Equicontinuous local dendrite maps

[EN] Let X be a local dendrite, and f : X → X be a map. Denote by E(X) the set of endpoints of X. We show that if E(X) is countable, then the following are equivalent:(1) f is equicontinuous;(2)  fn (X) = R(f);(3) f|  fn (X) is equicontinuous;(4) f| fn (X) is a pointwise periodic homeomorphism or is topologically conjugate to an irrational rotation of S 1 ;(5) ω(x, f) = Ω(x, f) for all x ∈ X.This result generalizes [17, Theorem 5.2], [24, Theorem 2] and [11, Theorem 2.8].Salem, AH.; Hattab, H.; Rejeiba, T. (2021). Equicontinuous local dendrite maps. Applied General Topology. 22(1):67-77. https://doi.org/10.4995/agt.2021.13446OJS6777221H. Abdelli, ω-limit sets for monotone local dendrite maps. Chaos, Solitons and Fractals, 71 (2015), 66-72. https://doi.org/10.1016/j.chaos.2014.12.003H. Abdelli and H. Marzougui, Invariant sets for monotone local dendrite maps, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 26, no. 9 (2016), 1650150 (10 pages). https://doi.org/10.1142/S0218127416501509E. Akin, J. Auslander and K. Berg, When is a transitive map chaotic?, in: Convergence in Ergodic Theory and Probability, Walter de Gruyter and Co., Berlin, 1996, pp. 25-40. https://doi.org/10.1515/9783110889383.25G. Askri and I. Naghmouchi, Pointwise recurrence on local dendrites, Qual. Theory Dyn Syst 19, 6 (2020). https://doi.org/10.1007/s12346-020-00347-8F. Balibrea, T. Downarowicz, R. Hric, L. Snoha and V. Spitalsky, Almost totally disconnected minimal systems, Ergodic Th. & Dynam Sys. 29, no. 3 (2009), 737-766. https://doi.org/10.1017/S0143385708000540F. Blanchard, B. Host and A. Maass, Topological complexity, Ergodic Th. & Dynam Sys. 20 (2000), 641-662. https://doi.org/10.1017/S0143385700000341A. M. Blokh, Pointwise-recurrent maps on uniquely arcwise connected locally arcwise connected spaces, Proc. Amer. Math. Soc. 143 (2015), 3985-4000. https://doi.org/10.1090/S0002-9939-2015-12589-0A. M. Blokh, The set of all iterates is nowhere dense in C([0,1],[0,1]), Trans. Amer. Math. Soc. 333, no. 2 (1992), 787-798. https://doi.org/10.1090/S0002-9947-1992-1153009-7W. Boyce, Γ-compact maps on an interval and fixed points, Trans. Amer. Math. Soc. 160 (1971), 87-102. https://doi.org/10.1090/S0002-9947-1971-0280655-1A. M. Bruckner and T. Hu, Equicontinuity of iterates of an interval map, Tamkang J. Math. 21, no. 3 (1990), 287-294.J. Camargo, M. Rincón and C. Uzcátegui, Equicontinuity of maps on dendrites, Chaos, Solitons and Fractals 126 (2019), 1-6. https://doi.org/10.1016/j.chaos.2019.05.033J. Cano, Common fixed points for a class of commuting mappings on an interval, Trans. Amer. Math. Soc. 86, no. 2 (1982), 336-338. https://doi.org/10.1090/S0002-9939-1982-0667301-2R. Gu and Z. Qiao, Equicontinuity of maps on figure-eight space, Southeast Asian Bull. Math. 25 (2001), 413-419. https://doi.org/10.1007/s100120100004A. Haj Salem and H. Hattab, Group action on local dendrites, Topology Appl. 247, no. 15 (2018), 91-99. https://doi.org/10.1016/j.topol.2018.08.002K. Kuratowski, Topology, vol. 2. New York: Academic Press; 1968.J. Mai, Pointwise-recurrent graph maps, Ergodic Th. & Dynam Sys. 25 (2005), 629-637. https://doi.org/10.1017/S0143385704000720J. Mai, The structure of equicontinuous maps, Trans. Amer. Math. Soc. 355, no. 10 (2003), 4125-4136. https://doi.org/10.1090/S0002-9947-03-03339-7C. A. Morales, Equicontinuity on semi-locally connected spaces, Topology Appl. 198 (2016), 101-106. https://doi.org/10.1016/j.topol.2015.11.011S. Nadler, Continuum Theory. Inc., New York: Marcel Dekker; 1992.G. Su and B. Qin, Equicontinuous dendrites flows, Journal of Difference Equations and Applications 25, no. 12 (2019), 1744-1754. https://doi.org/10.1080/10236198.2019.1694012T. Sun, Equicontinuity of σ-maps, Pure and Applied Math. 16, no. 3 (2000), 9-14.T. Sun, Z. Chen, X. Liu and H. G. Xi, Equicontinuity of dendrite maps, Chaos, Solitons and Fractals 69 (2014), 10-13. https://doi.org/10.1016/j.chaos.2014.08.010T. Sun, G. Wang and H. J. Xi, Equicontinuity of maps on a dendrite with finite branch points. Acta Mat. Sin. 33, no. 8 (2017), 1125-1130. https://doi.org/10.1007/s10114-017-6289-xT. Sun, Y. Zhang and X. Zhang, Equicontinuity of a graph map, Bull. Austral Math. Soc. 71 (2005), 61-67. https://doi.org/10.1017/S0004972700038016A. Valaristos, Equicontinuity of iterates of circle maps, Internat. J. Math. and Math. Sci. 21 (1998), 453-458. https://doi.org/10.1155/S016117129800062

Invasion by the Alien Tree Prunus serotina Alters Ecosystem Functions in a Temperate Deciduous Forest

Alien invasive species can affect large areas, often with wide-ranging impacts on ecosystem structure, function, and services. Prunus serotina is a widespread invader of European temperate forests, where it tends to form homogeneous stands and limits recruitment of indigenous trees. We hypotesized that invasion by P. serotina would be reflected in the nutrient contents of the native species' leaves and in the respiration of invaded plots as efficient resource uptake and changes in nutrient cycling by P. serotina probably underly its aggressive invasiveness. We combined data from 48 field plots in the forest of Compiègne, France, and data from an experiment using 96 microcosms derived from those field plots. We used general linear models to separate effects of invasion by P. serotina on heterotrophic soil and litter respiration rates and on canopy foliar nutrient content from effects of soil chemical properties, litter quantity, litter species composition, and tree species composition. In invaded stands, average respiration rates were 5.6% higher for soil (without litter) and 32% higher for soil and litter combined. Compared to indigenous tree species, P. serotina exhibited higher foliar N (+24.0%), foliar P (+50.7%), and lower foliar C:N (−22.4%) and N:P (−10.1%) ratios. P. serotina affected foliar nutrient contents of co-occuring indigenous tree species leading to decreased foliar N (−8.7 %) and increased C:N ratio (+9.5%) in Fagus sylvatica, decreased foliar N:P ratio in Carpinus betulus (−13.5%) and F. sylvatica (−11.8%), and increased foliar P in Pinus sylvestris (+12.3%) in invaded vs. uninvaded stands. Our results suggest that P. serotina is changing nitrogen, phosphorus, and carbon cycles to its own advantage, hereby increasing carbon turnover via labile litter, affecting the relative nutrient contents in the overstory leaves, and potentially altering the photosynthetic capacity of the long-lived indigenous broadleaved species. Uncontrolled invasion of European temperate forests by P. serotina may affect the climate change mitigation potential of these forests in the long term, through additive effects on local nutrient cycles

sPlotOpen – An environmentally balanced, open-access, global dataset of vegetation plots

Assessing biodiversity status and trends in plant communities is critical for understanding, quantifying and predicting the effects of global change on ecosystems. Vegetation plots record the occurrence or abundance of all plant species co-occurring within delimited local areas. This allows species absences to be inferred, information seldom provided by existing global plant datasets. Although many vegetation plots have been recorded, most are not available to the global research community. A recent initiative, called ?sPlot?, compiled the first global vegetation plot database, and continues to grow and curate it. The sPlot database, however, is extremely unbalanced spatially and environmentally, and is not open-access. Here, we address both these issues by (a) resampling the vegetation plots using several environmental variables as sampling strata and (b) securing permission from data holders of 105 local-to-regional datasets to openly release data. We thus present sPlotOpen, the largest open-access dataset of vegetation plots ever released. sPlotOpen can be used to explore global diversity at the plant community level, as ground truth data in remote sensing applications, or as a baseline for biodiversity monitoring. Main types of variable contained: Vegetation plots (n = 95,104) recording cover or abundance of naturally co-occurring vascular plant species within delimited areas. sPlotOpen contains three partially overlapping resampled datasets (c. 50,000 plots each), to be used as replicates in global analyses. Besides geographical location, date, plot size, biome, elevation, slope, aspect, vegetation type, naturalness, coverage of various vegetation layers, and source dataset, plot-level data also include community-weighted means and variances of 18 plant functional traits from the TRY Plant Trait Database. Spatial location and grain: Global, 0.01?40,000 m². Time period and grain: 1888-2015, recording dates. Major taxa and level of measurement: 42,677 vascular plant taxa, plot-level records.Fil: Sabatini, Francesco Maria. Martin-universität Halle-wittenberg; Alemania. German Centre For Integrative Biodiversity Research (idiv) Halle-jena-leipzig; AlemaniaFil: Lenoir, Jonathan. Université de Picardie Jules Verne; FranciaFil: Hattab, Tarek. Université de Montpellier; FranciaFil: Arnst, Elise Aimee. Manaaki Whenua - Landcare Research; Nueva ZelandaFil: Chytrý, Milan. Masaryk University; República ChecaFil: Giorgis, Melisa Adriana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto Multidisciplinario de Biología Vegetal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto Multidisciplinario de Biología Vegetal; ArgentinaFil: Vanselow, Kim André. University of Erlangen-Nuremberg; AlemaniaFil: Vásquez Martínez, Rodolfo. Jardín Botánico de Missouri Oxapampa; PerúFil: Vassilev, Kiril. Bulgarian Academy of Sciences; BulgariaFil: Vélez-Martin, Eduardo. ILEX Consultoria Científica; BrasilFil: Venanzoni, Roberto. University of Perugia; ItaliaFil: Vibrans, Alexander Christian. Universidade Regional de Blumenau; BrasilFil: Violle, Cyrille. Paul Valéry Montpellier University; FranciaFil: Virtanen, Risto. German Centre for Integrative Biodiversity Research; AlemaniaFil: von Wehrden, Henrik. Leuphana University of Lüneburg; AlemaniaFil: Wagner, Viktoria. University of Alberta; CanadáFil: Walker, Donald A.. University of Alaska; Estados UnidosFil: Waller, Donald M.. University of Wisconsin-Madison; Estados UnidosFil: Wang, Hua-Feng. Hainan University; ChinaFil: Wesche, Karsten. Senckenberg Museum of Natural History Görlitz; Alemania. Technische Universität Dresden; AlemaniaFil: Whitfeld, Timothy J. S.. University of Minnesota; Estados UnidosFil: Willner, Wolfgang. University of Vienna; AustriaFil: Wiser, Susan K.. Manaaki Whenua. Landcare Research; Nueva ZelandaFil: Wohlgemuth, Thomas. Swiss Federal Institute for Forest, Snow and Landscape Research; SuizaFil: Yamalov, Sergey. Russian Academy of Sciences; RusiaFil: Zobel, Martin. University of Tartu; EstoniaFil: Bruelheide, Helge. German Centre for Integrative Biodiversity Research; Alemani

Are we ready to track climate-driven shifts in marine species across international boundaries? - A global survey of scientific bottom trawl data

Marine biota are redistributing at a rapid pace in response to climate change and shifting seascapes. While changes in fish populations and community structure threaten the sustainability of fisheries, our capacity to adapt by tracking and projecting marine species remains a challenge due to data discontinuities in biological observations, lack of data availability, and mismatch between data and real species distributions. To assess the extent of this challenge, we review the global status and accessibility of ongoing scientific bottom trawl surveys. In total, we gathered metadata for 283,925 samples from 95 surveys conducted regularly from 2001 to 2019. We identified that 59% of the metadata collected are not publicly available, highlighting that the availability of data is the most important challenge to assess species redistributions under global climate change. Given that the primary purpose of surveys is to provide independent data to inform stock assessment of commercially important populations, we further highlight that single surveys do not cover the full range of the main commercial demersal fish species. An average of 18 surveys is needed to cover at least 50% of species ranges, demonstrating the importance of combining multiple surveys to evaluate species range shifts. We assess the potential for combining surveys to track transboundary species redistributions and show that differences in sampling schemes and inconsistency in sampling can be overcome with spatio-temporal modeling to follow species density redistributions. In light of our global assessment, we establish a framework for improving the management and conservation of transboundary and migrating marine demersal species. We provide directions to improve data availability and encourage countries to share survey data, to assess species vulnerabilities, and to support management adaptation in a time of climate-driven ocean changes.En prensa6,86

Towards a better understanding of the ecosystem impacts of global change on southern Mediterranean exploited species assemblages, application to the Gulf of Gabes (Tunisia) : from species distribution models to trophic consequences

La mer Méditerranée est un hotspot de biodiversité sous diverses influences où plusieurs perturbations agissent en synergie: réchauffement climatique, perte d'habitats et surpêche menacent la biodiversité marine et perturbent les équilibres écosystémiques. Afin d'assurer une gestion durable des écosystèmes marins côtiers, conformément aux prérogatives de l'Approche Ecosystémique des Pêches, il est nécessaire d'étudier les conséquences de ces perturbations sur les populations exploitées. Or, malgré la multiplicité des études relatives au changement global en Méditerranée, les conséquences écosystémiques de ces changements demeurent mal connues. Dans cette thèse, le Golfe de Gabès a été choisi comme modèle d'étude en raison des nombreuses perturbations qui y sont rencontrées et qui en font l'archétype de tendances plus généralisées en Mer Méditerranée. Cette thèse se propose d'abord de replacer l'écosystème du Golfe de Gabès dans son contexte biogéographique à travers l'étude de la phylobiogéographie des assemblages des poissons côtiers méditerranéens et la modélisation de la structure et du fonctionnement de l'écosystème du Golfe de Gabès. Par la suite, nous proposons de modéliser, en utilisant des modèles de niches écologiques, les modifications potentielles futures des assemblages biogéographiques d'espèces exploitées soumises aux changements climatiques et à la perte d'habitat, ainsi que les conséquences trophiques de ces modifications. En prenant en compte la taxonomie et l'histoire évolutive des espèces, nous avons mis en évidence le niveau de séparation entre les assemblages méditerranéens en proposant une nouvelle délimitation biogéographique du plateau continental. Par ailleurs, l'exploration des dissimilarités phylogénétiques à l'échelle des côtes tunisiennes a mis en évidence quatre zones biogéographiques majeures présentant une faible congruence avec le zonage adopté pour la gestion de la pêche en Tunisie. Les projections des futures aires de répartition des 60 principales espèces exploitées du Golfe de Gabès, grâce à l'implémentation du modèle climatique NEMOMED8, révèlent que pour la fin du siècle, 34 espèces pourraient contracter leurs aires de répartition parmi lesquelles 12 espèces pourraient s'éteindre à l'échelle du Golfe. Par ailleurs, en combinant des scénarios de régression d'herbier et de changement climatique, les projections montrent que les magnitudes des modifications d'aires de répartition induites par le changement climatique sont plus larges que celles résultant de la perte d'habitat. La mise en place d'un modèle trophique Ecopath nous a permis de décrire la structure et le fonctionnement de l'écosystème du Golfe de Gabès et de le comparer avec d'autres écosystèmes méditerranéens exploités. Ce modèle a intégré un large éventail d'espèces depuis le phytoplancton jusqu'aux top-prédateurs ainsi que les principales activités de pêche opérant dans la zone. Les résultats du modèle mettent en évidence que le chalutage benthique est l'activité ayant les conséquences écosystémiques les plus étendues avec un fort impact sur certaines espèces démersales exploitées. Enfin, pour étudier les conséquences trophiques des modifications des distributions spatiales des espèces exploitées, nous avons reconstruit les réseaux trophiques au sein des assemblages d'espèces en nous fondant sur la relation positive liant la taille du prédateur à celle de sa proie. Nous avons ainsi pu prédire les réseaux trophiques actuels et projeter les modifications potentielles de leurs structures. Nous avons constaté qu'une grande partie du Golfe pourrait connaître une augmentation de la connectance et un allongement des voies trophiques moyennes qui s'accompagnent d'une diminution du nombre de proies par prédateur et du nombre de prédateurs par proie. Cette thèse est une ouverture vers la compréhension du rôle de la biodiversité dans le maintien du fonctionnement des écosystèmes.The Mediterranean Sea is a marine biodiversity hot spot highly affected by several sources of disturbances interacting synergistically: global warming, habitat loss and overfishing threaten marine biodiversity and disrupt the ecosystem balance. To ensure a sustainable management of coastal marine ecosystems according to the Ecosystem Approach to Fisheries, it is necessary to study the ecosystem responses to these disturbances. However, despite the variety of global change studies in Mediterranean areas, ecosystems responses to these changes remain poorly understood and particularly at the southern part of the Mediterranean Sea. In this PhD thesis, the Gulf of Gabes was chosen as study area since it is one of the most affected regions by global change which makes it a mesocosm model of more regional patterns that occur in the Mediterranean Sea. In this study, as a first step, we replaced the Gulf of Gabes in its biogeographic and ecosystem regional context. This was achievied through a phylogenetic-based delineation of biogeographical species pools of coastal Mediterranean fishes and using an ecosystem model to describe its structure and functioning in comparison with other Mediterranean ecosystem model properties. We therefore projected potential future geographic ranges and assemblages composition of biogeographical exploited species pool according to global warming and habitat loss scenarios. Then we assessed their effects on food web structure. Taking into account the taxonomy and inter-species evolutionary relationships, we generate a new bioregionalisation of the continental shelf based on the turnover of lineages. Our results showed that climate is the major driver of species distribution and assemblage's composition. In addition, the exploration of phylogenetic dissimilarity across the Tunisian coast highlighted four major biogeographic areas showing a low spatial congruence with zoning used for fisheries management in Tunisia.Projected range shifts of the 60 main exploited species of the Gulf of Gabes through the implementation of a new climate model (NEMOMED8) revealed that, by the end of the century, 34 species could contract their ranges including 12 species that could become locally extinct across the Gulf of Gabes. Furthermore, by combining Posidonia meadows loss scenarios and climate change projections, our results showed that the magnitudes of the changes range induced by climate change are larger than those resulting from the loss of habitat.The Ecopath mass-balance model allowed us to describe the structure and functioning of the ecosystem of the Gulf of Gabes in comparison with other Mediterranean ecosystems. These models encompass the entire trophic spectrum from phytoplankton to higher trophic levels as well as the main fishing activities in the area. The model results showed that, among the fishing activities studied, bottom trawling was identified as the activity having the widest-ranging impacts across the different functional groups and the largest impacts on some commercially-targeted demersal fish species. Finally, to study the effects of species range shift on food web structure, we used a new methodology to infer trophic interactions between species. Based on the robust relationship between the size of prey and predators, we predicted the current food webs and project potential changes in their structures. We found that a significant portion of the Gulf of Gabes would face an increase of connectance and an extension of trophic pathways in parallel with a decrease in the number of prey per predator and the number of predators per prey. This PhD thesis paves the way towards the understanding of the role of biodiversity in maintaining ecosystem functioning

R script to perform a biogeographical regionalisation of the Adriatic Sea based on phylogenetic beta diversity

<p>This R code provides a computational framework to perform a biogeographical regionalisation based on phylogenetic beta diversity. For this purpose, we will use two data sets:</p> <p>-Distribution_Data.csv: a csv file with 1323 observations (sites located on the Adreatic Sea) on 161 binary variables (species).</p> <p>-Phylogenetic_Data.trd: a phylogenetic tree of 363 Mediterranean teleost species (see Meynard et al., 2012 for details: http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0036443).</p> <p>Two external functions are also required:</p> <p>-beta_pd_decompo.r: R function to quantify phylogenetic beta diversity (PBD) and its 'true' turnover and phylogenetic diversity (PD) components based on the UniFrac and PhyloSor indices.</p> <p>-A2R.r: R function for generating colored dendrograms which you can download here http://addictedtor.free.fr/packages/A2R/lastVersion/R/code.R.<br><br>For more details about this topic you can read the original article: </p> <p>Hattab, T., Albouy, C., Ben Rais Lasram, F., Le Loc'h, F., Guilhaumon, F., Leprieur, F. (2015), A biogeographical regionalization of coastal Mediterranean fishes. Journal of Biogeography. doi: 10.1111/jbi.12505</p> <p>1.Put all the documents in a single folder (this becomes your working directory)</p> <p>2. Install the necessary packages in R (see first part of the script)</p> <p>3. Define the working directory in the script (setwd(“C:/…/”), as indicated in the script)</p> <p>4. Run the script in R</p> <p> </p

A biogeographical regionalisation of coastal Mediterranean fishes

<p>A new biogeographic regionalisation of coastal Mediterranean fishes is available for download here in GIS shapefile format. The biogeographical regions were identified using quantitative analyses of taxonomic and phylogenetic data of 203 strictly coastal fish species. This shapefile is documented in this article :</p> <p>Hattab, T., Albouy, C., Ben Rais Lasram, F., Le Loc'h, F., Guilhaumon, F., Leprieur, F. (2015), A biogeographical regionalization of coastal Mediterranean fishes. Journal of Biogeography. doi: 10.1111/jbi.12505</p> <p> </p

Climatic microrefugia under anthropogenic climate change: implications for species redistribution

The role of modern climatic microrefugia is a neglected aspect in the study of biotic responses to anthropogenic climate change. Current projections of species redistribution at continental extent are based on climatic grids of coarse ( 1 km) resolutions that fail to capture spatiotemporal dynamics associated with climatic microrefugia. Here, we review recent methods to model the climatic component of potential microrefugia and highlight research gaps in accounting for the buffering capacity due to biophysical processes operating at very fine (< 1 m) resolutions (e.g. canopy cover) and the associated microclimatic stability over time (i.e. decoupling). To overcome this challenge, we propose a spatially hierarchical downscaling framework combining a free-air temperature grid at 1 km resolution, a digital elevation model at 25 m resolution and small-footprint light detection-and-ranging (LiDAR) data at 50 cm resolution with knowledge from the literature to mechanistically model sub-canopy temperatures and account for microclimatic decoupling. We applied this framework on a virtual sub-canopy species and simulated the impact of a warming scenario on its potential distribution. Modelling sub-canopy temperatures at 50 cm resolution and accounting for microclimatic stability over time enlarges the range of temperature conditions towards the cold end of the gradient, mitigates regional temperature changes and decreases extirpation risks. Incorporating these spatiotemporal dynamics into species redistribution models, being correlative, mechanistic or hybrid, will increase the probability of local persistence, which has important consequences in the understanding of the capacity of species to adapt. We finally provide a synthesis on additional ways that the field could move towards effectively considering potential climatic microrefugia for species redistribution