Calculating Time of Colonization

Dipteran larvae are poikilothermic, and therefore do not produce their own heat (Beck, 1983; Nation, 2011). Instead, they are affected by the ambient temperature, which determines how quickly or slowly they grow (Davidson, 1944; Beck, 1983; Nation, 2011). The warmer the ambient temperature, the faster they go through their instars and pupal stage. The slower the ambient temperature, the slower they go through their instars and pupal stage. It is this property that allows forensic entomologists to apply insect development data to determine a time of colonization estimation on animal remains. This also makes temperature the most important density independent factor for insects (Beck, 1983; Byrd & Castner, 2010).

Temperature has a profound effect on dipteran metabolic and developmental rate (Nation, 2011). Generally, within certain temperature ranges, larval development is accelerated as ambient temperature increases. This does not hold true at temperature extremes, however. Every insect has thermal activity and death thresholds—both lower and upper limits, below or above which they can no longer function (Block, 1982; Beck, 1983; Nation, 2011). These thermal thresholds are naturally different for different species. Those species that evolved in tropical or warmer areas will have higher upper limits than those that evolved in temperate or colder areas (Addo-Bediako et al., 2000). Therefore, there is a huge variation among species when it comes to temperature thresholds. The lower limits are better known than the upper limits and become important when mathematically calculating a time of colonization estimation (Block, 1982; Nation, 2011). Developmental thresholds for forensically important flies are usually between 6°C and 10°C and are experimentally determined. If a specific fly species developmental threshold is not available, a general rule of thumb is to use 6°C for winter species or flies in cold areas, and 10°C for warm weather species or flies in warmer areas (Davies & Ratcliffe, 1994; Anderson, 2000; Ames & Turner, 2003; Catts & Haskell, 2008).

Each stage of insect growth, from egg to adult, requires a certain amount of heat above a minimum temperature and below a maximum temperature (Davidson, 1944; Hagstrum & Milliken, 1988). This growth rate can be represented with a linear model that represents the amount of heat necessary for a given fly to go through each of its developmental stages. These linear models are called degree day or degree hour models, because development is recorded as the temperature above the minimum developmental threshold multiplied by time (days or hours) (Pruess, 1983; Yang et al., 1995; Megyesi et al., 2005; Michaud & Moreau, 2011).

This model allows us to calculate the time it takes a fly to develop using ambient temperature and this formula:

(Average Ambient Temperature — Minimum Threshold) x Unit of Time

This formula takes the average ambient temperature over a given time period, subtracts the minimum threshold for the insect species, and multiplies the result by a unit of time. The result is called a “degree day” (if the unit of time used was a day) or a "degree hour” (if the unit of time used was an hour). These are the two most common units of time seen in this type of model, because weather stations often record ambient temperature in daily or hourly intervals.

The formula may be used to calculate how many degree days (DD) or degree hours (DH) are necessary for an insect to get through various stages in its life cycle, as well as how many degree days have accumulated over time. The DD/DH necessary for an insect to get through its life cycle is determined by experiment. The data are recorded as hours needed for a species to develop at a given temperature, and these data may be converted into DD or DH by using the formula.

Table 5.2 shows several forensically important insects and the time it takes each insect to develop at various temperatures. Take, for example, the hours necessary for the black blowfly, Phormia regina, to develop at 27°C. According to research, it takes P. regina eggs 16 hours to go from freshly laid to hatching, 18 hours to go through the first larval instar, 11 hours to go through the second larval instar, and 36 hours to go through the third larval instar. To turn this information into degree hours, simply plug the data into the equation:

EggDH: '

• (27°C - 10°C) x 16 hours
• (17°C) x 16 hours
• 272 DH

In this case, it takes P. regina 272 DH to go through its entire egg stage. This same calculation may be used to determine DD.

Egg DD:

• (27°C - 10°C) x 0.67 days (17°C) x 0.67 days
• 11.39 DD

Table 5.2 Example of average ambient temperatures and calculated DD/ ADD from a weather station

The number of DD or DH necessary for each stage of P. regina development may be calculated in this same way.

First instar DH/DD:

• (27°C - 10°C) x 18 hours
• (17°C) x 18 hours
• 306 DH or 12.75 DD

Second instar DH/DD:

• (27°C - 10°C) x 11 hours
• (17°C) x 11 hours
• 180 DH or 7.5 DD

Third instar DH/DD:

• (27°C - 10°C) x 36 hours
• (17°C) x 36 hours
• 612 DH or 25.5 DD

The results may be summed up to determine the accumulated degree days (ADD) or accumulated degree hours (ADH necessary for P. regina to develop from freshly oviposited egg through the end of the third instar):

11.39 DD + 12.75 DD + 7.5 DD + 25.5 DD = 57.14 DD

This may be calculated for any range of developmental stages in an insect’s life cycle.

Once the ADD or ADH necessary for insect development is known, it is possible to calculate the time necessary for the DD to accumulate at recorded ambient temperatures. The species threshold temperature is used in the same DD formula, but the average temperature is a weather station recording over a given period of time.

If, for example, a weather station recorded an average temperature of 15°C over one day, then the DD accumulated over that one day may be calculated:

• (15°C - 10°C) x 1 day
• (5°C) x 1 day
• 5 DD

This calculation shows that five DDs accumulated over that one day. Each passing day may be calculated in the same way, and the results added up to produce the accumulated degree days over any given period of time:

Average temperature (°C) on 4 separate days: 15°C, 20°C, 21 °C, 18°C DD for each day: 5 DD, 10 DD, 11 DD, 8 DD

ADD over the 4 days: 5 DD + 10 DD +11 DD + 8 DD = 34 DD

Once all this information is calculated, the DD necessary for an insect species to develop is applied to the total DD accumulated over a period of time to determine how long it would take an insect to develop to an observed life stage given the recorded ambient temperature. This information is easiest when visualized in Table 5.2.

Notice that the dates in the table are listed in descending order; this method allows an entomologist to start with the date on which insect evidence was collected, and work backward in time to determine the minimum insect colonization interval. In Table 5.2, 11 DD were accumulated on May 15, 15 DD on May 14, 12 DD on May 13, etc., so 57.14 DD to get from egg through the end of the third instar.

If maggots at the very end of the third instar were found on an animal at the end of the day on May 15, the ADD necessary for those maggots to develop through the third instar may be used to determine when the eggs were laid. In this case, P. regina needs 57.14 DD to develop through the third instar. There were not enough DD accumulated on May 15 to reach that number, so the eggs could not have been laid on May 15 and had time to reach the observed life stage. Since only 25 DD accumulated between May 14 and 15, there still wasn’t enough time for the fly to reach its third instar. Enough DD accumulated between May 11 and May 15, however, for the insect to reach its observed life stage. In this instance, we can say the eggs had to have been laid sometime on May 11 or earlier to reach the third instar by May 15. This gives a minimum time of colonization estimation based on the life history of the flies colonizing an animal.

The efficacy of this method of the DD model of time of colonization estimation is dependent upon the availability of growth rate data for particular necrophagous species. These data are experimentally obtained and tend to be published as a life table or developmental rate of particular insect species. Table 5.3 represents a selection of published developmental data for commonly encountered forensically important flies.