Which function describes the species–area relationship best? A review and empirical evaluation

Aim The aims of this study are to resolve terminological confusion around different types of species–area relationships (SARs) and their delimitation from species sampling relationships (SSRs), to provide a comprehensive overview of models and analytical methods for SARs, to evaluate these theoretically and empirically, and to suggest a more consistent approach for the treatment of species–area data. Location Curonian Spit in north‐west Russia and archipelagos world‐wide. Methods First, I review various typologies for SARs and SSRs as well as mathematical models, fitting procedures and goodness‐of‐fit measures applied to SARs. This results in a list of 23 function types, which are applicable both for untransformed (S) and for log‐transformed (log S) species richness. Then, example data sets for nested plots in continuous vegetation (n = 14) and islands (n = 6) are fitted to a selection of 12 function types (linear, power, logarithmic, saturation, sigmoid) both for S and for log S. The suitability of these models is assessed with Akaike’s information criterion for S and log S, and with a newly proposed metric that addresses extrapolation capability. Results SARs, which provide species numbers for different areas and have no upper asymptote, must be distinguished from SSRs, which approach the species richness of one single area asymptotically. Among SARs, nested plots in continuous ecosystems, non‐nested plots in continuous ecosystems, and isolates can be distinguished. For the SARs of the empirical data sets, the normal and quadratic power functions as well as two of the sigmoid functions (Lomolino, cumulative beta‐P) generally performed well. The normal power function (fitted for S) was particularly suitable for predicting richness values over ten‐fold increases in area. Linear, logarithmic, convex saturation and logistic functions generally were inappropriate. However, the two sigmoid models produced unstable results with arbitrary parameter estimates, and the quadratic power function resulted in decreasing richness values for large areas. Main conclusions Based on theoretical considerations and empirical results, I suggest that the power law should be used to describe and compare any type of SAR while at the same time testing whether the exponent z changes with spatial scale. In addition, one should be aware that power‐law parameters are significantly influenced by methodology.     

Local–regional boundary shifts in oribatid mite (Acari: Oribatida) communities: species–area relationships in arboreal habitat islands of a coastal temperate rain forest, Vancouver Island, Canada

Aim This study investigates the species–area relationship (SAR) for oribatid mite communities of isolated suspended soil habitats, and compares the shape and slope of the SAR with a nested data set collected over three spatial scales (core, patch and tree level). We investigate whether scale dependence is exhibited in the nested sampling design, use multivariate regression models to elucidate factors affecting richness and abundance patterns, and ask whether the community composition of oribatid mites changes in suspended soil patches of different sizes. Location Walbran Valley, Vancouver Island, Canada. Methods A total of 216 core samples were collected from 72 small, medium and large isolated suspended soil habitats in six western redcedar trees in June 2005. The relationship between oribatid species richness and habitat volume was modelled for suspended soil habitat isolates (type 3) and a nested sampling design (type 1) over multiple spatial scales. Nonlinear estimation parameterized linear, power and Weibull function regression models for both SAR designs, and these were assessed for best fit using R² and Akaike's information criteria (ΔAIC) values. Factors affecting oribatid mite species richness and standardized abundance (number per g dry weight) were analysed by anova and linear regression models. Results Sixty‐seven species of oribatid mites were identified from 9064 adult specimens. Surface area and moisture content of suspended soils contributed to the variation in species richness, while overall oribatid mite abundance was explained by moisture and depth. A power‐law function best described the isolate SAR (S = 3.97 × A^0.12, R² = 0.247, F_1,70 = 22.450, P < 0.001), although linear and Weibull functions were also valid models. Oribatid mite species richness in nested samples closely fitted a power‐law model (S = 1.96 × A^0.39, R² = 0.854, F_1,18 = 2693.6, P < 0.001). The nested SAR constructed over spatial scales of core, patch and tree levels proved to be scale‐independent. Main conclusions Unique microhabitats provided by well developed suspended soil accumulations are a habitat template responsible for the diversity of canopy oribatid mites. Species–area relationships of isolate vs. nested species richness data differed in the rate of accumulation of species with increased area. We suggest that colonization history, stability of suspended soil environments, and structural habitat complexity at local and regional scales are major determinants of arboreal oribatid mite species richness.     

Daily age determination and growth rates of freshwater fish throughout a regulated lotic system of the Murray‐Darling Basin Australia

To facilitate future research in freshwater fish recruitment response to environmental flow delivery, size‐at‐age and growth models are presented for eight fish species occurring in south‐eastern Australia; three small‐bodied species and the juvenile 0+ age classes of five large‐bodied species. Otolith increments were used to estimate the daily age of golden perch Macquaria ambigua, bony bream Nematalosa erebi, common carp Cyprinus carpio; Murray cod Maccullochella peelii, freshwater eel‐tailed catfish Tandanus tandanus, Australian smelt Retropinna semoni, un‐specked hardyhead Craterocephalus stercusmuscarum fulvus and Murray–Darling rainbowfish Melanotaenia fluviatilis. Linear growth models provided the best fit for length‐at‐age data of juvenile 0+ age large‐bodied species; whereas von Bertalanffy growth functions provided the best fit to length‐at‐age data of small‐bodied species. The results provide novel baseline data for future research in this area.     

Species–area relationships in Mediterranean-climate plant communities

Aim To determine the best‐fit model of species–area relationships for Mediterranean‐type plant communities and evaluate how community structure affects these species–area models. Location Data were collected from California shrublands and woodlands and compared with literature reports for other Mediterranean‐climate regions. Methods The number of species was recorded from 1, 100 and 1000 m² nested plots. Best fit to the power model or exponential model was determined by comparing adjusted r² values from the least squares regression, pattern of residuals, homoscedasticity across scales, and semi‐log slopes at 1–100 m² and 100–1000 m². Dominance–diversity curves were tested for fit to the lognormal model, MacArthur's broken stick model, and the geometric and harmonic series. Results Early successional Western Australia and California shrublands represented the extremes and provide an interesting contrast as the exponential model was the best fit for the former, and the power model for the latter, despite similar total species richness. We hypothesize that structural differences in these communities account for the different species–area curves and are tied to patterns of dominance, equitability and life form distribution. Dominance–diversity relationships for Western Australian heathlands exhibited a close fit to MacArthur's broken stick model, indicating more equitable distribution of species. In contrast, Californian shrublands, both postfire and mature stands, were best fit by the geometric model indicating strong dominance and many minor subordinate species. These regions differ in life form distribution, with annuals being a major component of diversity in early successional Californian shrublands although they are largely lacking in mature stands. Both young and old Australian heathlands are dominated by perennials, and annuals are largely absent. Inherent in all of these ecosystems is cyclical disequilibrium caused by periodic fires. The potential for community reassembly is greater in Californian shrublands where only a quarter of the flora resprout, whereas three quarters resprout in Australian heathlands. Other Californian vegetation types sampled include coniferous forests, oak savannas and desert scrub, and demonstrate that different community structures may lead to a similar species–area relationship. Dominance–diversity relationships for coniferous forests closely follow a geometric model whereas associated oak savannas show a close fit to the lognormal model. However, for both communities, species–area curves fit a power model. The primary driver appears to be the presence of annuals. Desert scrub communities illustrate dramatic changes in both species diversity and dominance–diversity relationships in high and low rainfall years, because of the disappearance of annuals in drought years. Main conclusions Species–area curves for immature shrublands in California and the majority of Mediterranean plant communities fit a power function model. Exceptions that fit the exponential model are not because of sampling error or scaling effects, rather structural differences in these communities provide plausible explanations. The exponential species–area model may arise in more than one way. In the highly diverse Australian heathlands it results from a rapid increase in species richness at small scales. In mature California shrublands it results from very depauperate richness at the community scale. In both instances the exponential model is tied to a preponderance of perennials and paucity of annuals. For communities fit by a power model, coefficients z and log c exhibit a number of significant correlations with other diversity parameters, suggesting that they have some predictive value in ecological communities.     

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.     

Assessing biodiversity with species accumulation curves; inventories of small reptiles by pit‐trapping in Western Australia

Abstract We examined 11 non‐linear regression models to determine which of them best fitted curvilinear species accumulation curves based on pit‐trapping data for reptiles in a range of heterogeneous and homogenous sites in mesic, semi‐arid and arid regions of Western Australia. A well‐defined plateau in a species accumulation curve is required for any of the models accurately to estimate species richness. Two different measures of effort (pit‐trapping days and number of individuals caught) were used to determine if the measure of effort influenced the choice of the best model(s). We used species accumulation curves to predict species richness, determined the trapping effort required to catch a nominated percentage (e.g. 95%) of the predicted number of species in an area, and examined the relationship between species accumulation curves with diversity and rarity. Species richness, diversity and the proportion of rare species in a community influenced the shape of species accumulation curves. The Beta‐P model provided the best overall fit (highest r²) for heterogeneous and homogeneous sites. For heterogeneous sites, Hill, Rational, Clench, Exponential and Weibull models were the next best. For homogeneous habitats, Hill, Weibull and Chapman–Richards were the next best models. There was very little difference between Beta‐P and Hill models in fitting the data to accumulation curves, although the Hill model generally over‐estimated species richness. Most models worked equally well for both measures of trapping effort. Because the number of individuals caught was influenced by both pit‐trapping effort and the abundance of individuals, both measures of effort must be considered if species accumulation curves are to be used as a planning tool. Trapping effort to catch a nominated percentage of the total predicted species in homogeneous and heterogeneous habitats varied among sites, but even for only 75% of the predicted number of species it was generally much higher than the typical effort currently being used for terrestrial vertebrate fauna surveys in Australia. It was not possible to provide a general indication of the effort required to predict species richness for a site, or to capture a nominated proportion of species at a site, because species accumulation curves are heavily influenced by the characteristics of particular sites.     

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.     

Island biogeography of the Mediterranean sea: the species–area relationship for terrestrial isopods

Aim We looked at the biogeographical patterns of Oniscidean fauna from the small islands of the Mediterranean Sea in order to investigate the species–area relationship and to test for area‐range effects. Location The Mediterranean Sea. Methods We compiled from the literature a data set of 176 species of Oniscidea (terrestrial isopods) distributed over 124 Mediterranean islands. Jaccard's index was used as input for a UPGMA cluster analysis. The species–area relationship was investigated by applying linear, semi‐logarithmic, logarithmic and sigmoid models. We also investigated a possible ‘small island effect’ (SIE) by performing breakpoint regression. We used a cumulative and a sliding‐window approach to evaluate scale‐dependent area‐range effects on the log S/log A regression parameters. Results Based on similarity indexes, results indicated that small islands of the Mediterranean Sea can be divided into two major groups: eastern and western. In general, islands from eastern archipelagos were linked together at similarity values higher than those observed for western Mediterranean islands. This is consistent with a more even distribution of species in the eastern Mediterranean islands. Separate archipelagos in the western Mediterranean could be discriminated, with the exception of islets, which tended to group together at the lowest similarity values regardless of the archipelago to which they belong. Islets were characterized by a few common species with large ranges. The species–area logarithmic model did not always provide the best fit. Most continental archipelagos showed very similar intercepts, higher than the intercept for the Canary island oceanic archipelago. Sigmoid regression returned convex curves. Evidence for a SIE was found, whereas area‐range effects that are dependent on larger scale analyses were not unambiguously supported. Main conclusions The Oniscidea fauna from small islands of the Mediterranean Sea is highly structured, with major and minor geographical patterns being identifiable. Some but not all of the biogeographical complexity can be explained by interpreting the different shapes of species–area curves. Despite its flexibility, the sigmoid model tested did not always provide the best fit. Moreover, when the model did provide a good fit the curves looked convex, not sigmoid. We found evidence for a SIE, and minor support for scale‐dependent area‐range effects.     

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.     

The species–area relationship derived from species-specific incidence functions

The species–area relationship (SAR), describing the increase in species number (S) with increasing area (A), is one of the most robust patterns in ecology with great significance for conservation. The SAR is generally formulated as a power function, S = kA^z, although the semilogarithmic form S = a + b log A has often been used by botanists. Here we unite the two forms by deriving SARs from the incidence functions of the species that make up the community. We show how the decisive scaling parameters z and b relate to the properties of individual species, and highlight why the biological interpretation of SARs has been so enigmatic.     

The species–area relationship in centipedes (Myriapoda: Chilopoda): a comparison between Mediterranean island groups

The present study article examines the shapes of centipede species–area relationships (SARs) in the Mediterranean islands, compares the results of the linear form of the power model between archipelagos, discusses biological significance of the power model parameters with other taxa on the Aegean archipelago, and tests for a significant small‐island effect (SIE). We used 11 models to test the SARs and we compared the quality‐of‐fit of all candidate models. The power function ranked first and Z‐values was in the range 0.106–0.334. We assessed the presence of SIEs by fitting both a continuous and discontinuous breakpoint regression model. The continuous breakpoint regression functions never performed much better than the closest discontinuous model as a predictor of centipede species richness. We suggest that the relatively low Z‐values in our data partly reflect better dispersal abilities in centipedes than in other soil invertebrate taxa. Longer periods of isolation and more recent island formation may explain the somewhat lower constant c in the western Mediterranean islands compared to the Aegean islands. Higher breakpoint values in the western Mediterranean may also be a result of larger distance to the mainland and longer separation times. Despite the differences in the geological history and the idiosyncratic features of the main island groups considered, the overall results are quite similar and this could be assigned to the ability of centipedes to disperse across isolation barriers. © 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, 105 , 146–159.     

Mathematical modeling of appendicular bone growth in glaucous‐winged gulls

Development of locomotor activity is crucial in tetrapods. In birds, this development leads to different functions for hindlimbs and forelimbs. The emergence of walking and flying as very different complex behavior patterns only weeks after hatching provides an interesting case study in animal development. We measured the diaphyseal lengths and midshaft diameters of three wing bones (humerus, ulna, and carpometacarpus) and three leg bones (femur, tibiotarsus, and tarsometatarsus) of 79 juvenile (ages 0–42 days) and 13 adult glaucous‐winged gulls (Larus glaucescens), a semiprecocial species. From a suite of nine alternative mathematical models, we used information‐theoretic criteria to determine the best model(s) for length and diameter of each bone as a function of age; that is, we determined the model(s) that obtained the best tradeoff between the minimized sum of squared residuals and the number of parameters used to fit the model. The Janoschek and Holling III models best described bone growth, with at least one of these models yielding an R² ≥ 0.94 for every dimension except tarsometatarsus diameter (R² = 0.87). We used the best growth models to construct accurate allometric comparisons of the bones. Early maximal absolute growth rates characterize the humerus, femur, and tarsometatarsus, bones that assume adult‐type support functions relatively early during juvenile development. Leg bone lengths exhibit more rapid but less sustained relative growth than wing bone lengths. Wing bone diameters are initially smaller than leg bone diameters, although this relationship is reversed by fledging. Wing bones and the femur approach adult length by fledging but continue to increase in diameter past fledging; the tibiotarsus and tarsometatarsus approach both adult length and diameter by fledging. In short, the pattern of bone growth in this semiprecocial species reflects the changing behavioral needs of the developing organism. J. Morphol., 2009. © 2008 Wiley‐Liss, Inc.     

A test of the metapopulation model of the species–area relationship

Abstract Aim The species–area relationship is a ubiquitous pattern. Previous methods describing the relationship have done little to elucidate mechanisms producing the pattern. Hanski & Gyllenberg (Science, 1997, 275 , 397) have shown that a model of metapopulation dynamics yields predictable species–area relationships. We elaborate on the biological interpretation of this mechanistic model and test the prediction that communities of species with a higher risk of extinction caused by environmental stochasticity should have lower species–area slopes than communities experiencing less impact of environmental stochasticity. Methods We develop the mainland–island version of the metapopulation model and show that the slope of the species–area relationship resulting from this model is related to the ratio of population growth rate to variability in population growth of individual species. We fit the metapopulation model to five data sets, and compared the fit with the power function model and Williams's (Ecology, 1995, 76 , 2607) extreme value function model. To test that communities consisting of species with a high risk of extinction should have lower slopes, we used the observation that small‐bodied species of vertebrates are more susceptible to environmental stochasticity than large‐bodied species. The data sets were divided into small and large bodied species and the model fit to both. Results and main conclusions The metapopulation model showed a good fit for all five data sets, and was comparable with the fits of the extreme value function and power function models. The slope of the metapopulation model of the species–area relationship was greater for larger than for smaller‐bodied species for each of five data sets. The slope of the metapopulation model of the species–area relationship has a clear biological interpretation, and allows for interpretation that is rooted in ecology, rather than ad hoc explanation.     

Scoring ligand similarity in structure‐based virtual screening

Scoring to identify high‐affinity compounds remains a challenge in virtual screening. On one hand, protein–ligand scoring focuses on weighting favorable and unfavorable interactions between the two molecules. Ligand‐based scoring, on the other hand, focuses on how well the shape and chemistry of each ligand candidate overlay on a three‐dimensional reference ligand. Our hypothesis is that a hybrid approach, using ligand‐based scoring to rank dockings selected by protein–ligand scoring, can ensure that high‐ranking molecules mimic the shape and chemistry of a known ligand while also complementing the binding site. Results from applying this approach to screen nearly 70 000 National Cancer Institute (NCI) compounds for thrombin inhibitors tend to support the hypothesis. EON ligand‐based ranking of docked molecules yielded the majority (4/5) of newly discovered, low to mid‐micromolar inhibitors from a panel of 27 assayed compounds, whereas ranking docked compounds by protein–ligand scoring alone resulted in one new inhibitor. Since the results depend on the choice of scoring function, an analysis of properties was performed on the top‐scoring docked compounds according to five different protein–ligand scoring functions, plus EON scoring using three different reference compounds. The results indicate that the choice of scoring function, even among scoring functions measuring the same types of interactions, can have an unexpectedly large effect on which compounds are chosen from screening. Furthermore, there was almost no overlap between the top‐scoring compounds from protein–ligand versus ligand‐based scoring, indicating the two approaches provide complementary information. Matchprint analysis, a new addition to the SLIDE (Screening Ligands by Induced‐fit Docking, Efficiently) screening toolset, facilitated comparison of docked molecules' interactions with those of known inhibitors. The majority of interactions conserved among top‐scoring compounds for a given scoring function, and from the different scoring functions, proved to be conserved interactions in known inhibitors. This was particularly true in the S1 pocket, which was occupied by all the docked compounds. Copyright © 2009 John Wiley & Sons, Ltd.     

Species–area relationships of red-listed species in old boreal forests: a large-scale data analysis

Aim Species–area relationships are often applied, but not generally approved, to guide practical conservation planning. The specific species group analysed may affect their applicability. We asked if species–area curves constructed from extensive databases of various sectors of natural resource administration can provide insights into large‐scale conservation of boreal forest biodiversity if the analyses are restricted only to red‐listed species. Location Finland, northern Europe. Methods Our data included 12,645 records of 219 red‐listed Coleoptera and Fungi from the whole of Finland. The forest data also covered the entire country, 202,761 km². The units of species–area analyses were 224 municipalities where the red‐listed forest species have been observed. We performed a hierarchical partitioning analysis to reveal the relative importance of different potential explanatory variables. Based on the results, for all red‐listed species, species associated with coniferous trees and for Fungi, the area of economically over‐aged forests explained the best the variation in data. For species associated with deciduous trees and Coleoptera, the forest area explained better variation in data than the area of old forests. In the subsequent log–log species–area regression analyses, we used the best variables as the explanatory variable for each species group. Results There was a strong relationship between the number of all red‐listed species and the area of old forests remaining, with a z‐value of 0.45. The area explained better the number of species associated with conifer trees and Fungi than the number of species associated with deciduous trees and Coleoptera. Main conclusions The high z‐values of species–area curves indicate that the remaining old‐growth patches constitute a real archipelago for the conifer‐associated red‐listed species, since lower values had been expected if the surrounding habitat matrix were a suitable habitat for the species analysed.     

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.     

A model for the species–area–habitat relationship

Aim To propose a model (the choros model) for species diversity, which embodies number of species, area and habitat diversity and mathematically unifies area per se and habitat hypotheses. Location Species richness patterns from a broad scale of insular biotas, both from island and mainland ecosystems are analysed. Methods Twenty‐two different data sets from seventeen studies were examined in this work. The r² values and the Akaike's Information Criterion (AIC) were used in order to compare the quality of fit of the choros model with the Arrhenius species–area model. The classic method of log‐log transformation was applied. Results In twenty of the twenty‐two cases studied, the proposed model gave a better fit than the classic species–area model. The values of z parameter derived from choros model are generally lower than those derived from the classic species–area equation. Main conclusions The choros model can express the effects of area and habitat diversity on species richness, unifying area per se and the habitat hypothesis, which as many authors have noticed are not mutually exclusive but mutually supplementary. The use of habitat diversity depends on the specific determination of the ‘habitat’ term, which has to be defined based on the natural history of the taxon studied. Although the values of the z parameter are reduced, they maintain their biological significance as described by many authors in the last decades. The proposed model can also be considered as a stepping‐stone in our understanding of the small island effect.     

Predation by the carabid beetle Harpalus rufipes on the pest slug Deroceras reticulatum in the laboratory

The Harpalini species Harpalus rufipes, as many other generalist carabids, consume a wide variety of prey and it is known to feed on pest slugs such as the grey field slug Deroceras reticulatum, but quantitative data about the predatory activity of H. rufipes on slugs are very scarce. In laboratory experiments, we assessed the capability of male H. rufipes to kill eggs and different‐sized slugs of the pest species D. reticulatum in either the absence or the presence of alternative live prey (dipteran larvae and aphids). We also investigated the preference of H. rufipes for eggs and hatchlings of D. reticulatum in a choice experiment. H. rufipes killed considerable amounts of eggs and small juveniles (≤5.0 mg) of D. reticulatum, both in no‐choice and in choice situations. Medium‐sized juvenile slugs (10–20 mg) were seldom killed only in no‐choice situations, and no large juveniles (50–60 mg) were killed. Dipteran larvae and aphids were killed also in no‐choice and in choice situations. The type of alternative prey presented with slug eggs affected the survival of the eggs to H. rufipes predation. The presence of dipteran larvae as alternative prey did not affect the survival of juvenile slugs. When eggs and small juvenile slugs were offered together, the survivals of both items were similar. The obtained results under laboratory conditions suggest that the generalist predator H. rufipes might realise an important contribution to the control of pest slugs.     

Using functional traits to predict species growth trajectories,and cross‐validation to evaluate these models for ecological prediction

Modeling plant growth using functional traits is important for understanding the mechanisms that underpin growth and for predicting new situations. We use three data sets on plant height over time and two validation methods—in‐sample model fit and leave‐one‐species‐out cross‐validation—to evaluate non‐linear growth model predictive performance based on functional traits. In‐sample measures of model fit differed substantially from out‐of‐sample model predictive performance; the best fitting models were rarely the best predictive models. Careful selection of predictor variables reduced the bias in parameter estimates, and there was no single best model across our three data sets. Testing and comparing multiple model forms is important. We developed an R package with a formula interface for straightforward fitting and validation of hierarchical, non‐linear growth models. Our intent is to encourage thorough testing of multiple growth model forms and an increased emphasis on assessing model fit relative to a model's purpose.     

Shapes and functions of species–area curves: a review of possible models

Aim This paper reviews possible candidate models that may be used in theoretical modelling and empirical studies of species–area relationships (SARs). The SAR is an important and well‐proven tool in ecology. The power and the exponential functions are by far the models that are best known and most frequently applied to species–area data, but they might not be the most appropriate. Recent work indicates that the shape of species–area curves in arithmetic space is often not convex but sigmoid and also has an upper asymptote. Methods Characteristics of six convex and eight sigmoid models are discussed and interpretations of different parameters summarized. The convex models include the power, exponential, Monod, negative exponential, asymptotic regression and rational functions, and the sigmoid models include the logistic, Gompertz, extreme value, Morgan–Mercer–Flodin, Hill, Michaelis–Menten, Lomolino and Chapman–Richards functions plus the cumulative Weibull and beta‐P distributions. Conclusions There are two main types of species–area curves: sample curves that are inherently convex and isolate curves, which are sigmoid. Both types may have an upper asymptote. A few have attempted to fit convex asymptotic and/or sigmoid models to species–area data instead of the power or exponential models. Some of these or other models reviewed in this paper should be useful, especially if species–area models are to be based more on biological processes and patterns in nature than mere curve fitting. The negative exponential function is an example of a convex model and the cumulative Weibull distribution an example of a sigmoid model that should prove useful. A location parameter may be added to these two and some of the other models to simulate absolute minimum area requirements.