A general approach for postmortem interval based on uniformly distributed and interconnected qualitative indicators

Based on the results of previous pig carcass studies [26, 38‐40] and case histories [41‐44], a list of definitive insect species was prepared for the rural habitats of Central Europe (Online Resource: ESM 2). The only precondition the species had to meet was regular breeding in large cadavers. Species to be used in the validation tests were selected based on their distribution over PMI and availability of the necessary data.

Temperature models for PAI of developmental stages were estimated using previous methods [45] and data from previous studies [46, 47]. It was assumed that PAI starts at the moment of death and ends in the midpoint between the first collection of relevant insect specimen and the time when previous sample was taken. Although oviposition PAI of most carrion flies is poorly related to preceding temperature [46], it was assumed that the dependence of PAI on temperature will get stronger for later life stages due to the strong effect of temperature on the developmental rate of insects [5]. Accordingly, temperature models for PAI were also created for life stages of flies.

The method was validated using results of previous experiment [26, 27], with pig carcasses exposed in xerothermic grasslands (Western Poland, Europe; 52°31′N, 16°55′E) during spring, early, and late summer of 2012. Each seasonal block comprised eight cadavers (naked and clothed, cadaver mass 7–64 kg). Insects were sampled manually and with pitfall traps. Ground level temperatures were recorded at every carcass. The baseline data used to validate the method were different from the data used to develop the PAI models from the previous paragraph.

The validation procedure comprised several steps. First, relevant data were extracted from insect occurrence records of the baseline experiment; they included PMIs in which relevant configurations of life stages (presence/absence of subsequent stages) had been observed (hereafter referred as true PMI). In the second step, the current method was used to estimate PMI (hereafter referred as estimated PMI). Estimates were made for each day with relevant configuration of life stages. Temperature records were obtained from a local weather station and were retrospectively corrected to accommodate systematic differences between weather station and places where cadavers were exposed [48]. Then, using the temperature method, PAI for the present developmental stage was estimated [29]. The predictor temperature (i.e., temperature used to predict PAI with the model) was approximated using the following procedure. The average monthly PAI was extracted from a local carrion insect database. Temperature was averaged for this PAI starting from the day when the given configuration had been recorded and calculating backward. Corrected weather station temperatures were used in these calculations. The resultant average temperature was used as the first approximation of predictor temperature, and eventually the first PAI estimate was made. This procedure was iterated twice because such iterations were found to improve the approximation of predictor temperature and resultant estimate of PAI [29]. While iterating, in each case, the PAI estimate from the previous iteration was used to approximate predictor temperature in the next iteration. In the end, the 3rd estimate of PAI was used as the lower PMI. Using the same method and data, PAI for the absent life stage (defining upper PMI) was estimated. The third approximation of predictor temperature as used for the PAI of the present life stage in the previous step was used for this purpose. Average monthly PAIs were used instead of temperature estimates for these life stages that reveal a poor relationship between PAI and temperature. Monthly PAIs were calculated based on the same data from which temperature models were estimated. The midpoint between resultant lower and upper PMI is the estimated PMI. Next, error rate of the method was analyzed.

All analyzes were made at the 5% level of significance using Statistica 12 (StatSoft, Inc.).

Due to the finely uniform distribution of their life stages over PMI, L. caesar (Diptera: Calliphoridae), Thanatophilus sinuatus, and N. littoralis (Coleoptera: Silphidae) met the requirements to be included in the tests (Online Resource: ESM 1). Larval instars of the species and additionally the egg stage and the post-feeding larval stage of L. caesar were used as indicators. Consequently, eight configurations were tested (Table 1), covering about 20 days of decomposition. Temperature models for PAI were of acceptable quality for the 2nd and the 3rd larval stages (feeding and post-feeding phase) of L. caesar and for all the larval stages of T. sinuatus and N. littoralis (Online Resource: ESM 1-2). Due to the low quality of temperature models, the average monthly PAIs were used for the egg stage and the 1st larval stage of L. caesar (Online Resource: ESM 2).

PMI estimates were highly aggregated around the line representing perfectly accurate estimates in the entire PMI range (Fig. 4). A regression model for the relationship between estimated and true PMI (linear regression, estimated PMI = 0.6173 + 0.8934 * true PMI, t = 42.3, P < 0.001, r ² = 0.83, Fig. 4) only slightly deviated from the line representing perfect estimates (Fig. 4). Relative error of estimation decreased with an increase in PMI (Fig. 5). This finding suggests that configurations relevant for short PMI have higher estimation error than configurations relevant for long PMI. A formal comparison of configurations according to the error rate revealed highly significant differences (Kruskal-Wallis test, H_{(7, 371)} = 88.8, P < 0.001), with beetle configurations having lower error rates than fly configurations (Table 2, Online Resource: ESM 1). Error rates were not related to carcass mass (linear regression, relative error of estimation = 0.30057 − 0.000735 * carcass mass, t = −0.62, P = 0.535, r ² = 0.001, Online Resource: ESM 1).

Confidence intervals (Table 3) based on practical error rates (Online Resource: ESM 1) were narrower for beetle configurations than for fly configurations; they were reasonably small for beetle configurations, indicating that the method may give robust PMI estimates.

Current results demonstrate that insect successional indicators may produce accurate PMI estimates without using indicator persistence time (IPT). When they are interconnected and uniformly distributed over PMI, the presence and absence of subsequent indicators (here life stages of carrion insects) coupled with the estimation of their PAI gives a reliable and easily accessible knowledge of PMI.

The method has several advantages. First, it covers a wide range of PMI, similar to development-based entomological methods [5] or decomposition-based taphonomic methods [10]. Moreover, through the inclusion of other species and life stages, this range may be expanded outperforming development-based entomological methods. Stearibia nigriceps (Diptera: Piophilidae), Omosita colon (Coleoptera: Nitidulidae), species of Necrobia (Coleoptera: Cleridae) or Dermestes (Coleoptera: Dermestidae), and parasitoids of blowfly pupae, for example, Nasonia vitripennis (Hymenoptera: Pteromalidae), regularly colonize cadavers long after death [7, 26, 41, 49] and, from this point of view, may expand the range until about 3 months after death. Inclusion of eggs, pupae, and tenerals may have similar effect. Second, the method has a fine resolution, dividing PMI into many uniform and narrow subintervals. From this point of view, it outperforms decomposition-based taphonomic methods, in case of which subintervals enlarge with an increase in PMI [10]. Third, the method is accurate, particularly with these configurations for which PAI may be estimated using temperature methods. Although some methods have lower error rates, for example, methods based on cadaver temperature [50], accuracy of the current method is higher than some other approaches relevant for long PMI, for example, decomposition-based taphonomic methods [10, 51], or similar as compared to the others, for example, development-based entomological methods. Fourth, it may be easily applied in the forensic routine, as it needs only good insect sample and reliable temperature data. Fifth, accuracy of PMI estimation is unrelated to cadaver mass, and, from this point of view, the method outperforms other insect successional methods [17, 18, 52].

The method has, however, also some disadvantages. First, its good performance depends on the professional sampling of insects. Several life stages used are difficult to be sampled due to their small size (eggs or first instar larvae) or cryptic behavior (e.g., larvae of some beetle species). Although these effects may be reduced by including accessory species (i.e., species colonizing cadavers at time regimes similar to the major species), without standardized and professionalized sampling on a crime scene, the method may be ineffective. Second, the method needs sophisticated baseline data, that is, temperature models for PAI or average monthly or seasonal PAIs for particular life stages of carrion insects. Current protocols for decomposition studies cannot provide such data, and consequently, rebuilding them will be necessary. A framework for novel protocol was published recently [45]. Third, problems may arise with recolonizing taxa [12], as they may have two (or more) separated intervals during which the same configuration of indicators is present. A recent study revealed that species feeding on long-lasting carrion parts or arthropods present in such parts frequently recolonize on large cadavers [40]. Moreover, it was indicated that winter break in insect activity is necessary for the occurrence of recolonization [40]. Therefore, these estimation problems may occur for overwintered cadavers, for which the method seems to be inapplicable. Another possible disadvantage is the dependence of the method upon the environment in which cadaver was found. Because environments differ in composition of carrion fauna [53‐55], cadavers in different environments may have different definitive species. Moreover, when average monthly PAI is used instead of temperature estimates, the most accurate PMI estimates will be given from the PAI data specific for the environment in which cadaver was found. The questions whether average monthly or seasonal PAIs differ across environments and how large are these differences remain, however, open. From the other side, in the case of these taxa for which PAI may be estimated using temperature methods, validation studies for these methods [29, 56, 57] suggest that a single PAI model may be used across habitats. Moreover, previous data suggest that temperature models for PAI may give accurate estimates for insects from different geographic populations [56], and this finding indicates that the current PAI models may be to some extent used also across different geographic areas. All these problems need, however, further studies.

Although the method was calibrated for immature insects, it may be tempting to include adult insects. Most previous successional approaches for PMI used adult insects as primary indicators [9, 17, 52]. The inclusion of adult insects may be, however, problematic for two reasons. First, adult insects may be present on cadaver longer than all immature life stages. For this reason, the presence of adult stage and absence of 1st instar larval stage may occur twice, that is, at the beginning and at the end of adult stage residency, and this may decrease the accuracy of PMI estimation with the method. Second, there are carrion species that may be present on some cadavers exclusively as adult stage, for example, N. littoralis on some small or medium cadavers was found only as an adult stage [26]. In such cases, the time regime during which adult insects are present and 1st instar larval insects are absent may be distinctly prolonged, affecting the accuracy of estimation.

Although the method was tested only with insect successional markers, it may be similarly effective with other qualitative markers, in particular the ones that are reasonably interconnected and uniformly spaced over PMI. From this point of view, insect developmental indicators are very promising. Insect development may be easily represented as a sequence of qualitative changes uniformly spaced over insect life cycle and eventually over PMI. Forensic entomologists documented many examples of such stepwise distributions of external or internal morphological characters over the developmental timeline [14‐16, 58]. The current logic of estimation may be used to determine insect age from such distributions. Some morphological characters of immature insects may, however, also be used as direct PMI markers, similarly to the larval instars that were used here as primary indicators. Although modeling their occurrence along the PMI timeline will be challenging, the gain in resolution will compensate the necessary research efforts. Taphonomic markers are similarly promising. Cadaver decomposition may be described as a stepwise distribution of qualitative characters [1, 10], and some of them, for example, rigor mortis, bloating, or bone exposure, nicely fit the current approach for PMI. Moreover, it seems that all qualitative markers (entomological, taphonomic, etc.) may be combined in a single, multimarker method for PMI, incorporating the logic of estimation described in this article.