A stoichiometrically derived algal growth model and its global analysis

Xiong Li,Hao Wang

doi:10.3934/mbe.2010.7.825

Abstract

Organisms are composed of multiple chemical elements such as carbon, nitrogen, and phosphorus. The scarcity of any of these elements can severely restrict organismal and population growth. However, many trophic interaction models only consider carbon limitation via energy flow. In this paper, we construct an algal growth model with the explicit incorporation of light and nutrient availability to characterize both carbon and phosphorus limitations. We provide a global analysis of this model to illustrate how light and nutrient availability regulate algal dynamics.

Highlights

For growth and maintenance of organismal cells, carbon (C), nitrogen (N) and phosphorus (P) are vital chemical elements: C supplies energy, N is an essential component of proteins, and P is an essential component of nucleic acids
We obtain the following observations: 1) Algae go extinct if the nutrient is severely limiting; 2) Algae always survive with sufficient nutrient and any nonzero light intensity; 3) Whenever algae can survive, the unique internal steady state is globally attracting under strong light, whereas the boundary steady state with algal C at its carrying capacity is globally attracting under weak light
We find that algal quality is worse when light is stronger and algal quality is better when the nutrient availability is higher

Summary

Introduction

For growth and maintenance of organismal cells, carbon (C), nitrogen (N) and phosphorus (P) are vital chemical elements: C supplies energy, N is an essential component of proteins, and P is an essential component of nucleic acids. Stoichiometry, algae, phosphorus, carbon, nutrient, light, cell quota, global stability. To show the global stability of the origin, we devise a transformation to generate a new system that is defined at this steady state.

Results

Conclusion