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This paper develops a semi-Markov process model for describing ecological data, and demonstrates the utility of the model by fitting it to data on the migration of a marked population of shrimp. Gamma transit time distributions are selected for the model by reason of the qualitative properties of their transfer rate functions. Occupancy probabilities, mean residence times and other related parameters are estimated from the data for the assumed semi-Markov process model. These results are compared to those for a corresponding Markov process model which is widely used and was previously fitted to the same data. The semi-Markov process model provides a better fit for the data with substantial increases in the precision of corresponding parameter estimates. Further generalizations of this compartmental modeling approach to other semi-Markov process models are also discussed.