Species Assemblage Comparison with Abundance-based Data Using Zero-inflated Poisson Mixtures

Abstract

Species assemblage comparison is important in many ecological studies. In this paper, we develop a novel test for comparing species assemblages when abundance data from multiple quadrats are available. The test is based on the zero-inflated Poisson mixture model which we introduce to characterize the species assemblage given abundance data from multiple quadrats. We present a simulation study to evaluate the performance of our proposed test. The application of our test is further demonstrated on an ecological dataset. Comparison of species assemblages has important applications in ecology, since it provides crucial information about the spatial and temporal variations of ecosystems. There are two typical types of data collected in ecological studies: abundance-based data that contains the information of counts of each observed species in each sampling unit, and incidence-based data that only notes whether a species is present or absent in each sampling unit. Depending on the sampling procedure, the abundance-based data can be further divided into two categories. In one, the whole sampling area is treated as a single sampling unit, and the count information of each observed species is summarized for the whole area. The other has the sampling area divided into numerous plots, a sample of plots is randomly taken, and the count information of each observed species is recorded for each of the sampled plots. Following the terminology commonly used in ecology, we call those plots quadrats. We refer to the first type as abundance data from a single quadrat, and refer to the second type as abundance data from multiple quadrats. In the literature, mixture models are popular choices to model the ecological data due to their capabilities to account for heterogeneity among species (see, for example, Ord and Whitmore (1986), Bunge and Fitzpatrick (1993), Chao and Bunge (2002), Bohning and Schon (2005), Mao and Colwell (2005), Mao (2006)). More specifically, for incidence-based data, the binomial mixture model is usually