Environmental and Ecological Statistics, May 7, 2015
A sequence of jackknife estimators is developed to estimate the number of shared species in two c... more A sequence of jackknife estimators is developed to estimate the number of shared species in two communities. The estimators have simple and explicit formulae. A sequential testing criterion is also developed to determine a proper order for these jackknife estimators. The performance of the estimators is evaluated using empirical data on two forests from Malaysia, where 209 shared species present in both forests, and using simulated data. Results for the empirical data and simulated scenarios (for sampling fraction ranging from 0.5 to 20 %) show that the jackknife estimator, compared with other existing estimators, has a smaller bias and provides more reliable interval estimation in most cases. Additionally, two avian datasets from Taiwan and Hong Kong are used to demonstrate the proposed method. To extend the proposed method to three communities, we also list the first six orders of the jackknife estimators explicitly.
Journal of Agricultural Biological and Environmental Statistics, Sep 1, 2004
Consider a continuous-time stochastic model in which species arrive in the sample according to in... more Consider a continuous-time stochastic model in which species arrive in the sample according to independent Poisson processes and where the species discovery rates are heterogeneous. Based on an initial survey, we are concerned with the problem of predicting the number of new species that would be discovered by additional sampling. When the sampling time or sample size of the additional sample tends to infinity, this problem reduces to the prediction of the number of undetected species in the original sample, or equivalently, the estimation of species richness. The topic has a wide range of applications in various disciplines. We propose a simple prediction method and apply it to two datasets. One set of data deals with the capture counts of the Malayan butterfly and the other set deals with identification records of organic pollutants in a water environment. Simulation results are shown to investigate the performance of the proposed method and to compare it with the existing estimators.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
The species–area relationship (SAR) describes a law of species richness changes as the sampling a... more The species–area relationship (SAR) describes a law of species richness changes as the sampling area varies. SAR has been studied for more than 100 years and is of great significance in the fields of biogeography, population ecology, and conservation biology. Accordingly, there are many algorithms available for fitting the SARs, but their applicability is not numerically evaluated yet. Here, we have selected three widely used algorithms, and discuss three aspects of their applicability: the number of iterations, the time consumption, and the sensitivity to the initial parameter setting. Our results showed that, the Gauss–Newton method and the Levenberg–Marquardt method require relatively few iterative steps and take less time. In contrast, the Nelder–Mead method requires relatively more iteration steps and consumes the most time. Regarding the sensitivity of the algorithm to the initial parameters, the Gauss–Newton and the Nelder–Mead methods are more sensitive to the choice of init...
QuestionsEcologists collecting field samples of biological data have a keen interest in addressin... more QuestionsEcologists collecting field samples of biological data have a keen interest in addressing the following question: how many rare species are there in as‐yet unsurveyed additional samples? Depending on the size of a targeted additional sample, statistical models for estimating the number of rare species have not been systematically established and compared.LocationGlobal.MethodsFor fairly comparing and predicting rare‐species richness at the same sample‐size baseline, we systematically developed and compared four estimators for rarefaction and extrapolation of rare‐species richness with a given specific abundance. These four estimators included a uniformly minimum variance unbiased (UMVUE), Bayesian‐weighted, Chao‐derived unweighted and naïve estimator.ResultsAfter extensive numerical tests, for conducting rarefaction of rare‐species richness (i.e., when additional sample size was not larger than the original one) it is recommended to implement UMVUE, as it has zero bias and ...
Fig. S1 shows a flowchart for showing the transition dynamic between neighboring abundance states... more Fig. S1 shows a flowchart for showing the transition dynamic between neighboring abundance states for the stochastic models studied in the paper;Fig. S2 shows the impacts of initial abundance state on the resultant extinction probability over time;Fig. S3 shows the impacts of different combinations of emigration and immigration rates on the resultant extinction probability over time;Fig. S4 shows the similarity of the proposed biodiversity loss models used in the present study (Eq. 8 of the main text) and the previous study (Sgardeli et al. [3]);Fig. S5 shows the influence of parameter omega on determining the initial species abundance distribution and the likelihood for a species to be absent from the local target community in the area-based logseries model;Fig. S6 shows a shift in the emigration rate at the time point of habitat destruction and its influence on the magnitude of the extinction debt or species richness over time.
The file includes data for diet content, plant percent cover, fig production, and fig mass/number... more The file includes data for diet content, plant percent cover, fig production, and fig mass/number and bat activity (pellet and feces numbers). Plant abbreviations are as follows: Fs, Ficus septica; Ff, F. fistulosa; Fsj, F. superba var. japonica; Fm, F. microcarpa; Fa, F. ampelas; Ma, Morus australis; Dm, Diospyros maritima; As, Ardisia sieboldii; Pg, Psidium guajava; Tt, Turpinia ternata; Ej, Eurya japonica; Wb, Wedelia biflora
Interactions among multiple species form complex networks of interdependences and are considered ... more Interactions among multiple species form complex networks of interdependences and are considered primary factors in the generation and maintenance of biodiversity. Pteropodid bats are keystone species that provide important ecosystem services of pollination and seed dispersal in the tropics and subtropics. In this study, we investigated the utilization and preference of food resources by the insular frugivorous flying fox Pteropus dasymallus. We found that fig species constituted the major portion of the diet of the flying fox (94.6%). When foraging, the flying fox preferred seed figs from female trees over gall figs from male trees in functionally dioecious fig species. Germination experiments showed a significantly higher percentage of germination for fig seeds in feces than those from pellets and ripe figs (feces: 80.2%, pellets: 23.4%, ripe figs: 32.9%). Considering the active selection of seed figs and avoidance of gall figs by foraging flying foxes, we suggest that the abundance of seed figs accurately represents food availability for dioecy. This preference for seed figs or viable seeds can effectively promote the survival of pollinating wasps and might reinforce the evolution of dioecism in figs. In addition, the effects of gut passage on seed germination, in combination with the capacity of flying foxes to travel long distances, may substantially contribute to the efficiency of flying foxes as seed dispersers
Species richness has been viewed as the primary measure for understanding the biodiversity in a c... more Species richness has been viewed as the primary measure for understanding the biodiversity in a community for a long time. If the research interest focuses on a forest community, it is customary to collect data with a quadrat sampling. However, several well-known estimators cannot provide reliable consequences when the fraction of sampling domain is less than 5%, which is a common situation in practice. To meet the practical requirement, this study presents some promising methods that yield encouraging results in light of the various aspects of statistical criterion. Moreover, the evaluation of richness estimators employed two complete census datasets of forest plots to be testing populations rather than using artificial datasets.
Aim: Single‐species distributions are well known to present random, aggregate, or regular pattern... more Aim: Single‐species distributions are well known to present random, aggregate, or regular patterns. However, at the community level, multi‐species aggregate distribution patterns are not simply the lumped aggregate distribution of each species in the community. Actually, the superimposition of specimens of different species on a distribution map can present an interacting distributional pattern: different species may overlap with each other (or conversely, avoid each other). To this end, other than aggregation, it is necessary to further quantify distributionally overlapping patterns of different species at the community level.Methods and results: In this study, we combined the conspecific‐encounter index v and Moran's I index to disentangle community‐level distributional aggregation versus superimposition. Numerical simulations demonstrated that the two indices, calculated from biodiversity data collected using the sequential sampling of specimens along line transects, were eff...
Single‐species distributional patterns have been well studied and quantified using a negative bin... more Single‐species distributional patterns have been well studied and quantified using a negative binomial model. However, it is still unclear how to quantify multi‐species distribution patterns. A previous study (Chen et al. 2019) developed a simple conspecific‐encounter index for quantifying multi‐species distributional aggregation patterns when biodiversity data are collected in a consecutive scheme along line transects. Here, through simple derivation, we reported that the previously proposed conspecific‐encounter index had a close association with Moran's I index, which has been widely applied in spatial ecology for describing spatial autocorrelation of ecological data. Our proof unified the conspecific‐encounter index that is applied under the context of line‐transect sampling and Moran's I index that is applied under the context of spatial ecology. The unification sheds light on the development of new statistical metrics for quantifying biological diversity and distributi...
The distribution of individuals of different species across different sampling units is typically... more The distribution of individuals of different species across different sampling units is typically non-random. This distributional non-independence can be interpreted and modelled as a correlated multivariate distribution. However, this correlation cannot be modelled using a totally independent and random distribution such as the Poisson distribution. In this study, we utilized the negative multinomial distribution to overcome the problem encountered by the commonly used Poisson distribution and used it to derive insight into the implications of field sampling for rare species’ distributions. Mathematically, we derived, from the negative multinomial distribution and sampling theory, contrasting relationships between sampling area, and the proportions of locally rare and regionally rare species in ecological assemblages presenting multi-species correlated distribution. With the suggested model, we explored the cross-scale relationships between the spatial extent, the population thresh...
Ecologists have generally concluded that species distributions are not random (e.g. aggregate), b... more Ecologists have generally concluded that species distributions are not random (e.g. aggregate), based on single‐species studies that applied single‐species–based statistical methods, like the negative binomial model. Although it is common knowledge that some specific species in an ecological community present aggregate distributions, this does not necessarily imply that the entire community presents an aggregate distribution. Studying community‐level distributional aggregation patterns requires different statistical methods. Herein, by utilizing a novel conspecific‐encounter index derived from a multiple species Markov transition model that accounts for the non‐independent sampling of consecutive individuals along line transects, we were able to show that tree assemblages in tropical forest ecosystems can present a strong signal of extensive distributional interspersion. This interesting result is not unexpected, given the fact that neighbouring tree individuals in highly diverse tr...
Adequate postnatal growth is important for young bats to develop skilled sensory and locomotor ab... more 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.
A sequence of jackknife estimators is developed to estimate the number of shared species in two c... more A sequence of jackknife estimators is developed to estimate the number of shared species in two communities. The estimators have simple and explicit formulae. A sequential testing criterion is also developed to determine a proper order for these jackknife estimators. The performance of the estimators is evaluated using empirical data on two forests from Malaysia, where 209 shared species present in both forests, and using simulated data. Results for the empirical data and simulated scenarios (for sampling fraction ranging from 0.5 to 20 %) show that the jackknife estimator, compared with other existing estimators, has a smaller bias and provides more reliable interval estimation in most cases. Additionally, two avian datasets from Taiwan and Hong Kong are used to demonstrate the proposed method. To extend the proposed method to three communities, we also list the first six orders of the jackknife estimators explicitly.
Good-Turing frequency estimation (Good, ) is a simple, effective method for predicting detection ... more 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.
A biological community usually has a large number of species with relatively small abundances. Wh... more A biological community usually has a large number of species with relatively small abundances. When a random sample of individuals is selected and each individual is classified according to species identity, some rare species may not be discovered. This paper is concerned with the estimation of Shannon’s index of diversity when the number of species and the species abundances are
Journal of Agricultural, Biological, and Environmental Statistics, 2004
Consider a continuous-time stochastic model in which species arrive in the sample according to in... more Consider a continuous-time stochastic model in which species arrive in the sample according to independent Poisson processes and where the species discovery rates are heterogeneous. Based on an initial survey, we are concerned with the problem of predicting the number of new species that would be discovered by additional sampling. When the sampling time or sample size of the additional sample tends to infinity, this problem reduces to the prediction of the number of undetected species in the original sample, or equivalently, the estimation of species richness. The topic has a wide range of applications in various disciplines. We propose a simple prediction method and apply it to two datasets. One set of data deals with the capture counts of the Malayan butterfly and the other set deals with identification records of organic pollutants in a water environment. Simulation results are shown to investigate the performance of the proposed method and to compare it with the existing estimators.
Unambiguous classification is a prerequisite for the study of polymorphism, but accurate delimita... more 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.
Environmental and Ecological Statistics, May 7, 2015
A sequence of jackknife estimators is developed to estimate the number of shared species in two c... more A sequence of jackknife estimators is developed to estimate the number of shared species in two communities. The estimators have simple and explicit formulae. A sequential testing criterion is also developed to determine a proper order for these jackknife estimators. The performance of the estimators is evaluated using empirical data on two forests from Malaysia, where 209 shared species present in both forests, and using simulated data. Results for the empirical data and simulated scenarios (for sampling fraction ranging from 0.5 to 20 %) show that the jackknife estimator, compared with other existing estimators, has a smaller bias and provides more reliable interval estimation in most cases. Additionally, two avian datasets from Taiwan and Hong Kong are used to demonstrate the proposed method. To extend the proposed method to three communities, we also list the first six orders of the jackknife estimators explicitly.
Journal of Agricultural Biological and Environmental Statistics, Sep 1, 2004
Consider a continuous-time stochastic model in which species arrive in the sample according to in... more Consider a continuous-time stochastic model in which species arrive in the sample according to independent Poisson processes and where the species discovery rates are heterogeneous. Based on an initial survey, we are concerned with the problem of predicting the number of new species that would be discovered by additional sampling. When the sampling time or sample size of the additional sample tends to infinity, this problem reduces to the prediction of the number of undetected species in the original sample, or equivalently, the estimation of species richness. The topic has a wide range of applications in various disciplines. We propose a simple prediction method and apply it to two datasets. One set of data deals with the capture counts of the Malayan butterfly and the other set deals with identification records of organic pollutants in a water environment. Simulation results are shown to investigate the performance of the proposed method and to compare it with the existing estimators.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
The species–area relationship (SAR) describes a law of species richness changes as the sampling a... more The species–area relationship (SAR) describes a law of species richness changes as the sampling area varies. SAR has been studied for more than 100 years and is of great significance in the fields of biogeography, population ecology, and conservation biology. Accordingly, there are many algorithms available for fitting the SARs, but their applicability is not numerically evaluated yet. Here, we have selected three widely used algorithms, and discuss three aspects of their applicability: the number of iterations, the time consumption, and the sensitivity to the initial parameter setting. Our results showed that, the Gauss–Newton method and the Levenberg–Marquardt method require relatively few iterative steps and take less time. In contrast, the Nelder–Mead method requires relatively more iteration steps and consumes the most time. Regarding the sensitivity of the algorithm to the initial parameters, the Gauss–Newton and the Nelder–Mead methods are more sensitive to the choice of init...
QuestionsEcologists collecting field samples of biological data have a keen interest in addressin... more QuestionsEcologists collecting field samples of biological data have a keen interest in addressing the following question: how many rare species are there in as‐yet unsurveyed additional samples? Depending on the size of a targeted additional sample, statistical models for estimating the number of rare species have not been systematically established and compared.LocationGlobal.MethodsFor fairly comparing and predicting rare‐species richness at the same sample‐size baseline, we systematically developed and compared four estimators for rarefaction and extrapolation of rare‐species richness with a given specific abundance. These four estimators included a uniformly minimum variance unbiased (UMVUE), Bayesian‐weighted, Chao‐derived unweighted and naïve estimator.ResultsAfter extensive numerical tests, for conducting rarefaction of rare‐species richness (i.e., when additional sample size was not larger than the original one) it is recommended to implement UMVUE, as it has zero bias and ...
Fig. S1 shows a flowchart for showing the transition dynamic between neighboring abundance states... more Fig. S1 shows a flowchart for showing the transition dynamic between neighboring abundance states for the stochastic models studied in the paper;Fig. S2 shows the impacts of initial abundance state on the resultant extinction probability over time;Fig. S3 shows the impacts of different combinations of emigration and immigration rates on the resultant extinction probability over time;Fig. S4 shows the similarity of the proposed biodiversity loss models used in the present study (Eq. 8 of the main text) and the previous study (Sgardeli et al. [3]);Fig. S5 shows the influence of parameter omega on determining the initial species abundance distribution and the likelihood for a species to be absent from the local target community in the area-based logseries model;Fig. S6 shows a shift in the emigration rate at the time point of habitat destruction and its influence on the magnitude of the extinction debt or species richness over time.
The file includes data for diet content, plant percent cover, fig production, and fig mass/number... more The file includes data for diet content, plant percent cover, fig production, and fig mass/number and bat activity (pellet and feces numbers). Plant abbreviations are as follows: Fs, Ficus septica; Ff, F. fistulosa; Fsj, F. superba var. japonica; Fm, F. microcarpa; Fa, F. ampelas; Ma, Morus australis; Dm, Diospyros maritima; As, Ardisia sieboldii; Pg, Psidium guajava; Tt, Turpinia ternata; Ej, Eurya japonica; Wb, Wedelia biflora
Interactions among multiple species form complex networks of interdependences and are considered ... more Interactions among multiple species form complex networks of interdependences and are considered primary factors in the generation and maintenance of biodiversity. Pteropodid bats are keystone species that provide important ecosystem services of pollination and seed dispersal in the tropics and subtropics. In this study, we investigated the utilization and preference of food resources by the insular frugivorous flying fox Pteropus dasymallus. We found that fig species constituted the major portion of the diet of the flying fox (94.6%). When foraging, the flying fox preferred seed figs from female trees over gall figs from male trees in functionally dioecious fig species. Germination experiments showed a significantly higher percentage of germination for fig seeds in feces than those from pellets and ripe figs (feces: 80.2%, pellets: 23.4%, ripe figs: 32.9%). Considering the active selection of seed figs and avoidance of gall figs by foraging flying foxes, we suggest that the abundance of seed figs accurately represents food availability for dioecy. This preference for seed figs or viable seeds can effectively promote the survival of pollinating wasps and might reinforce the evolution of dioecism in figs. In addition, the effects of gut passage on seed germination, in combination with the capacity of flying foxes to travel long distances, may substantially contribute to the efficiency of flying foxes as seed dispersers
Species richness has been viewed as the primary measure for understanding the biodiversity in a c... more Species richness has been viewed as the primary measure for understanding the biodiversity in a community for a long time. If the research interest focuses on a forest community, it is customary to collect data with a quadrat sampling. However, several well-known estimators cannot provide reliable consequences when the fraction of sampling domain is less than 5%, which is a common situation in practice. To meet the practical requirement, this study presents some promising methods that yield encouraging results in light of the various aspects of statistical criterion. Moreover, the evaluation of richness estimators employed two complete census datasets of forest plots to be testing populations rather than using artificial datasets.
Aim: Single‐species distributions are well known to present random, aggregate, or regular pattern... more Aim: Single‐species distributions are well known to present random, aggregate, or regular patterns. However, at the community level, multi‐species aggregate distribution patterns are not simply the lumped aggregate distribution of each species in the community. Actually, the superimposition of specimens of different species on a distribution map can present an interacting distributional pattern: different species may overlap with each other (or conversely, avoid each other). To this end, other than aggregation, it is necessary to further quantify distributionally overlapping patterns of different species at the community level.Methods and results: In this study, we combined the conspecific‐encounter index v and Moran's I index to disentangle community‐level distributional aggregation versus superimposition. Numerical simulations demonstrated that the two indices, calculated from biodiversity data collected using the sequential sampling of specimens along line transects, were eff...
Single‐species distributional patterns have been well studied and quantified using a negative bin... more Single‐species distributional patterns have been well studied and quantified using a negative binomial model. However, it is still unclear how to quantify multi‐species distribution patterns. A previous study (Chen et al. 2019) developed a simple conspecific‐encounter index for quantifying multi‐species distributional aggregation patterns when biodiversity data are collected in a consecutive scheme along line transects. Here, through simple derivation, we reported that the previously proposed conspecific‐encounter index had a close association with Moran's I index, which has been widely applied in spatial ecology for describing spatial autocorrelation of ecological data. Our proof unified the conspecific‐encounter index that is applied under the context of line‐transect sampling and Moran's I index that is applied under the context of spatial ecology. The unification sheds light on the development of new statistical metrics for quantifying biological diversity and distributi...
The distribution of individuals of different species across different sampling units is typically... more The distribution of individuals of different species across different sampling units is typically non-random. This distributional non-independence can be interpreted and modelled as a correlated multivariate distribution. However, this correlation cannot be modelled using a totally independent and random distribution such as the Poisson distribution. In this study, we utilized the negative multinomial distribution to overcome the problem encountered by the commonly used Poisson distribution and used it to derive insight into the implications of field sampling for rare species’ distributions. Mathematically, we derived, from the negative multinomial distribution and sampling theory, contrasting relationships between sampling area, and the proportions of locally rare and regionally rare species in ecological assemblages presenting multi-species correlated distribution. With the suggested model, we explored the cross-scale relationships between the spatial extent, the population thresh...
Ecologists have generally concluded that species distributions are not random (e.g. aggregate), b... more Ecologists have generally concluded that species distributions are not random (e.g. aggregate), based on single‐species studies that applied single‐species–based statistical methods, like the negative binomial model. Although it is common knowledge that some specific species in an ecological community present aggregate distributions, this does not necessarily imply that the entire community presents an aggregate distribution. Studying community‐level distributional aggregation patterns requires different statistical methods. Herein, by utilizing a novel conspecific‐encounter index derived from a multiple species Markov transition model that accounts for the non‐independent sampling of consecutive individuals along line transects, we were able to show that tree assemblages in tropical forest ecosystems can present a strong signal of extensive distributional interspersion. This interesting result is not unexpected, given the fact that neighbouring tree individuals in highly diverse tr...
Adequate postnatal growth is important for young bats to develop skilled sensory and locomotor ab... more 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.
A sequence of jackknife estimators is developed to estimate the number of shared species in two c... more A sequence of jackknife estimators is developed to estimate the number of shared species in two communities. The estimators have simple and explicit formulae. A sequential testing criterion is also developed to determine a proper order for these jackknife estimators. The performance of the estimators is evaluated using empirical data on two forests from Malaysia, where 209 shared species present in both forests, and using simulated data. Results for the empirical data and simulated scenarios (for sampling fraction ranging from 0.5 to 20 %) show that the jackknife estimator, compared with other existing estimators, has a smaller bias and provides more reliable interval estimation in most cases. Additionally, two avian datasets from Taiwan and Hong Kong are used to demonstrate the proposed method. To extend the proposed method to three communities, we also list the first six orders of the jackknife estimators explicitly.
Good-Turing frequency estimation (Good, ) is a simple, effective method for predicting detection ... more 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.
A biological community usually has a large number of species with relatively small abundances. Wh... more A biological community usually has a large number of species with relatively small abundances. When a random sample of individuals is selected and each individual is classified according to species identity, some rare species may not be discovered. This paper is concerned with the estimation of Shannon’s index of diversity when the number of species and the species abundances are
Journal of Agricultural, Biological, and Environmental Statistics, 2004
Consider a continuous-time stochastic model in which species arrive in the sample according to in... more Consider a continuous-time stochastic model in which species arrive in the sample according to independent Poisson processes and where the species discovery rates are heterogeneous. Based on an initial survey, we are concerned with the problem of predicting the number of new species that would be discovered by additional sampling. When the sampling time or sample size of the additional sample tends to infinity, this problem reduces to the prediction of the number of undetected species in the original sample, or equivalently, the estimation of species richness. The topic has a wide range of applications in various disciplines. We propose a simple prediction method and apply it to two datasets. One set of data deals with the capture counts of the Malayan butterfly and the other set deals with identification records of organic pollutants in a water environment. Simulation results are shown to investigate the performance of the proposed method and to compare it with the existing estimators.
Unambiguous classification is a prerequisite for the study of polymorphism, but accurate delimita... more 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.
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