A novel mathematical model and application software for estimating the age of necrophagous fly larvae

The change in larval body length of necrophagous flies during their development is a key indicator for estimating larval age. However, existing forensic entomological models have limitations in this regard. In this study, a logistic algorithm was used to establish a general model for estimating the minimum postmortem interval (PMI_min) using larval body length. The new model was used to simulate the relationship between larval body length and developmental time of eight species of necrophagous flies. The model parameters of body length variation with developmental time of the different species were calculated. Computer software was developed based on the established logistic model. The advantage of the new model is that each parameter has a biological meaning and can be used to estimate the age of larvae at any temperature and any larval body length. Cross-validation of the model showed that the overall mean accuracy of the fitted growth curves for the eight necrophagous fly larvae was 82.7%, the mean accuracy of age extrapolations for seven necrophagous fly species ranged from 76.8% to 92.9%, while the accuracy of age extrapolations for only one species was lower (i.e., 63.3%). This study provides a new method to estimate the PMI_min based on larval body length, and the developed computer software will facilitate its application in forensic entomology.