Topographic depressions can provide climate and resource microrefugia for biodiversity.

Microrefugia are often located within topographically complex regions where stable environmental conditions prevail. Most of the studies concerning the distributions of climate change-sensitive species have emphasized the dominance of cold air pooling over other environmental factors, such as resource availability. There is a shortage of information on the relationships among topography-related microsite diversity, microclimate, resource availability, and species composition in microrefugia. To fill this knowledge gap, we studied the effects of microclimatic conditions and soil resources on plant species occurrence within and adjacent to 30 large topographic depressions (i.e., dolines) in two distant karst regions. Our results showed that both microclimate and soil resource availability may play a key role in maintaining climate change-sensitive species and biodiversity in dolines; therefore, they may simultaneously act as climate and resource microrefugia. Establishing climate-smart conservation priorities and strategies is required to maintain or increase the refugial capacity of such safe havens.

Empirical delineation of the forest-steppe zone is supported by macroclimate.

Eurasian forest-steppes form a 9000-km-long transitional zone between temperate forests and steppes, featuring a complex mosaic of herbaceous and woody habitats. Due to its heterogeneity regarding climate, topography and vegetation, the forest-steppe zone has been divided into several regions. However, a continental-scale empirical delineation of the zone and its regions was missing until recently. Finally, a map has been proposed by Erdos et al. based on floristic composition, physiognomy, relief, and climate. By conducting predictive distribution modeling and hierarchical clustering, here we compared this expert delineation with the solely macroclimate-based predictions and clusters. By assessing the discrepancies, we located the areas where refinement of the delineation or the inclusion of non-macroclimatic predictors should be considered. Also, we identified the most important variables for predicting the existence of the Eurasian forest-steppe zone and its regions. The predicted probability of forest-steppe occurrence showed a very high agreement with the expert delineation. The previous delineation of the West Siberia region was confirmed by our results, while that of the Inner Asia region was the one least confirmed by the macroclimate-based model predictions. The appropriate delineation of the Southeast Europe region from the East Europe region should be refined by further research, and splitting the Far East region into a southern and northern subregion should also be considered. The main macroclimatic predictors of the potential distribution of the zone and its regions were potential evapotranspiration (zone and regions), annual mean temperature (regions), precipitation of driest quarter (regions) and precipitation of warmest quarter (zone), but the importance of climatic variables for prediction showed great variability among the fitted predictive distribution models.

On the Spectral Form Factor for Random Matrices.

In the physics literature the spectral form factor (SFF), the squared Fourier transform of the empirical eigenvalue density, is the most common tool to test universality for disordered quantum systems, yet previous mathematical results have been restricted only to two exactly solvable models (Forrester in J Stat Phys 183:33, 2021. 10.1007/s10955-021-02767-5, Commun Math Phys 387:215-235, 2021. 10.1007/s00220-021-04193-w). We rigorously prove the physics prediction on SFF up to an intermediate time scale for a large class of random matrices using a robust method, the multi-resolvent local laws. Beyond Wigner matrices we also consider the monoparametric ensemble and prove that universality of SFF can already be triggered by a single random parameter, supplementing the recently proven Wigner-Dyson universality (Cipolloni et al. in Probab Theory Relat Fields, 2021. 10.1007/s00440-022-01156-7) to larger spectral scales. Remarkably, extensive numerics indicates that our formulas correctly predict the SFF in the entire slope-dip-ramp regime, as customarily called in physics.

Environmental heterogeneity increases the conservation value of small natural features in karst landscapes.

Local biodiversity hotspots are often located within regions where extreme and variable environmental - e.g., climatic and soil - conditions occur. These areas are conservation priorities. Although environmental heterogeneity is recognised as an important determinant of biodiversity, studies focusing on the effects of multiple environmental heterogeneity components in the same ecosystem are scarce. Here we investigate how topography and related microclimatic variables and soil properties may influence the biodiversity and conservation value of karst landscapes. Karst landscapes of the world contain millions of dolines (i.e. bowl- or funnel-shaped depressions) that may function as 'small natural features' with a disproportionately large role in maintaining biodiversity relative to their size. We assessed the diversity of microclimates, soils and vegetation and their relationships in six microhabitats (south-facing slopes, east-facing slopes, west-facing slopes, north-facing slopes and bottoms of dolines, and the adjacent plateau) for nine large dolines in a grassland ecosystem. Although there were remarkable differences among the conservation value of these microhabitats (e.g., representation of different species groups, presence of 'climate relicts'), each microhabitat had an important role in maintaining species that are rare or absent in other microhabitats in the landscape. We found that the studied dolines exhibited highly variable environmental conditions and promoted a high diversity of vegetation types with unique species composition, contributing to the topographic, climatic, soil, vegetation and land cover heterogeneity of karst landscapes. Therefore, our findings highlight that dolines may function as local biodiversity hotspots and have a crucial conservation importance. As dolines are widespread topographic features in many karst landscapes throughout the world, our results could be directly applied to other regions as well. An integrated approach is urgently needed to provide guidelines for landscape management, promoting the retention of the microhabitat diversity of small natural features for species vulnerable to climate change and/or various disturbances.

How to not trade water for carbon with tree planting in water-limited temperate biomes?

The most widespread nature-based solution for mitigating climate change is tree planting. When realized as forest restoration in historically forested biomes, it can efficiently contribute to the sequestration of atmospheric carbon and can also entail significant biodiversity and ecosystem service benefits. Conversely, tree planting in naturally open biomes can have adverse effects, of which water shortage due to increased evapotranspiration is among the most alarming ones. Here we assessed how soil texture affects the strength of the trade-off between tree cover and water balance in the forest-steppe biome, where the global pressure for afforestation is threatening with increasing tree cover above historical levels. Here we monitored vertical soil moisture dynamics in four stands in each of the most common forest types of lowland Hungary on well-drained, sandy (natural poplar groves, and Robinia and pine plantations) and on poorly drained, silty-clayey soils (natural oak stands and Robinia plantations), and neighboring grasslands. We found that forests on sand retain moisture in the topsoil (approx. 20 cm) throughout the year, but a thick dry layer develops below that during the vegetation period, significantly impeding groundwater recharge. Neighboring sandy grasslands showed an opposite pattern, with often dry topsoil but intact moisture reserves below, allowing deep percolation. In contrast, forests on silty-clayey soils did not desiccate lower soil layers compared neighboring grasslands, which in turn showed moisture patterns similar to sandy grasslands. We conclude that, in water-limited temperate biomes where landscape-wide water regime depends on deep percolation, soil texture should drive the spatial allocation of tree-based climate mitigation efforts. On sand, the establishment of new forests should be kept to a minimum and grassland restoration should be preferred. The trade-off between water and carbon is less pronounced on silty-clayey soils, making forest patches and wooded rangelands viable targets for both climate mitigation and ecosystem restoration.

How climate, topography, soils, herbivores, and fire control forest-grassland coexistence in the Eurasian forest-steppe.

Recent advances in ecology and biogeography demonstrate the importance of fire and large herbivores - and challenge the primacy of climate - to our understanding of the distribution, stability, and antiquity of forests and grasslands. Among grassland ecologists, particularly those working in savannas of the seasonally dry tropics, an emerging fire-herbivore paradigm is generally accepted to explain grass dominance in climates and on soils that would otherwise permit development of closed-canopy forests. By contrast, adherents of the climate-soil paradigm, particularly foresters working in the humid tropics or temperate latitudes, tend to view fire and herbivores as disturbances, often human-caused, which damage forests and reset succession. Towards integration of these two paradigms, we developed a series of conceptual models to explain the existence of an extensive temperate forest-grassland mosaic that occurs within a 4.7 million km2 belt spanning from central Europe through eastern Asia. The Eurasian forest-steppe is reminiscent of many regions globally where forests and grasslands occur side-by-side with stark boundaries. Our conceptual models illustrate that if mean climate was the only factor, forests should dominate in humid continental regions and grasslands should prevail in semi-arid regions, but that extensive mosaics would not occur. By contrast, conceptual models that also integrate climate variability, soils, topography, herbivores, and fire depict how these factors collectively expand suitable conditions for forests and grasslands, such that grasslands may occur in more humid regions and forests in more arid regions than predicted by mean climate alone. Furthermore, boundaries between forests and grasslands are reinforced by vegetation-fire, vegetation-herbivore, and vegetation-microclimate feedbacks, which limit tree establishment in grasslands and promote tree survival in forests. Such feedbacks suggest that forests and grasslands of the Eurasian forest-steppe are governed by ecological dynamics that are similar to those hypothesised to maintain boundaries between tropical forests and savannas. Unfortunately, the grasslands of the Eurasian forest-steppe are sometimes misinterpreted as deforested or otherwise degraded vegetation. In fact, the grasslands of this region provide valuable ecosystem services, support a high diversity of plants and animals, and offer critical habitat for endangered large herbivores. We suggest that a better understanding of the fundamental ecological controls that permit forest-grassland coexistence could help us prioritise conservation and restoration of the Eurasian forest-steppe for biodiversity, climate adaptation, and pastoral livelihoods. Currently, these goals are being undermined by tree-planting campaigns that view the open grasslands as opportunities for afforestation. Improved understanding of the interactive roles of climate variability, soils, topography, fire, and herbivores will help scientists and policymakers recognise the antiquity of the grasslands of the Eurasian forest-steppe.

Post-restoration grassland management overrides the effects of restoration methods in propagule-rich landscapes.

Grassland restoration is gaining momentum worldwide to tackle the loss of biodiversity and associated ecosystem services. Restoration methods and their effects on ecological community reassembly have been extensively studied across various grassland types, while the importance of post-restoration management has so far received less attention. Grassland management is an important surrogate for natural disturbances, with which most ancient grasslands have coevolved. Thus, without the reintroduction of management-related disturbance, restoration targets are unlikely to be achieved in restored grasslands. In this study, we aimed to explore how 20 yr of management by mowing once a year or light cattle grazing affects restoration success in Palearctic meadow-steppe grasslands restored by either sowing native grasses (sown sites), applying Medicago sativa as a nurse plant (Medicago sites), or allowing spontaneous succession (spontaneous sites). We found that, following mowing, sown sites maintained long-lasting establishment limitation, while Medicago sites experienced a delay in succession. These limitations resulted in low total and target species richness, low functional redundancy, and distinct species and functional composition compared to reference data from ancient grasslands. Spontaneous sites that were mowed reached a more advanced successional stage, although they did not reach reference levels regarding most vegetation descriptors. Sown and Medicago sites that were grazed had higher total and target species richness than those that were mowed, and showed restoration success similar to that of spontaneous sites, on which grazing had only moderate further positive effects. Grazed sites, irrespective of the restoration method, were uniformly species rich, functionally diverse, and functionally redundant, and thus became important biodiverse habitats with considerable resilience. We conclude that an optimally chosen post-restoration management may have an impact on long-term community reassembly comparable to the choice of restoration method. Restoration planners may, therefore, need to put more emphasis on future management than on the initial restoration method. However, our findings also imply that if local constraints, such as potentially high invasive propagule pressure, necessitate the application of restoration methods that could also hinder the establishment of target species, the long-term recovery of the grassland can still be ensured by wisely chosen post-restoration management.

Edge universality for non-Hermitian random matrices.

We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy-Widom distribution at the spectral edges of the Wigner ensemble.

Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.

For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner-Dyson-Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969).

Beyond the Forest-Grassland Dichotomy: The Gradient-Like Organization of Habitats in Forest-Steppes.

Featuring a transitional zone between closed forests and treeless steppes, forest-steppes cover vast areas, and have outstanding conservation importance. The components of this mosaic ecosystem can conveniently be classified into two basic types, forests and grasslands. However, this dichotomic classification may not fit reality as habitat organization can be much more complex. In this study, our aim was to find out if the main habitat types can be grouped into two distinct habitat categories (which would support the dichotomic description), or a different paradigm better fits this complex ecosystem. We selected six main habitats of sandy forest-steppes, and, using 176 relevés, we compared their vegetation based on species composition (NMDS ordination, number of common species of the studied habitats), relative ecological indicator values (mean indicators for temperature, soil moisture, and light availability), and functional species groups (life-form categories, geoelement types, and phytosociological preference groups). According to the species composition, we found a well-defined gradient, with the following habitat order: large forest patches, medium forest patches, small forest patches, north-facing edges, south-facing edges, and grasslands. A considerable number of species were shared among all habitats, while the number of species restricted to certain habitat types was also numerous, especially for north-facing edges. The total (i.e., pooled) number of species peaked near the middle of the gradient, in north-facing edges. The relative ecological indicator values and functional species groups showed mostly gradual changes from the large forest patches to the grasslands. Our results indicate that the widely used dichotomic categorization of forest-steppe habitats into forest and grassland patches is too simplistic, potentially resulting in a considerable loss of information. We suggest that forest-steppe vegetation better fits the gradient-based paradigm of landscape structure, which is able to reflect continuous variations.

Karst dolines provide diverse microhabitats for different functional groups in multiple phyla.

Fine-scale topographic complexity creates important microclimates that can facilitate species to grow outside their main distributional range and increase biodiversity locally. Enclosed depressions in karst landscapes ('dolines') are topographically complex environments which produce microclimates that are drier and warmer (equator-facing slopes) and cooler and moister (pole-facing slopes and depression bottoms) than the surrounding climate. We show that the distribution patterns of functional groups for organisms in two different phyla, Arthropoda (ants) and Tracheophyta (vascular plants), mirror this variation of microclimate. We found that north-facing slopes and bottoms of solution dolines in northern Hungary provided key habitats for ant and plant species associated with cooler and/or moister conditions. Contrarily, south-facing slopes of dolines provided key habitats for species associated with warmer and/or drier conditions. Species occurring on the surrounding plateau were associated with intermediate conditions. We conclude that karst dolines provide a diversity of microclimatic habitats that may facilitate the persistence of taxa with diverse environmental preferences, indicating these dolines to be potential safe havens for multiple phyla under local and global climate oscillations.

Large- and small-scale environmental factors drive distributions of cool-adapted plants in karstic microrefugia.

BACKGROUND AND AIMS: Dolines are small- to large-sized bowl-shaped depressions of karst surfaces. They may constitute important microrefugia, as thermal inversion often maintains cooler conditions within them. This study aimed to identify the effects of large- (macroclimate) and small-scale (slope aspect and vegetation type) environmental factors on cool-adapted plants in karst dolines of East-Central Europe. We also evaluated the potential of these dolines to be microrefugia that mitigate the effects of climate change on cool-adapted plants in both forest and grassland ecosystems. METHODS: We compared surveys of plant species composition that were made between 2007 and 2015 in 21 dolines distributed across four mountain ranges (sites) in Hungary and Romania. We examined the effects of environmental factors on the distribution and number of cool-adapted plants on three scales: (1) regional (all sites); (2) within sites and; (3) within dolines. Generalized linear models and non-parametric tests were used for the analyses. KEY RESULTS: Macroclimate, vegetation type and aspect were all significant predictors of the diversity of cool-adapted plants. More cool-adapted plants were recorded in the coolest site, with only few found in the warmest site. At the warmest site, the distribution of cool-adapted plants was restricted to the deepest parts of dolines. Within sites of intermediate temperature and humidity, the effect of vegetation type and aspect on the diversity of cool-adapted plants was often significant, with more taxa being found in grasslands (versus forests) and on north-facing slopes (versus south-facing slopes). CONCLUSIONS: There is large variation in the number and spatial distribution of cool-adapted plants in karst dolines, which is related to large- and small-scale environmental factors. Both macro- and microrefugia are therefore likely to play important roles in facilitating the persistence of cool-adapted plants under global warming.

Local Spectral Statistics of Gaussian Matrices with Correlated Entries.

We prove optimal local law, bulk universality and non-trivial decay for the off-diagonal elements of the resolvent for a class of translation invariant Gaussian random matrix ensembles with correlated entries.

Rigorous derivation of the Gross-Pitaevskii equation.

The time-dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schrödinger equation with a short-scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short-scale correlation structure in the condensate.