Are species–area relationships from entire archipelagos congruent with those of their constituent islands?

Aim To establish the extent to which archipelagos follow the same species–area relationship as their constituent islands and to explore the factors that may explain departures from the relationship. Location Thirty‐eight archipelagos distributed worldwide. Methods We used ninety‐seven published datasets to create island species–area relationships (ISARs) using the Arrhenius logarithmic form of the power model. Observed and predicted species richness of an archipelago and of each of its islands were used to calculate two indices that determined whether the archipelago followed the ISAR. Archipelagic residuals (ArcRes) were calculated as the residual of the prediction provided by the ISAR using the total area of the archipelago, standardized by the total richness observed in the archipelago. We also tested whether any characteristic of the archipelago (geological origin and isolation) and/or taxon accounts for whether an archipelago fits into the ISAR or not. Finally, we explored the relationship between ArcRes and two metrics of nestedness. Results The archipelago was close to the ISAR of its constituent islands in most of the cases analysed. Exceptions arose for archipelagos where (i) the slopes of the ISAR are low, (ii) observed species richness is higher than expected by the ISAR and/or (iii) distance to the mainland is small. The archipelago's geological origin was also important; a higher percentage of oceanic archipelagos fit into their ISAR than continental ones. ArcRes indicated that the ISAR underpredicts archipelagic richness in the least isolated archipelagos. Different types of taxon showed no differences in ArcRes. Nestedness and ArcRes appear to be related, although the form of the relationship varies between metrics. Main conclusions Archipelagos, as a rule, follow the same ISAR as their constituent islands. Therefore, they can be used as distinct units themselves in large‐scale biogeographical and macroecological studies. Departure from the ISAR can be used as a crude indicator of richness‐ordered nestedness, responsive to factors such as isolation, environmental heterogeneity, number and age of islands.     

Sampling design may obscure species–area relationships in landscape-scale field studies

We investigated 1) the role of area per se in explaining anuran species richness on reservoir forest islands, after controlling for several confounding factors. We also assessed 2) how sampling design affects the inferential power of island species–area relationships (ISARs) aiming to 3) provide guidelines to yield reliable estimates of area-induced species losses in patchy systems. We surveyed anurans with autonomous recording units at 151 plots located on 74 islands and four continuous forest sites at the Balbina Hydroelectric Reservoir landscape, central Brazilian Amazonia. We applied semi-log ISAR models to assess the effect of sampling design on the fit and slope of species–area curves. To do so, we subsampled our surveyed islands following both a 1) stratified and 2) non-stratified random selection of 5, 10, 15, 20 and 25 islands covering 1) the full range in island size (0.45–1699 ha) and 2) only islands smaller than 100 ha, respectively. We also compiled 25 datasets from the literature to assess the generality of our findings. Island size explained ca half of the variation in species richness. The fit and slope of species–area curves were affected mainly by the range in island size considered, and to a very small extent by the number of islands surveyed. In our literature review, all datasets covering a range of patch sizes larger than 300 ha yielded a positive ISAR, whereas the number of patches alone did not affect the detection of ISARs. We conclude that 1) area per se plays a major role in explaining anuran species richness on forest islands within an Amazonian anthropogenic archipelago; 2) the inferential power of island species–area relationships is severely degraded by sub-optimal sampling designs; 3) at least 10 habitat patches spanning three orders of magnitude in size should be surveyed to yield reliable species–area estimates in patchy systems.     

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.     

Species–area relationships in the Andaman and Nicobar Islands emerge because rarer species are disproportionately favored on larger islands

The island species–area relationship (ISAR) describes how the number of species increases with increasing size of an island (or island‐like habitat), and is of fundamental importance in island biogeography and conservation. Here, we use a framework based on individual‐based rarefaction to infer whether ISARs result from passive sampling, or whether some processes are acting beyond sampling (e.g., disproportionate effects and/or habitat heterogeneity). Using data on total and relative abundances of four taxa (birds, butterflies, amphibians, and reptiles) from multiple islands in the Andaman and Nicobar archipelago, we examine how different metrics of biodiversity (total species richness, rarefied species richness, and abundance‐weighted effective numbers of species emphasizing common species) vary with island area. Total species richness increased for all taxa, as did rarefied species richness controlling for a given sampling effort. This indicates that the ISAR did not result because of passive sampling, but that instead, some species were disproportionately favored on larger islands. For birds, frogs, and lizards, this disproportionate effect was only associated with species that were rarer in the samples, but for butterflies, both more common and rarer species were affected. Furthermore, for the two taxa for which we had plot‐level data (reptiles and amphibians), within‐island β‐diversity did not increase with island size, suggesting that within‐island compositional effects were unlikely to be driving these ISARs. Overall, our results indicate that the ISARs of these taxa are most likely driven by disproportionate effects, that is, where larger islands are important sources of biodiversity beyond a simple sampling expectation, especially through their influence on rarer species, thus emphasizing their role in the preservation and conservation of species.     

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.     

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.     

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.     

A global analysis of avian island diversity–area relationships in the Anthropocene

Research on island species–area relationships (ISAR) has expanded to incorporate functional (IFDAR) and phylogenetic (IPDAR) diversity. However, relative to the ISAR, we know little about IFDARs and IPDARs, and lack synthetic global analyses of variation in form of these three categories of island diversity–area relationship (IDAR). Here, we undertake the first comparative evaluation of IDARs at the global scale using 51 avian archipelagic data sets representing true and habitat islands. Using null models, we explore how richness-corrected functional and phylogenetic diversity scale with island area. We also provide the largest global assessment of the impacts of species introductions and extinctions on the IDAR. Results show that increasing richness with area is the primary driver of the (non-richness corrected) IPDAR and IFDAR for many data sets. However, for several archipelagos, richness-corrected functional and phylogenetic diversity changes linearly with island area, suggesting that the dominant community assembly processes shift along the island area gradient. We also find that archipelagos with the steepest ISARs exhibit the biggest differences in slope between IDARs, indicating increased functional and phylogenetic redundancy on larger islands in these archipelagos. In several cases introduced species seem to have ‘re-calibrated’ the IDARs such that they resemble the historic period prior to recent extinctions.     

On the general dynamic model of oceanic island biogeography

Aim To investigate the biological meaning of equations used to apply the general dynamic model (GDM) of oceanic island biogeography proposed by R. J. Whittaker, K. A. Triantis and R. J. Ladle. Location Analyses are presented for 17 animal groups living on the Aeolian Islands, a volcanic archipelago in the central Mediterranean, near Sicily. Methods In addition to the mathematical implementation of the GDM proposed by Whittaker, Triantis and Ladle, and termed here logATT² (, where S is species number or any other diversity metric, t is island age, A is island area, and a, b, c and d are fitted parameters), a new implementation based on the Arrhenius equation of the species–area relationship (SAR) is investigated. The new model (termed powerATT²) is: . For logATT² and powerATT² models, equations were developed to calculate (1) the expected number of species at equilibrium (i.e. when the island has reached maturity) per unit area (S_eq), and (2) the time required to obtain this value (t_eq). Whereas the intercept in the Gleason model (S = C + z log A) or the coefficient of the Arrhenius power model (S = CA^z) of the SAR can be considered measures of the expected number of species per unit area, this is not the case for the parameter a of the ATT² models. However, values of S_eq can be used for this purpose. The index of ‘colonization ability’ (CAB), calculated as the ratio , may provide a measure of the mean number of species added per unit area per unit time. Results Both ATT² models fitted most of the data well, but the powerATT² model was in most cases superior. Equilibrial values of species richness (S_eq) varied from c. 3 species km^?2 (reptiles) to 100 species km^?2 (mites). The fitted curves for the powerATT² model showed large variations in d, from 0.03 to 3. However, most groups had values of d around 0.2–0.4, as commonly observed for the z‐values of SARs modelled by a power function. Equilibration times ranged from about 170,000 years to 400,000 years. Mites and springtails had very high values of CAB, thus adding many more species per unit area per unit time than others. Reptiles and phytophagous scarabs showed very low values, being the groups that added fewest species per unit area per unit time. Main conclusions Values of equilibrial species richness per unit area are influenced by species biology (e.g. body size and ecological specialization). Theoretical and empirical evidence suggests that higher immigration rates should increase the z‐values of the Arrhenius model. Thus, in the same archipelago, groups with larger z‐values should be characterized by higher dispersal ability. Results obtained here for the parameter d conform to this prediction.     

Cross‐biome transplants of plant litter show decomposition models extend to a broader climatic range but lose predictability at the decadal time scale

We analyzed results from 10‐year long field incubations of foliar and fine root litter from the Long‐term Intersite Decomposition Experiment Team (LIDET) study. We tested whether a variety of climate and litter quality variables could be used to develop regression models of decomposition parameters across wide ranges in litter quality and climate and whether these models changed over short to long time periods. Six genera of foliar and three genera of root litters were studied with a 10‐fold range in the ratio of acid unhydrolyzable fraction (AUF, or ‘lignin’) to N. Litter was incubated at 27 field sites across numerous terrestrial biomes including arctic and alpine tundra, temperate and tropical forests, grasslands and warm deserts. We used three separate mathematical models of first‐order (exponential) decomposition, emphasizing either the first year or the entire decade. One model included the proportion of relatively stable material as an asymptote. For short‐term (first‐year) decomposition, nonlinear regressions of exponential or power function form were obtained with r² values of 0.82 and 0.64 for foliar and fine‐root litter, respectively, across all biomes included. AUF and AUF : N ratio were the most explanative litter quality variables, while the combined temperature‐moisture terms AET (actual evapotranspiration) and CDI (climatic decomposition index) were best for climatic effects. Regressions contained some systematic bias for grasslands and arctic and boreal sites, but not for humid tropical forests or temperate deciduous and coniferous forests. The ability of the regression approach to fit climate‐driven decomposition models of the 10‐year field results was dramatically reduced from the ability to capture drivers of short‐term decomposition. Future work will require conceptual and methodological improvements to investigate processes controlling decadal‐scale litter decomposition, including the formation of a relatively stable fraction and its subsequent decomposition.     

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.     

On the use of log‐transformation versus nonlinear regression for analyzing biological power laws

Xiao and colleagues re‐examined 471 datasets from the literature in a major study comparing two common procedures for fitting the allometric equation y = ax^b to bivariate data (Xiao et al., 2011). One of the procedures was the traditional allometric method, whereby the model for a straight line fitted to logarithmic transformations of the original data is back‐transformed to form a two‐parameter power function with multiplicative, lognormal, heteroscedastic error on the arithmetic scale. The other procedure was standard nonlinear regression, whereby a two‐parameter power function with additive, normal, homoscedastic error is fitted directly to untransformed data by nonlinear least squares. Xiao and colleagues articulated a simple (but explicit) protocol for fitting and comparing the alternative models, and then used the protocol to examine each of the datasets in their compilation. The traditional method was said to provide a better fit in 69% of the cases and an equivalent fit in another 15%, so the investigation appeared to validate findings from a large majority of prior studies on allometric variation. However, focus for the investigation by Xiao and colleagues was overly narrow, and statistical models apparently were not validated graphically in the scale of measurement. The present study re‐examined a subset of the cases using a larger pool of candidate models and graphical validation, and discovered complexities that were overlooked in their investigation. Some datasets that appeared to be described better by the traditional method actually were unsuited for use in an allometric analysis, whereas other datasets were not described adequately by a two‐parameter power function, regardless of how the model was fitted. Thus, conclusions reached by Xiao and colleagues are not well supported and their paradigm for fitting allometric equations is unreliable. Future investigations of allometric variation should adopt a more holistic approach and incorporate graphical validation on the original arithmetic scale. © 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 113 , 1167–1178.     

Allometric Models for Tree Volume and Total Aboveground Biomass in a Tropical Humid Forest in Costa Rica1

Allometric equations for the estimation of tree volume and aboveground biomass in a tropical humid forest were developed based on direct measurements of 19 individuals of seven tree species in Northern Costa Rica. The volume and the biomass of the stems represented about two‐thirds of the total volume and total aboveground biomass, respectively. The average stem volume varied between 4 and 11 Mg/tree and the average total aboveground biomass ranged from 4 to 10 mg/tree. The mean specific gravity of the sampled trees was 0.62 ± 0.06 (g/cm³). The average biomass expansion factor was 1.6 ± 0.2. The best‐fit equations for stem and total volume were of logarithmic form, with diameter at breast height (R²= 0.66 ? 0.81) as an independent variable. The best‐fit equations for total aboveground biomass that were based on combinations of diameter at breast height, and total and commercial height as independent variables had R² values between 0.77 and 0.87. Models recommended for estimating total aboveground biomass are based on diameter at breast height, because the simplicity of these models is advantageous. This variable is easy to measure accurately in the field and is the most common variable recorded in forest inventories. Two widely used models in literature tend to underestimate aboveground biomass in large trees. In contrast, the models developed in this study accurately estimate the total aboveground biomass in these trees.     

The maximal body mass–area relationship in island mammals

Aim A positive power relationship between maximal body mass and land area has previously been reported of the form M_max ∝ Area^0.5 whilst allometric scaling theory predicts either M_max ∝ Area^1.33 or M_max ∝ Area¹. We provide an analysis of the maximal mass–area relationship for four island systems, to test the hypothesis that community relaxation following isolation converges in each case to a slope of Area^0.5. Location Islands of the Japanese archipelago, the western Mediterranean, the Sea of Cortés and Southeast Asia. Methods We calculated the relationship between island area and the maximal body mass of the largest mammal species on the island using linear regression models with log‐transformed variables, and tested the hypothesis that the slopes were not significantly different from 0.5. Results We found a slope of 0.47 within the Japanese archipelago, 0.42 for western Mediterranean islands, 0.73 for the Sea of Cortés islands and 0.50 for Southeast Asian islands. None of these slopes were significantly different from 0.5. Main conclusions Our results provide further empirical support for previous findings of a general maximal body mass–area relationship of M_max ∝ Area^0.5, but they deviate from theoretical predictions. We hypothesize that this mass–area relationship was the ultimate end point of community relaxation initiated by the isolation of the mammal communities. Maximal body mass on each island today probably reflects the interaction between energetic constraints, home range size and island area.     

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.     

A general dynamic theory of oceanic island biogeography

Aim MacArthur and Wilson’s dynamic equilibrium model of island biogeography provides a powerful framework for understanding the ecological processes acting on insular populations. However, their model is known to be less successful when applied to systems and processes operating on evolutionary and geological timescales. Here, we present a general dynamic model (GDM) of oceanic island biogeography that aims to provide a general explanation of biodiversity patterns through describing the relationships between fundamental biogeographical processes – speciation, immigration, extinction – through time and in relation to island ontogeny. Location Analyses are presented for the Azores, Canaries, Galápagos, Marquesas and Hawaii. Methods We develop a theoretical argument from first principles using a series of graphical models to convey key properties and mechanisms involved in the GDM. Based on the premises (1) that emergent properties of island biotas are a function of rates of immigration, speciation and extinction, (2) that evolutionary dynamics predominate in large, remote islands, and (3) that oceanic islands are relatively short‐lived landmasses showing a characteristic humped trend in carrying capacity (via island area, topographic variation, etc.) over their life span, we derive a series of predictions concerning biotic properties of oceanic islands. We test a subset of these predictions using regression analyses based largely on data sets for native species and single‐island endemics (SIEs) for particular taxa from each archipelago, and using maximum island age estimates from the literature. The empirical analyses test the power of a simple model of diversity derived from the GDM: the log(Area) + Time + Time² model (ATT²), relative to other simpler time and area models, using several diversity metrics. Results The ATT² model provides a more satisfactory explanation than the alternative models evaluated (for example the standard diversity–area models) in that it fits a higher proportion of the data sets tested, although it is not always the most parsimonious solution. Main conclusions The theoretical model developed herein is based on the key dynamic biological processes (migration, speciation, extinction) combined with a simple but general representation of the life cycle of oceanic islands, providing a framework for explaining patterns of biodiversity, endemism and diversification on a range of oceanic archipelagos. The properties and predictions derived from the model are shown to be broadly supported (1) by the empirical analyses presented, and (2) with reference to previous phylogenetic, ecological and geological studies.     

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.     

Analytical Quantile Solution for the S‐distribution,Random Number Generation and Statistical Data Modeling

The selection of a specific statistical distribution as a model for describing the population behavior of a given variable is seldom a simple problem. One strategy consists in testing different distributions (normal, lognormal, Weibull, etc.), and selecting the one providing the best fit to the observed data and being the most parsimonious. Alternatively, one can make a choice based on theoretical arguments and simply fit the corresponding parameters to the observed data. In either case, different distributions can give similar results and provide almost equivalent models for a given data set. Model selection can be more complicated when the goal is to describe a trend in the distribution of a given variable. In those cases, changes in shape and skewness are difficult to represent by a single distributional form. As an alternative to the use of complicated families of distributions as models for data, the S‐distribution [Voit, E. O. (1992) Biom. J. 7 , 855–878] provides a highly flexible mathematical form in which the density is defined as a function of the cumulative. S‐distributions can accurately approximate many known continuous and unimodal distributions, preserving the well known limit relationships between them. Besides representing well‐known distributions, S‐distributions provide an infinity of new possibilities that do not correspond with known classical distributions. Although the utility and performance of this general form has been clearly proved in different applications, its definition as a differential equation is a potential drawback for some problems. In this paper we obtain an analytical solution for the quantile equation that highly simplifies the use of S‐distributions. We show the utility of this solution in different applications. After classifying the different qualitative behaviors of the S‐distribution in parameter space, we show how to obtain different S‐distributions that accomplish specific constraints. One of the most interesting cases is the possibility of obtaining distributions that acomplish P(X ≤ X_c) = 0. Then, we demonstrate that the quantile solution facilitates the use of S‐distributions in Monte‐Carlo experiments through the generation of random samples. Finally, we show how to fit an S‐distribution to actual data, so that the resulting distribution can be used as a statistical model for them.