Small‐Sample Estimation of Species Richness Applied to Forest Communities

Hwang, Wen‐Han; Shen, Tsung‐Jen

doi:10.1111/j.1541-0420.2009.01371.x

Cited by 15 publications

(26 citation statements)

References 39 publications

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“…See also McCrea and Morgan (2015). Ratio regression for the Poisson case has been suggested in Rocchetti et al (2011) and a special fractional polynomial model for the binomial ratio case by Hwang and Shen (2010). This paper develops the most general form of the ratio regression approach as it allows any member of the power series distribution as base distribution, a basically unlimited choice of regression model which is connected to the ratio of neighboring frequencies by a feasible link function.…”

Section: Extensions and Discussionmentioning

confidence: 99%

Ratio Plot and Ratio Regression with Applications to Social and Medical Sciences

Böhning¹

2016

Statist. Sci.

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Abstract. We consider count data modeling, in particular, the zerotruncated case as it arises naturally in capture-recapture modeling as the marginal distribution of the count of identifications of the members of a target population. Whereas in wildlife ecology these distributions are often of a well-defined type, this is less the case for social and medical science applications since study types are often entirely observational. Hence, in these applications, violations of the assumptions underlying closed capture-recapture are more likely to occur than in carefully designed capture-recapture experiments. In consequence, the marginal count distribution might be rather complex. The purpose of this note is to sketch some of the major ideas in the recent developments in ratio plotting and ratio regression designed to explore the pattern of the distribution underlying the capture process. Ratio plotting and ratio regression are based upon considering the ratios of neighboring probabilities which can be estimated by ratios of observed frequencies. Frequently, these ratios show patterns which can be easily modeled by a regression model. The fitted regression model is then used to predict the frequency of hidden zero counts. Particular attention is given to regression models corresponding to the negative-binomial, multiplicative binomial and the Conway-Maxwell-Poisson distribution.

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Section: Extensions and Discussionmentioning

confidence: 99%

Ratio Plot and Ratio Regression with Applications to Social and Medical Sciences

Böhning¹

2016

Statist. Sci.

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“…It is known that the number of observed forest tree species in regional or national forest monitoring programs typically underestimates the actual number of forest species present in the sampled forests (Cao, et al, 2004;Chiarucci, et al, 2003;Gimaret-Carpentier, et al, 1998;Hellmann & Fowler, 1999;Hwang & Shen, 2010;Lam & Kleinn, 2008;Magnussen & Boudewyn, 2008). The exceptions are in forests with few relatively rare species and in the absence of rare forest tree species.…”

Section: Journal Of Environment and Ecologymentioning

confidence: 99%

“…They are both easily modified to cope with repeat observations of species incidence data. The third model-based estimator   HW S  is the difference between a time two and a time one estimate of species richness obtained with the estimator proposed by Hwang and Shen (2010). This estimator cannot directly accommodate temporal covariances in species incidence data.…”

Section: Introductionmentioning

confidence: 99%

Estimating change in species richness from repeated sampling of incidence data

Magnussen

2011

JEE

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Forest tree species richness is an important indicator of sustainability. Forest monitoring allows stake-holders to track species richness over time. To test a hypothesis of whether an observed change in richness is significant or not, the analyst must choose a suitable estimator. Based on experience from comparative studies of potential estimators this study evaluates the performance of one design-based and three model-based estimators of change in species richness. The evaluation is done with Monte Carlo simulations of simple random sampling from four actual populations of forest tree species incidence data collected at two occasions from a fixed set of fixed-area forest inventory plots. The observed change in species richness (design-based) had the lowest root mean squared error, but was often more biased than estimates from the three model-based estimators. The bias issue and poor coverage of 95% confidence intervals dissuade the use of the design-based estimator (observed change). A newly developed urn-type estimator, easily adaptable to processing longitudinal data, was overall best in terms of bias and coverage.

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“…A maximum likelihood variance estimator is provided (Shen & He, 2008). The fourth estimator  hw S is a generalized jackknife estimator of richness (Hwang & Shen, 2010) expressed as the sum of SO and a prediction of the number of unseen species. The latter was obtained from an exponential regression model that predicts a scaled ratio of …”

Section: Estimators Of Species Richnessmentioning

confidence: 99%

“…Under these circumstances, few species richness estimators have performed well in Monte Carlo simulations with actual forest inventory data (Magnussen, 2011;Magnussen et al, 2010). Heretofore popular estimators of richness like the Jackknife, the bootstrap, and Chao's coverage-based estimators generally disappoint because they were not designed for sampling with multi-tree quadrants (Hellmann & Fowler, 1999;Hwang & Shen, 2010;Lam & Kleinn, 2008;Palmer, 1991;Schreuder et al, 2000;Schreuder et al, 1999).…”

Section: Introductionmentioning

confidence: 99%

Sample-based Estimation of Regional Forest Tree Species Richness

Magnussen¹

2011

ENRR

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Sample-based estimates of species richness for large heterogeneous regions may be affected by interactions between the sampling design and sub-regional heterogeneity in species richness and diversity. To investigate this issue a Monte Carlo simulation study was conducted with actual forest inventory tree species incidence data from two large regions, four estimators of species richness, three sampling designs, two sampling units (fixed area plots and tree nearest to plot center), and five sample sizes. The regions represent forested areas in central and eastern Canada and three states in the USA. Design effects in estimates of regional species richness were generally weak, of little practical import, and limited to settings with the smallest sample sizes. The study shows that accurate regional estimates of richness can be obtained by pooling sub-regional species incidence data. Sampling with fixed area plots was, with few estimator-dependent exceptions, considerably more efficient than sampling with one tree per sample location. A proposed ratio-based procedure for combining sub-regional estimates of richness broadens the options for regional estimation.

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Small‐Sample Estimation of Species Richness Applied to Forest Communities

Cited by 15 publications

References 39 publications

Ratio Plot and Ratio Regression with Applications to Social and Medical Sciences

Ratio Plot and Ratio Regression with Applications to Social and Medical Sciences

Estimating change in species richness from repeated sampling of incidence data

Sample-based Estimation of Regional Forest Tree Species Richness

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