Models are a flourishing and indispensable area of research in language evolution. Here we
highlight critical issues in using and interpreting models, and suggest viable approaches. First,
contrasting models can explain the same data and similar modelling techniques can lead to
diverging conclusions. This should act as a reminder to use the extreme malleability of
modelling parsimoniously when interpreting results. Second, quantitative techniques similar to
those used in modelling language evolution have proven themselves inadequate in other
disciplines. Cross-disciplinary fertilization is crucial to avoid mistakes which have previously
occurred in other areas. Finally, experimental validation is necessary both to sharpen models'
hypotheses, and to support their conclusions. Our belief is that models should be interpreted as
quantitative demonstrations of logical possibilities, rather than as direct sources of evidence.
Only an integration of theoretical principles, quantitative proofs and empirical validation can
allow research in the evolution of language to progress.