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 Pyhäjärvi in the northern hemisphere (Finland, northern Europe, lat. 60°54′–61°06′, long. 22°09′–22°22′). 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 8 years 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 (45 μgC L−1) and the upper limit for total phosphorus concentration (16 μg L−1) that satisfy with 0.95 probability our predefined water quality criteria (Cyanobacteria concentration during late summer period does not exceed the value 0.86 mg L−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.