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Transformation of data to normality may be illuminating and useful statistically. There are two standard families of transformations, power transformations for positive numbers, bounded at the left, and folded transformations for proportions, bounded both at the left and theright. It has been shown that there is no one satisfactory power transformation for range size data. However, such measures are limited to the right as well as the left, and we consider applying folded transformations to them. Seven data sets of range sizes recorded by 10 kmsquares are studied. Six are British (native and introduced plants, mammals, dragonflies and two breeding bird surveys) the seventh is ofSwiss breeding birds. Using these we show that the right hand limit of the distribution can be estimated and the best folded transformation found. In all cases the right hand limit is larger than the range size of the most widespread species and smaller than the notional scope of the survey. In all cases the logit or flog, the logarithmic folded transformation, is satisfactory; in five cases it is the best. Itis well known that abundance is approximately (though not exactly) log-normally distributed. The relationship of that to our discovery that range size data are approximately logit-normal is discussed. Thereis no fully satisfactory explanation for either observation at present. [ABSTRACT FROM AUTHOR]

The detailed forms of species-range size distributions in Britain are determined and contrasted for ten taxonomic assemblages (liverworts, vascular plants, molluscs [aquatic and terrestrial], dragonflies, macro-moths, butterflies, birds [breeding and wintering], mammals). All are strongly right-skewed when range sizes are untransformed. A logarithmic transformation fails to normalise the distribution for all but one group, and the distributions for several groups are not readily normalised at all. Taxa with larger median range sizes have species-range size distributions that are less strongly right-skewed. The median observed range sizes of species in each of the taxonomic groups fall, in terms of decreasing range size, in the sequence wintering birds > breeding birds > mammals > butterflies > terrestrial molluscs >dragonflies > aquatic molluscs > vascular plants > moths > liverworts. Despite the difficulties in deriving a simple and sensible mechanistic model for range size distributions, this is likely to be the most important next step towards understanding their forms. [ABSTRACT FROM AUTHOR]

Quantitative information on large scale spatial patterns of biodiversity remains poor, especially for pelagic systems. In this paper the regional diversity of procellariiforms is mapped worldwide at the species level. These seabirds do not display a conventional latitudinal gradient of decreasing species richness towards high latitudes, but rather are most speciose between 37 and 59S in all ocean basins. Basedon data for foraging ranges, areas with the highest species richnessand the most species with smaller range sizes are all found in the vicinity of New Zealand and its sub-Antarctic islands. In contrast, data for breeding ranges show islands in the southern Indian and Atlantic oceans to have the highest number of breeding species, while theseislands and New Zealand have the most species with smaller range sizes. No northern hemisphere regions are amongst the top ten grid cellsfor foraging and breeding species richness, although Hawaii has the highest species richness of procellariiforms north of the equator. Northern Baja California, Madeira, the Canary islands, and the west coast of South America are all important sites of narrow endemism in thenorthern hemisphere. High species richness and narrow endemism coincide with areas of significant longline fishing activity in the southern hemisphere. Near-minimum sets based on one and three representations demonstrate that if all procellariiform species are to be retained, large areas of the ocean and almost all breeding sites require conservation. [ABSTRACT FROM AUTHOR]

The relationship between the geographic distribution of consumers and of their hosts (foodplants) is examined using the resident butterfly fauna of Britain. On average, butterfly species that feed on more widely distributed hosts are themselves more widely distributed. However, the relationship is approximately triangular and the upper constraint imposed by the range sizes of hosts is not closely followed; some species have much more restricted ranges than their hosts have. There is no relationship between the proportion of the range of the foodplant that is occupied and the size of the range of the foodplant. Monophagous butterfly species have smaller range sizes than polyphagousspecies, probably as a consequence of the greater potential range sizes of the latter. Those plant species that are used as hosts by butterflies have larger range sizes than expected by chance, and individual polyphagous butterfly species tend disproportionately to be found in areas containing larger numbers of their host plant species. In sum, this study reveals a complex relationship between the distributionof butterflies and that of their resources (foodplants). [ABSTRACT FROM AUTHOR]

A general positive interspecific relationship between local abundance and geographic range size in animals has prompted speculation that a similar relationship might exist intraspecifically, such that a species is widespread at times when it is locally abundant, and more restricted in distribution when it is locally rare. Current evidence suggests that intraspecific relationships often are positive, but that there is considerable variation in the pattern exhibited by species. Here, we use data on British birds to test the hypotheses that speciesshowing a high mean or wide spread of local densities or range sizeswill be more likely to show strong intraspecific relationships between abundance and geographic range size. These data show only inconsistent support for an effect of the range of densities or of occupancies on intraspecific abundance-range size relationships. However, the strength of an intraspecific relationship does seem to be related to the mean occupancy of species, and whether or not a species exhibits temporal trends in density, with the strongest relationships found in species with simultaneous trends in both density and occupancy. We suggest that these results are explained by time lags in the loss or gain of species at occupied sites in response to reductions or increases in density. [ABSTRACT FROM AUTHOR]

A number of mechanisms have been proposed to explain the widely observed positive interspecific relationship between local abundance and extent of geographic distribution in animals. Here, we use data on British birds to assess two of these hypotheses: that the relationship results from the relative position of a study area with respect to the geographic ranges of the species which occur there, and that the relationship results from a simple difference between taxonomic groups,rather than any general tendency for more abundant species to have larger range sizes. We find support for neither hypothesis. Phylogenetically controlled comparative analyses reveal that the positive abundance-range size relationship is consistently found within taxa, even when abundance and range size are calculated at a variety of spatial and temporal scales. Analyses both across species and within taxa show that bird species for which Britain is near to the centre of their distribution in Europe tend to have larger British range sizes and higher abundances than do species where Britain is close to the edge oftheir range in Europe. However, these relationships do not cause that between abundance and range size, because this latter relationship persists within different range position categories. Whether a species is near the centre or edge of its geographic range in Britain may affect its position on the. abundance-range size relationship, but does not produce the relationship. Range position in Britain does, however, seem to be related to the magnitude of temporal changes in the range sizes of British birds. There is some evidence to suggest that species for which Britain is nearer to their European range centre haveshown smaller changes in distribution over the period 1970--1990 than have species for which Britain is close to their European range edge. [ABSTRACT FROM AUTHOR]

Knowledge of the distribution of biodiversity remains poor. This situation might more readily be resolved if the species richness of certain groups of organisms indicated the richness of other, less well known groups. Prendergast and Eversham (1997) perform a spatially explicit exploration of the pattern in the predictive power that one taxon(a potential 'indicator group') might have for the diversity of another. In this paper we respond to three important points that they raise. First, we describe an additional graphical technique for visualising spatial aspects of indicator relationships. Second, we examine some of the consequences of smoothing species richness data on observedindicator relationships. Third, we consider some of the factors thatmay contribute to strong indicator relationships. [ABSTRACT FROM AUTHOR]