Relative need for conservation assessments of vascular plant species among ecoregions

Aim (1) To determine the relative need for conservation assessments of vascular plant species among the world’s ecoregions given under‐assessed species distributions; (2) to evaluate the challenge posed by the lack of financial resources on species assessment efforts; and (3) to demonstrate the utility of nonlinear mixed‐effects models with both homoscedastic and heteroscedastic error structures in the identification of species‐rich ecoregions. Location Global. Methods We identified the world’s ecoregions that contain the highest vascular plant species richness after controlling for area using species–area relationship (SAR) models built within a mixed‐effects multi‐model framework. Using quantitative thresholds, ecoregions with the highest plant species richness, historical habitat loss and projected increase in human population density were deemed to be most in need of conservation assessments of plant species. We used generalized linear models to test if countries that overlap with highly important ecoregions are poorer compared with others. Results We classed ecoregions into nine categories based on the relative need for conservation assessments of vascular plant species. Ecoregions of highest relative need are found mostly in the tropics, particularly Southeast Asia, Central America, Tropical Andes and the Cerrado of South America, and the East African montane region and its surrounding areas. Countries overlapping with ecoregions deemed important for conservation assessments are poorer as measured by their capita gross national income than the other countries. The nonlinear mixed modelling framework was effective in reducing residual spatial autocorrelation compared with nonlinear models comprised of only fixed effects. In contrasting multiple SAR models to identify species‐rich ecoregions, there was not one SAR model that fitted best across all biomes. Not all SAR models displayed homoscedastic errors; therefore it is important to consider models with both homoscedastic and heteroscedastic error structures. Main conclusions We propose that conservation assessments should be conducted first in ecoregions with the greatest predicted species richness, historical habitat loss and future human population increase. As ecoregions deemed to be important for conservation assessments are located in the poorest countries, we urge international aid agencies and botanic gardens to cooperate with both local and international scientists to fund and implement conservation assessment programmes there.     

Global pattern and local variation in species–area relationships

Aim We conducted a meta‐analysis of species–area relationships (SARs) by combining several data sets and important covariates such as types of islands, taxonomic groups, latitude and spatial extent, in a hierarchical model framework to study global pattern and local variation in SARs and its consequences for prediction. Location One thousand nine hundred and eighteen islands from 94 SAR studies from around the world. Methods We developed a generalization of the power‐law SAR model, the HSARX model, which allows: (1) the inclusion of multiple focal parameters (intercept, slope, within‐study variance), (2) use of multiple effect modifiers based on a collection of SAR studies, and (3) modelling of the between‐ and within‐study variability. Results The global pattern in the SAR was the average of local SARs and had wide confidence intervals. The global SAR slope was 0.228 with 90% confidence limits of 0.059 and 0.412. The intercept, slope and within‐study variability of local SARs showed great heterogeneity as a result of the interaction of modifying covariates. Confidence intervals for these SAR parameters were narrower when other covariates in addition to area were accounted for, thus increasing the accuracy of the predictions for species richness. The significant effect of latitude and the interaction of latitude, taxa and island type on the SAR slope indicated that the ‘typical’ latitudinal diversity gradient can be reversed in isolated systems. Main conclusions The power‐law relationship underlying the HSARX model provides a good fit for non‐nested SARs across vastly different spatial scales by taking into account other covariates. The HSARX framework allows researchers to explore the complex interactions among SAR parameters and modifying variables, to explicitly study the scale dependence, and to make robust predictions on multiple levels (island, study, global) with associated prediction intervals. From a prediction perspective, it is not the global pattern but the local variation that matters.     

Animal movement tools (amt): R package for managing tracking data and conducting habitat selection analyses

Advances in tracking technology have led to an exponential increase in animal location data, greatly enhancing our ability to address interesting questions in movement ecology, but also presenting new challenges related to data management and analysis. Step‐selection functions (SSFs) are commonly used to link environmental covariates to animal location data collected at fine temporal resolution. SSFs are estimated by comparing observed steps connecting successive animal locations to random steps, using a likelihood equivalent of a Cox proportional hazards model. By using common statistical distributions to model step length and turn angle distributions, and including habitat‐ and movement‐related covariates (functions of distances between points, angular deviations), it is possible to make inference regarding habitat selection and movement processes or to control one process while investigating the other. The fitted model can also be used to estimate utilization distributions and mechanistic home ranges. Here, we present the R package amt (animal movement tools) that allows users to fit SSFs to data and to simulate space use of animals from fitted models. The amt package also provides tools for managing telemetry data. Using fisher (Pekania pennanti) data as a case study, we illustrate a four‐step approach to the analysis of animal movement data, consisting of data management, exploratory data analysis, fitting of models, and simulating from fitted models.     

mmSAR: an R‐package for multimodel species–area relationship inference

The species–area relationship (SAR) is one of the most fundamental tools in ecology. After almost a century of quantitative ecology, however, the quest for a “best SAR model” still remains elusive, with a substantial uncertainty about the best fitting SAR model frequently being observed. Recent research has required that this uncertainty be addressed, and a multimodel SAR framework has been devised. Here we introduce the mmSAR R‐package, which is a flexible and scalable implementation of the multimodel SAR framework for species‐area datasets, and provide some examples of its use. This R‐package provides functions for fitting SAR models, performing model selection, and the build up of multimodel SARs.     

multimark: an R package for analysis of capture–recapture data consisting of multiple “noninvasive” marks

I describe an open‐source R package, multimark , for estimation of survival and abundance from capture–mark–recapture data consisting of multiple “noninvasive” marks. Noninvasive marks include natural pelt or skin patterns, scars, and genetic markers that enable individual identification in lieu of physical capture. multimark provides a means for combining and jointly analyzing encounter histories from multiple noninvasive sources that otherwise cannot be reliably matched (e.g., left‐ and right‐sided photographs of bilaterally asymmetrical individuals). The package is currently capable of fitting open population Cormack–Jolly–Seber (CJS) and closed population abundance models with up to two mark types using Bayesian Markov chain Monte Carlo (MCMC) methods. multimark can also be used for Bayesian analyses of conventional capture–recapture data consisting of a single‐mark type. Some package features include (1) general model specification using formulas already familiar to most R users, (2) ability to include temporal, behavioral, age, cohort, and individual heterogeneity effects in detection and survival probabilities, (3) improved MCMC algorithm that is computationally faster and more efficient than previously proposed methods, (4) Bayesian multimodel inference using reversible jump MCMC, and (5) data simulation capabilities for power analyses and assessing model performance. I demonstrate use of multimark using left‐ and right‐sided encounter histories for bobcats (Lynx rufus) collected from remote single‐camera stations in southern California. In this example, there is evidence of a behavioral effect (i.e., trap “happy” response) that is otherwise indiscernible using conventional single‐sided analyses. The package will be most useful to ecologists seeking stronger inferences by combining different sources of mark–recapture data that are difficult (or impossible) to reliably reconcile, particularly with the sparse datasets typical of rare or elusive species for which noninvasive sampling techniques are most commonly employed. Addressing deficiencies in currently available software, multimark also provides a user‐friendly interface for performing Bayesian multimodel inference using capture–recapture data consisting of a single conventional mark or multiple noninvasive marks.     

Effects of sampling protocol on the shapes of species richness curves

Aim Scheiner (Journal of Biogeography, 2009, 36 , 2005–2008) criticized several issues regarding the typology and analysis of species richness curves that were brought forward by Dengler (Journal of Biogeography, 2009, 36 , 728–744). In order to test these two sets of views in greater detail, we used a simulation model of ecological communities to demonstrate the effects of different sampling schemes on the shapes of species richness curves and their extrapolation capability. Methods We simulated five random communities with 100 species on a 64 × 64 grid using random fields. Then we sampled species–area relationships (SARs, contiguous plots) as well as species–sampling relationships (SSRs, non‐contiguous plots) from these communities, both for the full extent and the central quarter of the grid. Finally, we fitted different functions (power, quadratic power, logarithmic, Michaelis–Menten, Lomolino) to the obtained data and assessed their goodness‐of‐fit (Akaike weights) and their extrapolation capability (deviation of the predicted value from the true value). Results We found that power functions gave the best fit for SARs, while for SSRs saturation functions performed better. Curves constructed from data of 32² grid cells gave reasonable extrapolations for 64² grid cells for SARs, irrespective of whether samples were gathered from the full extent or the centre only. By contrast, SSRs worked well for extrapolation only in the latter case. Main conclusions SARs and SSRs have fundamentally different curve shapes. Both sampling strategies can be used for extrapolation of species richness to a target area, but only SARs allow for extrapolation to a larger area than that sampled. These results confirm a fundamental difference between SARs and area‐based SSRs and thus support their typological differentiation.     

Tools for kinetic modeling of biochemical networks

The number of software packages for kinetic modeling of biochemical networks continues to grow. Although most packages share a common core of functionality, the specific capabilities and user interfaces of different packages mean that choosing the best package for a given task is not trivial. We compare 12 software packages with respect to their functionality, reliability, efficiency, user-friendliness and compatibility. Although most programs performed reliably in all numerical tasks tested, SBML compatibility and the set-up of multicompartmentalization are problematic in many packages. For simple models, GEPASI seems the best choice for non-expert users. For large-scale models, environments such as Jarnac/JDesigner are preferable, because they allow modular implementation of models. Virtual Cell is the most versatile program and provides the simplest and clearest functionality for setting up multicompartmentalization.     

From plots to islands: species diversity at different scales

Aim To investigate how plant diversity of whole islands (‘gamma’) is related to alpha and beta diversity patterns among sampling plots within each island, thus exploring aspects of diversity patterns across scales. Location Nineteen islands of the Aegean Sea, Greece. Methods Plant species were recorded at both the whole‐island scale and in small 100 m² plots on each island. Mean plot species richness was considered as a measure of alpha diversity, and six indices of the ‘variation’‐type beta diversity were also applied. In addition, we partitioned beta diversity into a ‘nestedness’ and a ‘replacement’ component, using the total species richness recorded in all plots of each island as a measure of ‘gamma’ diversity. We also applied 10 species–area models to predict the total observed richness of each island from accumulated plot species richness. Results Mean alpha diversity was not significantly correlated with the overall island species richness or island area. The range of plot species richness for each island was significantly correlated with both overall species richness and area. Alpha diversity was not correlated with most indices of beta diversity. The majority of beta diversity indices were correlated with whole‐island species richness, and this was also true for the ‘replacement’ component of beta diversity. The rational function model provided the best prediction of observed island species richness, with Monod’s and the exponential models following closely. Inaccuracy of predictions was positively correlated with the number of plots and with most indices of beta diversity. Main conclusions Diversity at the broader scale (whole islands) is shaped mainly by variation among small local samples (beta diversity), while local alpha diversity is not a good predictor of species diversity at broader scales. In this system, all results support the crucial role of habitat diversity in determining the species–area relationship.     

Plantecophys - An R Package for Analysing and Modelling Leaf Gas Exchange Data

Here I present the R package ''plantecophys'', a toolkit to analyse and model leaf gas exchange data. Measurements of leaf photosynthesis and transpiration are routinely collected with portable gas exchange instruments, and analysed with a few key models. These models include the Farquhar-von Caemmerer-Berry (FvCB) model of leaf photosynthesis, the Ball-Berry models of stomatal conductance, and the coupled leaf gas exchange model which combines the supply and demand functions for CO₂ in the leaf. The ''plantecophys'' R package includes functions for fitting these models to measurements, as well as simulating from the fitted models to aid in interpreting experimental data. Here I describe the functionality and implementation of the new package, and give some examples of its use. I briefly describe functions for fitting the FvCB model of photosynthesis to measurements of photosynthesis-CO₂ response curves (''A-C_i curves''), fitting Ball-Berry type models, modelling C3 photosynthesis with the coupled photosynthesis-stomatal conductance model, modelling C4 photosynthesis, numerical solution of optimal stomatal behaviour, and energy balance calculations using the Penman-Monteith equation. This open-source package makes technically challenging calculations easily accessible for many users and is freely available on CRAN.     

Robust methods for detecting a small island effect

Aim The small island effect (SIE), i.e. the hypothesis that species richness below a certain threshold area varies independently of island size, has become a widely accepted part of the theory of island biogeography. However, there are doubts whether the findings of SIEs were based on appropriate methods. The aim of this study was thus to provide a statistically sound methodology for the detection of SIEs and to show this by re‐analysing data in which an SIE has recently been claimed ( Sfenthourakis & Triantis, 2009 , Diversity and Distributions, 15 , 131–140). Location Ninety islands of the Aegean Sea (Greece). Methods First, I reviewed publications on SIEs and evaluated their methodology. Then, I fitted different species–area models to the published data of area (A) and species richness (S) of terrestrial isopods (Oniscidea), with log A as predictor and both S (logarithm function) and log S (power function) as response variables: (i) linear; (ii) quadratic; (iii) cubic; (iv) breakpoint with zero slope to the left (SIE model); (v) breakpoint with zero slope to the right; (vi) two‐slope model. I used non‐linear regression with R²_adj., AIC_c and BIC as goodness‐of‐fit measures. Results Many different methods have been applied for detecting SIEs, all of them with serious shortcomings. Contrary to the claim of the original study, no SIE occurs in this particular dataset as the two‐slope variants performed better than the SIE variants for both the logarithm and power functions. Main conclusions For the unambiguous detection of SIEs, one needs to (i) include islands with no species; (ii) compare all relevant models; and (iii) account for different model complexities. As none of the reviewed SIE studies met all these criteria, their findings are dubious and SIEs may be less common than reported. Thus, conservation‐related predictions based on the assumption of SIEs may be unreliable.     

Plants on small islands revisited: the effects of spatial scale and habitat quality on the species–area relationship

Understanding how species diversity is related to sampling area and spatial scale is central to ecology and biogeography. Small islands and small sampling units support fewer species than larger ones. However, the factors influencing species richness may not be consistent across scales. Richness at local scales is primarily affected by small‐scale environmental factors, stochasticity and the richness at the island scale. Richness at whole‐island scale, however, is usually strongly related to island area, isolation and habitat diversity. Despite these contrasting drivers at local and island scales, island species–area relationships (SARs) are often constructed based on richness sampled at the local scale. Whether local scale samples adequately predict richness at the island scale and how local scale samples influence the island SAR remains poorly understood. We investigated the effects of different sampling scales on the SAR of trees on 60 small islands in the Raja Ampat archipelago (Indonesia) using standardised transects and a hierarchically nested sampling design. We compared species richness at different grain sizes ranging from single (sub)transects to whole islands and tested whether the shape of the SAR changed with sampling scale. We then determined the importance of island area, isolation, shape and habitat quality at each scale on species richness. We found strong support for scale dependency of the SAR. The SAR changed from exponential shape at local sampling scales to sigmoidal shape at the island scale indicating variation of species richness independent of area for small islands and hence the presence of a small‐island effect. Island area was the most important variable explaining species richness at all scales, but habitat quality was also important at local scales. We conclude that the SAR and drivers of species richness are influenced by sampling scale, and that the sampling design for assessing the island SARs therefore requires careful consideration.     

ET come home: potential evapotranspiration in geographical ecology

Aim Many macroecological analyses are based on analyses of climatological data, within which evapotranspiration estimates are of central importance. In this paper we evaluate and review the use of evapotranspiration models and data in studies of geographical ecology to test the likely sensitivity of the analyses to variation in the performance of different metrics of potential evapotranspiration. Location Analyses are based on: (1) a latitudinal transect of sites (FLUXNET) for 11 different land‐cover types; and (2) globally gridded data. Methods First, we review the fundamental concepts of evapotranspiration, outline basic evapotranspiration models and describe methods with which to measure evapotranspiration. Next, we compare three different types of potential evapotranspiration models – a temperature‐based (Thornthwaite type), a radiation‐based (Priestley–Taylor) and a combination (Penman–Monteith) model – for 11 different land‐cover types. Finally, we compare these models at continental and global scales. Results At some sites the models differ by less than 7%, but generally the difference was greater than 25% across most sites. The temperature‐based model estimated 20–30% less than the radiation‐based and combination models averaged across all sites. The combination model often gave the highest estimates (22% higher than the radiation‐based model averaged across all sites). For continental and global averages, the potential evapotranspiration was very similar across all models. However, the difference in individual pixels was often larger than 150 mm year^?1 between models. Main conclusions The choice of evapotranspiration model and input data is likely to have a bearing on model fits and predictions when used in analyses of species richness and related phenomena at geographical scales of analysis. To assist those undertaking such analyses, we provide a guide to selecting an appropriate evapotranspiration model.     

The forestecology R package for fitting and assessing neighborhood models of the effect of interspecific competition on the growth of trees

1. Neighborhood competition models are powerful tools to measure the effect of interspecific competition. Statistical methods to ease the application of these models are currently lacking.
2. We present the forestecology package providing methods to (a) specify neighborhood competition models, (b) evaluate the effect of competitor species identity using permutation tests, and (cs) measure model performance using spatial cross‐validation. Following Allen and Kim (PLoS One, 15, 2020, e0229930), we implement a Bayesian linear regression neighborhood competition model.
3. We demonstrate the package''s functionality using data from the Smithsonian Conservation Biology Institute''s large forest dynamics plot, part of the ForestGEO global network of research sites. Given ForestGEO’s data collection protocols and data formatting standards, the package was designed with cross‐site compatibility in mind. We highlight the importance of spatial cross‐validation when interpreting model results.
4. The package features (a) tidyverse‐like structure whereby verb‐named functions can be modularly “piped” in sequence, (b) functions with standardized inputs/outputs of simple features sf package class, and (c) an S3 object‐oriented implementation of the Bayesian linear regression model. These three facts allow for clear articulation of all the steps in the sequence of analysis and easy wrangling and visualization of the geospatial data. Furthermore, while the package only has Bayesian linear regression implemented, the package was designed with extensibility to other methods in mind.

     

Arrhenius and Gleason revisited: new hybrid models resolve an old controversy

Aim Studies have typically employed species–area relationships (SARs) from sample areas to fit either the power relationship or the logarithmic (exponential) relationship. However, the plots from empirical data often fall between these models. This article proposes two complementary and hybrid models as solutions to the controversy regarding which model best fits sample‐area SARs. Methods The two models are and , where S_A is number of species in an area, A, where z, b, c₁ and c₂ are predetermined parameters found by calculation, and where d and n are parameters to be fitted. The number of parameters is reduced from six to two by fixing the model at either end of the scale window of the data set, a step that is justified by the condition that the error or the bias, or both, in the first and the last data points is negligible. The new hybrid models as well as the power model and the logarithmic model are fitted to 10 data sets. Results The two proposed models fit well not only to Arrhenius’ and Gleason’s data sets, but also to the other six data sets. They also provide a good fit to data sets that follow a sigmoid (or triphasic) shape in log–log space and to data sets that do not fall between the power model and the logarithmic model. The log‐transformation of the dependent variable, S, does not affect the curve fit appreciably, although it enhances the performance of the new models somewhat. Main conclusions Sample‐area SARs have previously been shown to be convex upward, convex downward (concave), sigmoid and inverted sigmoid in log–log space. The new hybrid models describe successfully data sets with all these curve shapes, and should therefore produce good fits also to what are termed triphasic SARs.     

Fast assessment of structural models of ion channels based on their predicted current–voltage characteristics

Computational prediction of protein structures is a difficult task, which involves fast and accurate evaluation of candidate model structures. We propose to enhance single‐model quality assessment with a functionality evaluation phase for proteins whose quantitative functional characteristics are known. In particular, this idea can be applied to evaluation of structural models of ion channels, whose main function ‐ conducting ions ‐ can be quantitatively measured with the patch‐clamp technique providing the current–voltage characteristics. The study was performed on a set of KcsA channel models obtained from complete and incomplete contact maps. A fast continuous electrodiffusion model was used for calculating the current–voltage characteristics of structural models. We found that the computed charge selectivity and total current were sensitive to structural and electrostatic quality of models. In practical terms, we show that evaluating predicted conductance values is an appropriate method to eliminate models with an occluded pore or with multiple erroneously created pores. Moreover, filtering models on the basis of their predicted charge selectivity results in a substantial enrichment of the candidate set in highly accurate models. Tests on three other ion channels indicate that, in addition to being a proof of the concept, our function‐oriented single‐model quality assessment method can be directly applied to evaluation of structural models of some classes of protein channels. Finally, our work raises an important question whether a computational validation of functionality should be included in the evaluation process of structural models, whenever possible. Proteins 2016; 84:217–231. © 2015 Wiley Periodicals, Inc.     

The power of time: spatiotemporal scaling of species diversity

The species–area relationship (SAR) provides the foundation for much of theoretical ecology and conservation practice. However, by ignoring time the SAR offers an incomplete model for biodiversity dynamics. We used long‐term data from permanent plots in Kansas grasslands, USA, to show that the increase in the number of species found with increasing periods of observation takes the same power‐law form as the SAR. A statistical model including time, area, and their interaction explains 98% of variation in mean species number and demonstrates that while the effect of time depends on area, and vice versa, time has strong effects on species number even at relatively broad spatial scales. Our results suggest equivalence of underlying processes in space and time and raise questions about the diversity estimates currently used by basic researchers and conservation practitioners.     

Exposure assessment in front of a multi-band base station antenna

This study investigates occupational exposure to electromagnetic fields in front of a multi‐band base station antenna for mobile communications at 900, 1800, and 2100 MHz. Finite‐difference time‐domain method was used to first validate the antenna model against measurement results published in the literature and then investigate the specific absorption rate (SAR) in two heterogeneous, anatomically correct human models (Virtual Family male and female) at distances from 10 to 1000 mm. Special attention was given to simultaneous exposure to fields of three different frequencies, their interaction and the additivity of SAR resulting from each frequency. The results show that the highest frequency—2100 MHz—results in the highest spatial‐peak SAR averaged over 10 g of tissue, while the whole‐body SAR is similar at all three frequencies. At distances >200 mm from the antenna, the whole‐body SAR is a more limiting factor for compliance to exposure guidelines, while at shorter distances the spatial‐peak SAR may be more limiting. For the evaluation of combined exposure, a simple summation of spatial‐peak SAR maxima at each frequency gives a good estimation for combined exposure, which was also found to depend on the distribution of transmitting power between the different frequency bands. Bioelectromagnetics 32:234–242, 2011. © 2010 Wiley‐Liss, Inc.     

CAD‐score: A new contact area difference‐based function for evaluation of protein structural models

Evaluation of protein models against the native structure is essential for the development and benchmarking of protein structure prediction methods. Although a number of evaluation scores have been proposed to date, many aspects of model assessment still lack desired robustness. In this study we present CAD‐score, a new evaluation function quantifying differences between physical contacts in a model and the reference structure. The new score uses the concept of residue–residue contact area difference (CAD) introduced by Abagyan and Totrov (J Mol Biol 1997; 268:678–685). Contact areas, the underlying basis of the score, are derived using the Voronoi tessellation of protein structure. The newly introduced CAD‐score is a continuous function, confined within fixed limits, free of any arbitrary thresholds or parameters. The built‐in logic for treatment of missing residues allows consistent ranking of models of any degree of completeness. We tested CAD‐score on a large set of diverse models and compared it to GDT‐TS, a widely accepted measure of model accuracy. Similarly to GDT‐TS, CAD‐score showed a robust performance on single‐domain proteins, but displayed a stronger preference for physically more realistic models. Unlike GDT‐TS, the new score revealed a balanced assessment of domain rearrangement, removing the necessity for different treatment of single‐domain, multi‐domain, and multi‐subunit structures. Moreover, CAD‐score makes it possible to assess the accuracy of inter‐domain or inter‐subunit interfaces directly. In addition, the approach offers an alternative to the superposition‐based model clustering. The CAD‐score implementation is available both as a web server and a standalone software package at http://www.ibt.lt/bioinformatics/cad‐score/ . Proteins 2013. © 2012 Wiley Periodicals, Inc.     

The gambin model provides a superior fit to species abundance distributions with a single free parameter: evidence,implementation and interpretation

The species abundance distribution (SAD) has been a central focus of community ecology for over fifty years, and is currently the subject of widespread renewed interest. The gambin model has recently been proposed as a model that provides a superior fit to commonly preferred SAD models. It has also been argued that the model's single parameter (α) presents a potentially informative ecological diversity metric, because it summarises the shape of the SAD in a single number. Despite this potential, few empirical tests of the model have been undertaken, perhaps because the necessary methods and software for fitting the model have not existed. Here, we derive a maximum likelihood method to fit the model, and use it to undertake a comprehensive comparative analysis of the fit of the gambin model. The functions and computational code to fit the model are incorporated in a newly developed free‐to‐download R package (gambin). We test the gambin model using a variety of datasets and compare the fit of the gambin model to fits obtained using the Poisson lognormal, logseries and zero‐sum multinomial distributions. We found that gambin almost universally provided a better fit to the data and that the fit was consistent for a variety of sample grain sizes. We demonstrate how α can be used to differentiate intelligibly between community structures of Azorean arthropods sampled in different land use types. We conclude that gambin presents a flexible model capable of fitting a wide variety of observed SAD data, while providing a useful index of SAD form in its single fitted parameter. As such, gambin has wide potential applicability in the study of SADs, and ecology more generally.     

The theory of the nested species–area relationship: geometric foundations of biodiversity scaling

The relationship between sampled area and the number of species within that area, the species–area relationship (SAR), is a major biodiversity pattern and one of a few law‐like regularities in ecology. While the SAR for isolated units (islands or continents) is assumed to result from the dynamics of species colonization, speciation and extinction, the SAR for contiguous areas in which smaller plots are nested within larger sample areas can be attributed to spatial patterns in the distribution of individuals. The nested SAR is typically triphasic in logarithmic space, so that it increases steeply at smaller scales, decelerates at intermediate scales and increases steeply again at continental scales. I will review current theory for this pattern, showing that all three phases of the SAR can be derived from simple geometric considerations. The increase of species richness with area in logarithmic space is generally determined by overall species rarity, so that the rarer the species are on average, the higher is the local slope z. Rarity is scale‐dependent: species occupy only a minor proportion of area at broad spatial scales, leading to upward accelerating shape of the SAR at continental scales. Similarly, species are represented by only a few individuals at fine spatial scales, leading to high SAR slope also at small areas. Geometric considerations reveal links of the SAR to other macroecological patterns, namely patterns of β‐diversity, the species–abundance distribution, and the relationship between energy availability (or productivity) and species richness. Knowledge of the regularities concerning nested SARs may be used for standardizing unequal areas, upscaling species richness and estimating species loss due to area loss, but all these applications have their limits, which also follow from the geometric considerations.