Introduction

Forensic pathologists and entomologists estimate the minimum post-mortem interval since a long time by describing the stage of succession and development of the necrophagous fauna (Amendt et al. 2004). From very simple calculations at the beginning, (Bergeret, see also Smith 1986) the discipline has evolved into a more mathematical one (e.g. Marchenko 2001; Grassberger and Reiter 2001, 2002) and tries to implement concepts like probabilities and confidence intervals (Lamotte and Wells 2000; Donovan et al. 2006; Tarone and Foran 2008, see also Villet et al. this book Chapter7). As pointed out by Tarone and Foran (2008) and Van Laerhoven (2008), the latter is one of the major tenets of the Daubert Standard (Daubert et al. v. Merrell Dow Pharmaceuticals (509 U.S. 579 (1993)).

Forensic Entomology deals with living systems and this means that we face problems related to influences depending e.g. on the time of the year, the ecosystem of the scene of crime or the geographic origin of the insects. Not surprisingly these varieties of possible impacts thwart the efforts to establish a statistically robust result in a forensic report, leading to strange situations in court, where the different methods and opinions of different experts may lead to different or inherent results and reports (Westerfield trial in San Diego, CA, USA (People v. Westerfield)). In a forensic context, this is simply a disaster for the reputation of the used method. The background of this problem is discussed in more detail by Villet et al. (this book Chapter7), and it can be stated that it is at least partly related to the application and misuse of statistical methods used in the past. In the present chapter we introduce methods which may help to better analyse forensic entomology data sets.

Highlands Statistics Ltd., 6 Laverock Road, AB41 6FN, Newburgh, Aberdeenshire, UK J. Amendt and H. Fremdt

Institute of Forensic Medicine, Kennedyallee 104, 60596, Frankfurt am Main, Germany A.A. Saveliev

Faculty of Geography and Ecology, Kazan State University, 18 Kremlevskaja Street, Kazan, 420008, Russia

J. Amendt et al. (eds.), Current Concepts in Forensic Entomology, 139

DOI 10.1007/978-1-4020-9684-6_8, © Springer Science + Business Media B.V. 2010

As mentioned above, several variables may influence the development of an insect, and certainly they sometimes don't just act simply by oneself, but in combination. This is valid as well for drugs, which are assimilated by maggots during feeding (see Lopes de Carvalho in this book Chapter 9). For the estimation of the post-mortem interval, it is always an important question to know if the presence of a particular drug causes an impairment of the development of the necrophagous insects. In a recent study, Fremdt (2008) showed the influence of an antemortem administration of a combination of two drugs on the insect successional patterns under natural conditions and the development on the blowfly Calliphora vicina. In this chapter, we use data from a similar study and show how to deal with interactions between three different types of drugs affecting the non-linear growth rates of the blowfly Calliphora vicina.

Our target audience is the reader who is familiar with linear regression models, tools which are still quite popular in forensic entomology. Traditional statistical methods like linear regression are based on a series of assumptions, some of which are violated for the data used here, as we will see later. We will discuss these assumptions; show how to verify them, and the implications of violating them. We also show how to solve the problems, and apply a series of methods that are all, in some way, extensions of linear regression. The underlying mathematics are not discussed here; the interested reader can consult Pinheiro and Bates (2000), Ruppert et al. (2003), or Wood (2006). Ecological applications can be found in Schabenberger and Pierce (2002), Crawley (2005), and Zuur et al. (2007, 2009), or for social science examples, see Keele (2008).

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