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The Lincoln-Peterson index is a method for deducing the population size of an elusive species. Many populations, such as those of many birds, insects, and ocean-going animals (from turtles to fish to whales), are very hard to count, due to their high mobility and wide dispersal. One common solution to this is to capture and tag a given number of individuals, re-release them into the wild, and then take random samples of the population at a later time. The simple way to think of this is that if you tag 100 animals, and later sample 100 animals, and you find only one tagged animal in your sample, you might guess that there are about 10,000 animals in the local population.
The Lincoln-Peterson index gives us a slightly more formal mathematical model for determining population size through our tagging and sampling process. It goes thusly:
M/N = m/n
Where:
- M = the number of individuals marked and released.
- N = the actual size of the study population.
- m = the number of marked individuals in the sample population.
- n = the total number of individuals in the sample.
We know M, m, and n, meaning that we can easily calculate N, the actual size of the study population. (To solve for N, we would write the equation as N=Mn/m).
As it happens, this index tends to overestimate the population size by a small amount. In order for this calculation to work accurately, no marked animals can be removed from the population (i.e., die) between the time they are tagged and the time that the sample is taken. As it happens, a population will constantly loose old (tagged) members, and gain new (untagged) members through the birth of new individuals. To account for this, a modified Lincoln-Peterson index was suggested:
N = M(n+1)/(m+1)
While the addition of the imaginary tagged animal to the sample size is a kludge that probably makes baby mathematician Jesus cry, it also results in more accurate estimations of population size, so it is frequently used. Another modification, known as the Schnabel index, is also often used: N=((M+1)x(n+1)/(m+1))-1.
For obvious reasons, the Lincoln-Peterson index is still the most popular when a quick and easy calculation is sufficient, but a modified form is more common in published works.
Lapsus calami is Latin for 'typo'. It literally means a 'lapse of the pen', and may refer to any transcription error or misspelling. It is used as a technical term in the field of biological nomenclature; any error in a published work is identified by one of a number of very specific terms. As you might expect, lapsus calami is not uncommon when dealing with long Latin names of families, species and various varieties.
Lapsus calami is synonymous with the less poetic and less common sphalma typographicum, literally a 'typographic error'. Despite what many sources will tell you, nomen nullum is not a synonym. A basic list of errors in scientific nomenclature would include:
If one moves away from the field of taxonomy, one might speak of other types of lapsus than those involving typos; a lapsus linguae would indicate that one misspoke, while a lapsus memoriae would indicate that one misremembered. Those, however, belong in other nodes.
3D printing is one of the most interesting technologies of our time, even if people do sometimes go overboard with their excitement about it - we are still a long way off having machines in our own homes that will just print us out a new phone on demand, but it is genuinely amazing that we can now upload a 3D file to a company that specialises in this stuff, and then pay to get it printed in plastic, ceramic or any of a range of different metals. Printing in this case usually means building up the piece layer by layer either by extruding the material from a tube, or some variant on selective laser sintering, which fuses fine powders into solid shapes using one or more lasers.
Medical applications are among the most fascinating uses for this technology. There has been a good deal of talk about printing whole organs in 3D, using cells taken from a patient's own body and grown in culture before spraying them into the shape of the organ in question. There have also been several successful dental implants and replacements of small bones with printed metal.
Now an 83-year-old woman suffering from chronic osteomyelitis has had an entire new jawbone created out of titanium. Using an MRI scan of her existing, badly deteriorated jaw, a metal replacement was created in exactly the right shape, allowing places for muscles to adhere and nerves to pass through. The titanium was coated with a kind of ceramic that the human body tolerates in implants, and was then successfully implanted by surgeons in the space of less than four hours - five times quicker than traditional reconstructive surgery would have been.
The patient was reportedly able to talk and swallow normally the day after the surgery. The team responsible for the operation at the Biomedical Research Institute at Hasselt University in Belgium, and the private company LayerWise which printed the jaw, are said to be extremely happy with the success of the operation, and excited about what this technology might hold for the future.
References
Did you think that this was another sentimental heart-broken node?
No, broken heart syndrome is an actual medical condition. It is also known as stress cardiomyopathy, transient apical ballooning cardiomyopathy or Takotsubo cardiomyopathy.
I first heard about broken heart syndrome in church a few years ago. At the joys and sorrows time, there was an announcement that a church member had been transferred from our local hospital to a larger one. That she had an unusual heart condition, was on a heart-lung machine and was expected to recover.
I thought, another zebra. It must be my patient. Then I scolded that part of my brain for a while, saying that other doctors in town see rare things too.
The cardiologist called me two days later because it was my patient.
Broken heart syndrome was first called Takotsubo cardiomyopathy because tako tsobu is the name of a round octopus trap and the shape that the heart takes when it suddenly gives way. The heart suddenly weakens and the muscle balloons. This causes severe heart failure because the stricken heart muscle cannot pump correctly. There is chest pain and it looks like a heart attack, but when a cardiac catheterization is done, the vessels usually are not blocked.
The heart is stricken by stress. In my patient's case, she was the primary caregiver to her husband, who had cancer. It is often triggered by the death of a beloved spouse; a break up; extreme fear, severe illness or even winning the lottery. It was first described in Japan in 1990. It is 7.5 times more likely to occur in women then men, according to a study at the University of Arkansas by Abhishek Dehmukh MD. He found 6229 cases in US hospitals in 2007, with 761 of the patients being male. It is theorized that a sudden rush of stress hormones damages the heart so that it balloons and that microvascular blockages may play a role.
My patient was on a heart-lung bypass machine, to pump for her heart, for three or four days. Her heart recovered. She spoke to our church and said that as a caregiver she had to learn to take care of herself too.
The poets are right. Our hearts can break, with a mortality rate of 1-2%. Take care.
National Institutes of Health
Mayo Clinic
Johns Hopkins
American Journal of Roentgenology
Daily mail
A picture
Art and science
For Science Quest 2012.
