systems.

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Dynamical shifts between the extremes of stability and collapse are hallmarks of ecological systems. These shifts are limited by and change with biodiversity, complexity, and the topology and hierarchy of interactions. Most ecological research has focused on identifying conditions for a system to shift from stability to any degree of instability-species abundances do not return to exact same values after perturbation. Real ecosystems likely have a continuum of shifting between stability and collapse that depends on the specifics of how the interactions are structured, as well as the type and degree of disturbance due to environmental change. Here we map boundaries for the extremes of strict stability and collapse. In between these boundaries, we find an intermediate regime that consists of single-species extinctions, which we call the extinction continuum. We also develop a metric that locates the position of the system within the extinction continuum-thus quantifying proximity to stability or collapse-in terms of ecologically measurable quantities such as growth rates and interaction strengths. Furthermore, we provide analytical and numerical techniques for estimating our new metric. We show that our metric does an excellent job of capturing the system's behaviour in comparison with other existing methods-such as May's stability criteria or critical slowdown. Our metric should thus enable deeper insights about how to classify real systems in terms of their overall dynamics and their limits of stability and collapse.

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The eelgrass Zostera marina is an important foundation species of coastal areas in the Northern Hemisphere, but is continuing to decline, despite management actions. The development of new management tools is therefore urgent in order to prioritize limited resources for protecting meadows most vulnerable to local extinctions and identifying most valuable present and historic meadows to protect and restore, respectively. We assessed 377 eelgrass meadows along the complex coastlines of two fjord regions on the Swedish west coast-one is currently healthy and the other is substantially degraded. Shoot dispersal for all meadows was assessed with Lagrangian biophysical modeling (scale: 100-1,000 m) and used for barrier analysis and clustering; a subset (n = 22) was also assessed with population genetic methods (20 microsatellites) including diversity, structure, and network connectivity. Both approaches were in very good agreement, resulting in seven subpopulation groupings or management units (MUs). The MUs correspond to a spatial scale appropriate for coastal management of "waterbodies" used in the European Water Framework Directive. Adding demographic modeling based on the genetic and biophysical data as a third approach, we are able to assess past, present, and future metapopulation dynamics to identify especially vulnerable and valuable meadows. In a further application, we show how the biophysical approach, using eigenvalue perturbation theory (EPT) and distribution records from the 1980s, can be used to identify lost meadows where restoration would best benefit the present metapopulation. The combination of methods, presented here as a toolbox, allows the assessment of different temporal and spatial scales at the same time, as well as ranking of specific meadows according to key genetic, demographic and ecological metrics. It could be applied to any species or region, and we exemplify its versatility as a management guide for eelgrass along the Swedish west coast.

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Maintaining and enabling evolutionary processes within meta-populations are critical to resistance, resilience and adaptive potential. Knowledge about which populations act as sources or sinks, and the direction of gene flow, can help to focus conservation efforts more effectively and forecast how populations might respond to future anthropogenic and environmental pressures. As a foundation species and habitat provider, Zostera marina (eelgrass) is of critical importance to ecosystem functions including fisheries. Here, we estimate connectivity of Z. marina in the Skagerrak-Kattegat region of the North Sea based on genetic and biophysical modelling. Genetic diversity, population structure and migration were analysed at 23 locations using 20 microsatellite loci and a suite of analytical approaches. Oceanographic connectivity was analysed using Lagrangian dispersal simulations based on contemporary and historical distribution data dating back to the late 19th century. Population clusters, barriers and networks of connectivity were found to be very similar based on either genetic or oceanographic analyses. A single-generation model of dispersal was not realistic, whereas multigeneration models that integrate stepping-stone dispersal and extant and historic distribution data were able to capture and model genetic connectivity patterns well. Passive rafting of flowering shoots along oceanographic currents is the main driver of gene flow at this spatial-temporal scale, and extant genetic connectivity strongly reflects the "ghost of dispersal past" sensu Benzie, 1999. The identification of distinct clusters, connectivity hotspots and areas where connectivity has become limited over the last century is critical information for spatial management, conservation and restoration of eelgrass.

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A perturbation method for computing quick estimates of the echo decay in pulsed spin echo gradient NMR diffusion experiments in the short gradient pulse limit is presented. The perturbation basis involves (relatively few) dipole distributions on the boundaries generating a small perturbation matrix in O(s(2)) time, where s denotes the number of boundary elements. Several approximate eigenvalues and eigenfunctions to the diffusion operator are retrieved. The method is applied to 1D and 2D systems with Neumann boundary conditions.

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