Research
Quantifying Statistical Uncertainty in Succession-Based
Entomological Estimates of the Postmortem Interval in
Death Scene Investigations: A Simulation Study
Kenneth Schoenly, M. Lee Goff, Jeffrey D. Wells, and Wayne D. Lord
ABSTRACT Timetables of carrion-arthropod
succession provide critical baseline data for calculating entomology-based
estimates of the
postmortem interval (PMI) in cases of natural and untimely death; however, statistical confidence intervals typically do not accompany such
estimates because of lack of methodology. Using 2 computer-intensive
sampled randomization
tests (the Jackknife and Bootstrap) and data
from 3 studies of carrion-arthropod
succession, we investigated the degree to which the PM"'-id'h (upper PMI limit - lower PMI limit + 1)
was affected by missing taxa, corpse age, and taxonomic resolution of baseline data. Results generated from these methods were nearly
identical. In each of the 3 studies, variability (uncertainty) in the PM"'-idthincreased as the number of missing taxa increased and as baseline
data decreased in taxonomic resolution. In 8 of 9 other trials, the PM"'-id'h increased as corpse age increased and as the number of taxa (3,
6, and 9) used for the estimate decreased; in the exceptional case, the PM~id'h decreased with corpse age when 6 taxa were used. We conclude
that randomization
methods are potentially useful tools in forensic entomology both for conducting sensitivity analyses of arthropod
successional data and for assessing statistical uncertainty of entomology-derived
PMI estimates.
C
ONTRARY TO THE POPULAR ADAGE, DEAD MEN (AND WOMEN) DO
tell tales (Maples and Browning 1994), particularly if crime
scene investigators can decipher the scientific evidet3ce that
often accumulates following human death. Since the early studies of
Megnin (1894), Johnston
and Villeneuve (1897), and Motter
(1898), entomologists have applied developmental and successional
data of carrion-associated
arthropods to assist medicolegal investigators in cases of homicide, suicide, and accidental death. The most
familar use of entomological evidence in crimina I investigations is in
estimation of the postmortem interval (PMI), the time from death to
discovery of the corpse. PMI estimates have special relevance in a
homicide investigation because such knowledge narrows the field of
possible suspects in the crime (Geberth 1990). Recent reviews,
books, and case studies on forensic entomology include reports by
Nuorteva (1977), Leclercq (1978), Keh (1985), Smith (1986), Lord
and Rodriguez
(1989), Catts and Haskell (1990), Greenberg
(1991), and Catts and Goff (1992).
Historically, statistical (and other mathematical)
developments
in forensic entomology have been outpaced by observational and
experimental approaches.
For example, no succession-based study
has used numerical methods to calculate statistical confidence intervals about a PMI estimate or included sensitivity tests of baseline
data to determine closeness (=precision) of repeated PMI estimates
under different ecological and methodological
situations. Towards
this goa I, one important test is to determine if 95 % confidence intervals, derived from numerical methods, capture the true PMI in 95%
of the samples drawn from successional data. Beyond forensic entomology and PMI estimation, confidence intervals provide important
guidelines of legal evidence that bear a heavy burden in the resolution of courtroom disputes (Solomon 1986). Such statistical parameters have found application in other medicolegal disciplines sLlch as
forensic anthropology
(Giles and Klepinger 1988).
Table 1 presents results of several applications of entomological
data to PMI estimation for a few selected cases that have come to
trial. These cases include instances where estimates were based on
accumulated degree-hours (ADH) of developing larvae and successiona I patterns of adults and developing larvae. ADH-based estimates are extrapolations
of laboratory-rearing
data for particular
species at constant temperatures
and photoperiods.
In each case,
106
A. Insects Collected from Animal
Model (=Baseline Fauna)
B. Insects Collected from Human
Remains (=Corpse Fauna)
•
C. The Estimation
Corpse
fauna
Procedure
Baseline
fauna
D. Courtroom
Testimony
PMI (in da)'s)
I 2 3 4 5 6 7 8
:
: :
: :
:
:
-
:
c==-.
:
:
~~
~~
:
PMI estimate = 3-5 days. P~lI.;'''h = 3 da)'s
Fig. 1. How to estimate the postmortem interval (PMI) of human
remains from carrion-arthropod successional data. (A) Baseline data are
collected from an animal model in a time-series investigation. (B) In a
subsequent death scene investigation, members of the corpse fauna
are sampled from human remains, reared to adulthood (if necessary),
and identified to species and life-history stage. (e) In the laboratory,
corpse taxa are matched to baseline taxa. The lower and upper PMI
limits correspond to the 1st and last days matching taxa cooccur in the
succession; PMlwidth is the difference between the upper and lower PMI
limits. (0) PMI statistics are recorded in the entomologist's case report
and offered in courtroom testimony, if required.
AMERICAN
ENTOMOLOGIST
•
Slimmer
1996
50
A Early & Goff (1986)
PMI =4t05days
40
I
~
30
20
0..
10
-
-.
• ----j-
. -- --.
0
2
15
12
9
~
6
.- -
3
----
- - - - - .- -.
-
4
B. Nabaglo (1973)
PMI = 8 to 9 days
••.....
~
C1l
~
t- --1- --1- --.1- --5
6
- - -7
8
+--\--
j-.----- -j- ---~-----\--------------------
----
0..
3
0
2
3
4
5
6
7
8
with data from decomposition studies conducted in similar habitats
at similar times of the year. The developmental
stage and both the
presence and absence of a taxon are of significance in successionbased PMI estimates.
Although no confidence intervals were set for these 8 cases, fina I
estimates for ADH and succession-based
cases fit well with the
known facts (Table 1). Close agreement between actual and entomology-based PMl's in most of these cases may be due in part to the
locality where most were reported {Hawaii}. Compared
to other
localities, the tropical environment of the Hawaiian Islands has a
relatively uniform annual climate. Under these conditions, seasonal
fIuctations in insect populations and successional patterns are less
pronounced in Hawaii than at other sites. Moreover, the development of a dense network of weather stations throughout the Hawaiian archipelago, motivated by the extensive cultivation of sugar and
pineapple in the region, permits finer-scale uses of regional climate
data for PMI estimation than may be available at other sites.
The introduction
of statistical confidence intervals in forensic
entomology is the subject of this paper. Here, we use 2 computerintensive resampling methods (the Bootstrap and .Jackknife) and
published successional data to investigate the effects of missing species, corpse age, and taxonomic resolution of baseline data on arthropod-based
PMI estimates. Statistical methods for calculating
confidence intervals from insect developmental data have been pursued elsewhere (Wells and Kurahashi
1994, Wells and Lamotte
1995) and are beyond the scope of this paper.
Data
30
Three published studies, 1 from the forensic entomology literature (Early and Goff 1986) and 2 from the carrion ecology literature
(Nabaglo 1973, McKinnerney 1978) constituted the baseline data
. in this analysis. These reports were chosen because they included a
large number of diverse, mostly species-specific, taxa whose taxo-
C. McKinnemey (1978)
PMI = 12 to 13 days
25
20
~
~
~
0..
nomic and ecological
15
t---li-
- - - - - - - -- - - - -- - - - --
----
10
5
0
0
2
4
3
5
6
Nurrber of Missing Taxa
7
8
Fig. 2 A-C.
Effect of missing taxa on PMIv.idlhobtained by jackknifing
successional data from 3 carrion-arthropod reports. Nine randomly
selected taxa provided the starting PMI estimate in each case (see
Appendix). Vertical bars depict the range of the bootstrapped upper and
lower PMI limits; solid symbols depict the median, over the bootstrapped values, of the midpoint of the PMI [(upper PMI limit - lower
PMI Iimit)/2]. Horizontal dashed lines enclose the starting PMI estimates
in each study. PMI, postmortem interval.
initial estimates were based on a particular time period required for
the most mature larva recovered from human remains to reach that
sta~e of development under laboratory conditions. Initial estimates
then were adjusted usin~ available climatic data from weather stations located near the discovery site of the remains to give the final
PMI estimates listed in Table 1. In each case, the range of ADH values is due to variation between individual laboratory rearings at
different temperatures. ]n many instances, development-based
studies have proven reliable in PMI estimation when ranges of days and
multiple species have been used. In succession-based cases, arthropod assemhla~es collected from human remains were compared
AMERICAN
ENTOMOLOCIST
•
Slimmer 1996
features satisfied our requirements
for the ran-
domization and aggregation trials we discuss below. Descriptive
statistics of these data sets and 20 other carrion-arthropod
assemblages are given in Schoenly (1992).
The authors of these studies sampled arthropods from surfaceplaced carcasses, during the summer, on mostly consecutive days:
Early and Goff (Diamond Head Crater, HI, cat carcasses), days
1-13,15,17,19,21,23,25,27,29,31,34,41,51,76;
Nabaglo
(Ojc6w National Park, Poland, vole carcasses), days 1-30; and
McKinnerney (Hueco Mountains, TX, rabbit carcasses), days 1-26.
Because these data were reported by different authors in different
locations with different carcass types, they provide an internal check
for the effects of habitat, carcass taxon, and investigator bias. If
consistent patterns emerge among the studies, we can conclude that
these patterns are robust in spite of these differences.
For each dataset, an occurrence matrix, containing S daily samples (columns) and T taxa (rows), was constructed from the corresponding succession figure or table in each published report. For
example, if taxon A was collected on the 1st d of sampling, a '1' was
inserted in row A and column 1; otherwise there was a '0' (Scboenly
1992).
Methods
Estimating the PMI. Succession-based PMI estimation is a 2-step
process (Schoenly et al. 1992). First, baseline taxa are collected from
an anima I model (for example, a pig carcass) in 1 or more time-series
investigations (Fig. lA) to record successional arrival, departure,
and residence times of each carrion-arthropod
species. Beyond recording baseline successional data, companion studies on laborato-
107
Table 1. Selected medicolegal cases litigated in U.S. courts that included entomology-based PMIa estimates
No. taxonomic
units used in
PMI estimateb
Locality
A. ADH-based cases'
Hawaii
2
Hawaii
3
California
6
B. Succession-based cases
Hawaii
Lower limit and upper
limit taxa
Chrysomya mfifades
Macquart
C. mfifacies Macquart
C. megacephala (Fabricius)
C. mfifacies Macquart
Phaellicia sericata ,:Meigen)
P. sericata (Meigen)
Actual PMI
in dayse
5-6
6 (LSA)
Goff et al. 1988
5-5.5
5 (LSA)
Goff et al. 1988
33-25
3.25 (C)
NP
Referenced
10.5-11
11(C)
NP
52+
53 (C)
Goff and adorn (1987)
19-20
20 (C)
Goff et al. (19R6)
Philollflms IOllgicomis Stephens
Hermetia iIIltcells (L.)
34-39
38 (LSA)
Goff and Flynn (1991)
Piopl}ila casei (L.)
H. illltcells (L.)
34-36
36 (LSA)
NP
5
C. mfifacies
C. mfifacies
6
Dermestes
Hawaii
9
Scenopinidae larvae
C. mfifacies Macquart
D. macltlattls DeGeer
Hawaii
11
Hawaii
20
Hawaii
Entomology-based
PMI in days
Macquart
Macquart
maCltlafllS DeGeer
apMl, postmortem interval.
bNumber of taxa, or life-history stages of a taxon, used for the PMI estimate.
eLSA, PMI based on when victim was last seen alive by a reliable source; C, PMl based on confession of a suspect.
dNP, data not publishable, at present, due to pending legal action.
'PM I estimate based on accumulated degree-hours (ADH) of developing flies.
ry rearing and age determination
of individual taxa also might be
conducted.
Second, corpse taxa collected from human remains in a subsequent death scene investigation are identified to species and life-history stage, reared to adulthood
(if necessary), and preserved as
evidence (Fig. I B). These taxa are then matched to the baseline taxa
whose successional timeta bles are known from the same region, season, and ecological circumstances
(Fig. IC). In the oversimplified
and hypothetical
example shown in Fig. 1, 4 corpse taxa match
members of the larger baseline fauna. The lower and upper limits of
the PMI correspond to the 1st and last days the matching taxa cooccur in the succession. Tn this example, the lower and upper PMT limits of the estimate are days 3 and 5, respectively, with a PMI"idth of 3
d ([upper limit - lower limit] + 1, because both limits are inclusive)
(Fig. lC). The PMTwidthprovides a simple and practical measure for
quantifying the precision of PMI estimates. PMI statistics and other
facts relevant to the case are incorporated in the entomologist's case
report (Catts 1990) and disclosed, if necessary, in courtroom testimony (Fig. lD).
Table 2. Effect of loss of taxonomic resolution on PMIwidthcalculated
from 1,000 random and independent draws of 4 taxa each
Level
of aggregation
Early and Goff
Nabaglo
McKinnerney
Original dara
Larva I level
Species level
Genus level
Family level
1-8-16
1-3-20
1-4-21
1-3-26
1-7-31
1-2-5
1-1-13
1-2-6
1-2-6
1-1-15
1-1-16
1-1-17
Each trio of numbers are PMIWidth
statistics: lower 95% confidence
limit - median PMlw;dth- upper 95% confidence limit (in days)(PMl =
postmortem interval). A blank cell in a given row indicates taxa that
could not be aggregated at that level of resolution.
108
However straightforward
the PMI estimation
procedure and
example may appear, application of these methods can be hampered
by biotic and abiotic factors. Complications
can arise due to the
presence of antemortem poisons and narcotics (Goff et al. 1993),
reoccurring baseline taxa (Schoenly 1992), the presence or absence
of predators and large scavengers (Wells and Greenberg 1994), and
unusual topographic, climatic, or other ecological circumstances at
the corpse discovery site (for example, Goff et al. 1991). These methods also assume that the pattern and process of carrion-arthropod
succession in a carrion model (for example, the domestic pig) is comparable to human remains. Because of obvious ethical considerations, only 1 field test of that assumption
(Haskell, Hall and
Schoenly, in preparation) has been conducted to date.
Sampled Randomization
Tests. To ascertain the degree to which
missing species, corpse age, and taxonomic resolution affect PMI
statistics, 2 computer-intensive
techniques, the Jackknife and Bootstrap, were used. These techniques are commonly used in various
scientific disciplines to test hypotheses, estimate bias, and compute
sampling distributions
and confidence intervals of population
parameters (Efron 1982). Uses of sampled randomization
tests in
biology have included cases where tests of significance are erected
for statistics of interest whose mathematical
distributions have not
been identified and in problem cases involving small or unbalanced
data sets for which analysis by conventional methods may be inappropriate or impractical (Manly 1991, Dixon 1993, Potvin and Roff
1993).
The Jackknife and Bootstrap share 2 characteristics (Efron 1982,
Manly 1991). First, each method recombines the origina I data /I
times, either through reshuffling or resampling, to produce /I computer-generated
pseudovalues of the parameter of interest. Second,
each method uses the resulting pseudovalues to calculate statistics of
central tendency or dispersion a bout the parameter of interest. The
'Jackknife' was introduced by Quenouille (1949) and Tukey (19S8l
as a method of bias reduction and arose from the jackknife's role as
an all-purpose tool. The 'Bootstrap'
introduced by Efron (1979),
A~1ERICAN ENTOMOLOGIST
•
Sllllllller
1996
arose from the adage "to pull oneself up by one's bootstraps"
to
mean th;1t a single sample can give rise to many others for use in
computing sampling distributions and confidence intervals of population parameters.
Unlike j:lckkn ife estimates, bootstra p estimates critica Ily depend
upon the number of randomizations
(NRAN) performed.
By the
law of large numbers, bootstrap estimates eventually converge on a
stable value as NRAN becomes large. Therefore, NRAN should be
large enough to capture most of the inherent variability of the estimate in a given case. For 95% confidence intervals, a minimum
NRAN of l,OOO is recommended (Manly 1991); thus, we performed
1.000 bootstrap estimates in each case.
Missin~ Species versus PMI,"idth' To eva luate the effect of missing
species on PMlwi.hh' 9 taxa were randomly selected from each dataset
and designated the "corpse fauna" (see Appendix). This selection
required that all 9 mxa overlapped each other on 2 d of the succession, after which PMI statistics (upper and lower PMllimits, PM 1w;d'h) were ca \culated using the PMI estimation
a Igorithm of
Schoenly et al. (1992). Nine taxa were chosen as the starting size in
each trial because this number lies close to the upper limit of corpse
taxa that have been used in calculating arthropod-based
PMI estimates (Goff and Flynn 1991).
To simulate the effect of missing species, we deleted one of the 9
taxa from the sta rting list at random and recomputed the PMIwidth
from the remaining 8 taxa. This process was repeated for all possible
deletions of 1 taxon, then 2 taxa, and so on, up to 8 independent deletions yielding n!/[r!(n-r)!]
ways of deleting r taxa from the n initial
taxa. From each of the 8 sets of deletions, we computed PMI statistics
from the distribution of jackknifed values. This procedure simulates
variable sampling effort that different entomologists might practice at
tht' crime scene or morgue. Variation in PMI as a function of missing
taxa was summarized by the median, over the jackknifed values, of the
midpoint of the PMI [(upper limit -lower limit)/2} and the range, over
a 1\jackknifed va lues, of the PMI upper and lower limits.
Corpse A~e Versus PMI,,'idlh'To assess the effect of carcass age on
PM1width'1 ,onn draws of 3,6, and 9 taxa each were randomly selected with replacement from each dataset yielding a total of 3,000 selections per study. As hefore, each selection required that all taxa
overlapped each other on 1 or more days of the succession, after
which PMI statistics (upper and lower PMI limits, midpoint of the
PMI) were calculated from these taxa. The midpoint of the PMI was
used as a single measure of corpse age. We then graphed PMIw;dthas
a function of corpse age, using the midpoint of the PMI as the x-axis
variable in each graph.
Taxonomic
Resolution Versus PMl.idth. To determine the effect
of taxonomic resolution on PMI".;dth' we resorted to progressive aggregation of taxonomic groups. In each dataset, taxonomic aggregation was performed
at each of 3 taxonomic
steps: species
-genus-family.
In the original data of Early and Goff, successional
records were recorded separately for different larval instars and the
adult stage of ClJ1')'soll1)'a mfifacies Macquart and C. megacephala
(Fabricius) (Calliphoridae:
Diptera); thus, these instar data permitted 1 additional step in the aggregation procedure (larval-level aggregation).
Aggrq~ating occurrence matrices to the rank of order
reduced their row totals to 7 or fewer taxa; thus, aggregation
ceased at the family level. Progressive aggregation of taxonomic
groups simulates a continuum of fine (species-level) to coarse (family-level) identification
different
entomologists
might practice
when characteri7.ing taxonomic
composition
of a carrion-arthropod assemblage.
Taxonomic aggregates were defined as the union of their constituent taxa with aggregates treated as single rows of the occurrence
matrix. For example, in the 1st step of aggregation of the Early and
Goff matrix the 3 larval instars for C. mfifacies and for C. megaAMPRICAN
ENTOMOl.O(;IST
•
Slimmer 1996
cephala were lumped into single rows, producing a slightly smaller
larval-level matrix. In the 2nd step, immature and adult stages of C.
rufifacies and C. megacephala were lumped to form a smaller species-Ievelmatrix; and so on. In each aggregated matrix, 1 member of
each aggregate group was arbitrarily chosen as the reference taxon
after which the successional records of the other members were added to the reference taxon and treated as 1. row of the matrix.
To estimate the effect of variable taxonomic resolution on PMIwidth'1,000 draws of 4 taxa each were randomly selected with replacement from the original and aggregated occurrence matrices.
From the frequency distribution of 1,000 pseuclovalues of PMlw;dth'
we calculated the median PMIwidthand the 2.5th and 97.5th percentile values to encompass the central 95% of the bootstrap distribution (that is, the 95% confidence interval on PMlwidth; Efron's
method).
Results and Discussion
Missing Species Versus PMI",idth' In each study, variability (uncertainty) in the median PMI and in the range of PMlwidth increased as
the number of missing taxa increased (Fig. 2 A-C). Of the 3 studies,
Early and Goff's data exhibited the widest systematic departure in
the range of PMIw;dth,' followed by McKinnerney and Nabaglo. In
the Early and Goff, Nabaglo and McKinnerney studies, the median
PMI first fell outside the starting PMI after 8, 5, and 5 taxa, respectively, were omitted. Tn sum, although systematic reduction of taxa
brought relatively small changes in the median PMI, systematically
larger ranges in PMIw;dthwere observed in each study following stepwise deletion of taxa.
Corpse Age Versus PMI,.;dth' In most plots of Fig. 3 A-I, the raw
data (not shown) described a triangle bound below by minimum
values of PMTwidth'a bove by maximum values of PMIwirlth'and on the
right by maximum PMI values of the succession. In 8 out of 9 cases,
the longer the corpse discovery time, the larger the scatter in PMIwidth;in the exceptional case (Nabaglo, 6 taxa case), PMIwidth decreased with corpse age (Fig. 3 E).
Log transformation
of Y-values did not correct the heteroscedasticity in values of PMIwid'hin the most variable cases of Fig. 3. Because heteroscedasticity
violates conventiona I assumptions
of
ordinary least-squares regression (Zar 1984), we drew error bars
from the 2.5th and 97.5th percentiles of the bootstrapped
distributions of PMIw;dth, sharing the same midpoint value to summarize
variability in the PMIw;dthwith corpse age. In each graph, qualitative
trends were summarized
using least-squares
linear regression
(dashed lines in Fig. 3 A-I), but without attaching levels of significance to the slope or fit of the relationship. Without supporting statistics, however, it is clear from Fig. 3 A-I that PMIw;dth is strongly
influenced by corpse age.
In 2 of the 3 studies, variability (uncertainty)
in PMIw;dth decreased as more corpse taxa were included in the estimation procedure (Fig. 3 A-C, G-I); in the exceptional study (Nabaglo, Fig. 3
D-F), the PMIwidthwas slightly more variable in the 9-taxa case than
the 6-taxa case. Corpse faunas of high species richness (9-taxa cases)
reduce the scatter along the X-axis more than low-richness faunas
(3-taxa cases) partly because older carcasses attract a lower species
richness of arthropod taxa and have lower species turnover than
fresh carcasses (Schoenly and Reid 1989), thus producing a tradeoff
between the number of corpse taxa used for PMI estimation and the
usefulness window of the successiona I timetable.
Taxonomic Resolution versus PMl.idth. In each study, systematic
loss of taxonomic resolution produced progressively larger confidence intervals in PMIwidth (Table 2). Of the 3 cases studied, PMI
statistics in Early and Goff showed the widest departure from the
original data. In this case, the median PMIwidthfluctuated from 8 d in
109
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Effect of corpse age on PMlwid1h obtained by 1,000 random draws each of 3, 6, and 9 taxa. (Above) (A-C).
Goff and Early (1985), 3, 6, and 9
taxa, respectively. (D-F). Nabaglo (1973), 3, 6, and 9 taxa, respectively. (Across) (G-I). McKinnerney (1978), 3, 6, and 9 taxa, respectively. The xaxis variable in each graph is the midpoint of the PMI [(upper limit - lower limit)/2]. Vertical bars are 95% confidence intervals about the mean.
the original matrix days to 3, 4, 3, and 7 d following larval-, species,
genus-, and family-level aggregation,
respectively, with the confidence interval about the PMlwidlh increasing from 15 d in the original data to twice that number after family-level aggregation (Table
2). PMI statistics in the other 2 studies were less sensitive to taxonomic aggregation,
with the median PMI remaining unchanged
and confidence intervals increasing by only 1-4 d (Table 2). The
wider range of PMIwidth, in Early and Goff's study may be due, in
large part, to a longer observation period and nonconsecutive
daily
sampling.
Conclusions and Implications for Succession-Based
Forensic Entomology
Nearly identical results in these 3 studies, revealed through sampled randomization
tests, suggest robust trends between PMI statistics and certain methodological
and ecological circumstances.
In
each of the 3 studies, variability (uncertainty) in the PMf"Widthin110
creased as the number of missing taxa increased and as the baseline
data decreased in taxonomic quality. In 8 of 9 other trials, the PMIwidthincreased as corpse age increased and as the number of taxa (3,
6, and 9) used for the estimate decreased; in the exceptional case
(Fig. 3 E), the PMlwidthdecreased with corpse age when 6 taxa were
used. Carrion studies with variable collection schedules, compared
to studies with fixed collection schedules, may exacerbate these effects. We conclude that randomization
tests are potentially useful
tools in forensic entomology both for conducting sensitivity tests of
baseline successional data and for assessing statistical uncertainty in
entomology-based
PMI estimates.
At least 4 implications for forensic entomology are suggested by
this study. First, the effects of missing taxa on PMlwidlhsuggests that
variable capture efforts practiced by different entomologists could
arrive at different PMI estimates even if sampling was conducted at
the same crime scene on the same day (but see below). Tighter enforcement to established standards of arthropod collection methods
at the crime scene or morgue (for example, Catts and Haskell 1990)
AMERICAN ENTOMOLOGIST
•
Slimmer
1996
G
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•
• •
1.·..•_·_--.-.
.. -...o
---
10
20
Midpoint of PMI (days)
References Cited
30
and field studies to validate these methods are 2 possible (partial)
remedies to this potential problem.
Second, the positive relationship
between corpse age and the
PMlwidth confirms the field intuitions of some medicolegal investigators (for example, Sopher 1973, Greenberg 1988, DiMaio and
DiMaio 1989, Geberth 1990) that the longer the PMI, the less accurate the PMI estimate becomes. Levelling the positive slope of the
relationship hetween the PMI and PMI"idth was accomplished when
additiona I taxa were recru ited in the estimation procedure (Fig. 3
A-C, (~-J); however, species recruitment was correlated negatively
with the length of the successional timetable for PMl estimation.
We hope that recognition of this tradeoff will not discourage community-level approaches
to PMl estimation.
Third, the loss of precision in PMJw;dth with increasing loss of
taxonomic
resolution
in the baseline data underscores
the need
for species- or genus-level
identification
for most if not all forensically-important
arthropod
groups (Smith 1986, Catts and
Haskell 1990). We hasten to note, however, that forensic investigators are unlikely to calculate PMI estimates based only on
coarsely-resolved
(genus- or family-level)
corpse or baseline
taxa (but sec Kulshrestha
and Chandra
1987); thus, the potentialusefulness
of bootstrapping
taxonomically
aggregated sucAMERICAN
Acknowledgments
The senior author thanks Joel E. Cohen (Rockefeller University) for providing financial, logistical, and intellectual support throughout his postdoctoral career. We thank Michael Grill (FBI Academy) and Paul Catts
(Washington State University) for providing technical and artistic assistance. We thank Paul Carts, Neal Haskell, and an anonymous reviewer for
providing constructive comments on an earlier draft. This study was supported under NSF grant BSR 87-05047 (to J. E. Cohen, Principal Investigator) and, more recently, National Institute of Justice grant 94-I]-CX-0039.
This is journal series no. 4087 of the Hawaii Institute of Tropical Agriculture
and Human Resources .
30
o
cessional records may be limited to between-study
comparisons
of baseline data.
Fourth, this study underscores the need for' greater statistical
study of entomology-based
PMI estimates. For example, the procedure of random draws of corpse taxa in this study assumes equal
sampling and catchability of taxa at the crime scene or morgue. This
assumption is unrealistic. Because feeding larvae are conspicuously
abundant, less mobile, and strongly associated with decomposing
remains, they are more catchable than soil or aerial arthropods.
Future studies should incorporate probabilistic estimates of arthropod capture based, perhaps, on species-abundance
rankings or
yield-effort studies conducted in the field. Also, no study has employed numerical probability tables, calculated from replicate carcasses, to estimate the likelihood of a fauna's association in the
succession (discussed in Wells and Greenberg 1994).
We hope these preliminary results will stimulate further dialogue
on the methods and practices of statistical confidence and sampled
randomization
tests in forensic entomology.
Also needed are
straightforward
and efficient approaches
forensic entomologists
can use to educate judges, juries, and litigators on the pros and cons
of entomology-based
PMI estimates (and confidence interva Is a bout
those estimates) when courtroom
reporting of such information
becomes necessary .
ENTOMOLOGIST
•
Slimmer
1996
Catts, E. P. 1990. The paper trail: case records and reports. 1/1 Entomology
and death: a procedural guide. E. P. Catts and N. H. Haskell [eds.], PI'.
138-144. Joyce's, Clemson, sc.
Catts, E. P., and M. L. Goff. 1992. Forensic entomology in criminal investigations. Ann. Rev. Entomo!. 37: 253-272.
Catts, E. P., and N. H. Haskell [eds.]. 1990. Entomology and death: a procedural guide. Joyce's. Clemson, Sc.
DiMaio, D. J., and J. M. DiMaio. 1989. Forensic Pathology. Elsevier, New
York.
Dixon, P. M. 1993. The bootstrap and jackknife: describing the precision of
ecological indices. 111 Design and analysis of ecological experiments. S.
M. Scheiner and J. Gurevitch [cds.], Pl'. 290-318. Chapman & Hall,
New York.
Early, M., and M. L. Goff. 1986. Arthropod succession patterns in exposed
carrion on the island of O'ahu, Hawaiian Islands, USA. J. Med. Entomol. 23: 520-531.
Efron, B. 1979. Bootstrap methods: another look at the jackknife. Ann.
Statist. 7: 1-26.
1982. The jackknife, the bootstrap and other resampling plans. Society for
Industrial and Applied Mathematics. Philadelphia, PA.
Geberth, V. J. 1990. Practical homicide investigation, 2nd cd. Elsevier, New
York.
Giles, E., and L. L. Klepinger. 1988. Confidence intervals for estimates
based on linear regression in forensic anthropology. J. Forensic Sci. 33:
1218-1222.
Goff, M. L., and M. M. Flynn. 1991. Determination of postmortem interval
by arthropod succession: a case from the Hawaiian Islands. J. Forensic
Sci. 36: 607-614.
111
Goff, M. L, and C. B. Odom. 1987. Forensic entomology in the Hawaiian
Islands. Three case studies. Am. J. Forensic Med. Path. 8: 4.\-50.
Goff, M. L., C. B. Odom, and M. Early. 1986. Estimation of postmortem
interval by entomological techniques: a case study from Oahu, Hawaii.
Bull. Soc. Vector Ecol. 11: 242-246.
Goff, M. L, A. I. Omori. and K. Gunatiklake. 1988. Estimarion of postmortem interval by arthropod succession: three case studies from the Hawaiian Islands. Am. J. Forensic Med. Pathol. 9: 220-225.
Goff, M. L, S. Charbonneau, and W. Sullivan. 1991. Presence of fecal
material in diapers as a potential source of error in estimations of postmortem interval using arthropod development rates. J. Forensic Sci. 36:
1603-1606.
Goff. M. L. W. A. Brown. A. I. Omori, and A. LaPointe. 1993. P:reliminary
observarions of the effects of Amitriptyline in decomposing tissues on the
development of P'1rIlsarcophaga mficomis
(Diptera: Sarc<>phagidae)
and implications of this effect to estimation of postmortem interval. J.
Forensic Sci. 38: 316-322.
Greenberg. B. 1988. Mostly flies (book review). J. N.Y. Entom01. Soc. 96:
489-491.
1991. Flies as forensic indicators. ]. Med. Entomol. 28: 565-577.
Johnston, W. and G. Villeneuve. 1897. On the medico-legal application of
entomology. Montreal Med. J. 26: 81-90.
Keh, n. 1985. Scope and applications of forensic entomology. Ann. Rev.
Entomol. 30: 137-154.
Kulshrestha, P., and H. Chandra. 1987. Time since death. An entomological
study on corpses. Am. J. Forensic Med. Path. 8: 233-238.
Leclercq, M. 1978. Entomologie et Medecine Legale: Datation de la Mort.
Masson, Paris.
Lord. W. D., and W. C. Rodriguez, Ill. 1989. Forensic entomology: the use
of insects in the investigation of homicide and untimely death. The Prosecutor 41-48 (Winter).
Manly, n.E]. 1991. Randomization and Monte Carlo methods in biology.
Chapman & Hall, New York.
Maples, W. R., and M. Browning. 1994. Dead men do tell tales. The strange
and fascinating cases of a forensic anthropologist. Doubleday Dell, New
York.
McKinnerney, M. 1978. Carrion communities in the northern Chihuahuan
Desert. Southwest. Nat. 23: 563-576.
Megnin, J.P. 1894. La Faune des Cadavres: Application e I'entomologie ala
Medecine Legale. Encyclopedie Scientifique des Aide-Memoire, Masson, Gauthiers-Villars et Fils, Paris.
Motter, M. G. 1898. A contribution to the study of the fauna of ,he grave.
A study of one-hundred and fifty disinterments with some additional
experimental observations. J. N.Y. Entomol. Soc. 6: 201-231.
Nabaglo, L 1973. Participation of invertebrates in decomposition of rodent
carcasses in forest ecosystems. £kol. Polska 21: 251-270.
Nuorteva, P. 1977. Sarcosaprophagous insects as forensic indicators. 111
Forensic medicine: a study in trauma and environmental hazards, vol 2.
C. G. Tedeschi,W.G. Eckert, and L.G. Tedeschi [eds.], Pl'. lC72-1095.
Saunders, Philadelphia.
Potvin, c.. and D. A. Roff. 1993. Distribution-free and robust statistical
methods: viable alternatives to parametric statistics? Ecology 74:
time of death. FBI Law Enforcement Bull. 10-31 (October).
Tukey, J. 1958. Bias and confidence in not quite large samples (abstract).
Ann. Math. Statist. 29: 614.
Wells, J. D., and B. Greenberg. 1994. Effect of the red imported fire ant
(Hymenoptera: Formicidae) and carcass type on the daily occurrence of
posrfeeding carrion-fly larvae (Diptera: Calliphoridae, Sarcophagidae).
J. Med. Entomol. 31: 171-174.
Wells,]. D., and H. Kurahashi, 1994. Chrysamya megacepha/a (Fabricius)
(Diptera: Calliphoridae) development: rate, variation and the implications for forensic entomology. Jpn. J. Sanit. Zoo!. 45: 303-.~09.
Wells,]. D., and L. R. Lamotte. 1995. Estimating maggot age from weight
using inverse prediction. J. For. Sci. 40: 573-578.
Zar, J. H. 1984. Biostatistica\ analysis, 2nd cd. Prentice-Hall, Englewood
Cliffs, N.J.
Receil1ed far ptlblicatian
26 Janllary 1995; accepted 3 JIIly 1995.
Appendix
Taxonomic identities of nine taxa drawn randomly from each of 3 carrion-arthropod studies to investigate effects of missing species on PMlw;dlb.1n
each case, taxonomic identities follow the original published report.
Early and Goff (1986): Dermestes spp. adults (Dermestidae: Coleoptera); Chrysomya megacepha/a (Fabricius) 1st instars (Calliphoridae:
Diptera); milichiids (Milichiidae: Diptera); Mllsca domestica L. adults
(Muscidae: Diptera); Mrlsca sorbells Wied. adults (Muscidae: Diptera);
Ophyra spp. adults (Muscidae: Diptera); sarcophagid adults (Sarcophagidae: Diptera)j Brachymeria fOllscolambei (DuFour) adults (Chalcidae:
Hymenoptera); isopod adults (Isopoda).
NabagIo (1973): Atheta sp. adults (Stapylinidae: Coleoptera); Nicraphams l1espi//aides Herbst adults (Silphidae: Coleoptera); teptocera sp.
adults (Sphaeroceridae: Diptera); collembolan adults (Collembola); Tachirills pallipes Gravenhorst adults (Staphylinidae: Coleoptera); Alliela /OIIf(icornis Gravenhorst adults (Staphylinidae: Coleoptera); coleopteran larvae
(Coleoptera); Orchese//a (lal'eSCerls (Bourlet) adults (Entomobryidae: Collembola); AcrOlrichis sp. adults (Ptilidae: Coleoptera).
McKinnerney (1978): Sapril1t1s discoida/is LeConte adults (Ilisteridae:
Coleoptera); Silpha Irtmcata Say adults (Silphidae: Coleoptera); Eleodes erltricattls eognaltls Haldeman adults (Tenebrionidae: Coleoptera); Cocb/iomyia
mace//aria
(Fabricius) adults (Calliphoridae: Diptera); C.
mace//aria (Fabricius) larvae (Calliphoridae: Diptera); Oxysarcodexia
ocliripyga (Wulp) larvae (Sarcophagidae: Diptera); So/eopsis XylOlli McCook adults (Formicidae: Hymenoptera); Rygchitlm a1ll1ll/,lIrllll all/llr/aftlm
(Say) adults (Vespidae: Hymenoptera); Dia/ictlls micro/epoides
(Ellis)
adults (Halictidae: Hymenoptera).
•
1617-1628.
QuenouiIle, N. 1949. Approximate tests of correlation in time seties. J. Roy.
Statist. Soc.Ser. B 11: 18-84.
Schoenly, K. 1992. A statistical analysis of successional patterns ill carrionarthropod assemblages: implications for forensic entomology and determination of the postmortem interval. J. Forensic Sci. 37: 1489-1513.
Schoenly, K., and W. Reid. 1989. Dynamics of heterotrophic succession in
carrion arthropod assemblages: discrete seres or a continuum of change?
Oecologia 73: 192-202.
Schoenly, K., M. 1. Goff, and M. Early. 1992. A BASIC algorithm ror calculating the postmortem interval from arthropod successional data. J. Forensic Sci. 37: 808-823.
Smith, K.G.V. 1986. A Manual of Forensic Entomology. Cornell University
Press, Ithaca, New York.
Solomon, H. 1986. Confidence intervals in legal settings. 111 Statistics and
the Law. M. H. DeGroot, S. E. Fienberg, and J. B. Kadane [eds.], pp.
455-473. Wile)', New York.
Sopher, I. M. 1973. The law enforcement officer and the determination of
112
Kenneth Schoenly is an assistant professor in the Department
of Biological Sciences, Louisiana Tech University, Ruston, LA
71272. On 1 January 1996, he assumed new job duties as insect
ecologist in the Entomology and Plant Pathology Division, International Rice Research Institute. P.O. Box 933, Manila, Philippines.
M. Lee Goff is a professor in the Department of Entomology, University of Hawaii. Honolulu. HI 96822. and to whom reprint requests and other correspondence should be addressed. Jeffrey D.
Wells is a postdoctoral associate in the Department of Medical Entomology, National Institute of Health, Toyama 1-23-1, Shinjukuku, Tokyo, 162, JAPAN. Wayne D. Lord is a supervisory special
agent in the Forensic Science Unit, Laboratory Division, FBI Academy, Quantico, VA 22135. All authors are active researchers,
workshop
participants, and case workers in forensic entomology.
AMERICAN ENTOMOLOGIST
•
Slimmer
1996