Unbiased Linear Property Estimation For Spheres From Sections Exhibiting Overprojection And Truncation

In the biological sciences, stereological techniques are frequently used to infer changes in structural parameters (volume fraction, for example) between samples from different populations or subject to differing treatment regimes. Non-homogeneity of these parameters is virtually guaranteed, both between experimental animals and within the organ under consideration. A two-stage strategy is then desirable, the first stage involving unbiased estimation of the required parameter, separately for each experimental unit, the latter being defined as a subset of the organ for which homogeneity can reasonably be assumed. In the second stage, these point estimates are used as data inputs to a hierarchical analysis of variance, to distinguish treatment effects from variability between animals, for example. Techniques are therefore required for unbiased estimation of parameters from potentially small numbers of sample profiles. This paper derives unbiased estimates of linear properties in one special case—the sampling of spherical particles by transmission microscopy, when the section thickness is not negligible and the resulting circular profiles are subject to lower truncation. The derivation uses the general integral equation formulation of Nicholson (1970); the resulting formulae are simplified, algebraically, and their efficient computation discussed. Bias arising from variability in slice thickness is shown to be negligible in typical cases. The strategy is illustrated for data examining the effects, on the secondary lysosomes in the digestive cells, of exposure of the common mussel to hydrocarbons. Prolonged exposure, at 30 μg 1−1 total oil-derived hydrocarbons, is seen to increase the average volume of a lysosome, and the volume fraction that lysosomes occupy, but to reduce their number.

The role of economics in ecosystem based management: The case of the EU Marine Strategy Framework Directive, First lessons learnt and way forward

The EU Marine Strategy Framework Directive (MSFD) sets out a plan of action relating to marine environmental policy and in particular to achieving ‘good environmental status’ (GES) in European marine waters by 2020. Article 8.1 (c) of the Directive calls for ‘an economic and social analysis of the use of those waters and of the cost of degradation of the marine environment’. The MSFD is ‘informed’ by the Ecosystem Approach to management, with GES interpreted in terms of ecosystem functioning and services provision. Implementation of the Ecosystem Approach is expected to be by adaptive management policy and practice. The initial socio-economic assessment was made by maritime EU Member States between 2011 and 2012, with future updates to be made on a regular basis. For the majority of Member States, this assessment has led to an exercise combining an analysis of maritime activities both at national and coastal zone scales, and an analysis of the non-market value of marine waters. In this paper we examine the approaches taken in more detail, outline the main challenges facing the Member States in assessing the economic value of achieving GES as outlined in the Directive and make recommendations for the theoretically sound and practically useful completion of the required follow-up economic assessments specified in the MSFD.

The role of economics in ecosystem based management: The case of the EU Marine Strategy Framework Directive, First lessons learnt and way forward

The EU Marine Strategy Framework Directive (MSFD) sets out a plan of action relating to marine environmental policy and in particular to achieving ‘good environmental status’ (GES) in European marine waters by 2020. Article 8.1 (c) of the Directive calls for ‘an economic and social analysis of the use of those waters and of the cost of degradation of the marine environment’. The MSFD is ‘informed’ by the Ecosystem Approach to management, with GES interpreted in terms of ecosystem functioning and services provision. Implementation of the Ecosystem Approach is expected to be by adaptive management policy and practice. The initial socio-economic assessment was made by maritime EU Member States between 2011 and 2012, with future updates to be made on a regular basis. For the majority of Member States, this assessment has led to an exercise combining an analysis of maritime activities both at national and coastal zone scales, and an analysis of the non-market value of marine waters. In this paper we examine the approaches taken in more detail, outline the main challenges facing the Member States in assessing the economic value of achieving GES as outlined in the Directive and make recommendations for the theoretically sound and practically useful completion of the required follow-up economic assessments specified in the MSFD.