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The thermal-summation model converts temperature records into accumulated degree days or degree hours, the currency forensic entomologists use to predict blow fly development rates and back-calculate colonisation dates from larval stage.
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A blow fly larva does not know the date. It does know, in the only sense that matters biologically, how much heat it has absorbed since it hatched. Development from egg to adult is not clocked by days on a calendar but by thermal units, the cumulative product of time and temperature above a threshold below which the biological machinery slows to a standstill. This is the thermal-summation model, and it is the engine under the hood of almost every precise PMI estimate in forensic entomology.
The model expresses thermal accumulation as accumulated degree days (ADD) or the finer-grained accumulated degree hours (ADH). Both measure the same thing: the sum of temperature above a species-specific base value, across the time interval since oviposition. Once a developing larva reaches the ADD or ADH required for its current stage, it moults. Once it reaches the total for the full developmental sequence, it pupates. The forensic entomologist works backward from the stage found to the heat accumulated, and from the heat accumulated to the date it was deposited.
That backward calculation requires two inputs beyond the larva itself: a reliable temperature record and the correct developmental dataset for the species in hand. Getting either of those wrong inflates the error on the final date estimate. This topic covers how the model works, how to source and correct the temperature data, and where the arithmetic can mislead a careful analyst who does not understand the model's limits.
Temperature does not just affect development speed. It defines it.
For most insects in the range between their lower and upper developmental thresholds, there is a near-linear relationship between temperature and development rate. A larva kept at 25 degrees Celsius will develop roughly twice as fast as one kept at 15 degrees Celsius (assuming a base of 5 degrees and ignoring the upper threshold for now). This linearity is what makes the thermal-summation model both mathematically simple and practically powerful.
The key experimental measurement is the thermal constant, also called K: the total ADD or ADH required to complete a developmental stage from egg hatch to moulting, or from oviposition to adult eclosion. Researchers determine K by rearing cohorts of the target species at several constant temperatures and recording the time to complete each stage. Plotting development rate (1/days) against temperature gives a straight line; the x-intercept is the base temperature and the reciprocal of the slope gives K. These constants are published in peer-reviewed literature for the main forensically important species and form the reference database the analyst uses.
Daily averages hide the variation that larvae actually experience.
ADD sums daily mean temperatures above the base temperature. If the daily mean at a scene on a given day was 20 degrees Celsius and the base temperature for the species is 4 degrees Celsius, that day contributes 16 DD to the cumulative total. The simplicity of ADD makes it attractive when only daily temperature records are available, which is the case for many older meteorological stations and rural locations.
The problem with ADD is that the daily mean smooths out variation that is biologically real. Consider a day with a high of 30 degrees and a low of 10 degrees at a base of 4 degrees. The mean is 20 degrees, giving ADD of 16. But if those temperatures held for equal hours, the 12 nighttime hours at 10 degrees contributed (10 minus 4) times 12 = 72 degree-hours, and the 12 daytime hours at 30 contributed (30 minus 4) times 12 = 312 degree-hours, for a total of 384 ADH, equivalent to 16 ADD. No error so far. But in reality, temperature curves through the day and the hourly breakdown is not symmetric. More critically, when nights fall below the base temperature, those hours contribute zero to development, and averaging them into a daily mean effectively attributes thermal units to periods when no development was occurring.
| Metric | ADD | ADH |
|---|---|---|
| Unit | Degree-days (DD) | Degree-hours (DH) |
| Data requirement | Daily mean temperature | Hourly temperature readings |
| Temporal resolution | 1 day | 1 hour |
| Error when nights are cold | Overestimates development | Correctly excludes sub-base hours |
| Preferred when | Only daily station data available | Hourly station or logger data available |
Modern meteorological networks and in-scene data loggers typically record at hourly or sub-hourly intervals. Where that data is available, ADH is preferred because it excludes sub-base hours directly rather than averaging them away. The difference between ADD and ADH matters most in continental climates with large diurnal temperature swings and in spring or autumn cases when night temperatures regularly fall below the base temperature.
The station reading is a proxy for the scene; treat it as such.
No weather station sits at the crime scene. The analyst must obtain historical temperature records from the nearest available station and use them as a proxy for the temperature the larvae actually experienced. Standard practice in most forensic entomology guidelines requires documenting the station used, its distance from the scene, its elevation relative to the scene, and any known systematic differences in exposure (urban versus rural, coast versus inland).
The arithmetic is simple; the discipline is in the inputs.
Once the analyst has a corrected scene temperature series and a species-specific developmental dataset, the back-calculation is straightforward. Starting from the examination date and working backward through the temperature series, ADD or ADH is accumulated hour by hour or day by day until the cumulative total matches the thermal requirement for the stage found. The date at which the total is reached is the estimated oviposition date, and it defines the floor on the mPMI.
In practice the calculation is performed in a spreadsheet or purpose-built software such as the PAST (Postmortem Arthropod Succession Tool) packages developed in academic laboratories, or the publicly available Estimating Postmortem Interval tool maintained by researchers at several European universities. The analyst inputs the examination date, the corrected temperature series, the base temperature, and the stage-specific thermal constant, and the tool outputs the back-calculated date range.
The result is presented as a date range rather than a single point, for two reasons. First, the developmental data themselves carry experimental variance. Second, the temperature correction introduces uncertainty. Good practice is to run the calculation using the lower and upper bounds of the developmental thermal constant and report the resulting date range with that uncertainty stated explicitly.
A precise calculation on imprecise inputs still gives an imprecise answer.
The thermal-summation model is well validated but its accuracy depends entirely on the quality of the inputs. The main error sources, in rough order of practical impact, are:
A blow fly species has a base temperature of 4 degrees Celsius. On a day with a mean temperature of 20 degrees Celsius, how many degree days does that day contribute to accumulated ADD?
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