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We relate the geometric Poisson brackets on the 2-Grassmannian in ℝ4 and on the (2, 2) Möbius sphere. We show that, when written in terms of local moving frames, the geometric Poisson bracket on the Möbius sphere does not restrict to the space of differential invariants of Schwarzian type. But when the concept of conformal natural frame is transported from the conformal sphere into the Grassmannian, and the Poisson bracket is written in terms of the Grassmannian natural frame, it restricts and results in either a decoupled system or a complexly coupled system of Korteweg–de Vries (KdV) equations, depending on the character of the invariants. We also show that the bi-Hamiltonian Grassmannian geometric brackets are equivalent to the non-commutative KdV bi-Hamiltonian structure. Both integrable systems and Hamiltonian structure can be brought back to the conformal sphere. [ABSTRACT FROM PUBLISHER]

In this paper we introduce a new infinite-dimensional pencil of Hamiltonian structures. These Poisson tensors appear naturally as the ones governing the evolution of the curvatures of certain flows of curves in 3-dimensional Riemannian manifolds with constant curvature. The curves themselves are evolving following arclength-preserving geometric evolutions for which the variation of the curve is an invariant combination of the tangent, normal, and binormal vectors. Under very natural conditions, the evolution of the curvatures will be Hamiltonian and, in some instances, bi-Hamiltonian and completely integrable. [ABSTRACT FROM AUTHOR]

Background: Progress in the field of evolutionary forest ecology has been hampered by the huge challenge of phenotyping trees across their ranges in their natural environments, and the limitation in high-resolution environmental information., Findings: The GenTree Platform contains phenotypic and environmental data from 4,959 trees from 12 ecologically and economically important European forest tree species: Abies alba Mill. (silver fir), Betula pendula Roth. (silver birch), Fagus sylvatica L. (European beech), Picea abies (L.) H. Karst (Norway spruce), Pinus cembra L. (Swiss stone pine), Pinus halepensis Mill. (Aleppo pine), Pinus nigra Arnold (European black pine), Pinus pinaster Aiton (maritime pine), Pinus sylvestris L. (Scots pine), Populus nigra L. (European black poplar), Taxus baccata L. (English yew), and Quercus petraea (Matt.) Liebl. (sessile oak). Phenotypic (height, diameter at breast height, crown size, bark thickness, biomass, straightness, forking, branch angle, fructification), regeneration, environmental in situ measurements (soil depth, vegetation cover, competition indices), and environmental modeling data extracted by using bilinear interpolation accounting for surrounding conditions of each tree (precipitation, temperature, insolation, drought indices) were obtained from trees in 194 sites covering the species' geographic ranges and reflecting local environmental gradients., Conclusion: The GenTree Platform is a new resource for investigating ecological and evolutionary processes in forest trees. The coherent phenotyping and environmental characterization across 12 species in their European ranges allow for a wide range of analyses from forest ecologists, conservationists, and macro-ecologists. Also, the data here presented can be linked to the GenTree Dendroecological collection, the GenTree Leaf Trait collection, and the GenTree Genomic collection presented elsewhere, which together build the largest evolutionary forest ecology data collection available., (© The Author(s) 2021. Published by Oxford University Press GigaScience.)

Knowledge about the vegetation history of Sardinia, the second largest island of the Mediterranean, is scanty. Here, we present a new sedimentary record covering the past ~ 8,000 years from Lago di Baratz, north-west Sardinia. Vegetation and fire history are reconstructed by pollen, spores, macrofossils and charcoal analyses and environmental dynamics by high-resolution element geochemistry together with pigment analyses. During the period 8,100-7,500 cal bp, when seasonality was high and fire and erosion were frequent, Erica arborea and E. scoparia woodlands dominated the coastal landscape. Subsequently, between 7,500 and 5,500 cal bp, seasonality gradually declined and thermo-mediterranean woodlands with Pistacia and Quercus ilex partially replaced Erica communities under diminished incidence of fire. After 5,500 cal bp, evergreen oak forests expanded markedly, erosion declined and lake levels increased, likely in response to increasing (summer) moisture availability. Increased anthropogenic fire disturbance triggered shrubland expansions (e.g. Tamarix and Pistacia ) around 5,000-4,500 cal bp. Subsequently around 4,000-3,500 cal bp evergreen oak-olive forests expanded massively when fire activity declined and lake productivity and anoxia reached Holocene maxima. Land-use activities during the past 4,000 years (since the Bronze Age) gradually disrupted coastal forests, but relict stands persisted under rather stable environmental conditions until ca. 200 cal bp, when agricultural activities intensified and Pinus and Eucalyptus were planted to stabilize the sand dunes. Pervasive prehistoric land-use activities since at least the Bronze Age Nuraghi period included the cultivation of Prunus , Olea europaea and Juglans regia after 3,500-3,300 cal bp, and Quercus suber after 2,500 cal bp. We conclude that restoring less flammable native Q. ilex and O. europaea forest communities would markedly reduce fire risk and erodibility compared to recent forest plantations with flammable non-native trees (e.g. Pinus , Eucalyptus ) and xerophytic shrubland (e.g. Cistus , Erica )., (© The Author(s) 2021.)