Mathematical Modeling and Applications to Riverine Ecosystems

Project: National Science and Technology CouncilNational Science and Technology Council Academic Grants

Project Details


Competition for resources is an important interaction between species, for which mathematical theory has been successful in predicting the persistence and coexistence of particular species based on their mechanisms of resource consumption. Several works have now considered populations and resources that are distributed in spatially variable habitats. It was found that even with one nutrient, coexistence of two competing species is possible for competition in the flow reactor habitat, with transport of nutrient and organisms by both advection and diffusion. The flow reactor model has been further included a hydraulic storage zone, again with similar outcomes for persistence and coexistence of competing populations. The flow reactor and its modifications are very important because they provide a simple model for riverine reservoirs. Many previous works provide useful results on competitive dynamics in spatially variable habitats, but have neglected some important biological facts. First, they only considered a single hydraulic storage zone in their systems. Models with multiple storage zones have been proposed or discussed in the existing engineering literature. Second, they have all assumed that consumption of nutrients and growth of populations are directly proportional though a quota constant, representing the amount nutrient contained in one individual. However, it is known that for many microorganisms the quota of nutrient per individual varies dynamically, so that nutrient is stored internally within organisms. Due to some difficulties, internal storage has been ignored in theoretical work for spatially variable habitats. Finally, the production of toxins that act against competing species, known as allelopathy, is also a crucial factor that potentially influences competitive outcomes. It will be biologically and mathematically interesting if we can incorporate allelopathy with internal storage of the nutrient in the dynamics of resource competition. To answer these three questions just summarized, we shall propose and study several models described by advection-dispersion-reaction systems or ordinary differential equations.

Project IDs

Project ID:PA10307-0653
External Project ID:MOST103-2115-M182-001-MY2
Effective start/end date01/08/1431/07/15


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