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.     

Macro‐scale bird species richness patterns of the East Asian mainland and islands: energy,area and isolation

Aim To create a map of bird species richness (BSR) in East Asia and to examine the effect of area, isolation, primary productivity, topographic heterogeneity, and human population density on BSR. Location East Asia (from 70° E to 180° E longitude), including the eastern half of the Palaearctic Region, the entire Oriental Region, and the entire Wallacea Subregion. Methods The breeding ranges of 2406 terrestrial bird species were mapped and overlaid to create a species richness map. The BSR map was transformed into a 100 × 100 km quadrat system, and BSR was analysed in relation to land area, average normalized difference vegetation index (NDVI), elevation range, and average population density. Results In general, BSR declined from the Tropics to the Arctic. In mainland East Asia, however, BSR was highest around the Tropic of Cancer, and fluctuated between 30° and 50° N. Islands had lower BSR than adjacent mainland areas. The NDVI was strongly positively correlated with BSR in mainland areas and on islands. For mainland areas, NDVI explained 65% of the BSR variation, and topographic heterogeneity explained an additional 6% in ordinary least‐squares regression. On islands, NDVI explained 66% of BSR variation, island area explained 13%, and distance to mainland accounted for 1%. Main conclusions In East Asia, we suggest that primary productivity is the key factor underpinning patterns of BSR. Primary productivity sets the upper limits of the capacity of habitats to support bird species. In isolated areas such as islands and peninsulas, however, BSR might not reach the richness limits set by primary productivity because the degree of isolation and area size also can affect species richness. Other factors, such as spatial heterogeneity, biotic interactions, and perturbations, may also affect species richness. However, their effects are secondary and are not as strong as primary productivity, isolation, and area size.     

The role of fire in terrestrial vertebrate richness patterns

Productivity is strongly associated with terrestrial species richness patterns, although the mechanisms underpinning such patterns have long been debated. Despite considerable consumption of primary productivity by fire, its influence on global diversity has received relatively little study. Here we examine the sensitivity of terrestrial vertebrate biodiversity (amphibians, birds and mammals) to fire, while accounting for other drivers. We analyse global data on terrestrial vertebrate richness, net primary productivity, fire occurrence (fraction of productivity consumed) and additional influences unrelated to productivity (i.e., historical phylogenetic and area effects) on species richness. For birds, fire is associated with higher diversity, rivalling the effects of productivity on richness, and for mammals, fire's positive association with diversity is even stronger than productivity; for amphibians, in contrast, there are few clear associations. Our findings suggest an underappreciated role for fire in the generation of animal species richness and the conservation of global biodiversity.     

Spatial patterns in the distribution of European springtails (Hexapoda: Collembola)

Using a large database on the spatial distribution of European springtails (Collembola) we investigated how range sizes and range distribution across European countries and major islands vary. Irrespective of ecological guild, islands tended to contain more endemic species than mainland countries. Nestedness and species co‐occurrence analysis based on country species lists revealed latitudinal and longitudinal gradients of species occurrences across Europe. Species range sizes were much more coherent and had fewer isolated occurrences than expected from a null model based on random colonization. We did not detect clear postglacial colonization trajectories that shaped the faunal composition across Europe. Our results are consistent with a multiregional postglacial colonization. © 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, 105 , 498–506.     

The island rule and a research agenda for studying ecogeographical patterns

We are currently experiencing a resurgence of interest in ecogeographical rules, which describe general trends in morphology and related traits along geographical gradients. In order to develop a more comprehensive understanding of the generality and underlying causal mechanisms for these patterns, we recommend a new, more integrated research agenda. In particular, we recommend studies that simultaneously consider different clines in morphology, geographical ranges and diversity as intricately related phenomena; all being ecological, evolutionary and biogeographical responses of organisms to selection regimes that vary non-randomly over space and time, and among species with different ecological and evolutionary histories.     

Island ecology and contingent theory: the role of spatial scale and taxonomic bias

Scale, the scale dependency of patterns and processes, and the ways that organisms scale their responses to these patterns and processes are central to island and landscape ecology. Here, we take a database of studies in island ecology and investigate how studies have changed over a 40-year period with respect to spatial scale and organisms studied. We demonstrate that there have been changes in the spatial scale of islands studied and that there is taxonomic bias in favour of vertebrates in island ecological studies when compared to scientific publications as a whole. We discuss how such taxonomic bias may have arisen and discuss the implications for ecology and biogeography.     

Continental and regional ranges of North American mammals: Rapoport's rule in real and null worlds

Aim To assess the relationship between species richness and distribution within regions arranged along a latitudinal gradient we use the North American mammalian fauna as a study case for testing theoretical models. Location North America. Methods We propose a conceptual framework based on a fully stochastic mid‐domain model to explore geographical patterns of range size and species richness that emerge when the size and position of species ranges along a one‐dimensional latitudinal gradient are randomly generated. We also analyse patterns for the mammal fauna of North America by comparing empirical results from a biogeographical data base with predictions based on randomization null models. Results We confirmed the validity of Rapoport's rule for the mammals of North America by documenting gradients in the size of the continental ranges of species. Additionally, we demonstrated gradients of mean regional range size that parallel those of continental range. Our data also demonstrated that mean range size, measured both as a continental or a regional variable, is significantly correlated with the geographical pattern in species richness. All these patterns deviated sharply from null models. Main conclusions Rapoport's statement of an areographic relationship between species distribution and richness is highly relevant in modern discussions about ecological patterns at the geographical scale.     

Spatial scale dependence of the species diversityin Tianmu Mountain and its relationship with spatial patterns by using multifractal analysis

This study took the Tianmu Mountain National Natural Preservation Area in western Zhejiang Province as an example 1) to quantify the species diversity with selected species indices including Shannon-Wiener index (H), Margalef index (K) and Evenness index (E) at different spatial scales, 2) to analyze the spatial distribution patterns of the species diversity by multifractal parameters such as the singularity index α, its fractal dimension f(α), the f(α)–α spectrum range (SR) and its symmetry (Dist) using the multifractal theory, and 3) to determine their relationships. Results of nonlinear regression analysis with power functions showed that increasing spatial scale resulted in increasing H but decreasing E and K, indicating that the scale dependence of species diversity existed. By using the multifractal method, it was indicated that species spatial distribution had multifractal features. Moreover, strong linear relationships of the diversity indices H, E and K with α_min and clear nonlinear associations of the diversity indices H, E and K with power functions for SR and Dist were found. Since interactions of the species diversity and the spatial characteristics are very complex, the above mentioned relationships need further validation along with precise explanations of any correlations among their ecological processes.     

Spatial scale dependence of the species diversityin Tianmu Mountain and its relationship with spatial patterns by using multifractal analysis

This study took the Tianmu Mountain National Natural Preservation Area in western Zhejiang Province as an example 1) to quantify the species diversity with selected species indices including Shannon-Wiener index (H), Margalef index (K) and Evenness index (E) at different spatial scales, 2) to analyze the spatial distribution patterns of the species diversity by multifractal parameters such as the singularity index α, its fractal dimension f(α), the f(α)–α spectrum range (SR) and its symmetry (Dist) using the multifractal theory, and 3) to determine their relationships. Results of nonlinear regression analysis with power functions showed that increasing spatial scale resulted in increasing H but decreasing E and K, indicating that the scale dependence of species diversity existed. By using the multifractal method, it was indicated that species spatial distribution had multifractal features. Moreover, strong linear relationships of the diversity indices H, E and K with α_min and clear nonlinear associations of the diversity indices H, E and K with power functions for SR and Dist were found. Since interactions of the species diversity and the spatial characteristics are very complex, the above mentioned relationships need further validation along with precise explanations of any correlations among their ecological processes.     

Temporal dynamics of stream fish assemblages and the role of spatial scale in quantifying change

1. Spatial grain of studies of communities is often based on arbitrary convention. Few studies have examined how spatial scaling of grain size affects estimates of compositional change over time, despite its broad implications.
2. Fish assemblage structure was compared between 1974 and 2014 at 33 sampling locations in the Muddy Boggy River drainage, USA. The two main objectives for this comparison were to quantify change in assemblage structure and to test for a relationship between compositional change and spatial scale. Spatial scale was manipulated by pooling assemblage data into a continuous range of groups, which increased in size from K = 33 pairs (i.e., local scale) to K = 1 pair (i.e., global scale), via clustering algorithm based on pair‐wise fluvial distance.
3. Local assemblages (stream reaches) varied in the degree of assemblage change over time (range = 0.10–0.99 dissimilarity; mean = 0.66). The global assemblage (drainage), however, remained relatively similar. A discontinuity in the relationship between compositional change and spatial scale occurred at K = 15 (mean dissimilarity = 0.56; p = .062), and this grouping is roughly the size of the headwater/tributary drainages (i.e., stream order ≤ 3) in the study system.
4. Spatial scale can impact estimates of biodiversity change over time. These results suggest assemblages are more dynamic at individual stream reaches than at the scale of the entire drainage. The decline in assemblage change at the spatial scale of K = 15 deserves further attention given the marginal significance, despite a small sample size (n = 15). This pattern could suggest regional and meta‐community processes become more important in shaping assemblage dynamics at the scale of headwater drainages, whereas the factors responsible for driving individual stream reach dynamics (e.g., stochasticity) become less important. Defining assemblages at a larger scale will result in different estimates of species persistence. Biodiversity monitoring efforts must take the effect of spatial scaling into consideration.

     

The influence of spatial scale on cross-taxon congruence patterns and prediction accuracy of species richness

A comparison of species richness patterns of butterflies and birds was made using data from two grids of squares (small squares 137.5 km on a side and large squares 275 km on a side) covering western North America. Using geostatistical procedures, we found that the spatial patterns of species richness of these two taxa were related. The influence of grain size on the strength of this relationship was investigated by analysing the two data sets. For both data sets, the number of butterfly species in a square was a statistically significant predictor of the corresponding number of bird species. However, cross-validation techniques showed that the marginal improvement in prediction accuracy due to including butterflies as a predictor was greater in the large-square data. We explored the effect of areal extent on cross-taxon congruencies by investigating species richness patterns in four subsets of the small-square data. In regions with smaller areal extent, the cross-taxon congruence patterns were not substantially different from the pattern found in the full data set. Finally, using data-splitting techniques, we explored the relationships between prediction accuracy of species richness, sample size, areal extent of the sample, and grain size.     

空间尺度对地形异质性-物种多样性关系的影响:粒度和幅度

空间尺度是影响我们理解生态学格局和过程的关键因素.目前已有多种关于物种多样性分布格局形成机制的假说且研究者未达成共识,原因之一是空间尺度对物种多样性分布格局的环境影响因子的解释力和相对重要性有重要影响.地形异质性是物种多样性分布格局的重要影响因素.本文综述了在地形异质性-物种多样性关系的研究中,不同空间粒度和幅度对研究...     

Biodiversity monitoring,earth observations and the ecology of scale

Human activity and land‐use change are dramatically altering the sizes, geographical distributions and functioning of biological populations worldwide, with tremendous consequences for human well‐being. Yet our ability to measure, monitor and forecast biodiversity change – crucial to addressing it – remains limited. Biodiversity monitoring systems are being developed to improve this capacity by deriving metrics of change from an array of in situ data (e.g. field plots or species occurrence records) and Earth observations (EO; e.g. satellite or airborne imagery). However, there are few ecologically based frameworks for integrating these data into meaningful metrics of biodiversity change. Here, I describe how concepts of pattern and scale in ecology could be used to design such a framework. I review three core topics: the role of scale in measuring and modelling biodiversity patterns with EO, scale‐dependent challenges linking in situ and EO data and opportunities to apply concepts of pattern and scale to EO to improve biodiversity mapping. From this analysis emerges an actionable approach for measuring, monitoring and forecasting biodiversity change, highlighting key opportunities to establish EO as the backbone of global‐scale, science‐driven conservation.