Research

DUWC Research–EPA Star Grant Project Develops a Bayesian Hierarchical Modeling Approach

Using part of the results from their larger, multi-year study of the Everglades, Duke University Wetland Center researchers Curtis J. Richardson and Song S. Qian won an EPA Science to Achieve Results (STAR) grant in 2005 to develop a Bayesian hierarchical modeling approach for estimating ecological thresholds. The hierarchical modeling approach is built on the Bayesian change point methods of Qian et al. (2003, 2004) for single species/metric. Single metric methods have been successfully used in the Everglades research (as described in a 2007 article by Richardson et al. in Environmental Science and Technology). Richardson and Qian’s STAR research is focused on the interaction among multiple metrics within the ecosystem of interest.

Initially, DUWC researchers discovered that the TP threshold for the Everglades varies by metrics. Even for a single metric, the estimated threshold varies over time. For example, Figure 1 shows how the bladderwort (Utricularia purpurea) stem density drops suddenly when TP concentration exceeds a certain value (the threshold) and that the threshold changes over time and season.

Figure 1: Observed total Utricularia stem counts are plotted against the previous 6 month average total phosphorus concentrations. The stem counts vary greatly by year and season. The stem counts also respond to the changes in phosphorus concentration, and the count is generally small when phosphorus concentration is high. A threshold is apparent in most year-seasons.

To understand the factors affecting the changes in TP threshold, conventional mathematical and statistical methods are insufficient and the Bayesian hierarchical modeling approach is necessary. This is because traditional methods can only analyze the threshold response using data specifically for a single metric observed from a single sampling event. There is no easy way to combine data from multiple metric and dates without some ecologically unrealistic assumptions. As part of the effort, Qian studied the application of the hierarchical (or multilevel) analysis of variance in ecological data analysis, publishing his results in a paper in the journal Ecology (Qian 2007). This effort led to a new statistical method for analyzing combined threshold data from multiple metrics and multiple sampling events. The new method preserves individual (metric, sampling event) specific features and can be used to study there interaction. Using this method, Qian and Richardson re-analyzed the bladderwort stem count data from all sampling events. They found that the varying threshold value is slowly converging to a stable value (Figure 2).

Figure 2: Estimated year-season interaction effects on TP threshold of total Utricularia stem count show the differences of year/season-specific thresholds from the overall average. The figure shows that the estimated year/season-specific threshold are gradually converging towards the overall mean, suggesting that the dosing system was gradually mature after initial dose of phosphorus.

The STAR project is nearing the end of the funding period. Researchers are preparing documents that will summarize several important findings:

1) The use of Bayesian hierarchical change point method for detecting and quantifying ecological threshold is feasible. This finding is an important contribution to the field in that it provides a series of quantitative methods for combining data from multiple sources to understand ecological responses at both individual metrics and ecosystem levels.

2) The Bayesian hierarchical method can also be used to account for interactions among species.

3) The hierarchical modeling approach also introduces an ecosystem-level response that can be easily integrated into a decision-making process.

Related Articles

Qian, S.S., and Z. Shen. 2007. Ecological applications of multilevel analysis of variants. Ecology 88 (10):2489-2495.

Richardson, C.J., R.S. King, S.S. Qian, P. Vaithiyanathan, R.G. Qualls, and C.A. Stow. 2007. Estimating ecological thresholds for phosphorus in the Everglades. Environmental Science and Technology 41 (23):8084-8091.

Richardson, C.J., and S. Qian. 1999. Long-term phosphorus assimilative capacity in freshwater wetlands: A new paradigm for maintaining ecosystem structure and function. Environmental Science and Technology 33 (10):1545-1551.

Qian, S.S., and C.J. Richardson. 1997. Estimating the long-term phosphorus accretion rate in the Everglades: A Bayesian approach with risk assessment. Water Resources Research 33:1681-1688.

Nicholas School of the Environment

DUWC Research–EPA Star Grant Project Develops a Bayesian Hierarchical Modeling Approach
Using part of the results from their larger, multi-year study of the Everglades, Duke University Wetland Center researchers Curtis J. Richardson and Song S. Qian won an EPA Science to Achieve Results (STAR) grant in 2005 to develop a Bayesian hierarchical modeling approach for estimating ecological thresholds. The hierarchical modeling approach is built on the Bayesian change point methods of Qian et al. (2003, 2004) for single species/metric. Single metric methods have been successfully used in the Everglades research (as described in a 2007 article by Richardson et al. in Environmental Science and Technology). Richardson and Qian’s STAR research is focused on the interaction among multiple metrics within the ecosystem of interest. Initially, DUWC researchers discovered that the TP threshold for the Everglades varies by metrics. Even for a single metric, the estimated threshold varies over time. For example, Figure 1 shows how the bladderwort (Utricularia purpurea) stem density drops suddenly when TP concentration exceeds a certain value (the threshold) and that the threshold changes over time and season. Figure 1: Observed total Utricularia stem counts are plotted against the previous 6 month average total phosphorus concentrations. The stem counts vary greatly by year and season. The stem counts also respond to the changes in phosphorus concentration, and the count is generally small when phosphorus concentration is high. A threshold is apparent in most year-seasons. To understand the factors affecting the changes in TP threshold, conventional mathematical and statistical methods are insufficient and the Bayesian hierarchical modeling approach is necessary. This is because traditional methods can only analyze the threshold response using data specifically for a single metric observed from a single sampling event. There is no easy way to combine data from multiple metric and dates without some ecologically unrealistic assumptions. As part of the effort, Qian studied the application of the hierarchical (or multilevel) analysis of variance in ecological data analysis, publishing his results in a paper in the journal Ecology (Qian 2007). This effort led to a new statistical method for analyzing combined threshold data from multiple metrics and multiple sampling events. The new method preserves individual (metric, sampling event) specific features and can be used to study there interaction. Using this method, Qian and Richardson re-analyzed the bladderwort stem count data from all sampling events. They found that the varying threshold value is slowly converging to a stable value (Figure 2).
		Figure 2: Estimated year-season interaction effects on TP threshold of total Utricularia stem count show the differences of year/season-specific thresholds from the overall average. The figure shows that the estimated year/season-specific threshold are gradually converging towards the overall mean, suggesting that the dosing system was gradually mature after initial dose of phosphorus.
The STAR project is nearing the end of the funding period. Researchers are preparing documents that will summarize several important findings: 1) The use of Bayesian hierarchical change point method for detecting and quantifying ecological threshold is feasible. This finding is an important contribution to the field in that it provides a series of quantitative methods for combining data from multiple sources to understand ecological responses at both individual metrics and ecosystem levels. 2) The Bayesian hierarchical method can also be used to account for interactions among species. 3) The hierarchical modeling approach also introduces an ecosystem-level response that can be easily integrated into a decision-making process. Related Articles *Qian, S.S., and Z. Shen. 2007. Ecological applications of multilevel analysis of variants. Ecology* 88 (10):2489-2495. Richardson*, C.J., R.S. King, S.S. Qian, P. Vaithiyanathan, R.G. Qualls, and C.A. Stow. 2007. Estimating ecological thresholds for phosphorus in the Everglades. Environmental Science and Technology* 41 (23):8084-8091. Richardson, C.J., and S. Qian. 1999. Long-term phosphorus assimilative capacity in freshwater wetlands: A new paradigm for maintaining ecosystem structure and function. Environmental Science and Technology 33 (10):1545-1551. *Qian, S.S., and C.J. Richardson. 1997. Estimating the long-term phosphorus accretion rate in the Everglades: A Bayesian approach with risk assessment. Water Resources Research* 33:1681-1688.**
	Nicholas School of the Environment