Effectiveness of spatial mosaic management for grassland breeding shorebirds

Since 2000, a new management technique has been introduced to stop the rapid decline of grassland breeding shorebirds in the Netherlands, called ‘mosaic management’. The most important difference from earlier Agri-Environment Schemes is that the mosaic management is conducted at a landscape scale (150–650 ha) rather than an individual farm scale (50–60 ha) and that there is purposeful planning of the spatial distribution and layout of management measures within a local area. We tested the effectiveness of the mosaic management by analysing breeding population trends of Northern Lapwing (Vanellus vanellus), Black-tailed Godwit (Limosa limosa), Redshank (Tringa totanus) and Oystercatcher (Haematopus ostralegus) in comparison with three other management types: individual management, regular farmland and nature reserves. After the introduction of mosaic management, populations of Black-tailed Godwit and Redshank stabilised and Northern Lapwing populations increased. Oystercatcher decreased, but this was also due to reduced winter survival. Populations in the mosaic management areas showed a greater annual improvement of 0–18% compared to other management types. The mosaic areas did not appear to be ‘sink’ areas as productivity in the mosaic areas seemed to be sufficient to support the observed densities. However, with the exception of Northern Lapwing, the change of trend was not greater in the mosaic areas than in the other management types. So, for the species other than Northern Lapwing, the good performance cannot be attributed to the mosaic management. The mosaic areas were good breeding habitats beforehand and continue to be so. It is possible that the mosaic management is part of the success, but not exclusively so. Our results show that modern farming can still be combined with grassland breeding shorebird management. However, further study of success factors is urgently needed for the conservation of the remaining good habitats on farmland and restoration of lost one

Vegetation development in sown field margins and on adjacent ditch banks

The creation of temporal and newly sown field margins for 6 years is a common agri-environment scheme (AES) in the Netherlands. Conservation profits resulting from AES vary over different areas and need further studying. We examined plant species richness in such field margins and adjacent ditch banks in the province of Zeeland, where these linear elements do not experience plant biomass removal after mowing as management strategy. First, during 2 years, we inventoried field margins sown with a wildflower mixture and related the species composition and richness to the age of the margins. In a second assessment, we studied plant species richness on ditch banks protected from arable fields by these margins. Major clusters in a principal component analysis (PCA) on species composition in the field margins showed a succession from sown and ruderal annual species (year 1), to sown perennial species (year 2) and ending with a dominance by tussock forming grass species and Urtica dioica (year 5–6). Total plant species richness decreased with increasing age of the margins, and this was caused by the combination of a decline in sown species and a stable number of not-sown species. The presence of field margins during several years did not result in an increase in plant species richness on adjacent ditch banks. In both the field margins and on the ditch banks, mowing management is not followed by the removal of the cuttings. For plant conservation, the results of these field margins are disappointing, probably due to the lack of a proper management. Therefore, we recommend implementing a hay-making and opening management, to increase plant richness and to reduce noxious weeds in the margins and on the ditch bank

A general realization theorem for matrix-valued Herglotz-Nevanlinna functions

New special types of stationary conservative impedance and scattering systems, the so-called non-canonical systems, involving triplets of Hilbert spaces and projection operators, are considered. It is established that every matrix-valued Herglotz-Nevanlinna function of the form V(z)=Q+Lz+\int_{\dR}(\frac{1}{t-z}-\frac{t}{1+t^2})d\Sigma(t) can be realized as a transfer function of such a new type of conservative impedance system. In this case it is shown that the realization can be chosen such that the main and the projection operators of the realizing system satisfy a certain commutativity condition if and only if L=0. It is also shown that $V(z)$ with an additional condition (namely, $L$ is invertible or L=0), can be realized as a linear fractional transformation of the transfer function of a non-canonical scattering $F_+$-system. In particular, this means that every scalar Herglotz-Nevanlinna function can be realized in the above sense. Moreover, the classical Livsic systems (Brodskii-Livsic operator colligations) can be derived from $F_+$-systems as a special case when $F_+=I$ and the spectral measure $d\Sigma(t)$ is compactly supported. The realization theorems proved in this paper are strongly connected with, and complement the recent results by Ball and Staffans.Comment: 28 page

Componentwise and Cartesian decompositions of linear relations

Let $A$ be a, not necessarily closed, linear relation in a Hilbert space \sH with a multivalued part \mul A. An operator $B$ in \sH with \ran B\perp\mul A^{**} is said to be an operator part of $A$ when A=B \hplus (\{0\}\times \mul A), where the sum is componentwise (i.e. span of the graphs). This decomposition provides a counterpart and an extension for the notion of closability of (unbounded) operators to the setting of linear relations. Existence and uniqueness criteria for the existence of an operator part are established via the so-called canonical decomposition of $A$. In addition, conditions are developed for the decomposition to be orthogonal (components defined in orthogonal subspaces of the underlying space). Such orthogonal decompositions are shown to be valid for several classes of relations. The relation $A$ is said to have a Cartesian decomposition if A=U+\I V, where $U$ and $V$ are symmetric relations and the sum is operatorwise. The connection between a Cartesian decomposition of $A$ and the real and imaginary parts of $A$ is investigated