# Interval estimation of thermal summation parameters in forensically important insects

## TL;DR

This paper introduces a new method for estimating insect development parameters with interval estimates, improving accuracy in forensic entomology.

## Contribution

A novel method using finite mixture Weibull distributions and EM algorithm for interval estimation of thermal summation parameters.

## Key findings

- The new method achieved 95% coverage for developmental data of two beetle species.
- Ikemoto and Takai’s method had only 59% and 75% coverage for the same species.
- The approach accounts for individual variability and identifies component populations in datasets.

## Abstract

Estimating time of death based on entomological evidence commonly relies on the “law of total effective temperature”, which requires developmental parameters of specific insect taxa. These are often calculated using the method of Ikemoto and Takai. However, this approach has key limitations. Most importantly, the lack of interval estimates may give the false impression of population homogeneity, which contradicts the substantial variation typically observed in insect populations. In this study, we propose an alternative method. It estimates interval values for developmental parameters while simultaneously identifying component populations within a dataset. The method involves fitting a finite mixture of Weibull distributions to development time data using the Expectation-Maximization (EM) algorithm. This allows for the inclusion of individual-level variability in the estimation process. We tested the method using previously published developmental data on two beetle species, Creophilus maxillosus and Necrodes littoralis (Staphylinidae). Our approach yielded 95% intervals with coverage close to the nominal level, in contrast to Ikemoto and Takai’s method, which captured only 59% and 75% of actual cases, respectively. These findings suggest that our method improves the accuracy of insect-based postmortem interval estimates in forensic entomology and, more broadly, provides a general framework for interval estimation of developmental parameters applicable in thermal ecology and applied entomology.