  Marine ecosystem models are developed to understand and simulate the
biogeochemical processes involved in marine ecosystems. Parekh, Follows and
Boyle introduced the $PO_4$-$DOP$-$Fe$ model of the coupled phosphorus and iron
cycles in 2005. Especially the part describing the phosphorus cycle
($PO_4$-$DOP$ model) is often applied in the context of parameter
identification. The mathematical analysis presented in this study is concerned
with the existence of solutions and the reconstruction of parameters from given
data. Both are important questions in the numerical model's assessment and
validation not answered so far. In this study, we obtain transient, stationary
and periodic solutions (steady annual cycles) of the $PO_4$-$DOP$-$Fe$ model
equations after a slight change in the equation modeling iron. This result
confirms the validity of the solutions computed numerically. Furthermore, we
present a calculation showing that four of the $PO_4$-$DOP$ model's parameters
are possibly dependent, i.e. different parameter values might be associated
with the same model output. Thereby, we identify a relevant source of
uncertainty in parameter identification. On the basis of the results, possible
ways to overcome this deficit can be proposed. In addition, the stated
mathematical conditions for solvability are universal and thus applicable to
the analysis of other ecosystem models as well.
