Bayesian modelling of algal mass occurrences - using adaptive MCMC methods with a lake water quality model

Our study aims to estimate confounded effects of nutrients and grazing zooplankton (Crustacea) on phytoplankton groups-specifically on nitrogen-fixing Cyanobacteria-in the shallow, mesotrophic Lake Pyhajarvi in the northern hemisphere (Finland, northern Europe, lat. 60^o54'-61^o06', long. 22^o09'-22^o22'). Phytoplankton is modelled with a non-linear dynamic model which describes the succession of three dominant algae groups (Diatomophyceae, Chrysophyceae, nitrogen-fixing Cyanobacteria) and minor groups summed together as a function of total phosphorus, total nitrogen, temperature, global irradiance and crustacean zooplankton grazing. The model is fitted using 8years of in situ observations and adaptive Markov chain Monte Carlo (MCMC) methods for estimation of model parameters. The approach offers a way to deal with noisy data and a large number of weakly identifiable parameters in a model. From our posterior simulations we calculate the lower limit for zooplankton carbon mass concentration ([email protected]^-^1) and the upper limit for total phosphorus concentration ([email protected]^-^1) that satisfy with 0.95 probability our predefined water quality criteria (Cyanobacteria concentration during late summer period does not exceed the value 0.86mgL^-^1). Within the observational range total phosphorus has marginal effect on Cyanobacteria compared to the zooplankton grazing effect, which is temperature-dependent. Extensive fishing efforts are needed to attain the criteria.

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