An examination of the thresholds of enrichment: a resource-based growth model

A model of single-species growth in the chemostat on two non-reproducing, growth-limiting, noninhibitory, perfectly substitutable resources is considered. The medium in the growth vessel is enriched by increasing the input concentration of one of the resources. Analytical methods are used to determine the effects of enrichment on the asymptotic behaviour of the model for different dilution rates. It is shown that there exists a threshold value for the dilution rate which depends on the maximal growth rate of the species on each of the resources. Provided the dilution rate is below the threshold, enrichment is beneficial in the sense that the carrying capacity of the environment is increased, regardless of which resource is used to enrich the environment. When the dilution rate is increased beyond the threshold, it becomes important to consider which resource is used for enrichment. For one of the resources it is shown that, while moderate enrichment can be beneficial, sufficient enrichment leads to the extinction of the microbial population. For the other resource, enrichment leads from washout or initial condition dependent outcomes to survival, and is thus beneficial. There are important implications of these results to the management of natural aquatic ecosystems. For example, while enrichment may be beneficial to the microbial species during the summer months, it can lead to their decimation during spring run-off, when the natural dilution rate is higher.