Water Control Policies in Lakes with Vertical Heterogeneity: an Algal Competition Modelling Approach

The algal competition between blue-green algae (cyanobacteria) and green algae (chlorophytes) is a topic that is widely treated both from the biological point of view and from that of the ecological modelling. The spread of blue-green algae in fresh waters, in fact, represents a problem of great interest linked to the quality of water and to the production by these organisms of cyanotoxins particularly toxic not only for the flora and fauna but also for humans. Moreover, blue-green algal blooms are associated with high levels of water turbidity and, due to their inedibility, less ecosystem biodiversity. Several models have been proposed to test algal competition and to propose different control strategies on the ecosystem that can lead to the disappearance of blue-green algae with consequent dominance of green algae. However, these models relate to spatially homogeneous lakes. Here, a more realistic algal competition model in a heterogeneous lake is proposed, by introducing a vertical stratification in the water body and assuming that organisms and nutrients can migrate (with mixing rate
$D$
) from the lower to the upper compartment and vice-versa. The analysis of the model not only shows that small/medium mixing rate
$D$
can promote algal coexistence, but also provides useful suggestions for the control of water quality that differ to a large extent from what has been achieved in the case of lake homogeneity.