An Incidence-Based Richness Estimator for Quadrats Sampled Without Replacement

Abstract

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.

Downscaling species occupancy from coarse spatial scales

“…Once it is calibrated at fine resolutions across multiple species, one could then predict the number of total species present inside the entire study region. Many different models have been proposed to upscale species richness from fine to coarse areas (see e.g., Ulrich and Ollik 2005, Shen and He 2008, Conlisk et al 2009). This approach provides an alternative method, defined within a unified and coherent framework, that may complement such predictions.…”

Sample-based Estimation of Regional Forest Tree Species Richness

“…The third estimator  sh S was developed by Shen and He for fixed-area plot wor sampling from a finite area population (Shen & He, 2008). A zero-truncated binomial distribution is assumed for the number of plots containing a given species, and a modified beta-distribution for the distribution of the probability of the plot-level presence/absence of a species.…”

“…After fitting the modified beta-distribution to the data, an explicit solution to the probability that a species occurred in x sample quadrats was obtained (EQ 4 p 2053) and used in a multinomial likelihood (Sanathanan, 1972) to estimate the number of unseen species. 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.…”

Estimating change in species richness from repeated sampling of incidence data

“…For the purpose of estimating forest tree species richness -at a given point in time  from a sample of species incidence data collected from fixed-area survey plots, the estimators by Shen and He (2008), Mingoti and Meeden (1992), Magnussen et al (2010), and Magnussen (2011) hold promise. Although any estimator of species richness can be used for estimation of change from repeat sample-based observation of species incidence data, the efficiency of the chosen estimator, in terms of variance, depends on how well it captures the temporal correlation of species incidence.…”

“…Estimating forest tree species richness from a forest inventory (monitoring) sample is a complex challenge with important issues related to temporal changes in the sample frame (Lister & Scott, 2009), sample size (Brose, Martinez, & Williams, 2003;Cao, et al, 2004;Hortal, Borges, & Gaspar, 2006), plot size (Brose, et al, 2003;Gimaret-Carpentier, Pelissier, Pascal, & Houllier, 1998;Shen & He, 2008), species identification (Archaux, 2009;Archaux et al, 2009), and choice of estimator (Mao & Lindsay, 2007;Walther & Morand, 1998). This study only deals with the last issue but fully recognizes that its importance depends critically on having satisfactory addressed all the other issues first.…”