  The Lotka-Volterra model is widely used to model interactions between two
species. Here, we generate synthetic data mimicking competitive, mutualistic
and antagonistic interactions between two tumor cell lines, and then use the
Lotka-Volterra model to infer the interaction type. Structural identifiability
of the Lotka-Volterra model is confirmed, and practical identifiability is
assessed for three experimental designs: (a) use of a single data set, with a
mixture of both cell lines observed over time, (b) a sequential design where
growth rates and carrying capacities are estimated using data from experiments
in which each cell line is grown in isolation, and then interaction parameters
are estimated from an experiment involving a mixture of both cell lines, and
(c) a parallel experimental design where all model parameters are fitted to
data from two mixtures simultaneously. In addition to assessing each design for
practical identifiability, we investigate how the predictive power of the
model-i.e., its ability to fit data for initial ratios other than those to
which it was calibrated-is affected by the choice of experimental design. The
parallel calibration procedure is found to be optimal and is further tested on
in silico data generated from a spatially-resolved cellular automaton model,
which accounts for oxygen consumption and allows for variation in the intensity
level of the interaction between the two cell lines. We use this study to
highlight the care that must be taken when interpreting parameter estimates for
the spatially-averaged Lotka-Volterra model when it is calibrated against data
produced by the spatially-resolved cellular automaton model, since baseline
competition for space and resources in the CA model may contribute to a
discrepancy between the type of interaction used to generate the CA data and
the type of interaction inferred by the LV model.
