We present a mathematical model based on differential equations describing the dynamics of nitrogen (NH4+, NO2-, NO3- and organic nitrogen in phytoplankton) in ponds of white shrimp (Litopenaeus vannamei), with low salinity and zero turnovers, from planting to harvest. The model predicts the results of commercial production in three ponds. We show that this culture system, without replacement, retains the nitrogen and shrimp produced a lower feed conversion in comparison with systems with replacement. The model can be used to define strategies for improved performance.