Modeling species distributions by breaking the assumption of self-similarity

Species distributions are commonly measured as the number of sites, or geographic grid cells occupied. These data may then be used to model species distributions and to examine patterns in both intraspecific and interspecific distributions. Harte et al. (1999) used a model based on a bisection rule and assuming self-similarity in species distributions to do so. However, this approach has also been criticized for several reasons. Here we show that the self-similarity in species distributions breaks down according to a power relationship with spatial scales, and we therefore adopt a power-scaling assumption for modeling species occupancy distributions. The outcomes of models based on these two assumptions (self-similar and power-scaling) have not previously been compared. Based on Harte's bisection method and an occupancy probability transition model under these two assumptions (self-similar and power-scaling), we compared the scaling pattern of occupancy (also known as the area-of-occupancy) and the spatial distribution of species. The two assumptions of species distribution lead to a relatively similar interspecific occupancy frequency distribution pattern, although the spatial distribution of individual species and the scaling pattern of occupancy differ significantly. The bimodality in occupancy frequency distributions that is common in species communities, is confirmed to a result for certain mathematical and statistical properties of the probability distribution of occupancy. The results thus demonstrate that the use of the bisection method in combination with a power-scaling assumption is more appropriate for modeling species distributions than the use of a self-similarity assumption, particularly at fine scales.     

Spatial and temporal variation in species-area relationships in the Fynbos biological hotspot

Species-area relations (SARs) are among the few recognized general patterns of ecology, are empirical relations giving the number of species found within an area of a given size and were initially formulated for island environments. The use of SARs has been extended to mainland environments, and to give baseline estimates of extinction rates attending habitat loss. Using current species distributions based on atlas data, we examined the spatial variation of rates of species accumulation and species-area curves for Proteaceae species for all one-minute by one-minute areas within the Cape Floristic Region, South Africa. We compared SARs for current distributions to those generated from modeled future Protea distributions following climate change. Within one biome and for two different scales, there exists a very large spatial variation in turnover rates for current Proteaceae distributions, and we show that these rates will not remain constant as climate warming progresses. As climate changes in coming years, some areas will gain species due to migration, as other areas lose species, and still other areas maintain current rates of species accumulation/turnover. Both current and future distributions show highly variable rates of species accumulation across the landscape. This means that an average species-area relationship will hide a very large interval of variation among SARs, for both current and future Proteaceae distributions. The use of species-area relations to estimate species extinctions following loss of current habitat, or loss of future climatically-suitable area is likely to result in erroneous predictions.     

History, island area and habitat availability determine land snail species richness of Aegean islands

Aim We examined the species-area relation of Aegean land snails, comparing different models to describe the relation. By examining those factors other than area that may also affect species richness, we tested whether the Aegean land snail fauna was more influenced by equilibrial migration and colonization processes, or rather is conservative and relictual. Location The Aegean archipelago (Greece). Methods Sixty-five islands were examined. Data were taken from own collections and from literature sources. Multiple regression analysis was used to test the null hypothesis of no relationship between species richness and island area, elevation, distance to the next larger island, and the presence and extent of calcareous substrate. Results The single most important factor determining land snail species number was area. While colonization-extinction dynamics have frequently been cited to explain this result, this conclusion was not tenable in this study as it was contradicted by species number not being related to the islands’ distances to neighbouring larger islands, after accounting for other factors affecting species number. We also found that habitat diversity affected species richness even after accounting for the effects of area: both increased elevation and greater extent of calcareous substrate on islands resulted in higher species number. This effect was most likely due to the fact that particular ecological conditions increased the probability that particular species could survive on an island. We compared the utility of the power and extreme-value function models of the species-area relation and found that both gave substantially the same results. However, fitting the power function model using nonlinear regression was of questionable utility. Main conclusions We conclude that the snail fauna of the Aegean is relictual, not equilibrial. The unusually high number of land snail species found on Crete is consistent with this conclusion. Crete is a currently united island which was separated into at least six smaller islands for 7–9 million years during the Neogene. Our results are consistent with the hypothesis that Crete still hosts a large number of endemic species of these paleoislands, resulting in a total number of species in excess of what would be expected based on area alone.     

小兴安岭阔叶红松林木本植物种-面积关系

种-面积关系研究是了解植物群落结构的重要途径,是群落生态学的基本问题。不同的研究方法对种-面积关系影响很大。利用黑龙江省小兴安岭两个10.4 hm2样地和5个1.0 hm2样地的调查数据,采用移动窗口法确定各样地的最小取样面积,避免了巢式取样法及随机样方法的不足。并采用4种种-面积关系模型进行拟合,评价各关系模型的适合度。在此基础上,基于最小面积进行模拟随机取样,探讨取样大小对物种数估计精度的影响。研究结果表明:由于拟合曲线模型的适用性及曲线外推可靠性问题的存在,采用拟合曲线的方法所估计的最小面积与实际值偏差较大。实际调查得到的各样地最小面积40 m×40 m—45 m×45 m,说明小兴安岭地区阔叶红松林群落所需的最小面积基本一致,但各样地群落结构的差异却在对取样数量的要求上体现出来。其中丰林与大亮子河样地物种数分布相对均匀,所需最小样方数量较少;而方正与胜山样地物种数分布异质性较大,差异的机理还有待于进一步研究。     

Habitat size and number in multi-habitat landscapes: a model approach based on species-area curves

This paper discusses species diversity in simple multi-habitat environments. Its main purpose is to present simple mathematical and graphical models on how landscape patterns affect species numbers. The idea is to build models of species diversity in multi-habitat landscapes by combining species-area curves for different habitats. Predictions are made about how variables such as species richness and species overlap between habitats influence the proportion of the total landscape each habitat should constitute, and how many habitats it should be divided into in order to be able to sustain the maximal number of species. Habitat size and numbers are the only factors discussed here, not habitat spatial patterns. Among the predictions are: 1) where there are differences in species diversity between habitats, optimal landscape patterns contain larger proportions of species rich habitats. 2) Species overlap between habitats shifts the optimum further towards larger proportions of species rich habitat types. 3) Species overlap also shifts the optimum towards fewer habitat types. 4) Species diversity in landscapes with large species overlap is more resistant to changes in landscape (or reserve) size. This type of model approach can produce theories useful to nature and landscape management in general, and the design of nature reserves and national parks in particular.     

How to resolve the SLOSS debate: Lessons from species-diversity models

The SLOSS debate - whether a single large reserve will conserve more species than several small - of the 1970s and 1980s never came to a resolution. The first rule of reserve design states that one large reserve will conserve the most species, a rule which has been heavily contested. Empirical data seem to undermine the reliance on general rules, indicating that the best strategy varies from case to case. Modeling has also been deployed in this debate. We may divide the modeling approaches to the SLOSS enigma into dynamic and static approaches. Dynamic approaches, covered by the fields of island equilibrium theory of island biogeography and metapopulation theory, look at immigration, emigration, and extinction. Static approaches, such as the one in this paper, illustrate how several factors affect the number of reserves that will save the most species.This article approaches the effect of different factors by the application of species-diversity models. These models combine species-area curves for two or more reserves, correcting for the species overlap between them. Such models generate several predictions on how different factors affect the optimal number of reserves. The main predictions are: Fewer and larger reserves are favored by increased species overlap between reserves, by faster growth in number of species with reserve area increase, by higher minimum-area requirements, by spatial aggregation and by uneven species abundances. The effect of increased distance between smaller reserves depends on the two counteracting factors: decreased species density caused by isolation (which enhances minimum-area effect) and decreased overlap between isolates. The first decreases the optimal number of reserves; the second increases the optimal number. The effect of total reserve-system area depends both on the shape of the species-area curve and on whether overlap between reserves changes with scale.The approach to modeling presented here has several implications for conservational strategies. It illustrates well how the SLOSS enigma can be reduced to a question of the shape of the species-area curve that is expected or generated from reserves of different sizes and a question of overlap between isolates (or reserves).     

Diversity patterns from ecological models at dynamical equilibrium

We study a dynamic model of ecosystems where an immigration flux assembles the species community and maintains its biodiversity. This framework is particularly relevant for insular ecosystems. Population dynamics is represented either as an individual-based model or as a set of deterministic equations for population abundances. Local extinctions and immigrations balance at a statistically stationary state where biodiversity fluctuates around a constant mean value. We find a number of scaling laws characterizing this stationary state. In particular, the number of species increases as a power law of the immigration rate. With additional assumptions on the immigration flux, we obtain species-area relationships in agreement with observations for archipelagos. We also find power-law distributions for species abundances and lifetimes.     

Self-similar land cover heterogeneity of temperate and tropical landscapes

Landscapes are complex objects often showing self-similar properties. For example, some power law exponents and fractal dimensions have been extensively used as global metrics for describing spatial arrangements of landscape land covers. This paper presents some newly found invariance properties for rural landscapes, with the hope to prepare further theory capable to link these properties mechanistically with generating processes. For this purpose, I propose a new surface-pattern analysis computing heterogeneity metrics into moving windows in a specific way. This generic method provides Multiscale Heterogeneity Maps (MHMs) and Heterogeneity Profiles (HPs) of almost any kind of landscape. Six landscapes, covering a wide range of observed mosaics have been analyzed by this way: four of them exhibit strong self-similar evenness (diversity) heterogeneity over two orders of magnitude with an apparent universality of the power law exponents (γ = ?0.19 ± 0.02). Such landscape self-organization is interpreted in terms of spatial arrangements of numerous land covers and fine scale patchy mosaics. This study suggests that most of terrestrial landscapes could exhibit power law behaviors in terms of evenness heterogeneity and could be the result of a hidden optimization of ecological and/or socio-economic processes.     

The species-area relation for archipelago biotas: Islands as samples from a species pool

If the immigration of species from a mainland or among islands is taken into account, each island of an archipelago can be regarded as a sample from a species pool. When two or more islands are combined so as to give larger samples, the resultant species-area relation does not differ from that observed in a continuous and homogeneous habitat on a mainland. This relation can be described by either of the two mathematical models proposed before (Kobayashi , 1975, 1976). A power function seems to be insufficient because the discrepancy between the observed and the calculated values becomes larger with the increasing area. In a log-log plot, the slope values for these alternatives to a power function vary continuously from 1 to 0 as the area increases. Owing to the spatially clumped distribution of each species, the number of species found on a single island is less than that found on several smaller islands of equivalent total area. Hence the species-area relation for individual islands has a smaller slope value than that obtained by combining the different numbers of islands and approaches a power function in form. From these results, it is concluded that the species-area data on archipelago biotas are equivalent to the case where separate samples of different sizes are drawn from a universe in which each species is spatially distributed in clumps. The properties of archipelago biotas which have so far been evidenced or predicted are consistent with this conclusion.     

Which Models Are Appropriate for Six Subtropical Forests: Species-Area and Species-Abundance Models

The species-area relationship is one of the most important topic in the study of species diversity, conservation biology and landscape ecology. The species-area relationship curves describe the increase of species number with increasing area, and have been modeled by various equations. In this paper, we used detailed data from six 1-ha subtropical forest communities to fit three species-area relationship models. The coefficient of determination and F ratio of ANOVA showed all the three models fitted well to the species-area relationship data in the subtropical communities, with the logarithm model performing better than the other two models. We also used the three species-abundance distributions, namely the lognormal, logcauchy and logseries model, to fit them to the species-abundance data of six communities. In this case, the logcauchy model had the better fit based on the coefficient of determination. Our research reveals that the rare species always exist in the six communities, corroborating the neutral theory of Hubbell. Furthermore, we explained why all species-abundance figures appeared to be left-side truncated. This was due to subtropical forests have high diversity, and their large species number includes many rare species.     

Self-organized instability in complex ecosystems

Why are some ecosystems so rich, yet contain so many rare species? High species diversity, together with rarity, is a general trend in neotropical forests and coral reefs. However, the origin of such diversity and the consequences of food web complexity in both species abundances and temporal fluctuations are not well understood. Several regularities are observed in complex, multispecies ecosystems that suggest that these ecologies might be organized close to points of instability. We explore, in greater depth, a recent stochastic model of population dynamics that is shown to reproduce: (i) the scaling law linking species number and connectivity; (ii) the observed distributions of species abundance reported from field studies (showing long tails and thus a predominance of rare species); (iii) the complex fluctuations displayed by natural communities (including chaotic dynamics); and (iv) the species-area relations displayed by rainforest plots. It is conjectured that the conflict between the natural tendency towards higher diversity due to immigration, and the ecosystem level constraints derived from an increasing number of links, leaves the system poised at a critical boundary separating stable from unstable communities, where large fluctuations are expected to occur. We suggest that the patterns displayed by species-rich communities, including rarity, would result from such a spontaneous tendency towards instability.     

Habitat fragmentation may not matter to species diversity

Conservation biologists worry that fragmenting a bloc of natural habitat might reduce its species diversity. However, they also recognize the difficulty and importance of isolating the effect of fragmentation from that of simple loss of area. Using two different methods (species-area curve and Fisher's alpha index of diversity) to analyse the species diversities of plants, tenebrionid beetles and carabid beetles in a highly fragmented Mediterranean scrub landscape, we decoupled the effect of degree of fragmentation from that of area loss. In this system, fragmentation by itself seems not to have influenced the number of species. Our results, obtained at the scale of hectares, agree with similar results at island and continent scales.     

Species-area curve,life history strategies,and succession: a field test of relationships

Changes of species richness along temporal and environmental gradients were investigated. Two data sets were used: a successional sere of old-field plant communities in the Bohemian Karst, and a set of plant communities under various intensities of disturbance in the Krkonoe (Giant) Mts, both in Czechoslovakia. The species richness of a plant community is a spatial phenomenon, and should be described by the species-area relationship (using e.g. the power function S=c\A ^z) rather than by a single number. In the old-field succession, the number of species in very small plots (0.1×0.1 m) tends to increase with successional age while the number of species in larger plots (4×4 m) decreases from the third year of succession. The plant community under the highest rate of disturbance of the Krkonoe Mts data set shows the lowest number of species on small plots and the highest number of species on large plots. The results may be explained using the distinction between founder-and dominance-controlled communities (Yodzis 1978, 1984). In accordance with this theory, the species-area relationship within a community is shaped mainly by the type of competitive interaction and may be predicted on the basis of life-history strategies of constituent species. Disturbance causes a shift from dominance to founder control. On the landscape scale, the species-area relationship is shaped by other factors, and so it is unjustified to extrapolate the relationship outside the range in which it was originally assessed.     

Orthopterans in small steppe patches: an investigation for the best-fit model of the species-area curve and evidences for their non-random distribution in the patches

Distribution of orthopterans were studied in 27 steppe patches in the Buda Hills, Hungary. The smallest patches were about 300 m², the largest ‘continents’ were over 100 000 m². We collected 692 imagoes of 32 species and 1 201 imagoes of 28 species in July 1992 and July 1993, respectively. We found that the best-fit models for the species-area curves were both the power function and exponential models. The multivariate regression model incorporated area and distance from large patches as significant factors in determining the number of species. The correlation analysis revealed that the elevation and the height of grass vegetation also influenced the distribution of species. We applied three methods for testing whether the distribution of orthopterans was random or not. First, we compared the observed species-area curves with the expected curves. Second, we compared the small-to-large and large-to-small cumulative curves. Finally, we compared the observed species-area curves with the rarefaction curves. All three methods for both years showed that the occurrence of orthopterans in the steppe patches was not random. A collection of small islands harboured more orthopteran species than one or two large patches of the same area.     

Dynamic relationships between body size,species richness,abundance, and energy use in a shallow marine epibenthic faunal community

We study the temporal variation in the empirical relationships among body size (S), species richness (R), and abundance (A) in a shallow marine epibenthic faunal community in Coliumo Bay, Chile. We also extend previous analyses by calculating individual energy use (E) and test whether its bivariate and trivariate relationships with S and R are in agreement with expectations derived from the energetic equivalence rule. Carnivorous and scavenger species representing over 95% of sample abundance and biomass were studied. For each individual, body size (g) was measured and E was estimated following published allometric relationships. Data for each sample were tabulated into exponential body size bins, comparing species‐averaged values with individual‐based estimates which allow species to potentially occupy multiple size classes. For individual‐based data, both the number of individuals and species across body size classes are fit by a Weibull function rather than by a power law scaling. Species richness is also a power law of the number of individuals. Energy use shows a piecewise scaling relationship with body size, with energetic equivalence holding true only for size classes above the modal abundance class. Species‐based data showed either weak linear or no significant patterns, likely due to the decrease in the number of data points across body size classes. Hence, for individual‐based size spectra, the SRA relationship seems to be general despite seasonal forcing and strong disturbances in Coliumo Bay. The unimodal abundance distribution results in a piecewise energy scaling relationship, with small individuals showing a positive scaling and large individuals showing energetic equivalence. Hence, strict energetic equivalence should not be expected for unimodal abundance distributions. On the other hand, while species‐based data do not show unimodal SRA relationships, energy use across body size classes did not show significant trends, supporting energetic equivalence.     

城市生物多样性分布格局研究进展

城市生物多样性分布格局由自然生态环境和城市化过程所决定;其动态和机理与自然生态系统迥然不同.城市生物多样性为城市生态系统提供了诸多生态系统功能和服务,对改善城市环境、维持城市可持续发展有着重要的意义和作用.城市化过程深刻改变了城市的生物多样性分布格局,导致了诸如本地物种多样性降低、外来物种多样性增加、物种同质化等一系列问题.近年来,城市生物多样性受到学界高度关注,大量研究结果既回答了一些关键性问题,又提出了诸多新的论题和挑战.分析了当前城市生物多样性分布格局研究的若干热点问题,总结了影响城市生物多样性格局的主要因素,探讨了城市生物多样性格局研究方法的关键问题,指出了未来城市生物多样性研究的发展方向,特别强调了城市生物多样性的生态系统功能研究在未来城市生物多样性研究中的重要地位.     

Cross-scale ecological dynamics and microbial size spectra in marine ecosystems

Evaluating the component features of 'scaling' planktonic size spectra, commonly observed in marine ecosystems, is crucial for understanding the ecological and evolutionary processes from which they emerge. Here, we develop a theoretical framework that describes such spectra in terms of the size distributions of individual species, and test it against actual datasets of microbial size spectra from the Atlantic Ocean. We describe characteristics of size probability distributions of component species that are sufficient to support the observational evidence and infer that, when a power law describes the community size spectrum (thus suggesting critical self-organization of microbial ecosystem structure and function), a related power law links the total number of individuals of a given species to its mean size.     

Temporal variation in species-area curves for invertebrates in clumps of an intertidal mussel

We examined the temporal variation in the relationships between the number of invertebrate species, and of total individuals inhabiting clumps of the intertidal mussel Brachidontes rostratus and the area of the clumps We collected clumps in four seasons - autumn, winter, spring and summer - from a rocky shore in south-eastern Australia Positive curvilinear relationships between species number and area were recorded for all seasons but fewer species for a given area were found in autumn and summer compared with winter and spring These species-area relationships were different from those predicted from a passive sampling model (Random Placement Model) Positive relationships between number of individuals and area were also recorded but these did not vary between seasons There was no short-term difference (i e between phases of tide and day) in species or individual number in clumps Seasonal variation, and small-scale spatial unpredictability in recruitment patterns are potentially important determinants of species numbers in this system The seasonal differences we have recorded for mussel clumps suggest that future studies on island systems particularly in marine habitats should consider temporal variation in species-area relationships and that conclusions from previous comparisons of species-area curves based on one-off sampling must only be tentative     

Self-similar patterns of nature: insect diversity at local to global scales

The insects are probably the most hyperdiverse and economically important metazoans on the planet, but there is no consensus on the best way to model the dimensions of their diversity at multiple spatial scales, and the huge amount of information involved hinders data synthesis and the revelation of 'patterns of nature'. Using a sample of more than 600k insect species in the size range 1-100mm, we analysed insect body sizes and revealed self-similar patterns persisting across spatial scales from several hectares to the World. The same patterns were found in both Northern and Southern Hemispheres. The patterns include: parallel rank-abundance distributions; flatter species-area curves in smaller insects-indicating their wider geographical distribution; the recurrence of the same species-rich family in the same body-size class at all spatial scales-which generates self-similar size-frequency distributions (SFDs)-and the discovery that with decreasing mean body size, local species richness represents an increasing fraction of global species richness. We describe how these 'rationalizing' patterns can be translated into methods for monitoring and predicting species diversity and community structure at all spatial scales.     

Evaluation of species-area functions using Sonoran Desert plant data: not all species-area curves are power functions

Ecologists have been studying the relationship between species richness and area for about a century. As area increases, more species are typically observed. Many mathematical functions have been proposed to describe the pattern of increase. Numerous researchers have assumed that the relationship is a power function despite the fact that there are many possible alternatives. There has been limited work in evaluating which species-area functions are most appropriate for field data. This study examines which of a variety of functions best describe how Sonoran Desert plant species richness of remnant habitat patches in the Phoenix metropolitan area vary with sampled area and the area of entire patches. No single species-area function was adequate for describing all empirical datasets. Sample curves of woody species were most frequently best described by the sigmoid logistic, Hill, and Lomolino functions, whereas herbaceous datasets were best fit by the sigmoid logistic or convex rational functions. A curve depicting the relationship between patch-level woody species richness and patch area was best fit by the convex exponential function. The power function provided the best fit for only one case. This study demonstrates the utility of testing alternative functions for statistical fit rather than assuming that any particular equation adequately describes the species-area relationship.