The FO (First Order) Laplacian-approximation-based method was developed around the 1970s and it was the first method used in population PK analysis [7].
The FO model engine
applies to Gaussian data only (the observation data is assumed to be Gaussian distributed),
is faster but less accurate than FOCE and Laplacian methods, producing results with poor statistical quality,
is useful for initial estimates but not recommended for final parameter estimates
requires a single minimization of an objective function representing an approximate negative marginal log likelihood,
uses population predictions with 
= 0, leading to less accurate estimates,
iterations involve the quasi-Newton optimization algorithm, repeating until the same log likelihood is achieved within a tolerance of 0.001.