A Bayesian observation error model to predict cyanobacterial biovolume from spring total phosphorus in Lake Mendota, Wisconsin

• Published in: Canadian journal of fisheries and aquatic sciences 1997-02, Vol.54 (2), p.464-473
• Main Authors: Stow, C A, Carpenter, S R, Lapthrop, R C
• Format: Article
• Language: English
• Subjects: Animal, plant and microbial ecology; Biological and medical sciences; Freshwater; Fundamental and applied biological sciences. Psychology; Marine biology; Microbial ecology; Phosphorus; Phosphorus compounds; Various environments (extraatmospheric space, air, water)
• ISSN: 0706-652X; 1205-7533
• DOI: 10.1139/f96-279

The fit of a simple linear model relating cyanobacterial biovolume (CBV) to spring total phosphorus concentration in lake Mendota was compared with the performance of a logistic single-parameter model in which CBV was related to an inverse exponential function of total phosphorus level. Historic data from 1976 to 1987 were used. Nonlinear least squares techniques were applied which demonstrated the superiority of the second model. The model was further refined by incorporating uncertainties in the sample estimates of the true mean phosphorus values. Bayes theorem was employed to assess model parameters and predictive uncertainty. When compared with a model which took no account of phosphorus uncertainty, the observation error model had a higher parameter variance but lower prediction uncertainty. This occurred because some of the noise in the data was resolved as phosphorus uncertainty, thus reducing the variance of the model disturbance term. The model resulted in less stringent phosphorus targets to meet acceptable CBV levels than the model which ignored uncertainty.