Estimating abundance from presence/absence maps

Abstract

Summary1. An important question in macroecology is: Can we estimate a species' abundance from its occurrence on landscape? Answers to this question are useful for estimating population size from more easily acquired distribution data and for understanding the macroecological occupancy-abundance relationship. 2. Several methods have recently been developed to address this question, but no method is general enough to provide a common solution to all species because of the wide variation in spatial distribution of species. 3. In this study, we developed a mixed Gamma-Poisson model that generalizes the negative binomial model and can characterize spatial dependence in the abundance distribution across cells. Under this framework, without any extra information, the clumping parameter and species abundance can be estimated using a map aggregation technique. This model was tested using a set of empirical census data consisting of 299 tree species from a 50-ha stem-mapped plot of Panama. 4. A comparison showed that the new method outperformed the previous methods to an appreciable degree. Particularly for abundant species in a finely gridded map (5 · 5 m), its bias is very small and the method can also reduce the root mean square error up to 30%. Like for previous methods, however, the new method's performance decreases with the increase in cell size. 5. As a by-product, the new method provides an approach to estimate spatial autocorrelation of species distribution which is otherwise difficult to estimate for presence ⁄ absence map.

Successional dynamics in Neotropical forests are as uncertain as they are predictable

“…This approximate AIC balances the goodness of fit (as measured by the log-likelihood of the regression relating observed and fitted values) and the number of parameters of the models (38). Because the nonlinear model (Eq.…”

Optimal design of butterfly occupancy surveys and testing if occupancy converts to abundance for sparse populations

“…In conservation, occupancy is typically regarded as inferior to abundance because it does not provide early warning of population declines (Pollock 2006;Joseph et al 2006). However, by assuming that a species' detectability is largely a function of its abundance, and recognizing that change in population size typically accompanies change in proportion of area occupied Longcore et al 2010), it is possible to reliably estimate abundance and population trend from occupancy data (He and Gaston 2000;Royle and Nichols 2003;Pollock 2006;Zhou and Griffiths 2007;Hui et al 2009;Hwang and He 2011;but see Strayer 1999). Detection/non-detection data tend to approximate patch-level processes with far less effort than abundance surveys (MacKenzie et al 2003;Zhou and Griffiths 2007), and may provide the best information under limited resources.…”

Consistent estimation of species abundance from a presence–absence map

“…When applied to forest census data (Condit et al, 1996), they showed that the estimator based on the generalized gamma Poisson model could improve estimation of abundance from occurrence data. To date, however, no statistical properties of the estimators of He and Gaston (2000) and Hwang and He (2011) are known. Even consistency has not been proven.…”

“…It is more appropriate to consider the spatial correlation of the λ ij over the cells so that the λ ij in neighboring cells are more similar than between those that are further apart. This observation motivated Hwang and He (2011) to model the mean levels as a gamma random field. Formally, let V st , s, t ∈ Z Z = {0, −1, 1, −2, 2, .…”

“…In addition, Conlisk (2007) showed that there is no solution from the negative binomial model under the correct distribution. To overcome the weaknesses of this approach, Hwang and He (2011) proposed an extension in the gamma-Poisson model framework. This extension yields a generalized gamma-Poisson mixtured model that has meaning in the ecological context.…”