PHYSIOLOGY: HARRIS AND BENEDICT tance less than 8ep from the point P, then X and P lie together in a connected sub-set of M every point of which is at a distance of less than e from the point P. The set M is said to be uniformly connected im kleinen if for every positive number e there exists a positive number 68 such that if P1 and P2 are two points of M at a distance apart less than 58 then they lie together in a connected sub-set of M every point of which is at a distance of less than e from P1.

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There is an increasing consensus that global climate change occurs and that potential changes in climate are likely to have important regional consequences for biota and ecosystems. Ecological restoration, including (re)-afforestation and rehabilitation of degraded land, is included in the array of potential human responses to climate change. However, the implications of climate change for the broader practice of ecological restoration must be considered. In particular, the usefulness of historical ecosystem conditions as targets and references must be set against the likelihood that restoring these historic ecosystems is unlikely to be easy, or even possible, in the changed biophysical conditions of the future. We suggest that more consideration and debate needs to be directed at the implications of climate change for restoration practice.

The extent of human‐induced change and damage to Earth's ecosystems renders ecosystem repair an essential part of our future survival strategy, and this demands that restoration ecology provide effective conceptual and practical tools for this task. We argue that restoration ecology has to be an integral component of land management in today's world, and to be broadly applicable, has to have a clearly articulated conceptual basis. This needs to recognize that most ecosystems are dynamic and hence restoration goals cannot be based on static attributes. Setting clear and achievable goals is essential, and these should focus on the desired characteristics for the system in the future, rather than in relation to what these were in the past. Goal setting requires that there is a clear understanding of the restoration options available (and the relative costs of different options). The concept of restoration thresholds suggests that options are determined by the current state of the system in relation to biotic and abiotic thresholds. A further important task is the development of effective and easily measured success criteria. Many parameters could be considered for inclusion in restoration success criteria, but these are often ambiguous or hard to measure. Success criteria need to relate clearly back to specific restoration goals. If restoration ecology is to be successfully practiced as part of humanity's response to continued ecosystem change and degradation, restoration ecologists need to rise to the challenges of meshing science, practice and policy. Restoration ecology is likely to be one of the most important fields of the coming century.

There are many ecological diversity measures, but their suitability for use with highly diverse bacterial communities is unclear and seldom considered. We assessed a range of species richness and evenness/dominance indices, and the use of species abundance models using samples of bacteria from zinc-contaminated and control soils. Bacteria were assigned to operational taxonomic units (OTUs) using amplified ribosomal DNA restriction analysis of 236 clones from each soil. The reduced diversity apparent in the contaminated soil was reflected by the diversity indices to varying degrees. The number of clones analysed and the weighting given to rare vs. abundant OTUs are the most important considerations when selecting measures. Our preferences, arrived at using theory and practical experience, include: the log series index alpha; the Q statistic (but only if coverage is 50% or more); the Berger-Parker and Simpson's indices, although their ecological relevance may be limited; and, unexpectedly, the Shannon-Wiener and Shannon evenness indices, even though their meanings may not be clear and their values inaccurate when coverage is low. For extrapolation, the equation for the log series distribution seems the best for extrapolating from OTU accumulation curves while non-parametric methods, such as Chao 1, show promise for estimating total OTU richness. Due to a preponderance of single-occurrence OTUs, none of the five species abundance models fit the OTU abundance distribution of the control soil, but both the log and log normal models fit the less diverse contaminated soil. Species abundance models are useful, irrespective of coverage, because they address the whole distribution of a sample, aiding comparison by revealing overall trends as well as specific changes in particular abundance classes.