A model of the species rank-abundance relation for a community in an open habitat

A mathematical model is proposed to describe the relationship between the abundance and the rank of species in order from the most abundant to the least in a community in an open habitat. This model is derived as a corollary of a species-area equation (Kobayashi , 1975) which could be expected in the case where the individuals of each species are uniformly distributed over a habitat area. Numerical simulation reveals that a rank-abundance curve for a universe results in different species-area or species-individual curves according to the spatial distribution of individuals, and that the relative abundance of each species in a sample varies with sample size unless the spatial distribution of individuals is uniform. A species-individual curve obtained bySanders 's (1968) rarefaction method agrees with that observed actually only for the spatially uniform distribution. Change in the pattern of rank-abundance curve with species diversity and with sample size is discussed in relation to the present model.     

The checkerboard score and species distributions

Summary There has been an ongoing controversy over how to decide whether the distribution of species is random — i.e., whether it is not greatly different from what it would be if species did not interact. We recently showed (Roberts and Stone (1990)) that in the case of the Vanuatu (formerly New Hebrides) avifauna, the number of islands shared by species pairs was incompatible with a random null hypothesis. However, it was difficult to determine the causes or direction of the community's exceptionality. In this paper, the latter problem is examined further. We use Diamond's (1975) notion of checkerboard distributions (originally developed as an indicator of competition) and construct a C-score statistic which quantifies checkerboardedness. This statistic is based on the way two species might colonise a pair of islands; whenever each species colonises a different island this adds 1 to the C-score. Following Connor and Simberloff (1979) we generate a control group of random colonisation patterns (matrices), and use the C-score to determine their checkerboard characteristics. As an alternative mode of enquiry, we make slight alterations to the observed data, repeating this process many times so as to obtain another control group. In both cases, when we compare the observed data for the Vanuatu avifauna and the Antillean bat communities with that given by their respective control group, we find that these communities have significantly large checkerboard distributions, making implausible the hypothesis that their species distributions are a product of random colonisation.     

Feedback control of a competitive mixed-culture system

Three feedback strategies for the on-line control of cell densities in a mixed-culture system have been examined. A competitive mixed-culture system of Candida utilis and Corynebacterium glutamicum grown on glucose as the limiting carbon source was modeled using Monod growth kinetics. First-order time constants were added to simulate transient growth effects. Multivariable feedback control of cell densities by manipulation of substrate feed and dilution rate was investigated. Feedback strategies directed to minimizing control interactions were found to be superior to classical feedback. Transients in the growth-rate response produced oscillations in cell density and required retuning of control constants. The relative time constants of the two species were important, with the largest oscillations resulting when the faster growing organism had the faster time constant.     

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.     

Coexistence of competitive species with a stage-structured life cycle

Ecological theory provides explanations for exclusion or coexistence of competing species. Most theoretical works on competition dynamics that have shaped current perspectives on coexistence assume a simple life cycle. This simplification, however, may omit important realities. We present a simple two-stage structured competition model to investigate the effects of life-history characteristics on coexistence. The achievement and the stability of coexistence depend not only on competition coefficients but also on a set of life-history parameters that reflect the viability of an individual, namely, adult death rate, maturation rate, and birth rate. High individual viability is necessary for a species to persist, but it does not necessarily facilitate coexistence. Intense competition at the juvenile or adult stage may require higher or lower viability, respectively, for stable coexistence to be possible. The stability mechanism can be explained by the refuge effect of the less competitive stage, and the birth performance, which preserves the less competitive stage as a refuge. Coexistence might readily collapse if the life-history characteristics, which together constitute individual viability, change, even though two species have an inherent competitive relation conducive to stable coexistence.     

Ensemble forecasting of species distributions

Concern over implications of climate change for biodiversity has led to the use of bioclimatic models to forecast the range shifts of species under future climate-change scenarios. Recent studies have demonstrated that projections by alternative models can be so variable as to compromise their usefulness for guiding policy decisions. Here, we advocate the use of multiple models within an ensemble forecasting framework and describe alternative approaches to the analysis of bioclimatic ensembles, including bounding box, consensus and probabilistic techniques. We argue that, although improved accuracy can be delivered through the traditional tasks of trying to build better models with improved data, more robust forecasts can also be achieved if ensemble forecasts are produced and analysed appropriately.     

The role of functional traits in species distributions revealed through a hierarchical model

Quantifying how functional traits relate to environmental gradients provides insight into mechanisms governing species distributions. Here, we bring together the fields of species distribution modelling and functional trait ecology with hierarchical modelling by explicitly incorporating traits into a multi‐species distribution model. We combined traits from the leaf‐height‐seed strategy scheme (specific leaf area (SLA), plant height and seed mass) with a distribution model for 20 eucalypt taxa in Victoria, Australia. The key insight of this approach is how traits modulate species responses to environmental gradients. The strongest link was between SLA and percent rock cover (species with low SLA had positive responses to rockiness, whereas high SLA species responded negatively to rockiness). We found evidence for complex yet potentially important interactions. For instance, the probability of species occurrence increased with rainfall and solar radiation on average yet the response varied depending on species height and SLA. Tall species were predicted to increase with rainfall and solar radiation across the range of SLA values (tall species with low SLA were especially sensitive to rainfall). Short species responded positively to rainfall and solar radiation only if they had low SLA. This framework readily accounts for interactions between combinations of traits and environmental variables unlike multi‐step approaches. Further application of this concept will contribute to a generalized mechanistic understanding of how traits influence species distributions along environmental gradients, with implications for understanding the response of species to global change.     

On plotting species abundance distributions

1. There has been a revival of interest in species abundance distribution (SAD) models, stimulated by the claim that the log-normal distribution gave an underestimate of the observed numbers of rare species in species-rich assemblages. This led to the development of the neutral Zero Sum Multinomial distribution (ZSM) to better fit the observed data. 2. Yet plots of SADs, purportedly of the same data, showed differences in frequencies of species and of statistical fits to the ZSM and log-normal models due to the use of different binning methods. 3. We plot six different binning methods for the Barro Colorado Island (BCI) tropical tree data. The appearances of the curves are very different for the different binning methods. Consequently, the fits to different models may vary depending on the binning system used. 4. There is no agreed binning method for SAD plots. Our analysis suggests that a simple doubling of the number of individuals per species in each bin is perhaps the most practical one for illustrative purposes. Alternatively rank-abundance plots should be used. 5. For fitting and testing models exact methods have been developed and application of these does not require binning of data. Errors are introduced unnecessarily if data are binned before testing goodness-of-fit to models.     

The effect of spring burning on competitive ranking of prairie species

Abstract. A common explanation for the changes in species abundance following a fire is a shift in competitive ranking. However, experimental tests have been inconsistent and generally do not support this explanation. I examined the competitive ability of an abundant C₄ grass, Andropogon gerardii, and a C₃ forb, Ratibida pinnata, in a prairie remnant in northern Ohio, USA, for each of three years following a spring burn in 1996. While the abiotic environment directly influenced both species similarly, relative competitive abilities in terms of growth changed markedly: in 1996 Andropogon was less inhibited by neighbors; in 1997 both Andropogon and Ratibida had similar competitive abilities; and in 1998 Ratibida was less inhibited by neighbors. This shift in competitive response ranking paralleled the changes in relative abundance for the two species. In contrast, the effect of neighbors on survival changed markedly over time but did not differ among the two species. Thus, fire may influence species abundance through changing species competitive response ranking, at least in terms of growth.     

Spatial scaling of species abundance distributions

Species abundance distributions are an essential tool in describing the biodiversity of ecological communities. We now know that their shape changes as a function of the size of area sampled. Here we analyze the scaling properties of species abundance distributions by using the moments of the logarithmically transformed number of individuals. We find that the moments as a function of area size are well fitted by power laws and we use this pattern to estimate the species abundance distribution for areas larger than those sampled. To reconstruct the species abundance distribution from its moments, we use discrete Tchebichef polynomials. We exemplify the method with data on tree and shrub species from a 50 ha plot of tropical rain forest on Barro Colorado Island, Panama. We test the method within the 50 ha plot, and then we extrapolate the species abundance distribution for areas up to 5 km². Our results project that for areas above 50 ha the species abundance distributions have a bimodal shape with a local maximum occurring for the singleton classes and that this maximum increases with sampled area size.     

Dynamics of species coexistence: maintenance of a plant-ant competitive metacommunity

The metacommunity approach is an adequate framework to study coexistence between interacting species at different spatial scales. However, empirical evidence from natural metacommunities necessary to evaluate the predictive power of theoretical models of species coexistence remains sparse. We use two African ant species, Cataulacus mckeyi and Petalomyrmex phylax , symbiotically associated with the myrmecophyte Leonardoxa africana africana , to examine spatio-temporal dynamics of species coexistence and to investigate which environmental and life-history parameters may contribute to the maintenance of species diversity in this guild of symbiotic ants. Using environmental niche partitioning as a conceptual framework, we combined data on habitat variation, social structure of colonies, and population genetics with data from a colonisation experiment and from observation of temporal dynamics. We propose that the dynamics of ant species colonisation and replacement at local and regional scales can be explained by a set of life history traits for which the two ants exhibit hierarchies, coupled with strong environmental differences between the different patches in the level of environmental disturbances. The role of the competition–colonisation tradeoff is discussed and we propose that interspecific tradeoffs for traits related to dispersal and to reproduction are also determinant for species coexistence. We therefore suggest that species-sorting mechanisms are predominant in the dynamics of this metacommunity, but we also emphasise that there may be many ways for two symbionts in competition for the same host to coexist. The results speak in favour of a more complete integration of the various metacommunity models in a single theoretical framework.     

Spatial distributions of tree species in a subtropical forest of China

The spatial dispersion of individuals in a species is an important pattern that is controlled by many mechanisms. In this study we analyzed spatial distributions of tree species in a large-scale (20 ha) stem-mapping plot in a species-rich subtropical forest of China. O-ring statistic was used to measure spatial patterns of species with abundance >10. Ω_0–10, the mean conspecific density within 10 m of a tree, was used as a measure of the intensity of aggregation of a species. Our results showed: (1) aggregated distribution was the dominant pattern in the plot. The percentage of aggregated species decreased with increased spatial scale. (2) The percentages of significantly aggregated species decreased from abundant to intermediate and to rare species. Rare species was more strongly aggregated than common species. Aggregation was weaker in larger diameter classes. (3) Seed traits determined the spatial patterns of trees. Seed dispersal mode can influence spatial patterns of species, with species dispersed by both modes being less clumped than species dispersed by animal or wind, respectively. Considering these results, we concluded that seed dispersal limitation, self-thinning and habitat heterogeneity primarily contributed to spatial patterns and species coexistence in the forest.     

Predicting species distributions in poorly-studied landscapes

Conservationists are increasingly relying on distribution models to predict where species are likely to occur, especially in poorly-surveyed but biodiverse areas. Modeling is challenging in these cases because locality data necessary for model formation are often scarce and spatially imprecise. To identify methods best suited to modeling in these conditions, we compared the success of three algorithms (Maxent, Mahalanobis Typicalities and Random Forests) at predicting distributions of eight bird and eight mammal species endemic to the eastern slopes of the central Andes. We selected study species to have a range of locality sample sizes representative of the data available for endemic species of this region and also that vary in their distribution characteristics. We found that for species that are known from moderate numbers (N = 38–94) of localities, the three methods performed similarly for species with restricted distributions but Maxent and Random Forests yielded better results for species with wider distributions. For species with small numbers of sample localities (N = 5–21), Maxent produced the most consistently successful results, followed by Random Forests and then Mahalanobis Typicalities. Because evaluation statistics for models derived from few localities can be suspect due to the poor spatial representation of the evaluation data, we corroborated these results with review by scientists familiar with the species in the field. Overall, Maxent appears to be the most capable method for modeling distributions of Andean bird and mammal species because of the consistency of results in varying conditions, although the other methods have strengths in certain situations. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

BIOMOD – a platform for ensemble forecasting of species distributions

BIOMOD is a computer platform for ensemble forecasting of species distributions, enabling the treatment of a range of methodological uncertainties in models and the examination of species-environment relationships. BIOMOD includes the ability to model species distributions with several techniques, test models with a wide range of approaches, project species distributions into different environmental conditions (e.g. climate or land use change scenarios) and dispersal functions. It allows assessing species temporal turnover, plot species response curves, and test the strength of species interactions with predictor variables. BIOMOD is implemented in R and is a freeware, open source, package.     

Switching effect of predation on competitive prey species

The fact that the predation pressure has a stabilizing effect on the community of competitive species is demonstrated by a mathematical model of two-preys and one-predator system which has the switching property of predation. By analyzing a dynamical system for these three species populations, it is shown that, in a wide range of parameter space, the system has stable coexisting equilibrium states and the manifold of stable stationary points exhibits a cusp catastrophe and there exist two stable stationary points in the cusp region in the parameter space. Thus, it has been shown that Cause's competitive exclusion is actually relaxed by the switching mechanism of predation.     

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.     

The role of stochastic processes in producing nested patterns of species distributions

Nestedness has received considerable attention in community ecology and conservation biology from both theoretical and empirical perspectives. This has lead to the creation of various metrics and null models to analyze nested subsets, all of which rely on the random placement of species to assess significance. However, if immigration and extinction are the processes that underlie species distributions on island systems, then null models might be better determined on the basis of randomly placed individuals. Consequently, we examined the effects of species–abundance distributions (uniform, dominance–decay, random–assortment, and dominance–preemption), island–size distributions (uniform and linear decrease), and total abundances (128, 256, 512, 1024, 2048, 4096 and 8192) on the degree of nestedness and its significance. Generally, matrices of species presence and absence created from the random placement of individuals were nested significantly according to null models based on the random placement of species. Island size and abundance had less of an effect on nestedness in systems dominated by only a few species than in systems in which abundances were distributed more evenly. Stochastic processes, such as the random placement of individuals, predispose systems to evince patterns of nestedness at the species level, which may account, in part, for the ubiquity of nestedness in nature.     

The vertical foliage distributions of six understory tree species in a Chamaecyparis obtusa Endl. forest

Summary The relationships between the amounts of foliage and heights of trees were studied for the dominant understory tree species, including three evergreen and three deciduous species, in a secondary forest of Chamaecyparis obtusa Endl. The relationships showed two phases: leaf increasing and stationary phases. In the leaf-increasing phase, the height growth allowed these species to expand the canopy by increasing the number of leaves. In the stationary phase, the number of leaves was relatively constant number irrespective of tree height from 160 to 400 cm. The number of leaves in the stationary phase represents the maximum number of leaves that can be supported by trees under shady conditions. From the analyses of vertical distributions of leaves in six species, mono- and multi-layer foliage distributions were detected. Two evergreen species, Eurya japonica and Cleyera japonica, showed multi-layer foliage distributions, whereas three deciduous species, Lyonia ovalifolia, Rhododendron reticulatum and Vaccinium hirtum, and one evergreen species, Pieris japonica, showed mono-layer foliage distributions. The relationships between the weights of non-photosynthetic and photosynthetic organs of the six species were examined. The proportion of non-photosynthetic organs increased with tree height. The understory species attained the stationary phase and were maintained by minimizing their investment in non-photosynthetic organs, i.e. their height growth was arrested by the shady conditions under the crown trees.     

Amphibian phylogeography: a model for understanding historical aspects of species distributions

Phylogeographic analysis has become a major tool for investigating historical aspects of biogeography and population genetic structure. Anuran amphibians are particularly informative subjects for phylogeographic research on account of their global distribution, high degree of population genetic structure and ease of sampling. Studies on all the world's inhabited continents have demonstrated the nature and locations of refugia, including the Gulf Coast in North America and the Mediterranean peninsulas in Europe during the Pleistocene glaciations; the importance of vicariance events such as the uplift of the Andes in shaping modern distributions; and colonization routes in temperate zones during postglacial climatic amelioration. Features identified as important to amphibian biogeography, notably mountain ranges, large rivers such as the Amazon and climatic fluctuations, are common to many other taxa. New analytical methods based on coalescent, Bayesian and likelihood approaches permit more rigorous hypothesis testing than has hitherto been possible and offer the prospect of even more detailed insights into species and population history in future work.