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

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.


Species richness, total abundance, and β1i values for early‐successional bird species in larch plantation patches. (A) Species richness and (B) total community abundance as a function of patch area. Solid and dotted black lines indicate the median and 95% CIs derived from multispecies abundance model (HM), respectively. Vertical line indicates the smallest area of our sampled patches. Estimated values smaller than this area are derived from extrapolation of the model. Solid and dotted gray lines were predictions from  models under constant density hypothesis. Due to high detection probability of bird species, observed species richness and abundances were equal to their estimated values. (C) Estimated values of β1i from the abundance model for each species. Solid line is the median and the inner and outer dotted lines are the 50% and 95% CIs, respectively. The rightmost box and vertical bar indicate the median, 50%, and 95% CIs of the estimated community‐level hyperparameter (mean value of β1i across species).
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ece32244-fig-0003: Species richness, total abundance, and β1i values for early‐successional bird species in larch plantation patches. (A) Species richness and (B) total community abundance as a function of patch area. Solid and dotted black lines indicate the median and 95% CIs derived from multispecies abundance model (HM), respectively. Vertical line indicates the smallest area of our sampled patches. Estimated values smaller than this area are derived from extrapolation of the model. Solid and dotted gray lines were predictions from models under constant density hypothesis. Due to high detection probability of bird species, observed species richness and abundances were equal to their estimated values. (C) Estimated values of β1i from the abundance model for each species. Solid line is the median and the inner and outer dotted lines are the 50% and 95% CIs, respectively. The rightmost box and vertical bar indicate the median, 50%, and 95% CIs of the estimated community‐level hyperparameter (mean value of β1i across species).

Mentions: Although we observed 39 bird species within patches and in mature forest adjacent to patches, mature forest species were transient and rarely detected on more than one visit. We encountered 150 territories of the 12 strictly early‐successional species. Community‐level detectability (individual‐level detection probability averaged across species, p¯), which was derived from the posterior median of the hyperparameter, was 0.66 (0.53–0.73). This suggests that each territory would be detected at least once if sites were visited five times (>99%). Indeed, estimated species richness and community‐level (total) abundance at each site were not different from the observed values (Fig. 3A,B). Estimated species richness increased with patch area as a saturating curve. The confidence intervals for the effect of area at individual and community levels (β1i and β¯1) included 1, indicating that all of these bird species showed no dependence of density on patch area (Fig. 3C). Indeed, predicted values of species richness and total abundance from multispecies models were quite similar to those from models assuming constant density (Fig. 3A,B).


Estimating species   –   area relationships by modeling abundance and frequency subject to incomplete sampling
Species richness, total abundance, and β1i values for early‐successional bird species in larch plantation patches. (A) Species richness and (B) total community abundance as a function of patch area. Solid and dotted black lines indicate the median and 95% CIs derived from multispecies abundance model (HM), respectively. Vertical line indicates the smallest area of our sampled patches. Estimated values smaller than this area are derived from extrapolation of the model. Solid and dotted gray lines were predictions from  models under constant density hypothesis. Due to high detection probability of bird species, observed species richness and abundances were equal to their estimated values. (C) Estimated values of β1i from the abundance model for each species. Solid line is the median and the inner and outer dotted lines are the 50% and 95% CIs, respectively. The rightmost box and vertical bar indicate the median, 50%, and 95% CIs of the estimated community‐level hyperparameter (mean value of β1i across species).
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getmorefigures.php?uid=PMC4979711&req=5

ece32244-fig-0003: Species richness, total abundance, and β1i values for early‐successional bird species in larch plantation patches. (A) Species richness and (B) total community abundance as a function of patch area. Solid and dotted black lines indicate the median and 95% CIs derived from multispecies abundance model (HM), respectively. Vertical line indicates the smallest area of our sampled patches. Estimated values smaller than this area are derived from extrapolation of the model. Solid and dotted gray lines were predictions from models under constant density hypothesis. Due to high detection probability of bird species, observed species richness and abundances were equal to their estimated values. (C) Estimated values of β1i from the abundance model for each species. Solid line is the median and the inner and outer dotted lines are the 50% and 95% CIs, respectively. The rightmost box and vertical bar indicate the median, 50%, and 95% CIs of the estimated community‐level hyperparameter (mean value of β1i across species).
Mentions: Although we observed 39 bird species within patches and in mature forest adjacent to patches, mature forest species were transient and rarely detected on more than one visit. We encountered 150 territories of the 12 strictly early‐successional species. Community‐level detectability (individual‐level detection probability averaged across species, p¯), which was derived from the posterior median of the hyperparameter, was 0.66 (0.53–0.73). This suggests that each territory would be detected at least once if sites were visited five times (>99%). Indeed, estimated species richness and community‐level (total) abundance at each site were not different from the observed values (Fig. 3A,B). Estimated species richness increased with patch area as a saturating curve. The confidence intervals for the effect of area at individual and community levels (β1i and β¯1) included 1, indicating that all of these bird species showed no dependence of density on patch area (Fig. 3C). Indeed, predicted values of species richness and total abundance from multispecies models were quite similar to those from models assuming constant density (Fig. 3A,B).

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.