Biodiversity survey and estimation for line-transect sampling.

Conducting biodiversity surveys using a fully randomised design can be difficult due to budgetary constraints (e.g., the cost of labour), site accessibility, and other constraints. To this end, ecologists usually select representative line transects or quadrats from a studied area to collect individuals of a given species and use this information to estimate the levels of biodiversity over an entire region. However, commonly used biodiversity estimators such as Rao's quadratic diversity index (and especially the Gini-Simpson index) were developed based on the assumption of independent sampling of individuals. Therefore, their performance can be compromised or even misleading when applied to species abundance datasets that are collected from non-independent sampling. In this study, we utilise a Markov chain model and derive an associated parameter estimator to account for non-independence in sequential sampling. Empirical tests on two forest plots in tropical (Barro Colorado, Island of Panama) and subtropical (Heishiding Nature Reserve of Guangdong, China) regions and the continental-scale spatial distribution of Acacia species in Australia showed that our estimators performed reasonably well. The estimated parameter measuring the degree of non-independence of subsequent sampling showed that a non-independent effect is very likely to occur when using line transects to sample organisms in subtropical regions at both local and regional spatial scales. In summary, based on a first-order Markov sampling model and using Rao's quadratic diversity index as an example, our study provides an improvement in diversity estimation while simultaneously accounting for the non-independence of sampling in field biodiversity surveys. Our study presents one possible solution for addressing the non-independent sampling of individuals in biodiversity surveys.

Population and Conservation Status of the Flying Fox Pteropus dasymallus in Taiwan.

Pteropus dasymallus is widely distributed on islands throughout the western edge of the Pacific Ocean. The Formosan flying fox, P. d. formosus, is an endemic subspecies in Taiwan found mainly on Lyudao; it was previously thought to have been extirpated. Since 2005, intensive surveys have been conducted to investigate the residency, population size and plant resource utilization of P. dasymallus in Taiwan. Interviews were carried out to investigate its former abundance and the causes of population decline. In Taiwan, P. dasymallus is in a state of ongoing oceanic dispersal and colonization and has considerably expanded its geographic range. In addition to remaining in its historic habitat on Lyudao, P. dasymallus has also established colonies on Gueishan Island and in Hualien on Taiwan's main island in the past few decades. The total population size is estimated to be 240 individuals, and this number is on the rise. Approximately three-quarters of the entire population (73.64%) was found on Gueishan Island. The sex ratio was strongly skewed toward males. A total of 40 plant species were recorded as being used by the flying fox for food, roosts or perches. More agricultural and horticultural plant species were used by the flying fox in urban Hualien. According to the interviews, flying foxes were abundant on Lyudao, but their number dramatically declined from the 1970s to the mid-1980s, mainly due to commercial hunting. Maintaining a sufficient population size and genetic variability is fundamental to the long-term survival of the flying fox. Enforcing conservation laws, restoring habitats, controlling invasive species and improving public awareness are the main steps in the recovery and sustainability of the flying fox population.

Extinction debt in local habitats: quantifying the roles of random drift, immigration and emigration.

We developed a time-dependent stochastic neutral model for predicting diverse temporal trajectories of biodiversity change in response to ecological disturbance (i.e. habitat destruction) and dispersal dynamic (i.e. emigration and immigration). The model is general and predicts how transition behaviours of extinction may accumulate according to a different combination of random drift, immigration rate, emigration rate and the degree of habitat destruction. We show that immigration, emigration, the areal size of the destroyed habitat and initial species abundance distribution (SAD) can impact the total biodiversity loss in an intact local area. Among these, the SAD plays the most deterministic role, as it directly determines the initial species richness in the local target area. By contrast, immigration was found to slow down total biodiversity loss and can drive the emergence of species credits (i.e. a gain of species) over time. However, the emigration process would increase the extinction risk of species and accelerate biodiversity loss. Finally but notably, we found that a shift in the emigration rate after a habitat destruction event may be a new mechanism to generate species credits.

A Bayesian-weighted approach to predicting the number of newly discovered rare species.

In natural ecological communities, most species are rare and thus susceptible to extinction. Consequently, the prediction and identification of rare species are of enormous value for conservation purposes. How many newly found species will be rare in the next field survey? We took a Bayesian viewpoint and used observed species abundance information in an ecological sample to develop an accurate way to estimate the number of new rare species (e.g., singletons, doubletons, and tripletons) in an additional unknown sample. A similar method has been developed for incidence-based data sets. Five seminumerical tests (3 abundance cases and 2 incidence cases) showed that our proposed Bayesian-weight estimator accurately predicted the number of new rare species with low relative bias and low relative root mean squared error and, accordingly, high accuracy. Finally, we applied the proposed estimator to 6 conservation-directed empirical data sets (3 abundance cases and 3 incidence cases) and found the prediction of new rare species was quite accurate; the 95% CI covered the true observed value very well in most cases. Our estimator performed similarly to or better than an unweighted estimator derived from Chao et al. and performed consistently better than the naïve unweighted estimator. We recommend our Bayesian-weight estimator for conservation applications, although the unweighted estimator of Chao et al. may be better under some circumstances. We provide an R package RSE (rare species estimation) at https://github.com/ecomol/RSE for implementation of the estimators.

Un Método con Ponderación Bayesiana para Predecir el Número de Especies Raras Recientemente Descubiertas Resumen En las comunidades ecológicas naturales, la mayoría de las especies son raras y por lo tanto susceptibles a la extinción. Como consecuencia, la predicción e identificación de las especies raras son de enorme valor para los propósitos de la conservación. ¿Cuántas especies recientemente descubiertas serán clasificadas como raras en el siguiente censo de campo? Tomamos un punto de vista bayesiano y utilizamos información de la abundancia observada de especies en una muestra ecológica para desarrollas una manera certera para estimar el número de nuevas especies raras (p. ej.: singleton, doubleton, y tripleton) en una muestra adicional desconocida. Un método similar se ha desarrollado para conjuntos de datos basados en la incidencia. Cinco pruebas semi-numéricas (tres casos de abundancia y dos casos de incidencia) mostraron que nuestra propuesta de estimador con ponderación bayesiana predijo con certeza el número de nuevas especies raras con un bajo sesgo relativo y un bajo error de la raíz cuadrada media relativa y, de manera acorde, una alta certeza. Finalmente, aplicamos el estimador propuesto a seis conjuntos de datos empíricos dirigidos hacia la conservación (tres casos de abundancia y tres casos de incidencia) y encontramos que la predicción de nuevas especies raras fue certera; el 95% del CI cubrió muy bien al verdadero valor observado en la mayoría de los casos. Nuestro estimador funcionó de manera similar o incluso mejor que un estimador sin ponderación derivado de Chao et al. (2015) y funcionó constantemente mejor que el simple estimador sin ponderación. Recomendamos nuestro estimador con ponderación bayesiana para ser aplicado en la conservación, aunque el estimador sin ponderación de Chao et al. (2015) puede ser mejor bajo ciertas circunstancias. Proporcionamos un paquete R para RSE (estimación de especies raras) en https://github.com/ecomol/RSE para la implementación de los estimadores.

Community-level species' correlated distribution can be scale-independent and related to the evenness of abundance.

The spatial distribution of species is not random; instead, individuals tend to gather, resulting in a non-random pattern. Previous studies used the independent negative binomial distribution (NBD) to model the distributional aggregation of a single species, in which the independence of the distribution of individuals of a species in different quadrats had been assumed. This way of analyzing aggregation will result in the scale-dependent estimation of the aggregation or shape parameter. However, because non-random (and therefore non-independent) distribution of individuals of a species in a finite area can be caused by either correlated or clumped distribution of individuals of a species between neighboring sites, an alternative model would assume that the distribution of individuals of a species over different sampling areas is multinomial. Here, we showed that, by assuming that regional species abundance followed a NBD while using a multinomial distribution to assign individuals of species in different non-overlapped sampling quadrats that are from a partition of the entire region (quantifying positive correlation or synchrony), the estimation of the shape parameter in this probabilistic model, which is the negative multinomial distribution (NMD), was scale-invariant (i.e., the estimated shape parameter is identical across different partitions of the study region). Accordingly, the estimation of the shape parameter was related to regional species distribution alone. This implied that, the shape parameter at the community level, using the NMD model, reflected the evenness of interspecific abundance. As a comparison, if the distribution of individuals of a single species followed independent NBDs as studied previously, the shape parameter would measure the evenness of intraspecific abundance (quantifying single-species' distributional aggregation). Moreover, our study highlighted the necessity for adjusting the model for the effects of unsampled species when studying community-level distributional patterns. Collectively, as long as a target area is partitioned into non-overlapping quadrats (no matter how their sizes vary), the proposed NMD model in this study, along with the independent NBDs model, can be jointly formulated as a framework to reconcile the scale-dependent debate on the shape parameter, unifying the relationship between inter- or intraspecific abundance and distributional patterns.

Evaluation of the estimate bias magnitude of the Rao's quadratic diversity index.

Rao's quadratic diversity index is one of the most widely applied diversity indices in functional and phylogenetic ecology. The standard way of computing Rao's quadratic diversity index for an ecological assemblage with a group of species with varying abundances is to sum the functional or phylogenetic distances between a pair of species in the assemblage, weighted by their relative abundances. Here, using both theoretically derived and observed empirical datasets, we show that this standard calculation routine in practical applications will statistically underestimate the true value, and the bias magnitude is derived accordingly. The underestimation will become worse when the studied ecological community contains more species or the pairwise species distance is large. For species abundance data measured using the number of individuals, we suggest calculating the unbiased Rao's quadratic diversity index.

Rarefaction and extrapolation of species richness using an area-based Fisher's logseries.

Fisher's logseries is widely used to characterize species abundance pattern, and some previous studies used it to predict species richness. However, this model, derived from the negative binomial model, degenerates at the zero-abundance point (i.e., its probability mass fully concentrates at zero abundance, leading to an odd situation that no species can occur in the studied sample). Moreover, it is not directly related to the sampling area size. In this sense, the original Fisher's alpha (correspondingly, species richness) is incomparable among ecological communities with varying area sizes. To overcome these limitations, we developed a novel area-based logseries model that can account for the compounding effect of the sampling area. The new model can be used to conduct area-based rarefaction and extrapolation of species richness, with the advantage of accurately predicting species richness in a large region that has an area size being hundreds or thousands of times larger than that of a locally observed sample, provided that data follow the proposed model. The power of our proposed model has been validated by extensive numerical simulations and empirically tested through tree species richness extrapolation and interpolation in Brazilian Atlantic forests. Our parametric model is data parsimonious as it is still applicable when only the information on species number, community size, or the numbers of singleton and doubleton species in the local sample is available. Notably, in comparison with the original Fisher's method, our area-based model can provide asymptotically unbiased variance estimation (therefore correct 95% confidence interval) for species richness. In conclusion, the proposed area-based Fisher's logseries model can be of broad applications with clear and proper statistical background. Particularly, it is very suitable for being applied to hyperdiverse ecological assemblages in which nonparametric richness estimators were found to greatly underestimate species richness.

Estimating species pools for a single ecological assemblage.

BACKGROUND: The species pool concept was formulated over the past several decades and has since played an important role in explaining multi-scale ecological patterns. Previous statistical methods were developed to identify species pools based on broad-scale species range maps or community similarity computed from data collected from many areas. No statistical method is available for estimating species pools for a single local community (sampling area size may be very small as ≤ 1 km2). In this study, based on limited local abundance information, we developed a simple method to estimate the area size and richness of a species pool for a local ecological community. The method involves two steps. In the first step, parameters from a truncated negative trinomial model characterizing the distributional aggregation of all species (i.e., non-random species distribution) in the local community were estimated. In the second step, we assume that the unseen species in the local community are most likely the rare species, only found in the remaining part of the species pool, and vice versa, if the remaining portion of the pool was surveyed and was contrasted with the sampled area. Therefore, we can estimate the area size of the pool, as long as an abundance threshold for defining rare species is given. Since the size of the pool is dependent on the rarity threshold, to unanimously determine the pool size, we developed an optimal method to delineate the rarity threshold based on the balance of the changing rates of species absence probabilities in the sampled and unsampled areas of the pool. RESULTS: For a 50 ha (0.5 km2) forest plot in the Barro Colorado Island of central Panama, our model predicted that the local, if not regional, species pool for the 0.5 km2 forest plot was nearly the entire island. Accordingly, tree species richness in this pool was estimated as around 360. When the sampling size was smaller, the upper bound of the 95% confidence interval could reach 418, which was very close to the flora record of tree richness for the island. A numerical test further demonstrated the power and reliability of the proposed method, as the true values of area size and species richness for the hypothetical species pool have been well covered by the 95% confidence intervals of the true values. CONCLUSIONS: Our method fills the knowledge gap on estimating species pools for a single local ecological assemblage with little information. The method is statistically robust and independent of sampling size, as proved by both empirical and numerical tests.

A general framework for predicting delayed responses of ecological communities to habitat loss.

Although biodiversity crisis at different spatial scales has been well recognised, the phenomena of extinction debt and immigration credit at a crossing-scale context are, at best, unclear. Based on two community patterns, regional species abundance distribution (SAD) and spatial abundance distribution (SAAD), Kitzes and Harte (2015) presented a macroecological framework for predicting post-disturbance delayed extinction patterns in the entire ecological community. In this study, we further expand this basic framework to predict diverse time-lagged effects of habitat destruction on local communities. Specifically, our generalisation of KH's model could address the questions that could not be answered previously: (1) How many species are subjected to delayed extinction in a local community when habitat is destructed in other areas? (2) How do rare or endemic species contribute to extinction debt or immigration credit of the local community? (3) How will species differ between two local areas? From the demonstrations using two SAD models (single-parameter lognormal and logseries), the predicted patterns of the debt, credit, and change in the fraction of unique species can vary, but with consistencies and depending on several factors. The general framework deepens the understanding of the theoretical effects of habitat loss on community dynamic patterns in local samples.

Postnatal growth and age estimation in Scotophilus kuhlii.

Adequate postnatal growth is important for young bats to develop skilled sensory and locomotor abilities, which are highly associated with their survival once independent. This study investigated the postnatal growth and development of Scotophilus kuhlii in captivity. An empirical growth curve was established, and the postnatal growth rate was quantified to derive an age-predictive equation. By further controlling the fostering conditions of twins, the differences in the development patterns between pups that received maternal care or were hand-reared were analyzed to determine whether the latter developed in the same manner as their maternally reared counterparts. Our results indicate that both forearm length and body mass increased rapidly and linearly during the first 4 weeks, after which the growth rate gradually decreased to reach a stable level. The first flight occurred at an average age of 39 days with a mean forearm length and body mass of 92.07% and 70.52% of maternal size, respectively. The developmental pattern of hand-reared pups, although similar to that of their maternally reared twin siblings, displayed a slightly faster growth rate in the 4th and 5th weeks. The heavier body mass of hand-reared pups during the pre-fledging period may cause higher wing loading, potentially influencing the flight performance and survival of the bats once independent.

Good-Turing frequency estimation in a finite population.

Good-Turing frequency estimation (Good, ) is a simple, effective method for predicting detection probabilities of objects of both observed and unobserved classes based on observed frequencies of classes in a sample. The method has been used widely in several disciplines, such as information retrieval, computational linguistics, text recognition, and ecological diversity estimation. Nevertheless, existing studies assume sampling with replacement or sampling from an infinite population, which might be inappropriate for many practical applications. In light of this limitation, this article presents a modification of the Good-Turing estimation method to account for finite population sampling. We provide three practical extensions of the modified method, and we examine performance of the modified method and its extensions in simulation experiments.

Delimitation of a continuous morphological character with unknown prior membership: application of a finite mixture model to classify scapular setae of Abacarus panticis.

Unambiguous classification is a prerequisite for the study of polymorphism, but accurate delimitation of continuous morphological characters can be challenging. Finite mixture modeling is a rigorous and flexible approach for delimiting continuous variables with unknown prior membership, but its application to morphological studies remains limited. In this study, the lengths of scapular setae of the eriophyoid mite Abacarus panticis Keifer collected from 18 sites in Taiwan were used as an example to evaluate the eligibility of finite mixture models. We then tested the hypothesis that longer scapular setae can facilitate dispersal. Lastly, we investigate morphological variation in various seta morphs by geometric morphometric techniques. Finite mixture models can satisfactorily classify scapular setae of A. panticis into long and short seta morphs. Abacarus panticis of the long morph only occurred in five sites whereas the short seta morph existed in all study sites. Geometric morphometric analyses revealed a more elongated coxal area in individuals of long morph than in those of short morph. Because the short morph is more widespread in geographical distribution than the long morph, longer scapular setae seem unlikely a specialized adaptation for dispersal. Further studies should capitalize on the finite mixture model in the delimitation of continuous morphological characters.

Small-sample estimation of species richness applied to forest communities.

Many well-known methods are available for estimating the number of species in a forest community. However, most existing methods result in considerable negative bias in applications, where field surveys typically represent only a small fraction of sampled communities. This article develops a new method based on sampling with replacement to estimate species richness via the generalized jackknife procedure. The proposed estimator yields small bias and reasonably accurate interval estimation even with small samples. The performance of the proposed estimator is compared with several typical estimators via simulation study using two complete census datasets from Panama and Malaysia.

An incidence-based richness estimator for quadrats sampled without replacement.

Most richness estimators currently in use are derived from models that consider sampling with replacement or from the assumption of infinite populations. Neither of the assumptions is suitable for sampling sessile organisms such as plants where quadrats are often sampled without replacement and the area of study is always limited. In this paper, we propose an incidence-based parametric richness estimator that considers quadrat sampling without replacement in a fixed area. The estimator is derived from a zero-truncated binomial distribution for the number of quadrats containing a given species (e.g., species i) and a modified beta distribution for the probability of presence-absence of a species in a quadrat. The maximum likelihood estimate of richness is explicitly given and can be easily solved. The variance of the estimate is also obtained. The performance of the estimator is tested against nine other existing incidence-based estimators using two tree data sets where the true numbers of species are known. Results show that the new estimator is insensitive to sample size and outperforms the other methods as judged by the root mean squared errors. The superiority of the new method is particularly noticeable when large quadrat size is used, suggesting that a few large quadrats are preferred over many small ones when sampling diversity.

Abundance-based similarity indices and their estimation when there are unseen species in samples.

A wide variety of similarity indices for comparing two assemblages based on species incidence (i.e., presence/absence) data have been proposed in the literature. These indices are generally based on three simple incidence counts: the number of species shared by two assemblages and the number of species unique to each of them. We provide a new probabilistic derivation for any incidence-based index that is symmetric (i.e., the index is not affected by the identity ordering of the two assemblages) and homogeneous (i.e., the index is unchanged if all counts are multiplied by a constant). The probabilistic approach is further extended to formulate abundance-based indices. Thus any symmetric and homogeneous incidence index can be easily modified to an abundance-type version. Applying the Laplace approximation formulas, we propose estimators that adjust for the effect of unseen shared species on our abundance-based indices. Simulation results show that the adjusted estimators significantly reduce the biases of the corresponding unadjusted ones when a substantial fraction of species is missing from samples. Data on successional vegetation in six tropical forests are used for illustration. Advantages and disadvantages of some commonly applied indices are briefly discussed.