In *MATLAB* Problem 3 (11 points) An active area of research is forensic entomol
ID: 3856151 • Letter: I
Question
In *MATLAB*
Problem 3 (11 points)
An active area of research is forensic entomology, i.e. the application and study of insect and other arthropod biology to crime scene investigations. The presence, growth, and development of insects and arthropods can be used to date crime scenes. An important consideration in this field is the temperature of a body, since temperature is a driving factor in the developmental cycles of most insects and arthropods. Techniques such as Newton's Law of Cooling can be used as a first order approximation of the object's temperature. Let's examine how Newton's Law of Cooling works using a cup of coffee as a convenient object of study.
Assuming a constant ambient temperature (i.e. the temperature of the environment), Newton's Law of Cooling is given as
Consider the following:
A cup of coffee is made at exactly 12:00 p.m. (noon).
The temperature of the room the coffee cup is in is 68.0 °F.
After two minutes, the coffee has cooled from an initial temperature of 180 °F to a temperature of 165 °F.
For this problem, complete the following:
Using the calculated proportionality constant:
Calculate an array of temperature values one at a time using a loop. You may not use vectorized techniques to accomplish this.
Note that you should get the same result for both approaches (1) and (2); if not, a mistake was made in one (or both) approaches. Use this information to check your work.
Experiment with the time step size, allowing the time step to become larger and smaller. Calculate the wall time (i.e. the "real time") for runs of both the vectorized and loop-based approaches as you vary the time step size.
Is one approach faster than the other? Does it depend on how big the data set is? Leave code for at least three numerical experiments in the project file you submit for a grade, but feel free to explore more scenarios than this.
Print your responses to these questions to a data file located on the desktop of the machine you are using; be sure to close that file when you are done. (When we grade your code, we will check to make sure this process would work for you on your machine, even if the file system on your machine does not match the file system on our own machines.) When you consider your responses, please remember that MATLAB's loop performance has improved over the years, so be sure to report what you actually observe; offer your reasoned explanation for why you are seeing what you are seeing.
Explanation / Answer
Forensic (or medico-legal) entomology[1] is the study of the insects associated with a human corpse in an effort to determine elapsed time since death. Insect evidence may also show that the body has been moved to a second site after death, or that the body has been disturbed at some time, either by animals, or by the killer returning to the scene of the crime. However, the primary purpose of forensic entomology today is to determine elapsed time since death.
Forensic entomology was first reported to have been used in 13th Century China and was used sporadically in the 19th Century and the early part of the 20th Century, playing a part in some very major cases. However, in the last 20 years, forensic entomology has become more and more common in police investigations. In 1996, some of us developed the American Board of Forensic Entomology, a certification Board for Forensic Entomologists, similar to the Board certification available for forensic odontologists and forensic anthropologists.
Most cases that involve a forensic entomologist are 72 h or more old, as up until this time, other forensic methods are equally or more accurate than the insect evidence. However, after three days, insect evidence is often the most accurate and sometimes the only method of determining elapsed time since death. Recently, I have also analyzed and testified in cases in which elapsed time since death was only a few hours previous to discovery.
There are two main ways of using insects to determine elapsed time since death : -
I - using successional waves of insects
II - using maggot age and development.
The method used is determined by the circumstances of each case. In general, the first method is used when the corpse has been dead for between a month up to a year or more, and the second method is used when death occurred less than a month prior to discovery.
The first method is based on the fact that a human body, or any kind of carrion, supports a very rapidly changing ecosystem going from the fresh state to dry bones in a matter of weeks or months depending on geographic region. During this decomposition, the remains go through rapid physical, biological and chemical changes, and different stages of the decomposition are attractive to different species of insects. Certain species of insects are often the first witnesses to a crime. They usually arrive within 24 h of death if the season is suitable i.e. spring, summer or fall in Canada and can arrive within minutes in the presence of blood or other body fluids. These first groups of insects are the Calliphoridae or blowflies and the Sarcophagidae (the fleshflies). Other species are not interested in the corpse when the body is fresh, but are only attracted to the corpse later such as the Piophilidae or cheese skippers which arrive later, during protein fermentation. Some insects are not attracted by the body directly, but arrive to feed on the other insects at the scene. Many species are involved at each decomposition stage and each group of insects overlaps the ones adjacent to it somewhat. Therefore, with a knowledge of the regional insect fauna and times of carrion colonization, the insect assemblage associated with the remains can be analyzed to determine a window of time in which death took place. This method is used when the decedent has been dead from a few weeks up to a year, or in some cases several years after death, with the estimated window of time broadening as time since death increases. It can also be used to indicate the season of death e.g. early summer. A knowledge of insect succession, together with regional, seasonal, habitat and meteorological variations, is required for this method to be successful.
The second method, that of using maggot age and development can give a date of death accurate to a day or less, or a range of days, and is used in the first few weeks after death. Maggots are larvae or immature stages of Diptera or two-winged flies. The insects used in this method are those that arrive first on the corpse, that is, the Calliphoridae or blowflies. These flies are attracted to a corpse very soon after death. They lay their eggs on the corpse, usually in a wound, if present, or if not, then in any of the natural orifices. Their development follows a set, predictable, cycle.
The insect egg is laid in batches on the corpse and hatches, after a set period of time, into a first instar (or stage) larva. The larva feeds on the corpse and moults into a second instar larva. The larva continues to feed and develop into a third instar larva. The stage can be determined by size and the number of spiracles (breathing holes). When in the third instar, the larva continues to feed for a while then it stops feeding and wanders away from the corpse, either into the clothes or the soil, to find a safe place to pupate. This non-feeding wandering stage is called a prepupa. The larva then loosens itself from its outer skin, but remains inside. This outer shell hardens, or tans, into a hard protective outer shell, or pupal case, which shields the insect as it metamorphoses into an adult. Freshly formed pupae are pale in colour, but darken to a deep brown in a few hours. After a number of days, an adult fly will emerge from the pupa and the cycle will begin again. When the adult has emerged, the empty pupal case is left behind as evidence that a fly developed and emerged.
Each of these developmental stages takes a set, known time. This time period is based on the availability of food and the temperature. In the case of a human corpse, food availability is not usually a limiting factor.
Insects are 'cold blooded', so their development is extremely temperature dependent. Their metabolic rate is increased with increased temperature, which results in a faster rate of development, so that the duration of development decreases in a linear manner with increased temperature, and vice-versa.
An analysis of the oldest stage of insect on the corpse and the temperature of the region in which the body was discovered leads to a day or range of days in which the first insects oviposited or laid eggs on the corpse. This, in turn, leads to a day, or range of days, during which death occurred. For example, if the oldest insects are 7 days old, then the decedent has been dead for at least 7 days. This method can be used until the first adults begin to emerge, after which it is not possible to determine which generation is present. Therefore, after a single blowfly generation has been completed, the time of death is determined using the first method, that of insect succession.
PROCEDURE
The first and most important stage of the procedure involved in forensic entomology involves careful and accurate collection of insect evidence at the scene. This involves a knowledge of the insects behaviour, therefore it is best performed by an entomologist. I am always willing to come to a scene if it is possible. Unfortunately, the entomologist is often not called until after the body has been removed from the death site. I usually see the remains at the morgue, and in some cases, do not actually see the remains at all, so my evidence is dependent on accurate collection by the investigating officers.
COLLECTING, PRESERVING AND PACKAGING SPECIMENS.
For further details, a video on insect collection is available from R.C.M.P. “E” Division Training – (604) 264 3619.
COLLECTION
Samples of insects of all stages should be collected from different areas of the body, from the clothing and from the soil/carpet etc. Insects will often congregate in wounds and in and around natural orifices.
The two main insect groups on bodies are flies (Diptera) and beetles (Coleoptera).
Both types of insect look very different at different stages of their lives.
Flies can be found as:-
- eggs (in egg masses usually)
- larvae or maggots (in a range of sizes from 1-2 mm to 17 mm)
- pupae and/or empty pupal cases
- adults.
EGGS - are very tiny, but are usually laid in clumps or masses, and are usually found in a wound or natural orifice, but may be found on clothing etc. They can be collected with a child’s paint brush dipped in water or with forceps. Half should be preserved in 75% alcohol or 50% isopropyl alcohol. The rest should be placed in a vial with a little damp tissue paper to prevent dehydration. If it will be more than a few hours before the entomologist receives them, they should also be given a small piece of beef liver. Make sure there is tissue or sawdust present if liver is added, to prevent drowning. They need some air. Newly emerged maggots can escape through holes, so a paper towel held over the top of the vial with a rubber band is excellent, as long as the vial stays upright! (No lid other than the paper towel is needed).
Eggs are only of value when no maggots or later insect stages are present. If maggots are already present, don’t worry about the eggs.
If no maggots are present, and the only insect evidence is eggs, then the eggs are very important and the time they hatch will be vital. Therefore, observe the live eggs every few hours and please note time when they first start hatching and the approximate percentage (e.g. 1015h 10% hatch, 1220 h 50% hatch, 1550 h 100% hatch).
MAGGOTS - collect a range of sizes. Maggots will be found crawling on or near the remains and may be in maggot masses. The masses generate a lot of heat, which speeds up development. Therefore, please note:-
Þ the site of maggot masses
Þ the temperature of each mass (thermometers can be acquired cheaply at drugstores) or if no thermometer available, please estimate size of mass.
Þ label which maggots come from a particular mass.
Large maggots are usually older so are most important, but smaller maggots may belong to a different species so both large and smaller maggots should be collected, with the emphasis on larger maggots.
Collect samples of maggots from different areas of the body and the surrounding area, and keep them separate.
As mentioned before, third instar larvae leave the food source to find a suitable area in which to pupate. They may wander some distance from the body so the soil for a metre or two around the body should be carefully sifted. Some may burrow down into leaf litter, so the soil below the corpse should be checked for several centimetres. If the remains were on a slope, the body fluids will seep downhill and insects will be found here, feeding on the fluids. This means that a very intensive search of the corpse, the clothes and the surrounding area must be made in order to get the entire picture.
When collected, the sample should be divided into two – half for preservation and half kept alive.
A proportion (approximately half) of the larvae should be preserved immediately for two reasons. Firstly, to show the entomologist, if s/he is not present at the scene, what stage the larvae were when collected, as if they are then placed on meat, they will continue to develop, giving a misleading impression to the entomologist when they are examined. Secondly, to produce as evidence in court.
If there are lots of maggots on the body, preserve approximately half of all sizes.
If there are only 20-30, preserve 1 or 2