Computing β-diversity with Rao's quadratic entropy: a change of perspective

Ecologists have traditionally viewed β-diversity as the ratio between γ-diversity and average α-diversity. More recently, an alternative way of partitioning diversity has been proposed for which β-diversity is obtained as the difference between γ-diversity and average α-diversity. Although this additive model of diversity decomposition is generally considered superior to its multiplicative counterpart, in both models β-diversity is a formally derived quantity without any self-contained ecological meaning; it simply quantifies the diversity excess of γ-diversity with respect to average α-diversity. Taking this excess as an index of β-diversity is a questionable operation. In this paper, we show that a particular family of α-diversity measures, the most celebrated of which is Rao's quadratic entropy, can be adequately used for summarizing β-diversity. Our proposal naturally leads to a new additive model of diversity for which, given two or more sets of plots, overall plot-to-plot species variability can be additively partitioned into two non-negative components: average variability in species composition within each set of plots and the species variability between the set of plots. For conservation purposes, the suggested change of perspective in the summarization of β-diversity allows for a flexible analysis of spatial heterogeneity in ecological diversity so that different hierarchical levels of biotic relevance (i.e. from the genetic to the landscape level) can be expressed in a significant and consistent way.     

Additive partitioning of rarefaction curves and species-area relationships: unifying alpha-, beta- and gamma-diversity with sample size and habitat area

Additive partitioning of species diversity is widely applicable to different kinds of sampling regimes at multiple spatial and temporal scales. In additive partitioning, the diversity within and among samples ( α and β ) is expressed in the same units of species richness, thus allowing direct comparison of α and β . Despite its broad applicability, there are few demonstrated linkages between additive partitioning and other approaches to analysing diversity. Here, we establish several connections between diversity partitions and patterns of habitat occupancy, rarefaction, and species–area relationships. We show that observed partitions of species richness are equivalent to sample-based rarefaction curves, and expected partitions from randomization tests are approximately equivalent to individual-based rarefaction. Additive partitions can also be applied to species–area relationships to determine the relative contributions of factors influencing the β -diversity among habitat fragments.     

Assessment of species diversity from species abundance distributions at different localities

We show how the spatial structure of species diversity can be analyzed using the correlation between the log abundances of the species in the communities, assuming that two communities at different localities can be described by a bivariate lognormal species abundance distribution. A useful property of this approach is that the log abundances of the species at two localities can be considered as samples from a bivariate normal distribution defined by only five parameters. The variances and the correlation can be estimated by maximum likelihood methods even if there is no information about the sampling intensity and the number of unobserved species. This method also enables estimation of over-dispersion in the sampling relative to a Poisson distribution that allows sampling adjustment of the estimate of β-diversity. Furthermore, we also obtain a partitioning of species diversity into additive components of α-, β- and γ-diversity. For instance, if the correlation between the log abundances of the species is close to one, the same species will be common and rare in the two communities and the β-diversity will be low. We illustrate this approach by analysing similarities of communities of rare and endangered species of oak-living beetles in south-eastern Norway. The number of recorded species was estimated to be only 48.1% of the total number of species actually present in these communities. The correlations among communities dropped rather quickly with distance with a scaling of order 200 km. This illustrates large spatial heterogeneity in species composition, which should be accounted for in the design of schemes of such devices for assessing species diversity in these habitat-types.     

Species diversity in neutral metacommunities: a network approach

Biologists seek an understanding of the processes underlying spatial biodiversity patterns. Neutral theory links those patterns to dispersal, speciation and community drift. Here, we advance the spatially explicit neutral model by representing the metacommunity as a network of smaller communities. Analytic theory is presented for a set of equilibrium diversity patterns in networks of communities, facilitating the exploration of parameter space not accessible by simulation. We use this theory to evaluate how the basic properties of a metacommunity – connectivity, size, and speciation rate – determine overall metacommunity γ -diversity, and how that is partitioned into α - and β -components. We find spatial structure can increase γ -diversity relative to a well-mixed model, even when θ is held constant. The magnitude of deviations from the well-mixed model and the partitioning into α - and β -diversity is related to the ratio of migration and speciation rates. γ -diversity scales linearly with metacommunity size even as α - and β -diversity scale nonlinearly with size.     

Species diversity in vertical, horizontal, and temporal dimensions of a fruit-feeding butterfly community in an Ecuadorian rainforest

To test the hypotheses that fruit-feeding nymphalid butterflies are randomly distributed in space and time, a community of fruit-feeding nymphalid butterflies was sampled at monthly intervals for one year by trapping 6690 individuals of 130 species in the canopy and understory of four forest habitats: primary, higraded, secondary, and edge. The overall species abundance distribution was well described by a lognormal distribution. Total species diversity (γ-diversity) was partitioned into additive components within and among community subdivisions (α-diversity and β-diversity) in vertical, horizontal and temporal dimensions. Although community subdivisions showed high similarity (1 —β-diversity/γ-diversity), significant β-diversity existed in each dimension. Individual abundance and observed species richness was lower in the canopy than in the understory. However, rarefaction analysis and species accumulation curves revealed that canopy had higher species richness than understory. Observed species richness was roughly equal in all habitats, but individual abundance was much greater in edge, largely due to a single, specialist species. Rarefaction analysis and species accumulation curves showed that edge had significantly lower species richness than all other habitats. Samples from a single habitat, height and time contained only a small fraction of the total community species richness. This study demonstrates the feasibility, and necessity, of large-scale, long-term sampling in multiple dimensions for accurately measuring species richness and diversity in tropical forest communities. We discuss the importance of such studies in conservation biology.     

On hierarchical diversity decomposition

Abstract. Question: According to Whittaker's proposal, ecologists have traditionally viewed β‐diversity as the ratio between γ‐diversity and average α‐diversity. More recently, an alternative way of partitioning diversity has been ‘rediscovered’for which β‐diversity is obtained as the difference between γ‐diversity and average α‐diversity. This additive way of partitioning diversity has rapidly become a very popular framework for hierarchical diversity decomposition at various spatial scales. The question for this study is: Can we highlight any relation between these two ways of partitioning diversity, or do these methods really capture different facets of spatial turnover in species composition? Methods: First the properties that a diversity measure should possess for enabling additive decomposition into α‐, β‐, and γ‐components are reviewed. Next, attention is drawn to the relationships between additive and multiplicative diversity decomposition. Results: It is shown that the additive model is closely related to its multiplicative counterpart through a simple logarithmic transformation. Conclusions: Contrary to the current assumption, both methods for partitioning diversity are not as different as they appear. Hence, the supposed superiority of additive diversity partition over multiplicative diversity decomposition is largely unjustified.     

Does the Existence of Bird's Nest Ferns Enhance the Diversity of Oribatid (Acari: Oribatida) Communities in a Subtropical Forest?

We examined the effects of the presence of bird's nest ferns on the species diversity of oribatid mites in the whole forest in terms of the three categories of species diversity (α-, β-, and γ-diversity) in a subtropical forest in south-western Japan. The species diversity (1 − D) of oribatid communities in the ferns was significantly lower than those in bark of trees and the forest-floor litter and soil, and was similar to that in the branches. The oribatid faunas in the litter in and the roots of the fern were more similar to those in both the forest-floor litter and soil than to the faunas in the other arboreal habitats. However, the ferns can be colonized by endemic oribatid species specialized to such environments. The number of oribatid species estimated for a hypothetical stand with no ferns was about 180 species from 80 samples; this value did not differ significantly from that in another hypothetical stand with ferns (ca. 190 species). Thus, the species richness of oribatid communities estimated for the whole forest (the γ-diversity) was not affected by the presence or absence of bird's nest ferns. The α- and β-diversities of oribatid communities on bird's nest ferns were lower than those in other habitats, and they might not dramatically raise the overall γ-diversity of invertebrate communities in the whole forest. The bird's nest ferns, however, can generate a unique habitat for specialized species, and this would help to maintain species diversities of invertebrates at the whole-forest scale in subtropical forests.     

Additive partition of parametric information and its associated beta-diversity measure

A desirable property of a diversity index is strict concavity. This implies that the pooled diversity of a given community sample is greater than or equal to but not less than the weighted mean of the diversity values of the constituting plots. For a strict concave diversity index, such as species richness S, Shannon's entropy H or Simpson's index 1-D, the pooled diversity of a given community sample can be partitioned into two non-negative, additive components: average within-plot diversity and between-plot diversity. As a result, species diversity can be summarized at various scales measuring all diversity components in the same units. Conversely, violation of strict concavity would imply the non-interpretable result of a negative diversity among community plots. In this paper, I apply this additive partition model generally adopted for traditional diversity measures to Aczél and Daróczy's generalized entropy of type . In this way, a parametric measure of -diversity is derived as the ratio between the pooled sample diversity and the average within-plot diversity that represents the parametric analogue of Whittaker's -diversity for data on species relative abundances.     

Diversity partitioning of moorland plant communities across hierarchical spatial scales

Understanding of the scaling of diversity is critical to enhance conservation strategies for subalpine moorland ecosystems vulnerable to future environmental changes. However, a paucity of quantitative data strongly limits such attempts. In this study, we used an additive diversity partitioning framework and quantified diversity patterns of moorland plant communities across hierarchical spatial scales, within- and between-sample transects, and between sites (corresponding to α and two levels of β diversity). Moorland sites markedly differed in size (range 1,000–160,000 m²) and were isolated from each other to varying extents within an inhospitable matrix (i.e., forests). We found that β diversity components were consistently higher, whereas the local α diversity component was consistently lower than expected by chance. We observed substantial contribution at the between-site scale to total species richness. By focusing on diversity patterns of moorland plant communities across multiple hierarchical spatial scales, we could thus identify the scale at which regional diversity is maximized. Our results suggest that protection of as many moorland sites as possible, to ensure beta diversity between sites, will effectively conserve total diversity. The use of additive diversity partitioning is a major step forward in providing strategies for the biological conservation of subalpine moorland ecosystems vulnerable to future environmental changes.     

Predators temper the relative importance of stochastic processes in the assembly of prey metacommunities

Communities assemble through a combination of stochastic processes, which can make environmentally similar communities divergent (high β-diversity), and deterministic processes, which can make environmentally similar communities convergent (low β-diversity). Top predators can influence both stochasticity (e.g. colonization and extinction events) and determinism (e.g. size of the realized species pool), in community assembly, and thus their net effect is unknown. We investigated how predatory fish influenced the scaling of prey diversity in ponds at local and regional spatial scales. While fish reduced both local and regional richness, their effects were markedly more intense at the regional scale. Underlying this result was that the presence of fish made localities within metacommunities more similar in their community composition (lower β-diversity), suggesting that fish enhance the deterministic, relative to the stochastic, components of community assembly. Thus, the presence of predators can alter fundamental mechanisms of community assembly and the scaling of diversity within metacommunities.     

Baidzharakhs (relic mounds) increase plant community diversity by interrupting zonal vegetation distribution along the Arctic Sea, northern Siberia

To understand how baidzharakhs (relic mounds enclosing polygonal ice blocks in permafrost) affect the zonal distribution of vegetation, vegetation was measured in 145 plots of area 50 cm × 50 cm on a coastal terrace facing the Arctic Ocean in northern Siberia. Cluster analysis classified five community types that were zonally distributed along the coastline. α-diversities (species richness and diversity) were not different among vegetation types except for vegetation close to the coastline. On and around baidzharakhs, burrows created by lemmings were frequently observed, and plant cover was low, suggesting that baidzharakhs support habitats for rodents. Disturbances by rodent habits caused plant cover to decline but did not change α-diversity. Two vegetation types that developed only on baidzharakhs were found at intermediate distances between the seacoast and inland areas. Because these two vegetation types are azonally distributed, β- and γ-diversities were increased by permafrost-derived topography, i.e., baidzharakh, and/or disturbance by rodents of which suitable nesting habitat is provided by baidzharakh.     

Spatial and Temporal Patterns in Macrofaunal Diversity Components Relative to Sea Floor Landscape Structure

We examined temporal changes in macrofaunal α- and β-diversity over several spatial scales (within patches, among patches, across landscapes and across regions) in Long Island Sound on the northeast USA coast. Regional ε-diversity was estimated at 144 taxa, however γ-diversity fluctuated over time as did α- and β-diversity components. Based on additive partitioning, patch- and region-scale β-diversity components generally had the highest contributions to γ-diversity; lower percentages were found at within-patch and landscape scales. Multiplicative diversity partitioning indicated highest species turnover at within- and among patch scales. For all partition results, within-patch and patch-scale β-diversity increased sharply when hypoxia impacted benthic communities. Spatial variation in diversity components can be attributed to the collection of different patch types at varying spatial scales and their associated habitats across the benthic landscapes, as well as gradients in depth and other estuarine-scale characteristics. Temporal variation in diversity components across spatial scales may be related to seasonal changes in habitat heterogeneity, species population dynamics, and seasonal disturbances. Rare species were significant and temporally consistent components of macrofaunal diversity patterns over different spatial scales. Our findings agree with other marine and terrestrial studies that show diversity components vary significantly over different spatial scales and the importance of habitat/landscape heterogeneity in supporting diversity. However, our results indicate that the relative contributions of scale-specific β-diversity components can also change significantly over time. Thus, studies of diversity patterns across patches and landscapes based on data collected at one time, or assembled into a single data set from different times, may not capture the full suite of diversity patterns that occur over varying spatial scales and any time-specific determinants of those patterns. Many factors that shape and maintain sedimentary communities vary temporally, and appear to play an important role in determining and maintaining macrofaunal diversity over different spatial scales.     

Structure and diversity of shallow soft-bottom benthic macrofauna in the Gulf of Lions (NW Mediterranean)

Samples of soft-sediment macrobenthos from 92 sites between 10 and 50 m depth were used to assess (1) the main soft-bottom macrofauna communities in the Gulf of Lions, (2) the different components of the diversity of benthic macrofauna in this area, and (3) the relevance of the use of major taxonomic groups as surrogates for the analysis of the structure and diversity of total macrofauna. Three main communities were identified by cluster analysis and associated procedures. These communities corresponded well to the assemblages recently identified on the basis of polychaete composition. The α-diversity indices were in accordance with those reported for similar communities in the Mediterranean. Conversely, the β-diversity value was higher than the few other data available in the literature for marine soft-bottom macrofauna. The total number of species in the studied area estimated by the “total species accumulation curve” (TS) method was 2,319, which was only 10% higher than the number obtained by extrapolation of the species–area curve. The similarity matrix based on polychaetes correlated best with the one based on total macrofauna. Polychaetes and crustaceans were also the best surrogates of total macrofauna when assessing α-diversity (except in the case of Δ*). Conversely, molluscs were the best surrogates of total macrofauna β-diversity. Our results show that the choice of an optimal surrogate for total benthic macrofauna depends on the characteristic of the benthic macrofauna to be studied. Moreover, this choice is also dependent on the environment to be studied.     

Community structure of arboreal caterpillars within and among four tree species of the eastern deciduous forest

Abstract.  1. A seasonally replicated experimental design was used to address the question of how differences within and among host tree species affect arboreal caterpillar communities.
2. Seasonal variation influenced caterpillar community composition most significantly, and the similarity among caterpillar assemblages did not necessarily follow the pattern of phylogenetic relatedness among host trees.
3. Species richness and abundance of caterpillars were higher on oaks and maples than on American beech. Diversity partitioning models revealed that β diversity was only occasionally greater or less than expected by chance alone.
4. When β diversity was significant, values tended to be greater than expected by chance among replicate trees within each species and lower than expected by chance among the four tree species.
5. Differences among trees appeared important for determining patterns of species presence/absence for rare species and influencing patterns of species dominance within caterpillar assemblages. Differences among tree species had a significant effect on overall lepidopteran community composition and mean species diversity (i.e. α diversity).
6. Because β diversity of caterpillars among host trees was lower than expected by chance, host specificity within the Lepidoptera may be less prevalent than thought previously.     

Community assembly along a species pool gradient: implications for multiple-scale patterns of species diversity

Various ecological processes influence patterns of species diversity at multiple spatial scales. One process that is potentially important but rarely considered is community assembly. I assembled model communities using species pools of differing size to examine how the history of community assembly may affect multi-scale diversity patterns. The model contained three scales at which diversity could be measured: local community, metacommunity, and species pool. Local species saturation occurred, as expected from the competition and predation built in the model. However, local communities did not become resistant to invasions except when the species pool was very small. Depending on dispersal rate and trophic level, the larger the species pool, the harder it was to predict which species invades which local community at a given time. Consequently, local-community dissimilarity maintained by assembly history increased linearly with pool size, even though local diversity was decoupled from pool size. These results have two implications for multi-scale diversity patterns. First, assembly history may provide an explanation for scale-dependent relationships between local and regional diversity: assembly causes the relationship to be curvilinear at one scale (local community), while linear at another (metacommunity). Second, assembly history influences how -diversity is partitioned into - and -diversity: assembly causes the relative contribution of to increase with pool size. Overall, this study suggests that community assembly history interacts with species pool size to regulate multi-scale patterns of species diversity.     

Patterns of bryophyte and vascular plant richness in European subalpine springs

The diversity of spring habitats can be determined not only by local environmental conditions, but also by large-scale biogeographical effects. The effects can differ across various groups of organisms. We compared α-, β- and γ-diversity patterns of bryophytes and vascular plants of (sub)alpine springs in three contrasting mountain ranges: Alps (Switzerland), Balkans (Bulgaria), Western Carpathians (Slovakia, Poland). We used univariate and multivariate statistics to test for the effects of pH, conductivity, altitude, slope, mean annual temperature and annual precipitation on diversity patterns of both taxonomic groups and compared diversity patterns among the regions for particular pH and conductivity classes. We identified acidophyte and basiphyte, calcifuge and calcicole species using species response modelling. All regions displayed significant relationship between conductivity and α-diversity of vascular plants. Bulgaria showed the highest α-diversity of vascular plants for the middle part of the conductivity gradient. For both taxonomic groups, the β-diversity in the middle part of gradient was highest in Swiss Alps. The total species pool was lowest in Bulgaria. The percentage of basiphyte and calcicole species was highest in the Alps. In (sub)alpine springs, mineral richness was a better determinant of vascular plant α-diversity than pH, and the extent of the alpine area did not coincide with α-diversity. Observed inter-regional differences in diversity patterns could be explained by the different proportion of limestone bedrock and different biogeographic history. The differences in α-diversity between both taxonomic groups are presumably result of the different rates of adaptation processes.     

Changes in aquatic plant communitieson the island of Valaam due to invasion by the muskrat Ondatra zibethicus L.(Rodentia, Mammalia)

Muskrat invaded Valaam Island (Northern part of European Russia) in the 1970s. Aquatic plant communities of 1962 and 1993 were compared on the same plots. Quantitative changes were tested with the help of jack-knifing estimates of most known inventory (-) diversity indicators. Qualitative transformations were assessed using -diversity values. The results demonstrated substantially more discriminant ability of diversity measures than classical methods of mathematical statistics. All of the -diversity values declined synchronously without exception. Species composition also changed greatly and those species which turn out to be more resistant to muskrat grazing became the main dominant plants. The activity of Ondatra became the over-riding ecological factor connecting the littoral plant communities of the Valaam. It is concluded that the sustainability of this ecosystem was damaged by muskrat's invasion and that the role of muskrat should not be underestimated when studying the ecology of freshwater littoral communities.     

美洲森林群落beta多样性的纬度梯度性

Beta多样性度量不同时空尺度物种组成的变化,是生物多样性的重要组成部分;理解其地理格局和形成机制已成为当前生物多样性研究的热点问题。基于Alwyn H. Gentry在美洲收集的131个森林样方数据,采用倍性和加性分配方法度量群落beta多样性,检验beta多样性随纬度的变化趋势,并分析其形成机制。研究表明:(1) 美洲森林群落beta多样性随纬度增加显著下降,热带和亚热带地区beta多样性高于温带地区;此格局可由物种分布范围的纬度梯度性和不同粒度(grain)下物种丰富度与纬度回归斜率的差异推论得出;(2) 加性分配方法表明beta多样性对各个温度带森林群落gamma多样性的相对贡献率平均为78.2%,并且随纬度升高而降低;(3) 美洲南半球森林群落beta多样性高于其北半球,这可能反映了区域间物种进化和环境变迁历史的差异。此外,还探讨了不同beta多样性计算方法的适用情景,首次证实了森林生态系统群落水平beta多样性的纬度梯度性,这对研究生物多样性的形成机制和生物多样性保护都具有重要的意义。     

Short Rotation Coppice (SRC) Plantations Provide Additional Habitats for Vascular Plant Species in Agricultural Mosaic Landscapes

Increasing loss of biodiversity in agricultural landscapes is often debated in the bioenergy context, especially with respect to non-traditional crops that can be grown for energy production in the future. As promising renewable energy source and additional landscape element, the potential role of short rotation coppice (SRC) plantations to biodiversity is of great interest. We studied plant species richness in eight landscapes (225 km²) containing willow and poplar SRC plantations (1,600 m²) in Sweden and Germany, and the related SRC α-diversity to species richness in the landscapes (γ-diversity). Using matrix variables, spatial analyses of SRC plantations and landscapes were performed to explain the contribution of SRC α-diversity to γ-diversity. In accordance with the mosaic concept, multiple regression analyses revealed number of habitat types as a significant predictor for species richness: the higher the habitat type number, the higher the γ-diversity and the lower the proportion of SRC plantation α-diversity to γ-diversity. SRC plantation α-diversity was 6.9 % (±1.7 % SD) of species richness on the landscape scale. The contribution of SRC plantations increased with decreasing γ-diversity. SRC plantations were dominated more by species adapted to frequent disturbances and anthropo-zoogenic impacts than surrounding landscapes. We conclude that by providing habitats for plants with different requirements, SRC α-diversity has a significant share on γ-diversity in rural areas and can promote diversity in landscapes with low habitat heterogeneity and low species pools. However, plant diversity enrichment is mainly due to additional species typically present in disturbed and anthropogenic environments.     

Plant species richness in grasslands: the relative importance of contemporary environment and land-use history since the Iron Age

The richness of vascular plants in all patches of dry semi-natural grassland within a landscape was investigated. The patch level richness was scaled up to the level of parish to match data on land-use intensity from Iron Age through historical time. Three measures of diversity were obtained: the local species pool, an area-independent diversity measure (the slope of the species number vs log area regression line), and the β-diversity, A gradient through the study area in the density of grassland and a corresponding clinal variation in grassland plant species diversity were found. Explanatory models were built by partial least squares regression and conventional stepwise multiple regression. Data on contemporary environmental conditions in the grassland patches and in the parish as a whole were added first, and then data on continuously older times in sequence. In the stepwise regression analyses the variables were also added in the opposite sequence. The results show that contemporary conditions are able to explain the major part of the variation in all diversity measures. Variables concerning former land-use do, however, add significantly to the explanation of variation in local species pool and in the area-independent diversity, but not in β-diversity. It is concluded that patterns of land-use intensity from the Iron Age and onwards have contributed significantly to the shaping of local species pools, and thereby the richness of grassland communities.