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Faculty Publications: Department of Entomology, Department of

2006

Effects of Temperature on Development of (Diptera: ) and Use of Developmental Data in Determining Time Intervals in

P. D. Nabity University of Nebraska-Lincoln

Leon G. Higley University of Nebraska-Lincoln, [email protected]

Tiffany M. Heng-Moss University of Nebraska-Lincoln, [email protected]

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Nabity, P. D.; Higley, Leon G.; and Heng-Moss, Tiffany M., "Effects of Temperature on Development of Phormia regina (Diptera: Calliphoridae) and Use of Developmental Data in Determining Time Intervals in Forensic Entomology" (2006). Faculty Publications: Department of Entomology. 277. https://digitalcommons.unl.edu/entomologyfacpub/277

This Article is brought to you for free and open access by the Entomology, Department of at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Faculty Publications: Department of Entomology by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. DIRECT INJURY,,FORENSICS Effects of Temperature on Development of Phormia regina (Diptera: Calliphoridae) and Use of Developmental Data in Determining Time Intervals in Forensic Entomology

1 P. D. NABITY, L. G. HIGLEY, AND T. M. HENG-MOSS

Department of Entomology, 202 Plant Industry, University of Nebraska, Lincoln, NE 68583Ð0816

J. Med. Entomol. 43(6): 1276Ð1286 (2006) ABSTRACT Precise developmental data for forensic indicator blow ßy are essential for accuracy in the estimate of the post-mortem interval (PMI). Why, then, does the determination of the PMI result in conßicting time frames when published conspeciÞc developmental data are used? To answer this question, we conducted constant temperature trials between the developmental minimum temperature and upper threshold temperatures (8Ð32ЊC) on the forensically important blow ßy species Phormia regina (Meigen) (Diptera: Calliphoridae). were reared using two designs to quantify sources of variation. We measured rearing container temperatures and internal growth chamber temperatures by using thermocouples to accurately record temperatures experi- enced by larvae and to construct a degree-day model. Differences in experimental design, as seen across temperature studies for this ßy species, did not signiÞcantly impact larval development. We also found that using set chamber temperatures rather than rearing container temperatures altered the Þnal degree-day model. Using any minimum threshold (including an empirically determined true mini- mum) other than that from linear interpolation (x-intercept) violated degree-day assumptions and invalidated estimates of the PMI. We observed the minimum developmental temperature to be higher (14ЊC) than that generated under the x-intercept method (5.46ЊC) by using data from oviposition to adult emergence. This difference along with the noted difference in accumulated degree-days (using different base temperatures) suggests a need for additional experimentation on other forensically important ßy species at low temperature thresholds to help with development of curvilinear models. Former and current estimates of the PMI may be inaccurate if the process to determine the time frame ignored degree-day model assumptions or was based upon questionable data sets.

KEY WORDS blow ßies, degree-day analysis, temperature thresholds, post-mortem interval

Forensic entomology is growing with the application Byrd and Allen 2001; Grassberger and Reiter 2001, of new technologies and the availability of new data on 2002a,b; Grassberger et al. 2003). forensically important species. Arguably, the key con- To use larval development in estimating PMI, ac- tribution of entomological information in criminal in- curate information on the development of individual vestigations is in the determination of the post-mor- species is essential. Currently, much of the available tem interval (PMI). Successional patterns of information comes from relatively few studies, often invasion may provide PMI indications over longer with limited data sets (Byrd and Allen 2001, Higley time intervals. For shorter periods, however, devel- and Haskell 2001). For example, data sets developed opmental rates of larvae are used. Decomposers such within limited temperature ranges (especially at low as blow ßies typically arrive and oviposit minutes after temperatures) (Nabity 2005) and data sets with only death. When correlated with environmental temper- single measures (no replication) exist for some tem- atures, development of these ßies can provide peratures. Byrd and Butler (1996, 1997, 1998) pro- a method for estimating the PMI. Consequently, pre- duced data sets by using cyclic temperatures spanning cise developmental data for forensic indicator species the median temperatures of the developmental spec- are essential for accuracy in the PMI estimate. Many trum (15.6Ð32.2ЊCin5.5ЊC intervals); and, Byrd and calliphorid and sarcophagid species have been studied Allen (2001) evaluated a greater temperature range because of their proliÞc occurrence on cadavers, eco- (10Ð40ЊC). However, neither study evaluated growth nomic importance, or role in succes- rates near the developmental threshold. Similarly, sion (Byrd and Butler 1996, 1997, 1998; Anderson 2000; Greenberg (1991) evaluated broad temperature ranges but produced data sets without regard for the minimum threshold and published data based upon 1 Corresponding author, e-mail: [email protected]. single measures. Developmental minima and maxima

0022-2585/06/1276Ð1286$04.00/0 ᭧ 2006 Entomological Society of America November 2006 NABITY ET AL.: P. regina DEVELOPMENT USED IN FORENSIC ENTOMOLOGY 1277 are not established for many forensic species, and Designs by Byrd and Butler (1996, 1997) also rep- developmental requirements, such as degree-days, licated larval containers within a chamber, rather than usually are not explicitly determined. More compre- between chambers. Grouping all rearing cups under hensive data are emerging for some species (e.g., the same environmental temperature, whether con- Byrd and Allen 2001, Grassberger et al. 2003), but stant or cyclic, may obscure the actual thermal envi- there remains a clear need for additional in-depth data ronment experience because of within cham- on development of forensically important insect spe- ber temperature variation. Additionally, there is little cies, such as Phormia regina (Meigen) (Diptera: Cal- if any mention of variability occurring in temperature liphoridae). studies, and only recently have investigators placed A further need is estimation of variation for con- electronic checks (thermocouples and data loggers) structing the PMI. One important issue is the assump- within experiments to monitor temperatures (Ander- tion that oviposition occurs shortly after death; yet, son 2000, Clarkson et al. 2004). Chamber effects may various circumstances (such as diurnal versus noctur- create the variation observed in data sets within and nal oviposition patterns, access to a body, or cold between studies on the same species (Kamal 1958, temperatures) may delay oviposition. Another major Greenberg 1991, Byrd and Allen 2001), and this vari- source of variation comes in determination of devel- ation needs to be investigated. opmental periods. Greenberg (1991), Byrd and Allen Traditionally, the experimental unit is deÞned as the (2001), and Clarkson et al. (2004) found ßuctuating entity to which a treatment is applied. However, in temperatures delayed larval development compared growth chamber studies involving temperature, the with constant temperature rearing. Thus, studies using treatment is not evenly applied (all locations within only cyclic temperatures to test development for some the chamber do not experience the same tempera- ßy species are incomplete. For example, Byrd and ture), and the presumed temperature (the set-cham- Butler (1996, 1997, 1998) tested development only ber temperature) may not match internal chamber under cycling temperatures with a period of 5.5ЊC, and temperatures. Thus, some investigators and statisti- one constant temperature (25ЊC). They argued for the cians have argued that within-chamber replications ßuctuating temperatures because specimens in nature are permissible if the treatments are recorded for each are subject to ßuctuating, not constant, temperatures. within chamber “replicate.” This argument assumes that temperature is the only signiÞcant factor affecting These studies also evaluated ßy development under replicates; otherwise, between-chamber replications various photoperiod settings; a concept that has not (to account for example, variability in light and rela- been directly tested in the literature. Although there tive humidity) would be necessary. The opposite in- are data to suggest photoperiod may inßuence devel- terpretation is that within chamber replicates, where opment (unpublished data) and investigators have temperature is the treatment, represent a lack of, or shown dipteran behavior to be augmented by light pseudoreplication (Hurlbert 1984). (e.g., Grassberger and Reiter 2001, 2002a,b), there are A less appreciated issue in the design of tempera- no conclusive studies testing the inßuence of light on ture studies is randomization. Typically, to compare a blow ßy development. number of temperature treatments, a complete set of Another important issue in determining develop- treatments would be randomized across chambers. mental periods is that of accurate temperature mea- Alternatively, a single treatment (temperature) may surement. Insect developmental rate increases lin- be applied to multiple chambers, with different treat- early, but only between the temperature extremes; ments being tested through time. In this second de- developmental rate becomes curvilinear at both high sign, the study is replicated, but because there could and low extremes with increases or decreases in tem- be an inßuence of time, the study is “pseudorandom- perature. Within the nonlinear portions of the tem- ized” (assignment of treatments is not random through perature development association, equal deviations time). from mean temperature (abscissa) result in unequal A Þnal point involves the goal of studies whose deviations in developmental time (ordinate). This is purpose is to determine a quantitative biological re- known as the rate summation effect, and it alters the sponse to temperature, such as determining temper- interpretation of data near thresholds when generated atureÐgrowth rate relationship. When determining under ßuctuating temperatures (Kaufmann 1932). Be- a mathematical relationship, regression, not treat- cause most environmental factors slow rather than ment comparison, is of utmost importance. From this increase development, with the exception of certain perspective, certain types of pseudoreplication and chemicals in the substrate (e.g., cocaine, Goff et al. pseudorandomization should be permissible. Unfor- 1989), it is important to have the fastest developmental tunately, failure to properly assess treatment (e.g., time when calculating the PMI. Thus, studies con- measure exact temperature insects experience in a ducted under nonconstant temperature regimes as- chamber) and failure to avoid bias (through use of sume a conservative developmental time, because lar- single chamber, pseudorandomization, and similar val developmental rate is slower (based upon studies) problems) may invalidate the points generated for along the linear portion and either faster than ex- regression. Finally, because regression relationships pected (at low temperatures) or slower than expected are highly dependent on the spread and range of (at high temperatures) within the curvilinear or values tested, clustered points (through the selection threshold portions (because of rate summation). of many temperatures in a narrow range and few 1278 JOURNAL OF MEDICAL ENTOMOLOGY Vol. 43, no. 6 outside this range) can distort or obscure the actual from 50 to 70%. Eggs were collected after oviposition relationship. on liver or hamburger (ground beef) substrate. We Because P. regina is well studied in the literature, used egg masses no older than 6 h for experiments. frequently associated with death scenes, and serves as Experiments began using ßies from the eighth and a primary specimen used to construct PMI, additional third generations for 2000 and 2004, respectively. We investigation of the temperatureÐdevelopmental time used emerged ßies to restock the colonies. relationship is merited. P. regina is a forensically im- We examined ßy development by using two differ- portant blow ßy common to Holarctic regions and ent designs to see whether bias occurred. The Þrst distributed in north of Mexico City. It series of experiments began in August 2000 and ended is abundant in the spring and fall when cooler tem- in August 2001. The second series began in August peratures are prevalent and in higher altitudes of 2003 and ended in December 2004. Experimental de- warmer areas (Hall 1948). P. regina readily visits de- signs differed between study years. The Þrst experi- composing material and frequents cadavers at crime ment used one rearing container within one growth scenes. Kamal (1958), Greenberg (1991), Anderson chamber; so, the experimental unit was the environ- (2000), and Byrd and Allen (2001) looked at devel- mental growth chamber. We tested seven tempera- opmental rates of P. regina, but they did not examine tures replicating chambers set at 32 and 26ЊC four potential sources of variation within their experi- times, 20, 14, 10, and 8ЊC twice; and 12ЊC once. In the ments. second design the experimental unit was the chamber The focus of this study was to gather additional data but with each temperature treatment replicated at the on P. regina developmental rates, especially on the same time across four chambers. The second series developmental minimum temperature threshold, and followed a completely randomized design when as- to determine an accurate low temperature measure- signing rearing containers to environmental growth ment. We selected two experimental designs, emulat- chambers. We tested Þve temperatures (12, 15, 20, 25, ing designs used on other forensically important ßy and 30ЊC) replicating each temperature over four species. Our Þrst objective was to test whether key chambers and with three subsamples (rearing con- environmental factors (e.g., photoperiod and sub- tainers) per chamber. Preliminary studies showed a strate) interacted in ways that altered larval develop- horizontal gradient from left to right inside the cham- mental time. We also examined how measures of stage ber, with signiÞcantly increased temperatures in the transition (by mode or Þrst 10%) altered estimates of end container relative to the middle container, be- developmental time. Our second objective was to de- cause of proximity to lights. Therefore, container termine whether experimental bias occurred by using placement was randomized when multiple subsamples temperatures set for growth chambers (hereafter set- occurred within chamber. chamber temperatures) rather than those measured In addition the experimental setups evaluated dif- within the rearing containers (hereafter rearing-con- ferent diets, photoperiods, and stage transition times. tainer temperatures). Our third objective was to com- We used two rearing substrates and diet media. In pare estimates based on the x-intercept versus an ob- 2001, larvae developed on 80% lean ground beef chuck served minimum developmental threshold. Finally, (hereafter meat) enclosed in foil pouches in sand- we examined the effects of any differences on the Þnal lined 2-liter containers. In 2004, larvae developed on degree-day model, because it is used in estimating the beef liver enclosed in foil pouches in 3.55-liter con- PMI. tainers lined with medium-grade vermiculite. All con- tainers were vented to allow for gas exchange. For photoperiod, in 2001 larvae developed under 16:8 Materials and Methods (L:D) h; in 2004, larvae developed under 24:0 (L:D) Flies for our experiments were collected on Uni- h. For population stage transition, we measured pupal versity of Nebraska East Campus in Lancaster County, and adult stage transition times under different crite- NE (40Њ 85Ј,96Њ 75Ј) by using baited traps (2000Ð ria. In 2001, we used modal developmental time. In 2004). Initially, traps were baited with liver, although 2004, we used the fastest developmental time (typi- additional traps in 2000 were baited with rotten ba- cally Յ10% of the population). nanas, mango, pears, and other noncitrus fruits (beer We used the same methods of recording tempera- was added to increase fermentation). P. regina were tures and calculating degree-days for both experi- identiÞed, separated, and placed in Þne wire mesh ments. We checked all chambers in 12-h intervals to cages (30-cm [length by width by height] cubes) in verify chamber function and to determine develop- laboratory growth chambers (models E-30B, I-35L, mental stage. We used thermocouples (TMC6-HB, LLVL, VLX, Percival ScientiÞc, Perry, IA). A contin- with 0Ð44ЊC range, Ϯ0.4ЊC accuracy at 20ЊC, and 0.2ЊC ual colony survived on water, sugar, and a mixture of resolution, and TMCx-HD, with Ϫ40 to 50ЊC range, powdered egg whites and powdered milk. We set Ϯ0.5ЊC accuracy at 20ЊC, and 0.41ЊC resolution) from colony temperatures from 20 to 25ЊC and assigned a a Hobo H8 outdoor/industrial four-channel external photoperiod of 16:8 (L:D) h for colonies used for the logger (Onset Computer Corp., Pocasset, MA) to Þrst experiments (in 2001) and 24:0 (L:D) h for col- record internal chamber and container temperatures. onies used in the second experiment (2004). The One thermocouple was placed within rearing con- photoperiod used for rearing was used for the exper- tainers to measure overall rearing container temper- iments that year. Relative humidity varied with season ature and account for any metabolic heat generated. November 2006 NABITY ET AL.: P. regina DEVELOPMENT USED IN FORENSIC ENTOMOLOGY 1279

Thus, three thermocouples recorded internal cham- Third, we calculated the thermal constant (accu- ber temperatures in 2001, and one thermocouple re- mulated degree-days; ADD) for the biological period corded chamber temperature in 2004. Temperatures of interest (here, development from egg to adult). For were recorded every 15 min to the nearest 0.1ЊC. each treatment temperature, this was (temperature Ϫ In a pseudoreplicated (one-chamber) pilot study in minimum) ϫ developmental time. 2004, we randomly assigned an egg cluster (of ages Յ6 Fourth, we conÞrmed that the calculated thermal Յ Њ Յ and 3 h old at 25 C, 0.5 ADD12 were 78 and 39, constants are independent of temperature. The slope respectively) to 16 opaque Dixie cups. We then Þtted of the linear regression of thermal constants versus three cups and the internal chamber with thermo- temperature was tested to determine whether it was couples and placed the setup in a growth chamber set signiÞcantly different from zero. to 11ЊC. Larval hatch was monitored to note occur- Finally, we determined the thermal constant either rence, and no developmental times were recorded. by slope of the thermal constant versus temperature The developmental minima, maxima, and thermal regression or the mean of the thermal constant across constants were determined to ensure that degree-day measured temperatures. These values should be ap- models were based solely on the linear portion of the proximately equal, and there is no a priori reason to developmental curve. Commonly, these values are choose one method over the other. However, because determined by regressing 1/developmental time ver- most literature values of thermal constants are based sus temperature and by using the intercept of this on means, we also used the mean for comparison. regression as a base temperature for calculating the Because temperature recordings were made every thermal constant. Because using the inverse of devel- 15 min, we calculated daily degree-days as the sum of opmental time skews the variance structure, this ap- these 15-min intervals over a day. Some variation in proach underestimates low temperature curvilinear- temperature occurred in chambers associated with ity, which can underestimate the slope of the actual normal chamber temperature regulation (the com- linear portion of the developmental curve. The num- pressor turning on and off) and ßuctuations associated ber of data points and the range of temperatures ex- with daily monitoring of larvae (typically this oc- amined also can inßuence the slope of the develop- curred over Ͻ5 min). In four chambers of the Þrst mental curve. Although no single procedure (short of experiment series, we noted temperatures were rou- having sufÞcient experimental points for a curvilinear tinely higher during photophase than during scoto- [sigmoidal] regression) can eliminate these problems, phase. we used a multiple step procedure to address these Data Analysis. For comparisons between measures issues. of temperature (rearing-container temperatures ver- First, we identiÞed the linear portion of the de- sus set-chamber temperatures), we analyzed data re- velopmental curve by iteratively checking for non- corded by thermocouples corresponding to their linearity in the lower and upper portions of the de- placement in the environmental growth chamber. We velopmental curve. SpeciÞcally, for regressions of averaged thermocouples by temperature treatment developmental time in days versus temperature and (30ЊC, 25ЊC, and so on) to determine within chamber of 1/d versus temperature we 1) used a runs test (a temperature variation and compared internal cham- statistical measure of unidirectional error, or nonran- ber temperatures to assess between chamber varia- domness) to identify signiÞcant nonlinearity in the tions. We compared developmental time under set- regression (GraphPad Prism 4 software, GraphPad chamber and rearing-container temperatures by using Software Inc., San Diego, CA), 2) examined R2 values an analysis of covariance (ANCOVA) with tempera- and patterns of residuals from regressions (GraphPad ture covariate at a signiÞcance level P Յ 0.05 (PROC Software Inc.), and 3) looked at 95% prediction bands MIXED, SAS Institute 2002). (indicating where 95% of data points fall between) for For comparisons between designs we used meta- observed data points in the 1/d versus temperature analysis, a statistical analysis integrating the results of regression. We used 95% prediction bands as opposed multiple studies (e.g., Hedges and Olkin 1985), be- to 95% conÞdence intervals, which result in many cause the studies occurred at two time periods. We points outside the bands, because the 95% conÞdence compared developmental times to pupation and adult interval is a measure of the true mean or relationship, emergence under the same parameters for compari- not a prediction of where points should be. Based on sons of temperature measures. We also correlated these criteria, we sequentially eliminated low and averaged container temperature to observed stage upper temperature points until the runs test was non- transition times to generate averaged development signiÞcant, the R2 showed no improvement, residuals data for P. regina (Table 1). showed a random distribution, and experimental For calculations of accumulated degree-days, we points were within 95% prediction bands of the re- used the regressed x-intercept as the base tempera- gression. ture. This temperature was determined from regres- Second, we determined the developmental mini- sion of data within the linear range according to mum from the x-intercept from a linear regression; the methods outlined above (by using the runs test once the appropriate temperature range was estab- in combination with the residual plots generated un- lished, we regressed 1/developmental time versus der the regression (GraphPad Software Inc.). ADD temperature to determine the appropriate develop- values from egg to adult emergence are denoted as e-a mental minimum. ADDx-int, and ADD from egg to pupation are de- 1280 JOURNAL OF MEDICAL ENTOMOLOGY Vol. 43, no. 6

Table 1. Mean ؎ SE developmental time to pupation and adult emergence by temperature for both 2001 and 2004 experiments

Temp (ЊC) Egg to Egg to Yr n a a Set Cont. pupation (d) adult (d) 2001 32 31.1 4 6.3 Ϯ 0.3 10.3 Ϯ 0.8 26 26.7 4 6.4 Ϯ 0.4 13.0 Ϯ 1.1 20 20.9 1 13.8 20.5 14 14.6 1 25.9 45.8 12 11.0 1 0 0 2004 30 30.0 4 (12) 7.2 Ϯ 0.3 11.8 Ϯ 0.3 25 24.7 8 (28) 8.4 Ϯ 0.3 14.3 Ϯ 0.4 20 20.3 5 (13) 11.9 Ϯ 0.5 19.1 Ϯ 0.8 15 15.1 4 (11) 23.8 Ϯ 1.4 39.6 Ϯ 1.8 12b 14.1 1 (1) 37.2 52.7 12 11.8 2 (5) 0 0

Time is measured as modal development time in 2001 and as Þrst 10% (minute duration) in 2004. The number of experimental units, or chambers used to calculate averages, is indicated by n. Total sub- samples or rearing containers within chambers are indicated by values in parentheses. a Averages include all chamber replications of equal set-chamber temperatures with one exception (see footnote b). b This set-chamber temperature deviated high enough from rear- ing-container temperature that development could occur. But be- cause development occurred near the observed minimum threshold, it was separated from containers (and chambers) where development did not occur (Ͻ12.2ЊC). Including this point with those of similar set-chamber temperatures (12ЊC) would be misrepresentative. Fig. 2. Nonlinear regression of developmental time from noted as e-pADD . When the base temperature re- egg to adult for P. regina by using rearing-container temper- x-int ature (A) and set-chamber temperature (B). A ϭϪ17.83 ϩ ßects a value different from the x-intercept, we deÞne Ϫ 2 ϭ ϭϪ ϩ Ϫ the terminology as ADD or ADD where the base 19.41x/(x 9.93), R 0.95; and B 65.65 60.43x/(x # Tb 6.19), R2 ϭ 0.92. The dashed line represents the cutoff to temperature (Tb) is a number. where linearity or, more aptly, approximated linearity be- comes statistically nonlinear (as temperatures decrease) Results based on the methods for the given data set. Set-chamber temperatures tended to be higher than rearing container temperatures, although not signiÞ- relation was higher using rearing-container tempera- ϭ cantly (P 0.43) (Fig. 1). This deviation resulted in tures (R2 ϭ 0.95) versus set-chamber temperatures Ͻ Ͼ a slope coefÞcient 1 (0.96) and an intercept 0. (R2 ϭ 0.92), indicating a slightly better x-axis distri- The nonlinear regression Þt to all data points bution. Even though rearing-chamber temperatures showed the developmental curve under rearing-con- explain 3% more of the variation, the difference is not tainer temperatures differed from the curve under biologically signiÞcant. set-chamber temperatures (Fig. 2A and B). The cor- When using nonlinear regression, variance struc- ture can become skewed if data points are averaged, and especially if the averages represent a different number of points. Consequently, Table 1 represents only averaged data for each different year and com- mentary on standard errors and conÞdence intervals is limited to unaveraged data (Fig. 2A and B). From the runs test, we identiÞed where the temperatureÐ developmental time relationship became nonlinear (17.5ЊC) for both adult and pupal development. When we generated the 95% prediction band, one point was removed from the adult developmental time data set (at 25.1ЊC), whereas three points were removed from the pupal developmental time data set (at 25.1, 25.9, and 28.1ЊC) (data not shown; see Nabity 2005). Developmental times did not differ for egg-to-adult emergence (P ϭ 0.13) between studies from 2001 and Fig. 1. Deviation in temperature between set chamber 2004. Similarly, developmental times from egg to pu- temperature and rearing container temperatures for both pation did not differ between studies (P ϭ 0.325), so studies. data sets were combined for all additional compari- November 2006 NABITY ET AL.: P. regina DEVELOPMENT USED IN FORENSIC ENTOMOLOGY 1281

Fig. 3. Linear regression of transformed (daysϪ1) devel- opmental time from egg to adult P. regina by using rearing- container (A) and set-chamber (B) temperatures. A ϭ 0.0036x Ϫ 0.0195, R2 ϭ 0.79; and B ϭ 0.0035x Ϫ 0.0175, R2 ϭ 0.74. For x-intercept, A ϭ 5.4ЊC and B ϭ 5.0ЊC. sons. Combined developmental rates from egg to pu- pation, however, were signiÞcantly faster than devel- opmental rate from egg to adult emergence (P ϭ 0.001). Comparisons between our measures of devel- Fig. 4. Accumulated degree-days plotted using the cal- opmental time, whether by mode or Þrst 10%, did not culated x-intercept (speciÞc to one studyÕs data; Green- differ. berg ϭϪ7.0ЊC, Byrd and Allen ϭϪ3.9ЊC, and Nabity et al. Data points along the linear portion of the nonlinear ϭ 5.4ЊC) as the base temperature (A), compared with various regression were transformed (daysϪ1) as is the stan- published base temperatures 10ЊC (B) and 0ЊC (C). As dis- dard in degree-day analyses (Arnold 1959) to con- cussed in the text, when the base temperature is above the Њ Ͼ Њ struct a relationship between developmental rate and x-intercept (e.g., 10 C 5.4 C for Nabity et al. 2007) the both rearing-container and set-chamber temperatures regression slope is positive and ADD values are lower; when the base temperature is below the x-intercept (e.g., 0ЊC Ͻ (Fig. 3A and B). Regression of set-chamber and rear- 5.4ЊC for Nabity et al. 2006) the regression slope is negative ing-container temperatures against developmental and ADD values are higher. rates generated nearly equal parameters (set temp. slope ϭ 0.00349, cont. temp. slope ϭ 0.00357), result- ing in similar x-intercepts (5.0 and 5.46ЊC, respec- x-intercepts are very different when developmental tively). When we evaluated pupal developmental rate times are averaged across replications (i.e., all devel- within its corresponding linear data set, we also found opmental data from chambers set to 12ЊC are averaged similar values between set and rearing-container tem- to yield one developmental time for that speciÞc peratures (set temp. slope ϭ 0.00582, x-int. ϭ 5.1ЊC; temperature). Whether using averages of replicates cont. temp.: slope ϭ 0.00574, x-int. ϭ 4.8ЊC). The trans- across equal set-chamber temperatures and regressing Њ Ϫ1 ϭ formation of rate to ADDx-int resulted in similar values with set-chamber temperatures (5.4 C, b 279), or e-a for averaged ADDx-int for both adult (281 ADD5.46) using the same developmental data and regressing e-p Њ Ϫ1 ϭ and pupal (174 ADD4.8) developmental times com- with rearing-container temperatures (7.3 C, b Ϫ1 e-a pared with the inverse slope (b : 280 ADD5.46; 174 253), both x-intercepts are valid for their respective e-p ADD4.8) of the regression line through development data sets. This relationship is what creates the differ- rate versus temperature (Fig. 4A). ences in base temperatures seen in Table 2. The value of the x-intercept depends upon the data Although the base temperature determined by x- being regressed. Therefore, the set versus container intercept must be used in degree-day calculations, 1282 JOURNAL OF MEDICAL ENTOMOLOGY Vol. 43, no. 6

Table 2. ADD to adult development by using averaged developmental time and selected base temperatures

Combined 2001 and Combined 2001 and 2004 (rearing- Byrd and Allen (2001)a Greenberg (1991) 2004 (set) container) Њ ϭ Њ Њ Ϫ Њ Њ Њ Ϫ Њ Њ Њ Њ b Њ ϭ Њ Њ Њ b Set ( C) Tb 10 C0C(4.0 C) 10 C0C(6.8 C) 10 C0C (5.4 C) Cont. CTb 10 C0C (7.3 C) 10c 0 0 0 11.0c 00 0 12cd 105 632 348 14.1c 216 743 356 14c 183 642 394 14.6c 211 660 333 15c 157 470 595 198 594 380 15.1c 202 598 307 19 142 300 407 20 181 362 434 193 387 282 20.3 205 398 256 22e 170 311 409 22.5e 187 336 438 25 214 356 413 215 358 280 24.8 210 353 248 26 207 337 267 26.7 217 346 251 29e 215 328 405 30 241 361 409 236 354 290 30.0 236 354 267 32 227 330 274 31.1 218 321 245 35 276 386 431 254 356 425 40 0 0 0 Avg 228 366 422 194 326 417 216 353 279 Avg 217 355 254 SD 40 14 12 43 22 14 17 22 9 SD 12 28 9

Base temperatures included both absolute and investigator preferred minimums (0 and 10ЊC) and empirically determined x-intercepts (through regression of daysϪ1 vs. temperature) from published data. The x-intercept calculated from the temperatures shown is represented by the value in parentheses. Average and standard deviation were calculated using only values within the linear range as determined by the methods. a Development times used to calculate ADD are means from Table 8 in Byrd and Allen (2001). b The x-intercepts calculated on combined 2001 and 2004 data are generated from Table 1. The difference between x-intercepts in Table 2 and data elsewhere in this article reßects a mathematical artifact from regressing data of similar yet different values. Consequently, x-intercept data here are only valid in the context of comparisons in this table. c Developmental time at this temperature is outside the linear range. d As seen in Table 1, one chamber from 2004 registered a rearing-container temp (14.1ЊC) high enough above set-chamber temperature Њ Њ e-a e-a e-a (12 C) for development to occur (at 12 C ADD10, ADD0, and ADD7.6 are 74, 446, and 164, respectively). But because this point is within the nonlinear portion (a), it is not used to Þgure averages. e Average of published values from Greenberg (1991). All times are average minimum duration from Tables 2, 6, and 7 in Greenberg (1991). it may not be biologically meaningful (Arnold 1959). P. regina to compare x-intercepts, replication, and P. regina development to adult (x-intercept ϭ 5.46ЊC) how differences in developmental data alter estima- was not observed at or below 14ЊC. Hatch occurred at tions of the PMI (Table 3). Given a temperature of 11ЊC and larval development progressed to pupation 23ЊC, our data suggest development from egg to adult at 12.2ЊC, although emergence did not occur. We then in 16.1 d, similar in agreement to Byrd and Allen e-a calculated ADDTb for each year of data by using (2001) (15.6) and Greenberg (1991) (14.0). set-chamber temperatures and base temperatures (0 and 10ЊC) found in published data sets from Green- Discussion berg (1991) and Byrd and Allen (2001). We also de- termined ADD by using the x-intercepts calculated Using linear regression analysis, a line can be Þtted from those studies and from our own averaged data to approximate a constant growth rate across median (Table 2). Finally, we combined our two studies to temperatures. Although this line yields an extrapo- show ADD calculated from rearing-container temper- lated developmental minimum, the actual develop- atures by using different base temperatures. Because mental minimum occurs at a higher temperature be- we averaged our data and then calculated the x-in- cause of curvilinear responses at low temperatures. tercept, our x-intercept base temperature (7.3ЊC) is We observed egg hatch at 11.7ЊC, cessation of larval higher than what was calculated using unaveraged development at and below 12ЊC (larvae died), and at data (5 or 46ЊC). Also, average and SD values are a temperature of 12.2ЊC larvae pupated but did not generated from only values within the linear portion emerge. We observed complete egg-to-adult de- of the temperatureÐdevelopmental time relationship. velopment at 14ЊC; therefore, our best estimate of The resulting linear regressions using investigator pre- the biological developmental minimum is 14ЊC. If a ferred values (10 or 0ЊC) yielded lines with positive deÞnitive minimum threshold exists (and a single slopes (Fig. 4 and 4C), whereas the same e-aADD threshold may not apply, given possible genetic vari- calculated using the x-intercept as the temperature ation among populations), our data indicate this base resulted in a horizontal regression line (Fig. 4A). value would lie between 12.2 and 14ЊC. Thus, when a

The theoretical relationship between ADDx-int and biologically meaningful lower developmental thresh- temperature is a horizontal line with the thermal con- old is needed, 14ЊC should be used rather than 10ЊC stant (or inverse slope) equal to the y-axis intercept as has been assumed in other studies (Kamal 1958, (Arnold 1959). Greenberg 1991, Byrd and Allen 2001). Note that We calculated regression parameters (x-intercept, the biological developmental threshold is different bϪ1, and ADD) of current published data sets on from the minimum threshold used for degree-day cal- November 2006 NABITY ET AL.: P. regina DEVELOPMENT USED IN FORENSIC ENTOMOLOGY 1283

Table 3. Experimental parameters of several studies on P. regina

No. Temp range Developmental ADD ADD ADD Time to reach Study Oviposition to Ϫ SE (d) temp (ЊC) min. by x-intercept (b 1) (mean) (SE) stage at 23ЊC (d) Greenberg (1991) Egg eclosion 2 22 and 29 Ϫ41.0 52.5 53 0.0 0.8 0.0 Pupation 2 22 and 29 Ϫ9.50 289 289 0.0 8.9 0.0 Adult emergence 8 19Ð35 Ϫ6.80 416 417 6.1 14.0 0.2 Byrd and Allen (2001) Egg eclosion 4 15Ð35 Ϫ23.6 39 39 0.1 0.8 0.0 Pupation 4 15Ð35 Ϫ0.06 222 223 12.3 9.6 0.5 Adult emergence 4 15Ð35 Ϫ4.00 421 422 6.2 15.6 0.2 Anderson (2000) Egg eclosion 2 16.1 and 23 9.20 12 12 Ñ 0.9 Ñ Pupation 2 16.1 and 23 9.38 123 123 Ñ 9.1 Ñ Adult emergence 2 16.1 and 23 8.76 219 219 Ñ 15.1 Ñ Nabity et al. (2006) Pupation 58 17.5Ð32.4 4.76 174 174 3.0 9.6 0.2 This study Adult emergence 61 17.5Ð32.4 5.46 280 281 3.6 16.1 0.2

The x-intercepts were determined using the range of linear data (as determined by the methods of this study) and subsequent ADD were calculated using x-intercepts as the base temperatures. Data were taken from published values (excepting data from this study). In one instance where only two temperatures were available (Anderson 2000), degree-day assumptions were not met (ADD were not independent of temperature). culations that must be the x-intercept threshold to Use of inappropriate minimum thresholds invali- meet assumptions underlying the degree-day method dates the basic assumption of linearity in degree-day (Arnold 1959). models (i.e., the developmental rate is not constant Grassberger and Reiter (2002b) noted a similar across temperature). For example, when values higher response in terraenovae (Robineau- than the x-intercept are used, the ADDÐtemperature Desvoidy); the regressed larval developmental mini- relationship has a positive slope, implying fewer ADD mum (8.9ЊC) was lower than the pupal (9.8ЊC) min- are needed for development than is actually the case. imum. However, their regression included a low Likewise, when values lower than the x-intercept are temperature point (15ЊC) from beyond the linear por- used, the ADDÐtemperature relationship has a nega- tion of the temperatureÐdevelopmental time relation- tive slope, implying more ADD are needed than the ship as deÞned by the methods in this article. By not true value. Thus, using observed minimum thresholds including this data point and comparing developmen- (14ЊC as in this study) or investigator selected tem- tal rates as presented, we see signiÞcant differences peratures (0 or 10ЊC as in other studies) for calcula- between egg developmental rates and both pupal and tions results in underestimating or overestimating ac- adult developmental rates (P Ͻ 0.01). Although we tual degree-days, which, correspondingly, transfers used averaged temperature data, developmental rate into the estimates of PMI. Unless speciÞed and for from egg to pupation also tended to be different from comparative purposes only, the base temperature for developmental rate from egg to adult (P ϭ 0.11). degree-day calculations must be derived from the x- Probably, an analysis of the original data set would intercept method to avoid adding bias to Þnal ADD generate similar results if not at a lower level of sig- tallies. niÞcance (using the raw, unaveraged data). Thus, What if the x-intercept is lower than the observed each stage of development for Pr. terraenovae and minimum threshold (as in this study) or a negative P. regina has a unique minimum threshold and devel- value (e.g., Greenberg 1991, Byrd and Allen 2001)? opmental rate. This phenomenon is common among The x-intercept has no biological meaning but merely other insects (e.g., Poston et al. 1977, Fantinou et al. serves as the parameter facilitating the linear trans- 2003) and likely occurs among all ßies of forensic formation of developmental rate versus temperature importance. into ADD versus temperature (Arnold 1959). Simply, The signiÞcance of an accurate developmental min- multiplying developmental time by an augmented imum is great, because it is the basis for degree-day temperature (in this case subtracting a constant is a calculations, which in turn directly affect the estimate linear transformation as opposed to the inverse time of the PMI. Previous studies on P. regina used a variety transformation which is nonlinear) rotates the graph of developmental minimums to determine ADD. of developmental rate until it is horizontal and with Greenberg (1991) and Anderson (2000) used 0ЊC, increased (scaled) y-axis values. Because this is a lin- whereas Byrd and Allen (2001) used an observed ear heat unit system, values outside the linear range do value of 10.0ЊC to calculate thermal constants. Not not satisfy the transformations, which becomes prob- surprisingly, the degree-day values generated were lematic when trying to estimate development under not constant, and linear regression of the Þnal tem- low temperatures that fall outside the linear range. peratureÐADD relationship showed a nonzero slope, Although according to the model, development oc- indicating an invalid degree-day model. When Tb used curs until the base temperature is reached, observa- for degree-day calculations is any value other than the tion and common sense tells us that development x-intercept, the resulting trend in degree-days will ceases at least below 0ЊC if not at low temperatures have an increasing or decreasing slope depending on (e.g., Ͻ6ЊC). Therefore, when calculating ADD by whether Tb is greater or less than the x-intercept. using temperatures outside the linear range, investi- 1284 JOURNAL OF MEDICAL ENTOMOLOGY Vol. 43, no. 6 gators must use caution; or rather include large de- stages across zoogeographic regions as calculated grees of variability until reliable curvilinear models are through x-intercepts regression (compared with developed on data sets spanning the entire tempera- Marchenko 2001). Although the same difference is ture range. shown for P. regina in this study, Grassberger and How does the minimum threshold alter the PMI? Reiter relied on extrapolation rather than direct ob- The PMI represents the time between when the in- servation, used data from outside the range where sects (and body) were sampled (discovered) and linearity holds, and generated data under manual tem- when the insects began their development (shortly perature checks (twice daily). These checks may have after death). Hence, the PMI calculated from ADD provided only a snapshot of the growth chamber func- represents the shortest time frame possible because tion and how it affected larval development. Based on intrinsic and extrinsic factors only slow, rather than the information presented in this study, and from the increase, developmental rate. Subsequently variation other regional studies on P. regina (Kamal 1958; from is assumed into the Þnal PMI and adjusted for scene Washington, Greenberg 1991; from Illinois, Byrd and context (e.g., weather phenomena and wrapped Allen 2001; from U.S. southeast), overall developmen- body). This is why PMI from insect development must tal rate of specimens from different geographic areas be considered an estimate and not an absolute time seems variable within species, and because of meth- frame. By incorrectly calculating ADD in violation of odology. If we plot temperature versus developmental the model assumptions, bias is introduced into the time for P. regina for all studies, all data points fall along estimate of the initial PMI based on ADD. Table 3 a similar curve, regardless of differences in experi- illustrates this point. Although developmental data mental design. Thus, although there may be variation from Anderson (2000) are similar in duration to other within the species regarding developmental rate be- data on P. regina, using only two points to establish a tween stages, geography does not seem to alter rates graphical relationship (whether time, timeϪ1,orADD along, at least, the linear portion of the developmental versus temperature) may introduce bias, especially curve. Where geography may play a role in altering when one of those points is in the curvilinear range for developmental time is along the curvilinear portions the species as 16.1ЊCisforP. regina. of the relationship or the real developmental mini- Table 3 illustrates how testing a broad range of mum where physiological limitations may be inßu- temperatures is essential in developing a more accu- enced by environment. Future studies should seek to rate model of insect development. For example, al- verify this hypothesis. though the calculated developmental minima (by x- The lack of statistical differences between rearing- intercept) and ADD are different between Byrd and container and set-chamber temperatures is probably Allen (2001) and our study, the application of both because of deviations occurring above and below set models in a development prediction (growth at a temperatures and the high correlation of the data constant 23ЊC) shows developmental predictions (both set-chamber and rearing-chamber temperature differing only by half a day for egg-to-adult devel- use the same developmental data). In our work, we opment. Table 3 also illustrates that the longer the used 16 different chambers across experiments; how- developmental period, the greater the degree of ever, if fewer chambers were used the likelihood of variation. Undoubtedly, these differences in develop- unidirectional bias in temperature would have been mental predictions would be greater under cyclic, greatly increased. Also, if the methods used to identify Þeld temperatures, given the greater variation associ- curvilinearity in the temperatureÐdevelopmental ated with Þeld temperature measurements and insect time relationship were used on set-chamber rather development. Because experimental procedures are than rearing-container temperatures, the resulting lin- so different, comparisons of predicted times of devel- ear regression would be based upon developmental opment seem the most appropriate and useful method times wrongly associated with higher temperatures of assessing the validity of different models. within the true curvilinear spectrum for the species. The comparisons in Table 3 also imply that differ- Rearing-container temperatures showed stronger ences between existing models (experimental deter- correlation than set-chamber temperatures to de- minations of development) lead to estimates differing velopmental time. This resulted in better x-axis dis- in over 2 d. Fortunately, the close agreement in pre- tribution, more indicative of the real curvilinear dictions from more robust data sets indicates that relationship. Also, because most forensic literature variation among models should probably be on the development studies do not replicate between cham- order of no Ͼ0.5 d, and probably much less for periods bers, variation in temperature data are not random, shorter than egg-to-adult development. Unfortu- but biased by the chamber. Because we measured nately, until those robust data sets are available for the temperature experienced by developing larvae all forensically important species, the validity of PMI within the chamber and across several chambers, our estimates from existing data is uncertain. temperatureÐdevelopmental time relationship more Greenberg (1991) and Grassberger and Reiter accurately represents the true relationship. Using (2001) suggest geographic variation may lead to dif- set-chamber temperatures would generate the wrong ferences in developmental times and thus develop- relationship between temperature and developmental mental minimums. In a related species, Grassberger time. The resulting data transformation (timeϪ1) and Reiter (2002b) found Pr. terraenovae has dif- would then include inappropriate data potentially bi- ferent minimum thresholds for similar developmental asing the regression parameters (and calculated November 2006 NABITY ET AL.: P. regina DEVELOPMENT USED IN FORENSIC ENTOMOLOGY 1285

ADD). When conducting any controlled temperature Data here provide developmental minima and de- experiments, we know variation in temperatures oc- gree-day accumulations for oviposition to pupation curs between chambers (when more than one cham- and oviposition to adult emergence. Additional exper- ber are used for a study) and within chambers. How- imentation is needed for degree-day requirements for ever, this error is not discussed in the literature larval stage and behavioral transitions (mature larval surrounding forensic entomology or degree-day anal- wandering before pupation). yses, which inherently depend upon controlled tem- To prevent future confusion regarding develop- peratures. mental studies on insects, but speciÞcally on forensi- All these sources of variation merge within the Þnal cally important insects where data are used to deter- ADD model presented for P. regina. Our Þnal model mine PMIs for legal use, we recommend 1) collecting e-a (Fig. 4A) showed ADDx-int versus temperature for developmental data across the entire temperature all tested data points (from this study) and other data spectrum; 2) disclosing all data for use in nonlinear on P. regina (Greenberg 1991, Byrd and Allen 2001). regression analyses; 3) investigating curvilinear ap- This regression line should be horizontal across me- proaches for degree-day calculations, especially for dian temperatures if physiological time is constant the nonlinear portions of the temperatureÐdevelop- across temperature. When the improper base temper- mental time relationship; 4) quantifying sources of atures are used (Fig. 4B and C), the slope coefÞcient variation whether in developmental time, experi- becomes nonzero, indicating a violation in model as- mental design, or regression analyses; and 5) limiting sumptions. Variance of data from the regression line use of degree-days only to temperatures within the is probably a result of intraspeciÞc variation that may linear portion of the temperatureÐdevelopmental depend upon physiological aspects such as nutrition, time relationship. hormonal regulation, thermoregulation, or stage- Through a thorough examination of the develop- speciÞc development (Higley et al. 1986, Higley and ment of forensically important ßy species, we can Haskell 2001). Variance also may result from inade- increase the practical applicability and accuracy of the quate characterization of the true experienced tem- time frames used in litigative processes. Until we ad- perature or approximations/assumption in laboratory dress these issues of variability, unreported data, and estimates of development (Higley et al. 1986). In other adhering to proper assumptions built into modeling forensic studies (Byrd 1996, 1997, 1998), variability in and interpretative processes, estimates of the PMI may thermal constants occur as well, within degree-hour not be accurate. temperature models when calculated under the proper assumptions. Finally, by taking raw (unaveraged) data through Acknowledgments the transformation process associated with calculating development rates and ADD, the Þnal ADD model We thank S. M. Louda and S. M. Spomer for constructive accurately depicts variability in development. From discussions and editorial remarks, and all who helped monitor this variability, standard errors or conÞdence intervals ßy development and colonies, especially T. R. Brosius, can be generated, thereby giving the initial estimate of L. D. Franzen, A. Gutsche, T. E. Huntington, and S. E. Svehla. This work was supported by the Nebraska Agricultural Ex- the PMI an increased degree of accuracy. By using periment Station (Projects NEB-17-078 and NEB-17-080) averaged data, no assessment of the variability can be and by awards to P.D.N. from the University of Nebraska made because the original variance structure is Pepsi Endowment and Program of Excellence Funds for skewed through the nonlinear transformation. Other Undergraduate and Creative Activities and Research Expe- studies published on averaged data are limited in this riences and from an Undergraduate Honors Grant from the fashion, signaling a need for additional developmental Agricultural Research Division, UN-L. This is paper 15101 of studies on forensically important ßy species, or pub- the journal series of the University of Nebraska Agricultural lication access to original raw data sets. Research Division. It is this estimation and application of errors in forensic sciences that is purported as the coming “paradigm shift” (Saks and Koehler 2005). Our results References Cited here strongly indicate the error in PMI estimates Anderson, G. S. 2000. Minimum and maximum develop- from degree-days is greater than has been previously ment rate of some forensically important Calliphoridae acknowledged. SpeciÞcally, 1) experimental error (Diptera). J. Forensic Sci. 45: 824Ð832. associated with temperature measurement within Arnold, C. Y. 1959. The determination and signiÞcance of chamber is a greater issue than error from pseudo- the base temperature in a linear heat unit system. Proc. randomization and pseudoreplication, per se; 2) use of Am. Soc. Hortic. Sci. 74: 430Ð445. minimum or modal development has no signiÞcance in Byrd, J. H., and J. C. Allen. 2001. The development of the Þnal estimates, as also seen by Byrd and Allen (2001) black blow ßy, Phormia regina (Meigen). Forensic Sci. and Huntington (2005); and 3) use of an improper Int. 120: 79Ð88. Byrd, J. H., and J. F. Butler. 1996. Effects of temperature on minimum developmental threshold (any value other Cochliomyia macellaria (Diptera: Calliphoridae) devel- than the x-intercept from a speciÞc set of development opment. J. Med. Entomol. 33: 901Ð905. data) both invalidates degree-day assumptions and Byrd, J. H., and J. F. Butler. 1997. Effects of temperature on leads to the largest errors in estimates of insect de- Sarcophaga haemorrhoidalis (Diptera: Sarcophagidae) velopment. development. J. Med. Entomol. 34: 694Ð698. 1286 JOURNAL OF MEDICAL ENTOMOLOGY Vol. 43, no. 6

Byrd, J. H., and J. F. Butler. 1998. Effects of temperature on J. L. Castner [eds.], Forensic entomology: the utility of Chrysomya rufifacies (Diptera: Calliphoridae) develop- in legal investigations. CRC, Boca Raton, FL. ment. J. Med. Entomol. 35: 353Ð358. Higley, L. G., L. P. Pedigo, and K. R. Ostlie. 1986. DEGDAY: Clarkson, C. A., N. R. Hobischak, and G. S. Anderson. 2004. A program for calculating degree days, and assumptions A comparison of the development rate of Protophormia behind the degree day approach. Environ. Entomol. 15: terraenovae (RobineauÐDesvoidy) raised under constant 999Ð1016. and ßuctuating temperature regimes. Can. Soc. Forensic Huntington, T. E. 2005. TemperatureÐdependent develop- Sci. 37: 95Ð101. ment of blow ßies of forensic importance and the effects Fantinou, A. A., D. Ch. Perdikis, and C. S. Chatzoglou. 2003. on the estimation of the postmortem interval. M.S. thesis, Development of immature stages of Sesamia nonagrioides University of Nebraska, Lincoln, NE. (Lepidoptera: Noctuidae) under alternating and con- Hurlbert, S. H. 1984. Pseudoreplication and the design of stant temperatures. Environ. Entomol. 32: 1337Ð1342. ecological Þeld experiments. Ecol. Monogr. 54: 187Ð211. Goff, M. L., A. I. Omori, and J. R. Goodbrod. 1989. Effect of Kamal, A. S. 1958. Comparative study of thirteen species of cocaine in tissues on the development rates of Boett- sarcosaprophagous Calliphoridae and Sarcophagidae cherisca peregrina (Diptera: Sarcophagidae). J. Med. (Diptera). I. Bionomics. Ann. Entomol. Soc. Am. 51: 261Ð Entomol. 26: 91Ð93. 270. Grassberger, M., and C. Reiter. 2001. Effect of temperature Kaufmann, O. 1932. Einige bemerkuungen uber den ein- on Lucilia sericata (Diptera: Calliphoridae) development ßuss von temperatureschwankungen auf die entwick- lungsdauer und streuung bei insekten und seine gra- with special reference to the isomegalen- and isomor- phische darstellung durch kettelinie und hyperbel. phen-diagram. Forensic Sci. Int. 120: 32Ð36. Z. Morph. Okol. Tiere 25: 353Ð361. Grassberger, M., and C. Reiter. 2002a. Effect of tempera- Marchenko, M. I. 2001. Medicolegal relevance of cadaver ture on development of Liopygia (ϭSarcophaga) argyr- entomofauna for the determination of the time since stoma (RobineauÐDesvoidy) (Diptera: Sarcophagidae) death. Forensic Sci. Int. 120: 89Ð109. and its forensic implications. J. Forensic Sci. 47: 1Ð5. Nabity, P. D. 2005. A comparison of abiotic and biotic fac- Grassberger, M., and C. Reiter. 2002b. Effect of tempera- tors on the physiological ecology of plants and insects. ture on development of the forensically important Hol- M.S. thesis, University of Nebraska, Lincoln, NE. arctic blow ßy (Robineau-Des- Nabity, P. D., L. G. Higley, and T. M. Heng-Moss. 2007. voidy) (Diptera: Calliphoridae). Forensic Sci. Int 128: Light-induced variability in the development of the fo- 177Ð182. rensically important blow ßy, Phormia regina (Meigen) Grassberger, M., E. Freidrich, and C. Reiter. 2003. The (Diptera: Calliphoridae). J. Med. Entomol. (in press). blowßy Chrysomya albiceps (Wiedemann) (Diptera: Cal- Poston, F. L., R. B. Hammond, and L. P. Pedigo. 1977. liphoridae) as a new forensic indicator in Central Europe. Growth and development of the painted lady on soy- Int. J. Leg. Med. 117: 75Ð81. beans (Lepidoptera: Nymphalidae). J. Kans. Entomol. Greenberg, B. 1991. Flies as forensic indicators. J. Med. Soc. 50: 31Ð36. Entomol. 28: 565Ð577. Saks, M. J., and J. J. Koehler. 2005. The coming paradigm Hall, D. G. 1948. The blowßies of North America. Thomas shift in forensic identiÞcation science. Science (Wash., Say Foundation, Baltimore, MD. D.C.) 309: 892Ð895. Hedges, L. V., and L. Olkin 1985. Statistical methods for SAS Institute. 2002. PROC userÕs manual, version 9.1. SAS meta-analysis. Academic, Orlando, FL. Institute, Cary, NC. Higley, L. G., and N. H. Haskell. 2001. Insect development and forensic entomology, pp. 287Ð302. In J. H. Byrd and Received 12 May 2006; accepted 4 August 2006.