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Calcium imaging with fluorescent protein sensors is widely used to record activity in neuronal populations. The transform between neural activity and calcium-related fluorescence involves nonlinearities and low-pass filtering, but the effects of the transformation on analyses of neural populations are not well understood. We compared neuronal spikes and fluorescence in matched neural populations in behaving mice. We report multiple discrepancies between analyses performed on the two types of data, including changes in single-neuron selectivity and population decoding. These were only partially resolved by spike inference algorithms applied to fluorescence. To model the relation between spiking and fluorescence we simultaneously recorded spikes and fluorescence from individual neurons. Using these recordings we developed a model transforming spike trains to synthetic-imaging data. The model recapitulated the differences in analyses. Our analysis highlights challenges in relating electrophysiology and imaging data, and suggests forward modeling as an effective way to understand differences between these data.