Invasiveness does not predict impact: response of native land snail communities to plant invasions in riparian habitats.

Studies of plant invasions rarely address impacts on molluscs. By comparing pairs of invaded and corresponding uninvaded plots in 96 sites in floodplain forests, we examined effects of four invasive alien plants (Impatiens glandulifera, Fallopia japonica, F. sachalinensis, and F.× bohemica) in the Czech Republic on communities of land snails. The richness and abundance of living land snail species were recorded separately for all species, rare species listed on the national Red List, and small species with shell size below 5 mm. The significant impacts ranged from 16-48% reduction in snail species numbers, and 29-90% reduction in abundance. Small species were especially prone to reduction in species richness by all four invasive plant taxa. Rare snails were also negatively impacted by all plant invaders, both in terms of species richness or abundance. Overall, the impacts on snails were invader-specific, differing among plant taxa. The strong effect of I. glandulifera could be related to the post-invasion decrease in abundance of tall nitrophilous native plant species that are a nutrient-rich food source for snails in riparian habitats. Fallopia sachalinensis had the strongest negative impact of the three knotweeds, which reflects differences in their canopy structure, microhabitat humidity and litter decomposition. The ranking of Fallopia taxa according to the strength of impacts on snail communities differs from ranking by their invasiveness, known from previous studies. This indicates that invasiveness does not simply translate to impacts of invasion and needs to be borne in mind by conservation and management authorities.

Between geometry and biology: the problem of universality of the species-area relationship.

The species-area relationship (SAR) is considered to be one of a few generalities in ecology, yet a universal model of its shape and slope has remained elusive. Recently, Harte et al. argued that the slope of the SAR for a given area is driven by a single parameter, the ratio between total number of individuals and number of species (i.e., the mean population size across species at a given scale). We provide a geometric interpretation of this dependence. At the same time, however, we show that this dependence cannot be universal across taxa: if it holds for a taxon composed from two subsets of species and also for one of its subsets, it cannot simultaneously hold for the other subset. Using three data sets, we show that the slope of the SAR considerably varies around the prediction. We estimate the limits of this variation by using geometric considerations, providing a theory based on species spatial turnover at different scales. We argue that the SAR cannot be strictly universal, but its slope at each particular scale varies within the constraints given by species' spatial turnover at finer spatial scales, and this variation is biologically informative.

Analytical evidence for scale-invariance in the shape of species abundance distributions.

The distribution of species abundances within an ecological community provides a window into ecological processes and has important applications in conservation biology as an indicator of disturbance. Previous work indicates that species abundance distributions might be independent of the scales at which they are measured which has implications for data interpretation. Here we formulate an analytically tractable model for the species abundance distribution at different scales and discuss the biological relevance of its assumptions. Our model shows that as scale increases, the shape of the species abundance distribution converges to a particular shape given uniquely by the Jaccard index of spatial species turnover and by a parameter for the spatial correlation of abundances. Our model indicates that the shape of the species abundance distribution is taxon specific but does not depend on sample area, provided this area is large. We conclude that the species abundance distribution may indeed serve as an indicator of disturbances affecting species spatial turnover and that the assumption of conservation of energy in ecosystems, which is part of the Maximum Entropy approach, should be re-evaluated.

Rarity, commonness, and the contribution of individual species to species richness patterns.

Common species have a greater effect on observed geographical patterns of species richness than do rare ones. Here we present a theory of the relationship between individual species occurrence patterns and patterns in species richness, which allows purely geometrical and statistical causes to be distinguished from biological ones. Relationships between species occupancy and the correlation of species occurrence with overall species richness are driven by the frequency distribution of species richness among sites. Moreover, generally positive relationships are promoted by the fact that species occupancy distributions are mostly right skewed. However, biological processes can lead to deviations from the predicted pattern by changing the nestedness of a species' spatial distribution with regard to the distributions of other species in an assemblage. We have applied our theory to data for European birds at several spatial scales and have identified the species with significantly stronger or weaker correspondence with the overall richness pattern than that predicted by the null model. In sum, whereas the general macroecological pattern of a stronger influence of common species than of rare species on species richness is predicted by mathematical considerations, the theory can reveal biologically important deviations at the level of individual species.

Species abundance distribution results from a spatial analogy of central limit theorem.

The frequency distribution of species abundances [the species abundance distribution (SAD)] is considered to be a fundamental characteristic of community structure. It is almost invariably strongly right-skewed, with most species being rare. There has been much debate as to its exact properties and the processes from which it results. Here, we contend that an SAD for a study plot must be viewed as spliced from the SADs of many smaller nonoverlapping subplots covering that plot. We show that this splicing, if applied repeatedly to produce subplots of progressively larger size, leads to the observed shape of the SAD for the whole plot regardless of that of the SADs of those subplots. The widely reported shape of an SAD is thus likely to be driven by a spatial parallel of the central limit theorem, a statistically convergent process through which the SAD arises from small to large scales. Exact properties of the SAD are driven by species spatial turnover and the spatial autocorrelation of abundances, and can be predicted using this information. The theory therefore provides a direct link between SADs and the spatial correlation structure of species distributions, and thus between several fundamental descriptors of community structure. Moreover, the statistical process described may lie behind similar frequency distributions observed in many other scientific fields.

Rapoport's rule, species tolerances, and the latitudinal diversity gradient: geometric considerations.

The most pervasive species-richness pattern, the latitudinal gradient of diversity, has been related to Rapoport's rule, i.e., decreasing latitudinal extent of species' ranges toward the equator. According to this theory, species can have narrower tolerances in more stable climates, leading to smaller ranges and allowing coexistence of more species. We show, using a simple geometric model, that the postulated decrease of species' potential range sizes toward the tropics would itself lead to a latitudinal gradient opposite to that observed. In contrast, an increase in extent of potential ranges toward the tropics would lead to the observed diversity gradient. Moreover, in the presence of geographic barriers constraining actual species' ranges, Rapoport's rule emerges if the latitudinal trend in extents of potential ranges (as defined by climatic tolerance) is opposite to that postulated or if variability in potential range extents decreases toward the poles. A strong implicit latitudinal diversity gradient (i.e., higher concentration of midpoints of species' potential ranges in the tropics), however, produces both observed macroecological patterns without the contribution of any latitudinal trends in species climatic tolerances or in potential range sizes. Our model underscores the necessity of discriminating theoretical processes and principles from the patterns we observe, and it is well supported by data on global distribution of species' range sizes.

The quest for a null model for macroecological patterns: geometry of species distributions at multiple spatial scales.

There have been several attempts to build a unified framework for macroecological patterns. However, these have mostly been based either on questionable assumptions or have had to be parameterized to obtain realistic predictions. Here, we propose a new model explicitly considering patterns of aggregated species distributions on multiple spatial scales, the property which lies behind all spatial macroecological patterns, using the idea we term 'generalized fractals'. Species' spatial distributions were modelled by a random hierarchical process in which the original 'habitat' patches were randomly replaced by sets of smaller patches nested within them, and the statistical properties of modelled species assemblages were compared with macroecological patterns in observed bird data. Without parameterization based on observed patterns, this simple model predicts realistic patterns of species abundance, distribution and diversity, including fractal-like spatial distributions, the frequency distribution of species occupancies/abundances and the species-area relationship. Although observed macroecological patterns may differ in some quantitative properties, our concept of random hierarchical aggregation can be considered as an appropriate null model of fundamental macroecological patterns which can potentially be modified to accommodate ecologically important variables.