The presence of heavy metals influences the efficiency of anaerobic fermentation and results in the variations of the relationships among the fermentation parameters. In this study, the impacts of elevated Cu2+ concentrations on relationships among biogas properties, process stability, substrate biodegradation, and enzyme activity were analysed by Pearson correlation analysis based on the experimental data of a mesophilic anaerobic co-fermentation with mixed acid pretreated Phragmites australis straw and raw cow dung as feedstocks. The results showed that in the absence of Cu2+, the cumulative biogas yields were positively related to pH values (0.780, p < 0.05) and negatively related to oxidation-reduction potential values (−0.909, p < 0.01) and cellulase activity (−0.937, p < 0.01). The coenzyme F420 activity was negatively related to volatile fatty acid (VFA) concentrations (−0.756, p < 0.05). In the presence of 30 mg/l Cu2+, correlation coefficients between the cumulative biogas yields and pH values, ammonia nitrogen (NH4+-N), VFA, chemical oxygen demand, hemicellulose, and cellulose were higher than the control group, indicating the efficient hydrolysis, acidogenesis, and acetogenesis stages. High Cu2+ concentrations (500 mg/l) resulted in almost completely different impacts on these relationships from the low Cu2+ concentrations, especially on the hydrolysis stage. [ABSTRACT FROM AUTHOR]