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.     

Should we use proportional sampling for species–area studies?

Aim In this paper we aim to show that proportional sampling can detect species–area relationships (SARs) more effectively than uniform sampling. We tested the contribution of alpha and beta diversity in ant communities as explanations for the SAR. Location Tropical forest remnants in Viçosa, Minas Gerais, Brazil (20 °45′ S, 42 °50′ W). Methods We sampled 17 forest remnants with proportional sampling. To disentangle sampling effects from other mechanisms, species richness was fitted in a model with remnant size, number of samples (sampling effects) and an interaction term. Results A SAR was observed independent of the number of samples, discarding sampling effects. Alpha diversity was not influenced by remnant size, and beta diversity increased with remnant size; evidence to the fact that habitat diversity within remnants could be the dominant cause of the SAR. Such a relationship between beta diversity and remnant area may have also arisen due to the combined effects of territoriality and aggregation of ant species. Main conclusions The proposed model, together with proportional sampling, allowed the distinction between sampling effects and other mechanisms.     

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.     

Evaluation of different observational sampling regimes for use in zoological parks

Observational sampling methods provide clearly-defined guidelines for collection and analysis of behavioral data. In some situations, use of formal sampling regimes may be impractical or impossible. A case in point is data collection conducted by animal care staff at zoological parks and aquaria. Often, time is sufficiently limited that data collection is perceived as a task that cannot be accomplished given the normal constraints of the day. Here, we explore the efficacy and validity of using more variable and abridged sampling regimes in an effort to identify the appropriateness of such observation schemes for systematic monitoring of behavior. We describe the results of studies on three species (two polar bears, an Atlantic bottlenose dolphin calf, and two brown bears), conducted over a period of several years at the Brookfield Zoo, Brookfield, Illinois, USA. Data collection schemes varied both within and across groups in order to provide a basis of comparison. In all cases, there were significant differences based on sampling regime for rare behaviors (those that individually comprised <15% of the activity budget), but not for common behaviors. Subsampling from larger data sets indicated that data reliability increases with increasing observation number. We discuss the strengths and weaknesses of such sporadic sampling methods, and suggest that, in many instances such limited data collection may yet yield an accurate picture of animal activity and should not be overlooked as a viable management tool.     

Sequential sampling: a novel method in farm animal welfare assessment

Lameness in dairy cows is an important welfare issue. As part of a welfare assessment, herd level lameness prevalence can be estimated from scoring a sample of animals, where higher levels of accuracy are associated with larger sample sizes. As the financial cost is related to the number of cows sampled, smaller samples are preferred. Sequential sampling schemes have been used for informing decision making in clinical trials. Sequential sampling involves taking samples in stages, where sampling can stop early depending on the estimated lameness prevalence. When welfare assessment is used for a pass/fail decision, a similar approach could be applied to reduce the overall sample size. The sampling schemes proposed here apply the principles of sequential sampling within a diagnostic testing framework. This study develops three sequential sampling schemes of increasing complexity to classify 80 fully assessed UK dairy farms, each with known lameness prevalence. Using the Welfare Quality herd-size-based sampling scheme, the first ‘basic’ scheme involves two sampling events. At the first sampling event half the Welfare Quality sample size is drawn, and then depending on the outcome, sampling either stops or is continued and the same number of animals is sampled again. In the second ‘cautious’ scheme, an adaptation is made to ensure that correctly classifying a farm as ‘bad’ is done with greater certainty. The third scheme is the only scheme to go beyond lameness as a binary measure and investigates the potential for increasing accuracy by incorporating the number of severely lame cows into the decision. The three schemes are evaluated with respect to accuracy and average sample size by running 100 000 simulations for each scheme, and a comparison is made with the fixed size Welfare Quality herd-size-based sampling scheme. All three schemes performed almost as well as the fixed size scheme but with much smaller average sample sizes. For the third scheme, an overall association between lameness prevalence and the proportion of lame cows that were severely lame on a farm was found. However, as this association was found to not be consistent across all farms, the sampling scheme did not prove to be as useful as expected. The preferred scheme was therefore the ‘cautious’ scheme for which a sampling protocol has also been developed.     

Random placement models predict species–area relationships in duck communities despite species aggregation

Species–area relationships are the product of many ecological processes and their interactions. Explanations for the species–area relationship (SAR) have focused on separating putative niche‐based mechanisms that correlate with area from sampling effects caused by patches with more individuals containing more species than patches with fewer individuals. We tested the hypothesis that SARs in breeding waterfowl communities are caused by sampling effects (i.e. random placement from the regional species pool). First, we described observed SARs and patterns of species associations for fourteen species of ducks on ponds in prairie Canada. Second, we used null models, which randomly allocated ducks to ponds, to test if observed SARs and patterns of species associations differed from those expected by chance. Consistent with the sampling effects hypothesis, observed SARs were accurately predicted by null models in three different years and for diving and dabbling duck guilds. This is the first demonstration that null models can predict SARs in waterbirds or any other aquatic organisms. Observed patterns of species association, however, were not well predicted by null models as in all years there was less observed segregation among species (i.e. more aggregation) than under the random expectation, suggesting that intraspecific competition could play a role in structuring duck communities. Taken together, our results indicate that when emergent properties of ecological communities such as the SAR appear to be caused by random processes, analyses of species associations can be critical in revealing the importance of niche‐based processes (e.g. competition) in structuring ecological communities.     

Linking species richness curves from non-contiguous sampling to contiguous-nested SAR: An empirical study

The species–area relationship (SAR) is one of the few generalizations in ecology. However, many different relationships are denoted as SARs. Here, we empirically evaluated the differences between SARs derived from nested-contiguous and non-contiguous sampling designs, using plants, birds and butterflies datasets from Great Britain, Greece, Massachusetts, New York and San Diego. The shape of SAR depends on the sampling scheme, but there is little empirical documentation on the magnitude of the deviation between different types of SARs and the factors affecting it. We implemented a strictly nested sampling design to construct nested-contiguous SAR (SA_CR), and systematic nested but non-contiguous, and random designs to construct non-contiguous species richness curves (SA_SRs for systematic and SACs for random designs) per dataset. The SA_CR lay below any SA_SR and most of the SACs. The deviation between them was related to the exponent f of the power law relationship between sampled area and extent. The lower the exponent f, the higher was the deviation between the curves. We linked SA_CR to SA_SR and SAC through the concept of “effective” area (A_e), i.e. the nested-contiguous area containing equal number of species with the accumulated sampled area (A_S) of a non-contiguous sampling. The relationship between effective and sampled area was modeled as log(A_e) = klog(A_S). A Generalized Linear Model was used to estimate the values of k from sampling design and dataset properties. The parameter k increased with the average distance between samples and with beta diversity, while k decreased with f. For both systematic and random sampling, the model performed well in predicting effective area in both the training set and in the test set which was totally independent from the training one. Through effective area, we can link different types of species richness curves based on sampling design properties, sampling effort, spatial scale and beta diversity patterns.     

Pitfalls in Small-Scale Species-Area Sampling and Analysis

Analyses of the dependency of species richness (S) on area (A), the so-called species-area relationships (SARs), are widespread approaches to characterize and compare biodiversity patterns. This article highlights – with a focus on small-scale SARs of plants in continuous ecosystems – how inappropriate sampling methods or theoretical misconceptions can create artifacts and thus may lead to wrong conclusions. Most of these problems have been recognized before but continue to appear regularly in the scientific literature. The following main points are reviewed and discussed: i) Species richness values and SARs depend on the measurement method (any-part vs. grid-point system); ii) Species-richness values depend on the shape of the analyzed plots; iii) Many published SARs are not true SARs but instead represent species sampling curves or their data points consist of richness totals for incontiguous subplots; iv) Nested-plot design is the preferred sampling method for SARs (the claim that this approach would cause pseudoreplication is erroneous); v) SARs should be constructed using mean values of several counts for the smaller areas; vi) SAR functions can be fitted and selected both in the S- and the log S-space but this must be done consistently for all compared function types. It turns out that the finding of non-power function SARs in many studies is due to a lack of awareness of one or several of the named points. Thus, power-function SARs are even more widespread than a recent review would suggest. I therefore propose to use the power law as a universal model for all types of SARs but to test whether the slope z varies with spatial scale. Finally, I urge readers to be aware of the many pitfalls in SAR studies, to fully disclose methodology, and to apply a meaningful and consistent terminology, especially by restricting the terms “species-area relationship” and “species density” to situations in which each data point represents a contiguous area.     

Building anisotropic sampling schemes for the estimation of anisotropic dispersal

Anisotropy, a structural property of dispersal, is observed in dispersal patterns occurring for a wide range of biological systems. While dispersal models more and more often incorporate anisotropy, the sampling schemes required to collect data for validation usually do not account for the anisotropy of dispersal data. Using a parametric model already published to describe the spatial spread of a plant disease, the wheat yellow rust, we carry out a study aimed at recommending an appropriate sampling scheme for anisotropic data. In a first step, we show with a simulation study that prior knowledge of dispersal anisotropy can be used to improve the sampling scheme. One of the main guidelines to be proposed is the orientation of the sampling grid around the main dispersal directions. In a second step, we propose a sequential sampling procedure (SSP) used to automatically build anisotropic sampling schemes adapted to the actual anisotropy of dispersal. The SSP is applied to simulated and real data. The proposed methodology is expected to be adapted easily to any kind of organisms with wind-borne propagule dispersal because it does not require the inclusion of biological features specific of the considered organism.     

Age structure in neutral theory resolves inconsistencies related to reproductive-size threshold

Aims Neutral theory consists of a suite of models that assume ecological equivalence among individual organisms. They have been most commonly applied to tropical forest tree communities either as null models or as approximations. Neutral models typically only include reproductive adults; therefore, fitting to empirical tree community data requires defining a reproductive-size threshold, which for trees is usually set arbitrarily to a diameter at breast height (DBH) of 100 mm. The inevitable exclusion of some reproductive adults and inclusion of some saplings cause a non-random sampling bias in neutral model fits. Here, we investigate this problem and resolve it by introducing simple age structure into a neutral model.Methods We compared the performance and sensitivity of DBH threshold of three variants of a spatially explicit neutral model: the traditional model, a model incorporating random sampling and a model with two distinct age classes—reproductive adults and saplings. In the age-structured model, saplings are offspring from adults that disperse according to a Gaussian dispersal kernel around the adults. The only extra parameter is the ratio of adults to saplings, which is not a free parameter but directly measurable. We used species–area relationships (SARs) to explore the predicted effect of saplings on the species richness at different scales in our model. We then evaluated the three model variations to find the parameters required to maintain the observed level of species richness in the 50-ha plot on Barro Colorado Island (BCI). We repeated our analysis filtering the data at different minimum tree-size thresholds in order to find the effect this threshold has on our results. Lastly, we used empirical species–individual relationships (SIRs) to test the pre-existing hypothesis that environmental filtering is the primary cause of differences between the assemblage of saplings and that of adults on BCI.Important findings Our age-structured neutral model was characterized by SARs that were insensitive to the presence of saplings at large scales and highly sensitive to them at small scales. Both models without age structure were highly sensitive to the DBH threshold chosen in a way that could not be explained based on random samplings alone. The age-structured neutral model, which allowed for non-random sampling based on life stage, was consistent with species richness observations. Our analysis of empirical SIRs did not support environmental filtering as a dominant force, but it did show evidence for other differences between age classes. Age can now be easily incorporated into future studies of neutral models whenever there is a concern that a sample is not entirely composed of reproductive adult individuals. More generally, we suggest that modeling studies using tree data subject to a minimum size threshold should consider the sensitivity of their results to that threshold.     

Evolutionary species–area curves as revealed by single-island endemics: insights for the inter-provincial species–area relationship

The species–area relationship (SAR) between different biological provinces is one of the most interesting, but least explored aspects of the well-known species–area pattern. Following the usage that a biological province is a region whose species have for the most part evolved within it, rather than immigrating from somewhere else, we propose that islands can be considered equivalent to biological provinces for single island endemic species (SIEs). Hence, analyses of the relationships between numbers of SIEs and island area can be used as model systems to explore the form of inter-provincial SARs. We analyzed 13 different data sets derived from 11 sources, using the power (log–log) model. Eleven of the SIE–area relationships were statistically significant, explaining high proportions of the variance in SIE numbers (R² 0.57–0.95). The z-values (slopes) of the statistically significant SIE–area relationships ranged from 0.47 to 1.13, with a mean value of 0.80 (SD±0.24).
All the island systems in which SIE represent >50% of species exhibited z-values for the SARs of native species higher than those deemed typical of archipelagic SARs. The SIE–area slopes are quite similar to those previously calculated for inter-provincial SARs, indicating that, when speciation becomes the dominant process adding to the species richness of assemblages, high z-values should be anticipated, regardless of the biogeographical scale of the study system.     

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.     

Freshwater bacterioplankton richness in oligotrophic lakes depends on nutrient availability rather than on species–area relationships

A central goal in ecology is to grasp the mechanisms that underlie and maintain biodiversity and patterns in its spatial distribution can provide clues about those mechanisms. Here, we investigated what might determine the bacterioplankton richness (BR) in lakes by means of 454 pyrosequencing of the 16S rRNA gene. We further provide a BR estimate based upon a sampling depth and accuracy, which, to our knowledge, are unsurpassed for freshwater bacterioplankton communities. Our examination of 22 669 sequences per lake showed that freshwater BR in fourteen nutrient-poor lakes was positively influenced by nutrient availability. Our study is, thus, consistent with the finding that the supply of available nutrients is a major driver of species richness; a pattern that may well be universally valid to the world of both micro- and macro-organisms. We, furthermore, observed that BR increased with elevated landscape position, most likely as a consequence of differences in nutrient availability. Finally, BR decreased with increasing lake and catchment area that is negative species–area relationships (SARs) were recorded; a finding that re-opens the debate about whether positive SARs can indeed be found in the microbial world and whether positive SARs can in fact be pronounced as one of the few ‘laws'' in ecology.     

Phylogenetic relationships among seed plants: Persistent questions and the limits of molecular data

Trees inferred from DNA sequence data provide only limited insight into the phylogeny of seed plants because the living lineages (cycads, Ginkgo, conifers, gnetophytes, and angiosperms) represent fewer than half of the major lineages that have been detected in the fossil record. Nevertheless, phylogenetic trees of living seed plants inferred from sequence data can provide a test of relationships inferred in analyses that include fossils. So far, however, significant uncertainty persists because nucleotide data support several conflicting hypotheses. It is likely that improved sampling of gymnosperm diversity in nucleotide data sets will help alleviate some of the analytical issues encountered in the estimation of seed plant phylogeny, providing a more definitive test of morphological trees. Still, rigorous morphological analyses will be required to answer certain fundamental questions, such as the identity of the angiosperm sister group and the rooting of crown seed plants. Moreover, it will be important to identify approaches for incorporating insights from data that may be accurate but less likely than sequence data to generate results supported by high bootstrap values. How best to weigh evidence and distinguish among hypotheses when some types of data give high support values and others do not remains an important problem.     

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.     

Species–area relationship and a tentative interpretation of the function coefficients in an ecosystem simulation

In this paper, we identified the best species–area relationship (SAR) models from amongst 28 different models gathered from the literature, using an artificial predator–prey simulation (EcoSim), along with investigating how sampling approaches and sampling scales affect SARs. Further, we attempted to determine a plausible interpretation of SAR model coefficients for the best performing SAR models. This is the most extensive quantitatively based investigation of the species–area relationship so far undertaken in the literature.We gathered 28 different models from the literature and fitted them to sampling data from EcoSim using non-linear regression and ΔAICc as the goodness-of-fit criterion. Afterwards, we proposed a machine-learning approach to find plausible relationships between the models’ coefficients and the spatial information that likely affect SARs, as a basis for extracting rules that provide an interpretation of SAR coefficients.We found the power function family to be a reasonable choice and in particular the Plotkin function based on ΔAICc ranking. The Plotkin function was consistently in the top three in terms of the best ranked SAR functions. Furthermore, the simple power function was the best-ranked model in nested sampling amongst models with two coefficients. We found that the Plotkin, quadratic power, Morgan–Mercer–Floid and the generalized cumulative Weibull functions are the best ranked models for small, intermediate, large, and very large scales, respectively, in nested sampling, while Plotkin (in small to intermediate scales) and Chapman–Richards (in large to very large scales) are the best ranked functions in random sampling. Finally, based on rule extractions using machine-learning techniques we were able to find interpretations of the coefficients for the simple and extended power functions. For instance, function coefficients corresponded to sampling scale size, patch number, fractal dimension, average patch size, and spatial complexity.Our main conclusions are that SAR models are highly dependent on sampling scale and sampling approach and that the shape of the best ranked SAR model is convex without an asymptote for smaller scales (small, intermediate) and it is sigmoid for larger scales (large and very large). For some of the SAR model coefficients, there are clear correlations with spatial information, thereby providing an interpretation of these coefficients. In addition, the slope z measuring the rate of species increase for SAR models in the power function family was found to be directly proportional to beta diversity, which confirms the view that beta diversity and SAR models are to some extent both measures of species richness.     

Sampling design and the shape of species–area curves on the regional scale

Species–area relationships (SARs) are one of the fundamental patterns in ecology. However, how the way they were constructed influences resulting SAR shapes has gained astonishingly little attention. We use data of the distribution atlas of Polish butterflies to compare SARs constructed from four different designs: adding up species numbers of independent areas (species accumulation curves using contiguous and non-contiguous areas), using a nested design, and comparing species numbers of independent areas of different sizes. It appeared that the way of constructing SARs influences the outcome. We attribute this influence to the pronounced faunal dissimilarities of more distant areas (spatial species turnover). The nested design resulted in significantly higher slopes and lower intercepts of power function SARs than the other designs. SARs from all four sampling designs showed a pronounced downward curvature on small spatial scales. Only the nested design predicted species densities correctly. The implications of these results for the use of SARs in bioconservation are discussed.     

Gauging the effects of sampling failure in biogeographical analysis

Aim Various methods are employed to recover patterns of area relationships in extinct and extant clades. The fidelity of these patterns can be adversely affected by sampling error in the form of missing data. Here we use simulation studies to evaluate the sensitivity of an analytical biogeographical method, namely tree reconciliation analysis (TRA), to this form of sampling failure. Location Simulation study. Methods To approximate varying degrees of taxonomic sampling failure within phylogenies varying in size and in redundancy of biogeographical signal, we applied sequential pruning protocols to artificial taxon–area cladograms displaying congruent patterns of area relationships. Initial trials assumed equal probability of sampling failure among all areas. Additional trials assigned weighted probabilities to each of the areas in order to explore the effects of uneven geographical sampling. Pruned taxon–area cladograms were then analysed with TRA to determine if the optimal area cladograms recovered match the original biogeographical signal, or if they represent false, ambiguous or uninformative signals. Results The results indicate a period of consistently accurate recovery of the true biogeographical signal, followed by a nonlinear decrease in signal recovery as more taxa are pruned. At high levels of sampling failure, false biogeographical signals are more likely to be recovered than the true signal. However, randomization testing for statistical significance greatly decreases the chance of accepting false signals. The primary inflection of the signal recovery curve, and its steepness and slope depend upon taxon–area cladogram size and area redundancy, as well as on the evenness of sampling. Uneven sampling across geographical areas is found to have serious deleterious effects on TRA, with the accuracy of recovery of biogeographical signal varying by an order of magnitude or more across different sampling regimes. Main conclusions These simulations reiterate the importance of taxon sampling in biogeographical analysis, and attest to the importance of considering geographical, as well as overall, sampling failure when interpreting the robustness of biogeographical signals. In addition to randomization testing for significance, we suggest the use of randomized sequential taxon deletions and the construction of signal decay curves as a means to assess the robustness of biogeographical signals for empirical data sets.     

Drivers of moth species richness on tropical altitudinal gradients: a cross-regional comparison

Aims We examine the role of species–area relationships (SARs), climatic parameters and phylogeny in shaping the altitudinal species richness patterns of moths. With respect to SARs, we investigate whether habitat heterogeneity is a probable mechanism for mediating area effects. We investigate the consistency of patterns by comparing several discrete regions. Location Nine mountainous regions in tropical Asia and the Malay Archipelago. Methods Presence‐only records for 292 species of the Lepidopteran family Sphingidae were used to measure interpolated species richness in 200‐m altitudinal bands. Species richness was correlated with area measures, which were calculated from both two‐dimensional map projections and three‐dimensional digital elevation models (DEMs). We used data simulations of homogeneous communities to test for effects of sample (i.e. habitat) heterogeneity as a mechanism causing SARs. Species richness patterns were compared among regions and between the two major sphingid clades, and were related to regional climatic characteristics. Results The area of altitudinal bands was a strong (statistical) explanation of species richness, particularly if area was calculated from three‐dimensional DEMs, but SARs often over‐predict species richness in lowland areas. There was no evidence for habitat heterogeneity as a mechanism of altitudinal SARs (tested for Borneo only). Species richness patterns varied considerably between the nine regions, which may, as an alternative to SARs, be explained by climatic differences such as (temperature) seasonality. Phylogenetic clades differed in species richness patterns exhibited. Main conclusion SARs provide strong empirical explanations for (regional) altitudinal patterns of species richness, but lack of evidence for the most likely mechanism cautions against a priori ‘corrections’ of species richness data for area. Furthermore, SARs are often not a sufficient explanation for the drop in species richness towards lowlands. Climate, or other collinear variables, may offer alternative explanations for altitudinal SARs. More research is needed to understand the mechanisms for SARs in an altitudinal context in order to evaluate their importance in the face of parameter collinearity.     

Estimating incident population distribution from prevalent data

A prevalent sample consists of individuals who have experienced disease incidence but not failure event at the sampling time. We discuss methods for estimating the distribution function of a random vector defined at baseline for an incident disease population when data are collected by prevalent sampling. Prevalent sampling design is often more focused and economical than incident study design for studying the survival distribution of a diseased population, but prevalent samples are biased by design. Subjects with longer survival time are more likely to be included in a prevalent cohort, and other baseline variables of interests that are correlated with survival time are also subject to sampling bias induced by the prevalent sampling scheme. Without recognition of the bias, applying empirical distribution function to estimate the population distribution of baseline variables can lead to serious bias. In this article, nonparametric and semiparametric methods are developed for distribution estimation of baseline variables using prevalent data.