Long-term dynamics of the iconic old-forest lichen Usnea longissima in a protected landscape

Long-term data on spatial dynamics of epiphytic lichens associated with old-growth forests are fundamental for understanding how environmental factors drive their extinction and colonization in heterogeneous landscapes. This study focuses on Usnea longissima, a flagship species for biodiversity conservation. By using a long-term data set (37 yr.) of U. longissima in old Picea abies forests in Skuleskogen National Park, Sweden, we examined changes in the number of host trees, population size (sum of thallus length), extinction, colonization, dispersal, and distribution in a protected landscape. We surveyed the lichen in 1984-1985 by applying a line transect inventory and a total population inventory and tagged 355 occupied trees with an aluminium plate buried in the ground. We repeated the survey in 2021 using a metal detector and recorded GPS-position of host trees, tree and lichen population characteristics. We also measured the structure and age (tree-ring data) of the forest to understand how disturbance history influenced lichen populations. Usnea longissima occurred on 66 of the tagged trees and we recorded 141 new host trees. The number of host trees decreased with 41.7% and the population size with 41.9%. One third of the decline was caused by deterministic extinction (treefalls) and two thirds by stochastic extinction on standing trees. The probability of stochastic extinction on live trees decreased with population size in logistic regression. The decline in the sites with largest populations (35-87% loss) was more influenced by limited colonization than extinction. Colonization was highest in humid north-facing hillslopes with multi-layered forests driven by gap dynamics. The lichen was strongly dispersal-limited, with a median effective horizontal dispersal of only 3.8 m in 37 yr., explaining its strong dependence of long continuity of forest cover. The populations were clustered and had substantial local turnover, yet with stable distribution at landscape scale. The tree-ring index, growth releases and gap recruitments indicate extensive harvesting similar to 1860-1900, but without major disturbances during the last 70-80 yr. Instead, the decline of U. longissima was probably driven by air pollution, climate change (autumn/winter mortality and heatwaves) and denser forests. Our findings highlight that the long-term survival of this lichen may be at risk even in forests having a strong level of protection

The accuracy of merging approximation in generalized St. Petersburg games

Merging asymptotic expansions of arbitrary length are established for the distribution functions and for the probabilities of suitably centered and normalized cumulative winnings in a full sequence of generalized St. Petersburg games, extending the short expansions due to Cs\"org\H{o}, S., Merging asymptotic expansions in generalized St. Petersburg games, \textit{Acta Sci. Math. (Szeged)} \textbf{73} 297--331, 2007. These expansions are given in terms of suitably chosen members from the classes of subsequential semistable infinitely divisible asymptotic distribution functions and certain derivatives of these functions. The length of the expansion depends upon the tail parameter. Both uniform and nonuniform bounds are presented.Comment: 30 pages long version (to appear in Journal of Theoretical Probability); some corrected typo

A forest typology for monitoring sustainable forest management: The case of European Forest Types

Sustainable forest management (SFM) is presently widely accepted as the overriding objective for forest policy and practice. Regional processes are in progress all over the world to develop and implement criteria and indicators of SFM. In continental Europe, a set of 35 Pan-European indicators has been endorsed under the Ministerial Conference on the Protection of Forests in Europe (MCPFE) to measure progress towards SFM in the 44 countries of the region. The formulation of seven indicators (forest area, growing stock, age structure/diameter distribution, deadwood, tree species composition, damaging agents, naturalness) requires national data to be reported by forest types. Within the vast European forest area the values taken by these indicators show a considerable range of variation, due to variable natural conditions and anthropogenic influences. Given this variability, it is very difficult to grasp the meaning of these indicators when taken out of their ecological background. The paper discusses the concepts behind, and the requirements of, a classification more soundly ecologically framed and suitable for MCPFE reporting than the three (un-informative) classes adopted so far: broadleaved forest, coniferous forest, mixed broadleaved and coniferous forest. We propose a European Forest Types scheme structured into a reasonably higher number of classes, that would improve the specificity of the indicators reported under the MCPFE process and its understanding.L'articolo è disponibile sul sito dell'editore www.tandf.co.uk/journals

An improvement of the Berry--Esseen inequality with applications to Poisson and mixed Poisson random sums

By a modification of the method that was applied in (Korolev and Shevtsova, 2009), here the inequalities $$\rho(F_n,\Phi)\le\frac{0.335789(\beta^3+0.425)}{\sqrt{n}}$$ and $$\rho(F_n,\Phi)\le \frac{0.3051(\beta^3+1)}{\sqrt{n}}$$ are proved for the uniform distance $\rho(F_n,\Phi)$ between the standard normal distribution function $\Phi$ and the distribution function $F_n$ of the normalized sum of an arbitrary number $n\ge1$ of independent identically distributed random variables with zero mean, unit variance and finite third absolute moment $\beta^3$. The first of these inequalities sharpens the best known version of the classical Berry--Esseen inequality since $0.335789(\beta^3+0.425)\le0.335789(1+0.425)\beta^3<0.4785\beta^3$ by virtue of the condition $\beta^3\ge1$, and 0.4785 is the best known upper estimate of the absolute constant in the classical Berry--Esseen inequality. The second inequality is applied to lowering the upper estimate of the absolute constant in the analog of the Berry--Esseen inequality for Poisson random sums to 0.3051 which is strictly less than the least possible value of the absolute constant in the classical Berry--Esseen inequality. As a corollary, the estimates of the rate of convergence in limit theorems for compound mixed Poisson distributions are refined.Comment: 33 page

Fractal iso-contours of passive scalar in smooth random flows

We consider a passive scalar field under the action of pumping, diffusion and advection by a smooth flow with a Lagrangian chaos. We present theoretical arguments showing that scalar statistics is not conformal invariant and formulate new effective semi-analytic algorithm to model the scalar turbulence. We then carry massive numerics of passive scalar turbulence with the focus on the statistics of nodal lines. The distribution of contours over sizes and perimeters is shown to depend neither on the flow realization nor on the resolution (diffusion) scale $r_d$ for scales exceeding $r_d$. The scalar isolines are found fractal/smooth at the scales larger/smaller than the pumping scale $L$. We characterize the statistics of bending of a long isoline by the driving function of the L\"owner map, show that it behaves like diffusion with the diffusivity independent of resolution yet, most surprisingly, dependent on the velocity realization and the time of scalar evolution

Lectures on Gaussian approximations with Malliavin calculus

In a seminal paper of 2005, Nualart and Peccati discovered a surprising central limit theorem (called the "Fourth Moment Theorem" in the sequel) for sequences of multiple stochastic integrals of a fixed order: in this context, convergence in distribution to the standard normal law is equivalent to convergence of just the fourth moment. Shortly afterwards, Peccati and Tudor gave a multidimensional version of this characterization. Since the publication of these two beautiful papers, many improvements and developments on this theme have been considered. Among them is the work by Nualart and Ortiz-Latorre, giving a new proof only based on Malliavin calculus and the use of integration by parts on Wiener space. A second step is my joint paper "Stein's method on Wiener chaos" (written in collaboration with Peccati) in which, by bringing together Stein's method with Malliavin calculus, we have been able (among other things) to associate quantitative bounds to the Fourth Moment Theorem. It turns out that Stein's method and Malliavin calculus fit together admirably well. Their interaction has led to some remarkable new results involving central and non-central limit theorems for functionals of infinite-dimensional Gaussian fields. The current survey aims to introduce the main features of this recent theory. It originates from a series of lectures I delivered at the Coll\`ege de France between January and March 2012, within the framework of the annual prize of the Fondation des Sciences Math\'ematiques de Paris. It may be seen as a teaser for the book "Normal Approximations Using Malliavin Calculus: from Stein's Method to Universality" (jointly written with Peccati), in which the interested reader will find much more than in this short survey.Comment: 72 pages. To be published in the S\'eminaire de Probabilit\'es. Mild update: typos, referee comment