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Estimating species   –   area relationships by modeling abundance and frequency subject to incomplete sampling

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ABSTRACT

Models and data used to describe species–area relationships confound sampling with ecological process as they fail to acknowledge that estimates of species richness arise due to sampling. This compromises our ability to make ecological inferences from and about species–area relationships. We develop and illustrate hierarchical community models of abundance and frequency to estimate species richness. The models we propose separate sampling from ecological processes by explicitly accounting for the fact that sampled patches are seldom completely covered by sampling plots and that individuals present in the sampling plots are imperfectly detected. We propose a multispecies abundance model in which community assembly is treated as the summation of an ensemble of species‐level Poisson processes and estimate patch‐level species richness as a derived parameter. We use sampling process models appropriate for specific survey methods. We propose a multispecies frequency model that treats the number of plots in which a species occurs as a binomial process. We illustrate these models using data collected in surveys of early‐successional bird species and plants in young forest plantation patches. Results indicate that only mature forest plant species deviated from the constant density hypothesis, but the model suggested that the deviations were too small to alter the form of species–area relationships. Nevertheless, results from simulations clearly show that the aggregate pattern of individual species density–area relationships and occurrence probability–area relationships can alter the form of species–area relationships. The plant community model estimated that only half of the species present in the regional species pool were encountered during the survey. The modeling framework we propose explicitly accounts for sampling processes so that ecological processes can be examined free of sampling artefacts. Our modeling approach is extensible and could be applied to a variety of study designs and allows the inclusion of additional environmental covariates.

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Conceptual framework of ecological and sampling processes involved in modeling species–area relationships (SARs). Abundance of individual species in the area of interest is determined by their densities and its area, and true species richness is a consequence of these abundances. Unless sampling plots cover the area entirely, only individuals in the sampling plots are exposed to sampling. During field surveys, some individuals may be undetected because of imperfect detection. SARs are traditionally estimated using only detected species. In this study, we propose a sampling model to consider these two sources of incomplete sampling separately. To account for unobserved species due to incomplete sampling, “potential” species with zero detected individuals are augmented, and combined detection histories of detected and potential species are analyzed to estimate abundances of individual species (including unobserved species) in each area (denoted by “*”). Our estimate of species richness is obtained as a derived parameter (†, i.e., the posterior distribution of the number of species with at least one individual). Based on these quantities across the species (including unobserved species), the total abundance of communities and the species richness are estimated.
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ece32244-fig-0002: Conceptual framework of ecological and sampling processes involved in modeling species–area relationships (SARs). Abundance of individual species in the area of interest is determined by their densities and its area, and true species richness is a consequence of these abundances. Unless sampling plots cover the area entirely, only individuals in the sampling plots are exposed to sampling. During field surveys, some individuals may be undetected because of imperfect detection. SARs are traditionally estimated using only detected species. In this study, we propose a sampling model to consider these two sources of incomplete sampling separately. To account for unobserved species due to incomplete sampling, “potential” species with zero detected individuals are augmented, and combined detection histories of detected and potential species are analyzed to estimate abundances of individual species (including unobserved species) in each area (denoted by “*”). Our estimate of species richness is obtained as a derived parameter (†, i.e., the posterior distribution of the number of species with at least one individual). Based on these quantities across the species (including unobserved species), the total abundance of communities and the species richness are estimated.

Mentions: Here, we propose a framework to model SARs accounting for incomplete sampling using hierarchical community models (Royle and Dorazio 2008; Iknayan et al. 2014). Hierarchical community models are ensembles of species‐level models from which community‐level state variables such as species richness can be derived (Royle and Dorazio 2008). Hierarchical community models contain both a model for the ecological process of interest, the abundances or frequencies of individual species at each site, and a model for the sampling process by which the data were generated. The central concept of our approach is to simultaneously estimate SARs and abundances or frequencies of individual species, using a model that accounts for the imperfect detection of individuals in the sampled area and the incomplete spatial coverage of the study area by sampling plots. Furthermore, we consider the contributions to SARs of species undetected throughout the survey using data augmentation (Royle and Dorazio 2008) (see Fig. 2 for a conceptualization of our modeling framework). Because hierarchical community models can include species‐level covariates, our modeling framework can relax the assumption of constant density. For example, we can allow for positive or negative density–area relationships (DARs) for individual species, which prevail in many landscapes (Bender et al. 1998; Connor et al. 2000; Brotons et al. 2003).


Estimating species   –   area relationships by modeling abundance and frequency subject to incomplete sampling
Conceptual framework of ecological and sampling processes involved in modeling species–area relationships (SARs). Abundance of individual species in the area of interest is determined by their densities and its area, and true species richness is a consequence of these abundances. Unless sampling plots cover the area entirely, only individuals in the sampling plots are exposed to sampling. During field surveys, some individuals may be undetected because of imperfect detection. SARs are traditionally estimated using only detected species. In this study, we propose a sampling model to consider these two sources of incomplete sampling separately. To account for unobserved species due to incomplete sampling, “potential” species with zero detected individuals are augmented, and combined detection histories of detected and potential species are analyzed to estimate abundances of individual species (including unobserved species) in each area (denoted by “*”). Our estimate of species richness is obtained as a derived parameter (†, i.e., the posterior distribution of the number of species with at least one individual). Based on these quantities across the species (including unobserved species), the total abundance of communities and the species richness are estimated.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4979711&req=5

ece32244-fig-0002: Conceptual framework of ecological and sampling processes involved in modeling species–area relationships (SARs). Abundance of individual species in the area of interest is determined by their densities and its area, and true species richness is a consequence of these abundances. Unless sampling plots cover the area entirely, only individuals in the sampling plots are exposed to sampling. During field surveys, some individuals may be undetected because of imperfect detection. SARs are traditionally estimated using only detected species. In this study, we propose a sampling model to consider these two sources of incomplete sampling separately. To account for unobserved species due to incomplete sampling, “potential” species with zero detected individuals are augmented, and combined detection histories of detected and potential species are analyzed to estimate abundances of individual species (including unobserved species) in each area (denoted by “*”). Our estimate of species richness is obtained as a derived parameter (†, i.e., the posterior distribution of the number of species with at least one individual). Based on these quantities across the species (including unobserved species), the total abundance of communities and the species richness are estimated.
Mentions: Here, we propose a framework to model SARs accounting for incomplete sampling using hierarchical community models (Royle and Dorazio 2008; Iknayan et al. 2014). Hierarchical community models are ensembles of species‐level models from which community‐level state variables such as species richness can be derived (Royle and Dorazio 2008). Hierarchical community models contain both a model for the ecological process of interest, the abundances or frequencies of individual species at each site, and a model for the sampling process by which the data were generated. The central concept of our approach is to simultaneously estimate SARs and abundances or frequencies of individual species, using a model that accounts for the imperfect detection of individuals in the sampled area and the incomplete spatial coverage of the study area by sampling plots. Furthermore, we consider the contributions to SARs of species undetected throughout the survey using data augmentation (Royle and Dorazio 2008) (see Fig. 2 for a conceptualization of our modeling framework). Because hierarchical community models can include species‐level covariates, our modeling framework can relax the assumption of constant density. For example, we can allow for positive or negative density–area relationships (DARs) for individual species, which prevail in many landscapes (Bender et al. 1998; Connor et al. 2000; Brotons et al. 2003).

View Article: PubMed Central - PubMed

ABSTRACT

Models and data used to describe species–area relationships confound sampling with ecological process as they fail to acknowledge that estimates of species richness arise due to sampling. This compromises our ability to make ecological inferences from and about species–area relationships. We develop and illustrate hierarchical community models of abundance and frequency to estimate species richness. The models we propose separate sampling from ecological processes by explicitly accounting for the fact that sampled patches are seldom completely covered by sampling plots and that individuals present in the sampling plots are imperfectly detected. We propose a multispecies abundance model in which community assembly is treated as the summation of an ensemble of species‐level Poisson processes and estimate patch‐level species richness as a derived parameter. We use sampling process models appropriate for specific survey methods. We propose a multispecies frequency model that treats the number of plots in which a species occurs as a binomial process. We illustrate these models using data collected in surveys of early‐successional bird species and plants in young forest plantation patches. Results indicate that only mature forest plant species deviated from the constant density hypothesis, but the model suggested that the deviations were too small to alter the form of species–area relationships. Nevertheless, results from simulations clearly show that the aggregate pattern of individual species density–area relationships and occurrence probability–area relationships can alter the form of species–area relationships. The plant community model estimated that only half of the species present in the regional species pool were encountered during the survey. The modeling framework we propose explicitly accounts for sampling processes so that ecological processes can be examined free of sampling artefacts. Our modeling approach is extensible and could be applied to a variety of study designs and allows the inclusion of additional environmental covariates.

No MeSH data available.


Related in: MedlinePlus