Aims In ecology and conservation biology, the number of species counted in a biodiversity study is a key metric but is usually a biased underestimate of total species richness because many rare species are not detected. Moreover, comparing species richness among sites or samples is a statistical challenge because the observed number of species is sensitive to the number of individuals counted or the area sampled. For individual-based data, we treat a single, empirical sample of species abundances from an investigator-defined species assemblage or community as a reference point for two estimation objectives under two sampling models: estimating the expected number of species (and its unconditional variance) in a random sample of (i) a smaller number of individuals (multinomial model) or a smaller area sampled (Poisson model) and (ii) a larger number of individuals or a larger area sampled. For sample-based incidence (presence–absence) data, under a Bernoulli product model, we treat a single set of species incidence frequencies as the reference point to estimate richness for smaller and larger numbers of sampling units.
Methods The first objective is a problem in interpolation that we address with classical rarefaction (multinomial model) and Coleman rarefaction (Poisson model) for individual-based data and with sample-based rarefaction (Bernoulli product model) for incidence frequencies. The second is a problem in extrapolation that we address with sampling-theoretic predictors for the number of species in a larger sample (multinomial model), a larger area (Poisson model) or a larger number of sampling units (Bernoulli product model), based on an estimate of asymptotic species richness. Although published methods exist for many of these objectives, we bring them together here with some new estimators under a unified statistical and notational framework. This novel integration of mathematically distinct approaches allowed us to link interpolated (rarefaction) curves and extrapolated curves to plot a unified species accumulation curve for empirical examples. We provide new, unconditional variance estimators for classical, individual-based rarefaction and for Coleman rarefaction, long missing from the toolkit of biodiversity measurement. We illustrate these methods with datasets for tropical beetles, tropical trees and tropical ants.
Important findings Surprisingly, for all datasets we examined, the interpolation (rarefaction) curve and the extrapolation curve meet smoothly at the reference sample, yielding a single curve. Moreover, curves representing 95% confidence intervals for interpolated and extrapolated richness estimates also meet smoothly, allowing rigorous statistical comparison of samples not only for rarefaction but also for extrapolated richness values. The confidence intervals widen as the extrapolation moves further beyond the reference sample, but the method gives reasonable results for extrapolations up to about double or triple the original abundance or area of the reference sample. We found that the multinomial and Poisson models produced indistinguishable results, in units of estimated species, for all estimators and datasets. For sample-based abundance data, which allows the comparison of all three models, the Bernoulli product model generally yields lower richness estimates for rarefied data than either the multinomial or the Poisson models because of the ubiquity of non-random spatial distributions in nature.

Aim Site occupancy probabilities of target species are commonly used in various ecological studies, e.g. to monitor current status and trends in biodiversity. Detection error introduces bias in the estimators of site occupancy. Existing methods for estimating occupancy probability in the presence of detection error use replicate surveys. These methods assume population closure, i.e. the site occupancy status remains constant across surveys, and independence between surveys. We present an approach for estimating site occupancy probability in the presence of detection error that requires only a single survey and does not require assumption of population closure or independence. In place of the closure assumption, this method requires covariates that affect detection and occupancy.
Methods Penalized maximum-likelihood method was used to estimate the parameters. Estimability of the parameters was checked using data cloning. Parametric boostrapping method was used for computing confidence intervals.
Important findings The single-survey approach facilitates analysis of historical datasets where replicate surveys are unavailable, situations where replicate surveys are expensive to conduct and when the assumptions of closure or independence are not met. This method saves significant amounts of time, energy and money in ecological surveys without sacrificing statistical validity. Further, we show that occupancy and habitat suitability are not synonymous and suggest a method to estimate habitat suitability using single-survey data.

Aims Fits of species-abundance distributions to empirical data are increasingly used to evaluate models of diversity maintenance and community structure and to infer properties of communities, such as species richness. Two distributions predicted by several models are the Poisson lognormal (PLN) and the negative binomial (NB) distribution; however, at least three different ways to parameterize the PLN have been proposed, which differ in whether unobserved species contribute to the likelihood and in whether the likelihood is conditional upon the total number of individuals in the sample. Each of these has an analogue for the NB. Here, we propose a new formulation of the PLN and NB that includes the number of unobserved species as one of the estimated parameters. We investigate the performance of parameter estimates obtained from this reformulation, as well as the existing alternatives, for drawing inferences about the shape of species abundance distributions and estimation of species richness.
Methods We simulate the random sampling of a fixed number of individuals from lognormal and gamma community relative abundance distributions, using a previously developed 'individual-based' bootstrap algorithm. We use a range of sample sizes, community species richness levels and shape parameters for the species abundance distributions that span much of the realistic range for empirical data, generating 1?000 simulated data sets for each parameter combination. We then fit each of the alternative likelihoods to each of the simulated data sets, and we assess the bias, sampling variance and estimation error for each method.
Important findings Parameter estimates behave reasonably well for most parameter values, exhibiting modest levels of median error. However, for the NB, median error becomes extremely large as the NB approaches either of two limiting cases. For both the NB and PLN,>90% of the variation in the error in model parameters across parameter sets is explained by three quantities that corresponded to the proportion of species not observed in the sample, the expected number of species observed in the sample and the discrepancy between the true NB or PLN distribution and a Poisson distribution with the same mean. There are relatively few systematic differences between the four alternative likelihoods. In particular, failing to condition the likelihood on the total sample sizes does not appear to systematically increase the bias in parameter estimates. Indeed, overall, the classical likelihood performs slightly better than the alternatives. However, our reparameterized likelihood, for which species richness is a fitted parameter, has important advantages over existing approaches for estimating species richness from fitted species-abundance models.

Aims A common assumption in ecology is that where a species is found to be most abundant must correspond to the environmental context in which the species performs the best (i.e. optimal niche space). This assumption is central to common conservation and management tools such as habitat suitability assessment and species distribution modeling. I test this hypothesis.
Methods I use the US Forest Inventory Assessment data for the abundance of trees across eastern North America. I use the FORAST tree-ring dataset for ontogenetic growth rate (tree-ring increment), a measure of niche performance and correlated with intrinsic rate of increase, r .
Important findings I find that across 15 species, there are significantly more negative correlations than expected by chance. This negative correlation between abundance and performance across space contradicts common assumptions but is consistent with an inclusive niche structuring of the community.

Aims Mechanisms contributing to species coexistence have at least one of two modes of action: (i) stabilization of populations through restoring forces and (ii) equalization of fitness across individuals of different species. Recently, ecologists have begun gleaning the relative roles of these by testing the predictions of neutral theory, which predicts the properties of communities under pure fitness equalization. This null hypothesis was rejected for forests of southern Ontario based on large-scale (~100 km) spatial synchrony evident in the fossil pollen record over the entire Holocene, and the argument that a species' relative abundance would instead vary independently at such distances in the absence of stabilizing mechanisms. This test of neutral theory was criticized based on the idea that the synchrony might be produced by dispersal alone. Here, I revisit this test of neutral theory by explicitly calculating the synchrony expected in these forests using a novel simulation method enabling examination of the distribution of a species over large spatial and temporal scales.
Methods A novel neutral simulation algorithm tracking only the focal species was used to calculate the neutral expectation for spatial synchrony properties examined empirically by Clark and MacLachlan [(2003) Stability of forest biodiversity. Nature 423 :635–8] using fossil pollen data from eight lake sites. The coefficient of variation (CV) in a species' relative abundance across the eight sites (initiated at about 10% with a small CV) was calculated for 10 runs over a 10?000 year time interval. The CV reflects the level of spatial synchrony in that less synchronous dynamics should lead to more variation across space (a higher equilibrium CV), and in particular, a greater increase in the CV over time from a small initial value. A 'two dimensional t' fat-tailed dispersal kernel was assumed with parameters set to the median derived from seed trap data for deciduous wind-dispersed trees. Robustness of results to assumed dispersal distance, density of trees on the landscape, site sizes, age at maturity and starting spatial distribution were checked.
Important findings In contrast to the prediction of Clark and MacLachlan that, in the absence of stabilization, the CV across the sites should increase over time from levels observed at the beginning of the Holocene, under fat-tailed dispersal my neutral model robustly predicted only a brief (50 years) and small increase in the CV. I conclude that purely fitness-equalized species coexistence cannot be rejected based on the observed lack of increase in the CV across the eight sites in southern Ontario over the Holocene. Synchronous variation in environmental factors could alternatively explain the observed synchrony without the need for stabilization. However, neither dispersal nor environmental synchrony seems likely explanations for the quick widespread recovery of Tsuga in the Holocene after its seeming decimation, likely due to a pest outbreak.

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.

Aims The neutral theory of biodiversity provides a powerful framework for modeling macroecological patterns and interpreting species assemblages. However, there remain several unsolved problems, including the effect of relaxing the assumption of strict neutrality to allow for empirically observed variation in vital rates and the 'problem of time'—empirically measured coexistence times are much shorter than the prediction of the strictly neutral drift model. Here, we develop a nearly neutral model that allows for differential birth and death rates of species. This model provides an approach to study species coexistence away from strict neutrality.
Methods Based on Moran's neutral model, which assumes all species in a community have the same competitive ability and have identical birth and death rates, we developed a model that includes birth–death trade-off but excludes speciation. This model describes a wide range of asymmetry from strictly neutral to nearly neutral to far from neutral and is useful for analyzing the effect of drift on species coexistence. Specifically, we analyzed the effects of the birth–death trade-off on the time and probability of species coexistence and quantified the loss of biodiversity (as measured by Simpson's diversity) due to drift by varying species birth and death rates.
Important findings We found (i) a birth–death trade-off operating as an equalizing force driven by demographic stochasticity promotes the coexistence of nearly neutral species. Species near demographic trade-offs (i.e. fitness equivalence) can coexist even longer than that predicted by the strictly neutral model; (ii) the effect of birth rates on species coexistence is very similar to that of death rates, but their compensatory effects are not completely symmetric; (iii) ecological drift over time produces a march to fixation. Trade-off-based neutral communities lose diversity more slowly than the strictly neutral community, while non-neutral communities lose diversity much more rapidly; and (iv) nearly neutral systems have substantially shorter time of coexistence than that of neutral systems. This reduced time provides a promising solution to the problem of time.

Aims Much recent theory has focused on the role of neutral processes in assembling communities, but the basic assumption that all species are demographically identical has found little empirical support. Here, we show that the framework of the current neutral theory can easily be generalized to incorporate species differences so long as fitness equivalence among individuals is maintained through trade-offs between birth and death.
Methods Our theory development is based on a careful reformulation of the Moran model of metacommunity dynamics in terms of a non-linear one-step stochastic process, which is described by a master equation.
Important findings We demonstrate how fitness equalization through demographic trade-offs can generate significant macroecological diversity patterns, leading to a very different interpretation of the relation between Fisher's α and Hubbell's fundamental biodiversity number. Our model shows that equal fitness (not equal demographics) significantly promotes species diversity through strong selective sieving of community membership against high-mortality species, resulting in a positive association between species abundance and per capita death rate. An important implication of demographic trade-off is that it can partly explain the excessively high speciation rates predicted by the neutral theory of the stronger symmetry. Fitness equalization through demographic trade-offs generalizes neutral theory by considering heterospecific demographic difference, thus representing a significant step toward integrating the neutral and niche paradigms of biodiversity.

Aims The neutral theory of biodiversity has been criticized for being fragile with even slight deviations from its basic assumption of equal fitness among species. In response to this criticism, Hubbell ((2001) The Unified Neutral Theory of Biodiversity and Biogeography. Princeton, NJ: Princeton University Press) proposed that competitive exclusion can be infinitely delayed by dispersal and recruitment limitation, thus making species effectively neutral. But the theoretical foundation for this claim still remains unclear and controversial, and the effects of dispersal and recruitment limitation are often confounded, especially in field studies. This study aims to provide an affirmative theoretical answer to the question of whether dispersal limitation and recruitment limitation can separately or jointly overwhelm the effects of fitness differences among species and lead to neutral community dynamics.
Methods Computer simulations were used to investigate the effects of dispersal and recruitment limitation on delaying competitive exclusion in a homogeneous habitat in a spatially explicit context.
Important findings We found that even a slight competitive asymmetry would require extremely strong dispersal and recruitment limitation for neutrality to emerge. Most importantly, when the effects of dispersal and recruitment limitation were set apart, it is found that recruitment limitation is more effective in delaying competitive exclusion, whereas dispersal limitation tends to have a stronger impact on the general shape of both species abundance distributions and species–area relationships.

Aims We compare performance of ecosystem classification maps and provincial forest inventory data derived from air photography in reflecting ground beetle (Coleoptera: Carabidae) biodiversity patterns that are related to the forest canopy mosaic. Our biodiversity surrogacy model based on remotely sensed tree canopy cover is validated against field-collected ground data.
Methods We used a systematic sampling grid of 198 sites, covering 84 km 2 of boreal mixedwood forest in northwestern Alberta, Canada. For every site, we determined tree basal area, characterized the ground beetle assemblage and obtained corresponding provincial forest inventory and ecosystem classification information. We used variation partitioning, ordination and misclassification matrices to compare beetle biodiversity patterns explained by alternative databases and to determine model biases originating from air photo-interpretation.
Important findings Ecosystem classification data performed better than canopy cover derived from forest inventory maps in describing ground beetle biodiversity patterns. The biodiversity surrogacy models based on provincial forest inventory maps and field survey generally detected similar patterns but inaccuracies in air photo-interpretation of relative canopy cover led to differences between the two models. Compared to field survey data, air photo-interpretation tended to confuse two Picea species and two Populus species present and homogenize stand mixtures. This generated divergence in models of ecological association used to predict the relationship between ground beetle assemblages and tree canopy cover. Combination of relative canopy cover from provincial inventory with other geo-referenced land variables to produce the ecosystem classification maps improved biodiversity predictive power. The association observed between uncommon surrogates and uncommon ground beetle species emphasizes the benefits of detecting these surrogates as a part of landscape management. In order to complement conservation efforts established in protected areas, accurate, high resolution, wide ranging and spatially explicit knowledge of landscapes under management is primordial in order to apply effective biodiversity conservation strategies at the stand level as required in the extensively harvested portion of the boreal forest. In development of these strategies, an in-depth understanding of vegetation is key.

Aims Australia is among one of the world's wealthiest nations; yet, its relatively small human population (22.5 million) has been responsible for extensive deforestation and forest degradation since European settlement in the late 18th century. Despite most (~75%) of Australia's 7.6 million-km 2 area being covered in inhospitable deserts or arid lands generally unsuitable to forest growth, the coastal periphery has witnessed a rapid decline in forest cover and quality, especially over the last 60 years. Here I document the rates of forest loss and degradation in Australia based on a thorough review of existing literature and unpublished data.
Important findings Overall, Australia has lost nearly 40% of its forests, but much of the remaining native vegetation is highly fragmented. As European colonists expanded in the late 18th and the early 19th centuries, deforestation occurred mainly on the most fertile soils nearest to the coast. In the 1950s, southwestern Western Australia was largely cleared for wheat production, subsequently leading to its designation as a Global Biodiversity Hotspot given its high number of endemic plant species and rapid clearing rates. Since the 1970s, the greatest rates of forest clearance have been in southeastern Queensland and northern New South Wales, although Victoria is the most cleared state. Today, degradation is occurring in the largely forested tropical north due to rapidly expanding invasive weed species and altered fire regimes. Without clear policies to regenerate degraded forests and protect existing tracts at a massive scale, Australia stands to lose a large proportion of its remaining endemic biodiversity. The most important implications of the degree to which Australian forests have disappeared or been degraded are that management must emphasize the maintenance of existing primary forest patches, as well as focus on the regeneration of matrix areas between fragments to increase native habitat area, connectivity and ecosystem functions.