Discussion

Many variables that influence the rate of development of insects are not usually incorporated into the commonly-applied models for estimating PMImin, largely because of the paucity of relevant data. At present forensic entomologists generally estimate a PMImin using a reliable, simplified model and then account for confounding variables using qualitative estimates of their bias and precision (Table 7.1) derived from peer-reviewed scientific literature, ad hoc experimentation and their experience.

Fortunately, not all of the confounding variables are equally prevalent or equally significant (Table 7.1). For example, inaccuracy arising from using incubator temperature setting instead of direct measurement of maggots' temperatures overshadows any affect that lighting has on development (Nabity et al. 2007).

Table 7.1 Reported qualitative worst-case estimates of the bias and precision in PMI . associated with different confounding variables affecting insect development in corpses, ranked by the magnitude of the error. The effects are not necessarily additive, and can be ameliorated under some conditions

Source

Bias

Minimum precision

Modelling

Variable

Variable

Circadian Rhythms

Variable

Hours

Light-induced variability

Variable

Hours

Precocious development

Overestimated (temperature-

Hours, up to duration of

dependent)

embryonic developm

Preservation and measurement

Variable

Hours to days

Promptness of arrival

Underestimated in general

Hours to days

Overestimated with myiasis

Days to weeks

Diet

Variable (tissue- and species-

Days

dependant)

Drugs

Variable (drug- and species-

Days

dependant)

Competition

Underestimated by size

Days

Overestimated by

Days

developmental events

Wandering

Underestimated

Days

Maggot-generated heat

Overestimated

Days

Developmental plasticity

Variable

Days

Chilling

Underestimated

Days

Overestimated

Weeks

Diapause

Underestimated

Months

Ruling out some variables is easier in earlier stages of development because they have not had time to manifest themselves, while variation has also had less time to accumulate, which simplifies estimation. The disadvantage of working with early stages is that an error of, say, 24 h may represent a relative error of 100% in the first day of development, but only 4.5% by the time of eclosion. Thus, precocious development is most problematic in young larvae (because of the large relative error), while maggot-generated heat becomes an increasingly serious problem as larvae age. This emphasises the collection of data at an appropriate resolution to minimise relative error (Richards and Villet 2008; Richards and Villet 2009) and processing entomological evidence as soon after its discovery as possible.

The sources of error are not necessarily additive; lesser errors may be subsumed within greater ones. In particular, the resetting of the developmental clock by circa-dian rhythms can effectively resynchronise development at several points in insects' life cycles, helping to eradicate the accumulating variation due to other factors. Furthermore, errors counteract one another in some cases because of their opposing biases (Table 7.1). Maggot-generated heat and competition may have opposing effects on growth rates as maggot densities increase, and errors in the estimation of the parameters of thermal accumulation models tend to cancel out because the two model parameters (K and D0) are inversely correlated (Trudgill et al. 2005).

There is scope for research on the interaction of confounding variables that operate on comparable time scales.

The complexity of integrating all of the parameters discussed in this chapter into an accurate mathematical model is daunting; assessing the interactions amongst their varying precisions is even more of a Gordian knot. However, it is undue cause for gloom. First, akin to Zeno's paradoxes, there is a finite envelope of possibility for diapause-free insect development, outlined quite literally in isomorphen diagrams (Grassberger and Reiter 2001; Midgley and Villet 2009b; Richards and Villet 2009; Richards et al. 2008; Richards et al. 2009b). In many worst-case situations, one can still estimate bounds on a PMImn. Second, the physical model provided by dead pigs achieves all of this integration without needing as much parameterization (Turner and Wiltshire 1999). Pigs provide simulations of ecological succession that appear to be both repeatable and representative of the processes on human corpses (Schoenly et al. 1991; Schoenly et al. 1996; Schoenly et al. 2005; Schoenly et al. 2007; Shahid et al. 2003), and can very probably serve the same role in providing a valid model for development. Even simulations using minced meat can provide realistic estimates (Faucherre et al. 1999). Third, statistical models are becoming increasingly sophisticated (Ieno et al. 2010), and await suitable data to test their capabilities (Richards and Villet 2008; Richards et al. 2008; VanLaerhoven 2008). Even given these reasons for optimism, it is likely that the inherent variation (or estimate precision) of insect development will limit the accuracy of estimates of PMI to about 5-15% of the true elapsed time. Whether this is satisfactory will min r J

depend on the contingencies of the particular case.

Finally, there is great scope for the development and validation of standard methods and best practices (Amendt et al. 2007; Peters et al. 2007). Some progress has been made in this direction in terms of rearing techniques (e.g. (Ireland and Turner 2005; Nabity et al. 2007; Tarone and Foran 2006)), entomotoxicological validation (Peters et al. 2007) and experimental design (Richards and Villet 2008). It is particularly desirable that the sampling, measuring and estimation methods used to handle case material are closely similar to those used to generate benchmark data, so that the validity, precision, bias and reliability of estimates of PMImin are not disputed.

Acknowledgements We thank Lucy Glover and Kerri-Lynne Kriel for helping with the experiment in Fig. 7.4; Kendall Crous, Martin Grassberger, Mervyn Mansell, Iain Patterson and Ben Price for their input on various topics in this chapter; and Susan Abraham for help with graphics.

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