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Repeated surveys of vegetation plots offer a viable tool to detect fine‐scale responses of vegetation to environmental changes. In this study, our aim was to explore how the species composition and species richness of dry grasslands changed over a period of 17 years, how these changes relate to environmental changes and how the presence of spring ephemerals, which may react to short‐term weather fluctuations rather than long‐term climatic trends, may influence the results. A total of 95 plots was surveyed in 2005 and resurveyed in 2022 in dry grasslands of the Kiskunság Sand Ridge (Hungary, Eastern Central Europe), where there has been a significant increase in mean annual temperature during the last decades, while no trends in precipitation can be identified. Db‐RDA was performed to reveal compositional changes. The changes in environmental conditions and naturalness state were assessed using ecological and naturalness indicator values. We also compared per‐plot richness of all species, native species and non‐native species of the old and the new relevés. All analyses were repeated after removing all spring ephemerals. We found clear temporal changes in species composition. Mean temperature indicator values increased, while mean soil moisture indicator values decreased during the 17 years. Also, decreasing per‐plot richness was detected both for all species and for native species, while mean naturalness increased. After the removal of spring ephemerals, the compositional changes were less obvious although still significant. The increase in the temperature indicator values remained significant even without the spring ephemerals. However, the decrease in the moisture indicator values, the decrease in the number of all species and native species, as well as the increase in naturalness indicator values disappeared when spring ephemerals were excluded from the analyses. Our study demonstrates that between‐year weather differences and long‐term environmental trends both contribute to observed vegetation changes. [ABSTRACT FROM AUTHOR]

We consider N×N$N\times N$ non‐Hermitian random matrices of the form X+A$X+A$, where A$A$ is a general deterministic matrix and NX$\sqrt {N}X$ consists of independent entries with zero mean, unit variance, and bounded densities. For this ensemble, we prove (i) a Wegner estimate, that is, that the local density of eigenvalues is bounded by N1+o(1)$N^{1+o(1)}$ and (ii) that the expected condition number of any bulk eigenvalue is bounded by N1+o(1)$N^{1+o(1)}$; both results are optimal up to the factor No(1)$N^{o(1)}$. The latter result complements the very recent matching lower bound obtained by Cipolloni et al. and improves the N$N$‐dependence of the upper bounds by Banks et al. and Jain et al. Our main ingredient, a near‐optimal lower tail estimate for the small singular values of X+A−z$X+A-z$, is of independent interest. [ABSTRACT FROM AUTHOR]

We consider the spectral radius of a large random matrix X with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the celebrated circular law. The coefficients in this asymptotics are universal but they differ from a similar asymptotics recently proved for the rightmost eigenvalue of X in Cipolloni et al., Ann. Probab. 51(6), 2192–2242 (2023). To access the more complicated spectral radius, we need to establish a new decorrelation mechanism for the low-lying singular values of X − z for different complex shift parameters z using the Dyson Brownian Motion. [ABSTRACT FROM AUTHOR]

Aims: Ecological strategies can provide information about plant community assembly and its main drivers. Our aim was to reveal the dominant strategies of the vegetation types of forest–grassland mosaics and to deduce the assembly processes responsible for their species composition. Location: Hungary. Methods: We investigated eight vegetation types of Hungarian forest–steppes. The trade‐off between three key traits related to leaf size and economics was used to calculate Grime's competitive–stress tolerance–ruderal (CSR) value for each species, based on which the mean value for each vegetation type was determined. Detrended correspondence analysis (DCA) ordination was used to reveal the compositional differences among the vegetation types under study. To analyze how ecological strategies correlate with the compositional gradient, we used linear regression between plot ordination scores (the first DCA scores) and each strategy (C, S, and R). Linear mixed‐effect models were used to evaluate the differences between the vegetation types regarding each strategy (C, S, and R). Results: Each vegetation type was dominated by the stress‐tolerator strategy, indicating the prominent role of environmental filtering in community assembly. However, ecological strategies differed significantly among the communities. The importance of the stress‐tolerator strategy decreased toward the less harsh end of the gradient (i.e., from grasslands to forests), while the competitor strategy showed a reverse pattern. The ruderal strategy was weakly correlated with the gradient, although its proportion increased toward the harsh end of the gradient. Conclusions: With ongoing climate change, an increasing importance of environmental filtering is expected in the assembly of the vegetation types in the studied forest–grassland mosaics. We suggest that CSR strategies offer a useful tool for studying plant‐community assembly rules along environmental gradients. [ABSTRACT FROM AUTHOR]

We consider large non‐Hermitian random matrices X with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having 2+ϵ derivatives. Previously this result was known only for a few special cases; either the test functions were required to be analytic [72], or the distribution of the matrix elements needed to be Gaussian [73], or at least match the Gaussian up to the first four moments [82, 56]. We find the exact dependence of the limiting variance on the fourth cumulant that was not known before. The proof relies on two novel ingredients: (i) a local law for a product of two resolvents of the Hermitisation of X with different spectral parameters and (ii) a coupling of several weakly dependent Dyson Brownian motions. These methods are also the key inputs for our analogous results on the linear eigenvalue statistics of real matrices X that are presented in the companion paper [32]. © 2021 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]