Deterministic and stochastic plankton dynamics: Effects of contamination, refuge, and additional food sources

Studying plankton systems encompasses different interests, including understanding ecological cycles and developing sustainable strategies in aquaculture research regarding food security. Zooplankton farming is economically valuable, and its production may depend primarily on the availability of phytoplankton and other external food sources. However, diverse factors may affect overall phytoplankton–zooplankton interactions. For example, phytoplankton’s defense mechanisms, such as finding refuge and releasing toxins or low phytoplankton’s sustainable environments, can decrease zooplankton populations. Another critical factor is the adverse effects of pollution on plankton systems, which are more frequently present in water bodies. Still, zooplankton may survive harsh conditions if present pollutants are in low concentrations and external sources, including animal waste, are available. The partial understanding of these trophic interactions depends on initial assumptions, and using stochastic approaches may reduce the gap between deterministic mathematical outcomes and reality. In this work, we have mathematically described a planktonic system under the above assumptions using a deterministic model as well as its stochastic version. Our findings suggest that zooplankton growth is possible under polluted environments by providing them with external food sources, complementing phytoplankton availability. However, in these circumstances, random external environmental factors may cause the phytoplankton population to collapse. Through stochastic numerical experiments, we estimate which possible scenarios are more likely to induce phytoplankton extinction in these plankton systems.