How was the cama's life expectancy computed?

How was the cama's life expectancy computed?

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A cama is a hybrid between a male dromedary camel and a female llama. The first cama was born on January 14, 1998, yet on the Wikipedia page it is said that a cama's life span is 30-40 years. How was that number determined? Is it simply the average between a camel's and a llama's life spans?

Since no source is given for the 30 - 40 years estimate in Wikipedia, we can't find out how the authors of the Wiki page reached that estimate, but 'someone made an educated guess' seems likely. There are a few reasonable ways that one might educatedly guess the longevity of the cama, but there are good reasons to treat those educated guesses with caution.

First, as you suggested, you could just estimate the cama's longevity from the life expectancy of camels and llamas. This is likely to fall in the right ball-park, but should be interpreted with caution: ligers (lion - tiger hybrids) are reputed to have high rates of premature death, and the same may well apply to camas.

Second, you could plug the animal's body measurements, metabolic-rate measurements, or similar measurements into a model which relates species' attributes to a measure of their longevity. Many different models of lifespan have been built (e.g. here), and if your goal is to get a rough estimate of how long a member of a particular species will live, those models are not a bad way of making a first guess. The 'this is a weird hybrid and might have issues with premature death' caveat still applies, though.

Life span

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Life span, the period of time between the birth and death of an organism.

It is a commonplace that all organisms die. Some die after only a brief existence, like that of the mayfly, whose adult life burns out in a day, and others like that of the gnarled bristlecone pines, which have lived thousands of years. The limits of the life span of each species appear to be determined ultimately by heredity. Locked within the code of the genetic material are instructions that specify the age beyond which a species cannot live given even the most favourable conditions. And many environmental factors act to diminish that upper age limit.


The mule is valued because, while it has the size and ground-covering ability of its dam, it is stronger than a horse of similar size and inherits the endurance and disposition of the donkey sire, tending to require less food than a horse of similar size. Mules also tend to be more independent than most domesticated equines other than its parental species, the donkey.

The median weight range for a mule is between about 370 and 460 kg (820 and 1,000 lb). [5] While a few mules can carry live weight up to 160 kg (353 lb), the superiority of the mule becomes apparent in their additional endurance. [6]

In general, a mule can be packed with dead weight of up to 20% of its body weight, or approximately 90 kg (198 lb). [6] Although it depends on the individual animal, it has been reported that mules trained by the Army of Pakistan can carry up to 72 kilograms (159 lb) and walk 26 kilometres (16.2 mi) without resting. [7] The average equine in general can carry up to approximately 30% of its body weight in live weight, such as a rider. [8]

A female mule that has estrus cycles and thus, in theory, could carry a fetus, is called a "molly" or "Molly mule", though the term is sometimes used to refer to female mules in general. Pregnancy is rare, but can occasionally occur naturally as well as through embryo transfer. A male mule is properly called a horse mule, though often called a john mule, which is the correct term for a gelded mule. A young male mule is called a mule colt, and a young female is called a mule filly. [9]

With its short thick head, long ears, thin limbs, small narrow hooves, and a short mane, the mule shares characteristics of a donkey. In height and body, shape of neck and rump, uniformity of coat, and teeth, it appears horse-like. [10] The mule comes in all sizes, shapes and conformations. There are mules that resemble huge draft horses, sturdy quarter horses, fine-boned racing horses, shaggy ponies and more.

The mule is an example of hybrid vigor. [11] Charles Darwin wrote: "The mule always appears to me a most surprising animal. That a hybrid should possess more reason, memory, obstinacy, social affection, powers of muscular endurance, and length of life, than either of its parents, seems to indicate that art has here outdone nature." [12]

The mule inherits from its sire the traits of intelligence, sure-footedness, toughness, endurance, disposition, and natural cautiousness. From its dam it inherits speed, conformation, and agility. [13] : 5–6,8 Mules are reputed to exhibit a higher cognitive intelligence than their parent species. That said, there is a lack of robust scientific evidence to back up these claims. There is preliminary data from at least two evidence based studies, but they rely on a limited set of specialized cognitive tests and a small number of subjects. [14] [15] Mules are generally taller at the shoulder than donkeys and have better endurance than horses, although a lower top speed. [16] [14]

Handlers of working animals generally find mules preferable to horses: mules show more patience under the pressure of heavy weights, and their skin is harder and less sensitive than that of horses, rendering them more capable of resisting sun and rain. [10] Their hooves are harder than horses', and they show a natural resistance to disease and insects. Many North American farmers with clay soil found mules superior as plow animals.

A mule does not sound exactly like a donkey or a horse. Instead, a mule makes a sound that is similar to a donkey's but also has the whinnying characteristics of a horse (often starts with a whinny, ends in a hee-haw). Mules sometimes whimper.

Color and size variety Edit

Mules come in a variety of shapes, sizes and colors, from minis under 200 lb (91 kg) to over 1,000 lb (454 kg), and in many different colors. The coats of mules come in the same varieties as those of horses. Common colors are sorrel, bay, black, and grey. Less common are white, roans, palomino, dun, and buckskin. Least common are paint mules or tobianos. Mules from Appaloosa mares produce wildly colored mules, much like their Appaloosa horse relatives, but with even wilder skewed colors. The Appaloosa color is produced by a complex of genes known as the Leopard complex (Lp). Mares homozygous for the Lp gene bred to any color donkey will produce a spotted mule.

Distribution and use Edit

Mules historically were used by armies to transport supplies, occasionally as mobile firing platforms for smaller cannons, and to pull heavier field guns with wheels over mountainous trails such as in Afghanistan during the Second Anglo-Afghan War. [17]

The Food and Agriculture Organization of the United Nations (FAO) reports that China was the top market for mules in 2003, closely followed by Mexico and many Central and South American nations.

Mules and hinnies have 63 chromosomes, a mixture of the horse's 64 and the donkey's 62. The different structure and number usually prevents the chromosomes from pairing up properly and creating successful embryos, rendering most mules infertile.

A few mare mules have produced offspring when mated with a purebred horse or donkey. [18] [19] Herodotus gives an account of such an event as an ill omen of Xerxes' invasion of Greece in 480 BC: "There happened also a portent of another kind while he was still at Sardis—a mule brought forth young and gave birth to a mule" (Herodotus The Histories 7:57), and a mule's giving birth was a frequently recorded portent in antiquity, although scientific writers also doubted whether the thing was really possible (see e.g. Aristotle, Historia animalium, 6.24 Varro, De re rustica, 2.1.28).

As of October 2002, there had been only 60 documented cases of mules birthing foals since 1527. [19] In China in 2001, a mare mule produced a filly. [20] In Morocco in early 2002 and Colorado in 2007, mare mules produced colts. [19] [21] [22] Blood and hair samples from the Colorado birth verified that the mother was indeed a mule and the foal was indeed her offspring. [22]

A 1939 article in the Journal of Heredity describes two offspring of a fertile mare mule named "Old Bec", which was owned at the time by Texas A&M University in the late 1920s. One of the foals was a female, sired by a jack. Unlike her mother, she was sterile. The other, sired by a five-gaited Saddlebred stallion, exhibited no characteristics of any donkey. That horse, a stallion, was bred to several mares, which gave birth to live foals that showed no characteristics of the donkey. [23]

The mule is "the most common and oldest known manmade hybrid." [24] [25] It was likely invented in ancient times in what is now Turkey. They were common in Egypt by 3000 BCE. [24] Homer noted their arrival in Asia Minor in the Iliad in 800 BCE. Mules are mentioned in the Bible (Samuel 2:18:9, Kings 1:18:5, Zacharia 14:15, Psalms 32:9). Christopher Columbus brought mules to the new world. [25] George Washington is known as the Father of the American Mule due to his success in producing 57 mules at his home at Mount Vernon. At the time, mules were not common in the United States, but Washington understood their value as they were "more docile than donkeys and cheap to maintain." [26] In the nineteenth century they were used in various capacities as draft animals: on farms, especially where clay made the soil slippery pulling canal boats and famously for pulling, often in teams of twenty animals, wagonloads of borax out of Death Valley, California from 1883 to 1889. The wagons were among the largest ever pulled by draft animals, designed to carry 10 short tons (9 metric tons) of borax ore at a time. [27]

In the second half of the 20th century, widespread usage of mules declined in industrialized countries. The use of mules for farming and transportation of agricultural products largely gave way to steam then gasoline powered tractors and trucks.

Mules are still used extensively to transport cargo in rugged roadless regions, such as the large wilderness areas of California's Sierra Nevada mountains or the Pasayten Wilderness of northern Washington state. Commercial pack mules are used recreationally, such as to supply mountaineering base camps, and also to supply trail building and maintenance crews, and backcountry footbridge building crews. [28] As of July 2014, there are at least sixteen commercial mule pack stations in business in the Sierra Nevada. [29] The Angeles chapter of the Sierra Club has a Mule Pack Section that organizes hiking trips with supplies carried by mules. [30]

During the Soviet–Afghan War, mules were used to carry weapons and supplies over Afghanistan's rugged terrain to the mujahideen. [31]

Approximately 3.5 million donkeys and mules are slaughtered each year for meat worldwide. [32]

Mule trains have been part of working portions of transportation links as recently as 2005 by the World Food Programme. [33]

With the reform of the Corps of Alpini, the last mules were sold at auction in 1993. Nowadays there is little use in the mountains for agricultural and sylvan needs. Some specimens are used in hippotherapy and, for this purpose, we try to re-evaluate mules with ad hoc projects.

The last mule of the Alpine baggage Edit

Iroso, the last of the mules used by the Alpine Corps, died in 2019. [34] The mule had been in the force of the 7th Alpine Regiment. In 1993 it was bought at auction by a former Alpine who had looked after it ever since. The last public appearance recorded was that for the celebrations of his 40th birthday, which took place in Anzano, a hamlet of Cappella Maggiore (TV), on January 13, 2019.[1]

Iroso, now almost blind and bruised by the weight of the years, died on April 29, 2019.[2]

Integrated Population Biology and Modeling, Part A

Subrata Lahiri , in Handbook of Statistics , 2018

1.7 Recent Contributions of Arni S. R. Srinivasa Rao and James R. Carey on Stationary Population and Other Related Issues

In continuation of the publications of “Carey's Equality and Fundamental Theorem on Stationary Population Models” (vide ) and “New theorem determines the age distribution of population from fruit flies to humans” (vide ), Rao (2014) and Rao and Carey (2015) (see also Rao, 2012 ) have shown very interesting and new ideas and concepts on population stationary as well as on population stability and momentum.

The paper by Rao (2014) develops a new theory to understand the stability of populations. The argument is that when subpopulations will have presence of population momentum, then the local stability of the total population could become unstable. This paper also proposes mathematical conditions under which subpopulation growth and momentum to decide whether or not the total population remains stable.

The research paper by Rao and Carey (2015) presents a novel theorem in stationary populations that states under certain conditions, two graphs, one constructed based on captured data and other on age at capture, are equal. They gave an innovative proof which uses sets and graphs and concepts of Carey's Equality. The concepts and ideas of the two research publications, mentioned above, may be followed up for further in demographic research.


The physical manifestations of TSC are due to the formation of hamartia (malformed tissue such as the cortical tubers), hamartomas (benign growths such as facial angiofibroma and subependymal nodules), and very rarely, cancerous hamartoblastomas. The effect of these on the brain leads to neurological symptoms such as seizures, intellectual disability, developmental delay, and behavioral problems. [ citation needed ]

Neurological Edit

Three types of brain tumours are associated with TSC:

  • Giant cell astrocytoma: (grows and blocks the cerebrospinal fluid flow, leading to dilatation of ventricles causing headache and vomiting)
  • Cortical tubers: after which the disease is named
  • Subependymal nodules: form in the walls of ventricles

Classic intracranial manifestations of TSC include subependymal nodules and cortical/subcortical tubers. [5]

The tubers are typically triangular in configuration, with the apex pointed towards the ventricles, and are thought to represent foci of abnormal neuronal migration. The T2 signal abnormalities may subside in adulthood, but will still be visible on histopathological analysis. On magnetic resonance imaging (MRI), TSC patients can exhibit other signs consistent with abnormal neuron migration such as radial white matter tracts hyperintense on T2WI and heterotopic gray matter. [ citation needed ]

Subependymal nodules are composed of abnormal, swollen glial cells and bizarre multinucleated cells which are indeterminate for glial or neuronal origin. Interposed neural tissue is not present. These nodules have a tendency to calcify as the patient ages. A nodule that markedly enhances and enlarges over time should be considered suspicious for transformation into a subependymal giant cell astrocytoma, which typically develops in the region of the foramen of Monro, in which case it is at risk of developing an obstructive hydrocephalus. [ citation needed ]

A variable degree of ventricular enlargement is seen, either obstructive (e.g. by a subependymal nodule in the region of the foramen of Monro) or idiopathic in nature. [ citation needed ]

Neuropsychiatric Edit

About 90% of people with TSC develop a range of neurodevelopmental, behavioural, psychiatric, and psychosocial difficulties. The "TSC‐associated neuropsychiatric disorders" are abbreviated TAND. These difficulties are less frequently identified and thus undertreated when compared with the neurological symptoms. [6] Most problems are associated with more severe intellectual delay or associated with childhood and adolescence, and some (for example depressed mood) may be unreported if the person is unable to communicate. TAND can be investigated and considered at six levels: behavioural, psychiatric, intellectual, academic, neuropsychological, and psychosocial. [6]

Behavioural problems most commonly seen include overactivity, impulsivity and sleeping difficulties. Also common are anxiety, mood swings, and severe aggression. Less common are depressed mood, self-injury, and obsessional behaviours. [6]

People with TSC are frequently also diagnosed with psychiatric disorders: autism spectrum disorder (ASD), attention deficit hyperactivity disorder (ADHD), anxiety disorder and depressive disorder. TSC is one of the most common genetic causes of autism spectrum disorder, which affects nearly half of people with TSC. ASD is more common in TSC2 than TSC1 and more common with earlier and more severe epilepsy, and with lower intellectual ability. ADHD is nearly as frequently seen in TSC as ASD (up to half of all people with TSC). Anxiety and depressive disorders, when they occur, are typically diagnosed in early adulthood and among those intellectually able to express their moods. [6] Schizophrenia (and symptoms like hallucinations or psychosis) is no more common in TSC than the general population. [ citation needed ]

The intellectual ability of people with TSC varies enormously. About 40–50% have a normal IQ. A normal IQ is much more commonly seen in TSC1 than TSC2, and profound intellectual disability seen in 34% of TSC2 compared with 10% of TSC1 in one study. Many studies have examined whether early onset, type and severity of epilepsy associates with intellectual ability. Academic issues occur even in people with TSC who have normal intellectual ability. These are often specific learning disorders such as dyscalculia (understanding mathematics), but also include other aspects affecting school life such as anxiety, lack of social skills or low self-esteem. [6]

About half of people with TSC, when assessed for neuropsychological skills, are in the bottom 5th percentile in some areas, which indicates a severe impairment. These include problems with attention (for example, being able to concentrate on two separate things like looking and listening), memory (particularly recall, verbal and spatial working memory) and executive function (for example, planning, self-monitoring, cognitive flexibility). [6]

The psychosocial impacts of TSC include low self-esteem and self-efficacy in the individual, and a burden on the family coping with a complex and unpredictable disorder. [6]

Kidneys Edit

Between 60 and 80% of TSC patients have benign tumors (once thought hamartomatous, but now considered true neoplasms) of the kidneys called angiomyolipomas frequently causing hematuria. These tumors are composed of vascular (angio–), smooth muscle (–myo–), and fat (–lip-) tissue. Although benign, an angiomyolipoma larger than 4 cm is at risk for a potentially catastrophic hemorrhage either spontaneously or with minimal trauma. Angiomyolipomas are found in about one in 300 people without TSC. However, those are usually solitary, whereas in TSC they are commonly multiple and bilateral. [ citation needed ]

About 20-30% of people with TSC have renal cysts, causing few problems. However, 2% may also have autosomal dominant polycystic kidney disease. [ citation needed ]

Lungs Edit

Patients with TSC can develop progressive replacement of the lung parenchyma with multiple cysts, known as lymphangioleiomyomatosis (LAM). Recent genetic analysis has shown that the proliferative bronchiolar smooth muscle in TSC-related lymphangioleiomyomatosis is monoclonal metastasis from a coexisting renal angiomyolipoma. Cases of TSC-related lymphangioleiomyomatosis recurring following lung transplant have been reported. [7]

Heart Edit

Small tumours of the heart muscle, called cardiac rhabdomyomas, are rare in the general population (perhaps 0.2% of children) but very common in people with TSC. Around 80% of children under two-years-old with TSC have at least one rhabdomyoma, and about 90% of those will have several. The vast majority of children with at least one rhabdomyoma, and nearly all children with multiple rhabdomyomas will be found to have TSC. Prenatal ultrasound, performed by an obstetric sonographer specializing in cardiology, can detect a rhabdomyoma after 20 weeks. Rhabdomyoma vary in size from a few millimetres to several centimetres, and are usually found in the lower chambers (ventricles) and less often in the upper chambers (atria). They grow in size during the second half of pregnancy, but regress after birth, and are seen in only around 20% of children over two years old. [8]

Most rhabdomyomas cause no problems but some may cause heart failure in the foetus or first year of life. Rhabdomyomas are believed to be responsible for the development of heart arrhythmia later in life, which is relatively common in TSC. Arrhythmia can be hard to spot in people with TSC, other than by performing routine ECG. For example, arrhythmia may cause fainting that is confused with drop seizures, and symptoms of arrhythmia such as palpitations may not be reported in an individual with developmental delay. [8]

Skin Edit

Some form of dermatological sign is present in 96% of individuals with TSC. Most cause no problems, but are helpful in diagnosis. Some cases may cause disfigurement, necessitating treatment. The most common skin abnormalities include:

  • Hypomelanic macules ("ash leaf spots") are present in about 90% of people with TSC. [9] These small white or lighter patches of skin may appear anywhere on the body, and are caused by a lack of melanin. They are usually the only visible sign of TSC at birth. In fair-skinned individuals, a Wood's lamp (ultraviolet light) may be required to see them. On the scalp, the effect may be a white patch of hair (poliosis). Patches smaller than 3mm are known as "confetti" skin lesions. [9]
  • Facial angiofibromas are present in about 75% of people with TSC. [9] These are a rash of reddish spots or bumps on the nose and cheeks in a butterfly distribution, which consist of blood vessels and fibrous tissue. This potentially socially embarrassing rash starts to appear during childhood.
  • Ungual fibromas: Also known as Koenen's tumors, these are small fleshy tumors that grow around and under the toenails or fingernails. These are rare in childhood, but common by middle age. [10] They are generally more common on toes than on fingers, develop at 15–29 years, and are more common in women than in men.
  • Fibrous cephalic plaques are present in about 25% of people with TSC. [9] These are raised, discoloured areas usually found on the forehead, but sometimes on the face or elsewhere on the scalp. are present in about half of people with TSC, appearing in childhood. [9] They are areas of thick leathery skin that are dimpled like an orange peel, and pigmented, they are usually found on the lower back or nape of the neck, or scattered across the trunk or thighs. The frequency of these lesions rises with age. pits are found in almost all adults with TSC. [9]
  • Intraoral fibromas are small surface-tumours found in the gums, inside the cheeks or tongue. Gum (gingival) fibromas are found in about 20-50% of people with TSC, more commonly in adults. [9]

Eyes Edit

Retinal lesions, called astrocytic hamartomas (or "phakomas"), which appear as a greyish or yellowish-white lesion in the back of the globe on the ophthalmic examination. Astrocytic hamartomas can calcify, and they are in the differential diagnosis of a calcified globe mass on a CT scan. [11]

Nonretinal lesions associated with TSC include:

Pancreas Edit

Pancreatic neuroendocrine tumours have been described in rare cases of TSC. [12]

Variability Edit

Individuals with TSC may experience none or all of the clinical signs discussed above. The following table shows the prevalence of some of the clinical signs in individuals diagnosed with TSC.

TSC is a genetic disorder with an autosomal dominant pattern of inheritance, variable expressivity, and incomplete penetrance. [10] [14] Two-thirds of TSC cases result from sporadic genetic mutations, not inheritance, but their offspring may inherit it from them. Current genetic tests have difficulty locating the mutation in roughly 20% of individuals diagnosed with the disease. So far, it has been mapped to two genetic loci, TSC1 and TSC2. [ citation needed ]

TSC1 encodes for the protein hamartin, is located on chromosome 9 q34, and was discovered in 1997. [15] TSC2 encodes for the protein tuberin, is located on chromosome 16 p13.3, and was discovered in 1993. [16] TSC2 is contiguous with PKD1, the gene involved in one form of polycystic kidney disease (PKD). Gross deletions affecting both genes may account for the 2% of individuals with TSC who also develop polycystic kidney disease in childhood. [17] TSC2 has been associated with a more severe form of TSC. [18] However, the difference is subtle and cannot be used to identify the mutation clinically. Estimates of the proportion of TSC caused by TSC2 range from 55% to 90%. [2]

TSC1 and TSC2 are both tumor suppressor genes that function according to Knudson's "two hit" hypothesis. That is, a second random mutation must occur before a tumor can develop. This explains why, despite its high penetrance, TSC has wide expressivity. [ citation needed ]

Hamartin and tuberin function as a complex which is involved in the control of cell growth and cell division. The complex appears to interact with RHEB GTPase, thus sequestering it from activating mTOR signalling, part of the growth factor (insulin) signalling pathway. Thus, mutations at the TSC1 and TSC2 loci result in a loss of control of cell growth and cell division, and therefore a predisposition to forming tumors. TSC affects tissues from different germ layers. Cutaneous and visceral lesions may occur, including angiofibroma, cardiac rhabdomyomas, and renal angiomyolipomas. The central nervous system lesions seen in this disorder include hamartomas of the cortex, hamartomas of the ventricular walls, and subependymal giant cell tumors, which typically develop in the vicinity of the foramina of Monro. [ citation needed ]

Molecular genetic studies have defined at least two loci for TSC. In TSC1, the abnormality is localized on chromosome 9q34, but the nature of the gene protein, called hamartin, remains unclear. No missense mutations occur in TSC1. In TSC2, the gene abnormalities are on chromosome 16p13. This gene encodes tuberin, a guanosine triphosphatase–activating protein. The specific function of this protein is unknown. In TSC2, all types of mutations have been reported new mutations occur frequently. Few differences have yet been observed in the clinical phenotypes of patients with mutation of one gene or the other. [ citation needed ]

Cells from individuals with pathogenic mutations in the TSC2 gene display abnormal accumulation of glycogen that is associated with depletion of lysosomes and autophagic impairment. The defective degradation of glycogen by the autophagy-lysosome pathway is, at least in part, independent of impaired regulation of mTORC1 and is restored, in cultured cells, by the combined use of PKB/Akt and mTORC1 pharmacological inhibitors. [19]

Tuberous sclerosis complex is diagnosed with clinical and genetic tests. There are many different mutations in the TSC1 and TSC2 genes that have been identified in individuals with TSC. A pathogenic mutation in the gene prevents the proteins from being made or inactivates the proteins. If such a pathogenic mutation is found then this alone is sufficient to diagnose TSC. However, some mutations are less clear in their effect, and so not sufficient alone for diagnosis. Between 1 in 10 and 1 in 4 of individuals with TSC have no mutation that can be identified. Once a particular mutation is identified in someone with TSC, this mutation can be used to make confident diagnoses in other family members. [9]

For clinical diagnosis, there isn't one sign that is unique (pathognomonic) to TSC, nor are all signs seen in all individuals. Therefore, several signs are considered together, classed as either major or minor features. An individual with two major features, or one major feature and at least two minor features can be given a definite diagnosis of TSC. If only one major feature or at least two minor features are present, the diagnosis is only regarded as possibly TSC. [9]

Diagnostic Criteria for Tuberous Sclerosis Complex [9]
Major Features
Location Sign Onset [20] Note
1 Skin Hypomelanotic macules Infant – child At least three, at least 5 mm in diameter.
2 Head Facial angiofibromas or fibrous cephalic plaque Infant – adult At least three angiofibromas
3 Fingers and toes Ungual fibroma Adolescent – adult At least two
4 Skin Shagreen patch (connective tissue nevus) Child
5 Eyes Multiple retinal nodular hamartomas Infant
6 Brain Cortical dysplasias Fetus (includes tubers and cerebral white matter radial migration lines)
7 Brain Subependymal nodule Child – adolescent
8 Brain Subependymal giant cell astrocytoma Child – adolescent
9 Heart Cardiac rhabdomyoma Fetus
10 Lungs Lymphangioleiomyomatosis Adolescent – adult
11 Kidneys Renal angiomyolipoma Child – adult At least two. Together, 10 and 11 count as one major feature.
Minor Features
Location Sign Note
1 Skin "Confetti" skin lesions
2 Teeth Dental enamel pits At least three
3 Gums Intraoral fibromas At least two
4 Eyes Retinal achromic patch
5 Kidneys Multiple renal cysts
6 Liver, spleen and other organs Nonrenal hamartoma

TSC can be first diagnosed at any stage of life. Prenatal diagnosis is possible by chance if heart tumours are discovered during routine ultrasound. In infancy, epilepsy, particularly infantile spasms, or developmental delay may lead to neurological tests. The white patches on the skin may also first become noticed. In childhood, behavioural problems and autism spectrum disorder may provoke a diagnosis. During adolescence, the skin problems appear. In adulthood, kidney and lung problems may develop. An individual may also be diagnosed at any time as a result of genetic testing of family members of another affected person. [21]

Tuberous sclerosis complex affects multiple organ systems so a multidisciplinary team of medical professionals is required. [ citation needed ]

In suspected or newly diagnosed TSC, the following tests and procedures are recommended by 2012 International Tuberous Sclerosis Complex Consensus Conference. [22]

  • Take a personal and family history covering three generations. Genetic counselling and tests determine if other individuals are at risk.
  • A magnetic resonance imaging (MRI) of the brain to identify tubers, subependymal nodules (SEN) and sub-ependymal giant cell astrocytomas (SEGA).
  • Children undergo a baseline electroencephalograph (EEG) and family educated to identify seizures if/when they occur.
  • Assess children for behavioural issues, autism spectrum disorder, psychiatric disorders, developmental delay, and neuropsychological problems.
  • Scan the abdomen for tumours in various organs, but most importantly angiomyolipomata in the kidneys. MRI is superior to CT or ultrasound. Take blood pressure and test renal function.
  • In adult women, test pulmonary function and perform a high-resolution computed tomography (HRCT) of the chest.
  • Examine the skin under a Wood's lamp (hypomelanotic macules), the fingers and toes (ungual fibroma), the face (angiofibromas), and the mouth (dental pits and gingival fibromas).
  • In infants under three, perform an echocardiogram to spot rhabdomyomas, and electrocardiogram (ECG) for any arrhythmia.
  • Use a fundoscope to spot retinal hamartomas or achromic patches.

The various symptoms and complications from TSC may appear throughout life, requiring continued surveillance and adjustment to treatments. The following ongoing tests and procedures are recommended by 2012 International Tuberous Sclerosis Complex Consensus Conference. [22]

  • In children and adults younger than 25 years, a magnetic resonance imaging (MRI) of the brain is performed every one to three years to monitor for subependymal giant cell astrocytoma (SEGA). If a SEGA is large, growing or interfering with ventricles, the MRI is performed more frequently. After 25 years, if there are no SEGAs then periodic scans may no longer be required. A SEGA causing acute symptoms are removed with surgery, otherwise either surgery or drug treatment with an mTOR inhibitor may be indicated.
  • Repeat screening for TSC-associated neuropsychiatric disorders (TAND) at least annually. Sudden behavioural changes may indicate a new physical problem (for example with the kidneys, epilepsy or a SEGA).
  • Routine EEG determined by clinical need.
  • Infantile spasms are best treated with vigabatrin and adrenocorticotropic hormone used as a second-line therapy. Other seizure types have no TSC-specific recommendation, though epilepsy in TSC is typically difficult to treat (medically refractory).
  • Repeat MRI of abdomen every one to three years throughout life. Check renal (kidney) function annually. Should angiomyolipoma bleed, this is best treated with embolisation and then corticosteroids. Removal of the kidney (nephrectomy) is strongly to be avoided. An asymptomatic angiomyolipoma that is growing larger than 3 cm is best treated with an mTOR inhibitor drug. Other renal complications spotted by imaging include polycystic kidney disease and renal cell carcinoma.
  • Repeat chest HRCT in adult women every five to 10 years. Evidence of lymphangioleiomyomatosis (LAM) indicates more frequent testing. An mTOR inhibitor drug can help, though a lung transplant may be required.
  • A 12-lead ECG should be performed every three to five years.

The mTOR inhibitor everolimus was approved in the US for treatment of TSC-related tumors in the brain (subependymal giant cell astrocytoma) in 2010 and in the kidneys (renal angiomyolipoma) in 2012. [23] [24] Oral everolimus (rapalog) reduces tumour size, is effective in terms of response to skin lesions and does not increase the risk of adverse events. [25] Everolimus also showed evidence of effectiveness at treating epilepsy in some people with TSC. [26] [27] In 2017, the European Commission approved everolimus for treatment of refractory partial-onset seizures associated with TSC. [28]

Neurosurgical intervention may reduce the severity and frequency of seizures in TSC patients. [29] [30] Embolization and other surgical interventions can be used to treat renal angiomyolipoma with acute hemorrhage. Surgical treatments for symptoms of lymphangioleiomyomatosis (LAM) in adult TSC patients include pleurodesis to prevent pneumothorax and lung transplantation in the case of irreversible lung failure. [22]

Other treatments that have been used to treat TSC manifestations and symptoms include a ketogenic diet for intractable epilepsy and pulmonary rehabilitation for LAM. [31] Facial angiofibromas can be reduced with laser treatment and the effectiveness of mTOR inhibitor topical treatment is being investigated. Laser therapy is painful, requires anaesthesia, and has risks of scarring and dyspigmentation. [32]

The prognosis for individuals with TSC depends on the severity of symptoms, which range from mild skin abnormalities to varying degrees of learning disabilities and epilepsy to severe intellectual disability, uncontrollable seizures, and kidney failure. Those individuals with mild symptoms generally do well and live long, productive lives, while individuals with the more severe form may have serious disabilities. However, with appropriate medical care, most individuals with the disorder can look forward to normal life expectancy. [3]

A study of 30 TSC patients in Egypt found, ". earlier age of seizures commencement (<6 months) is associated with poor seizure outcome and poor intellectual capabilities. Infantile spasms and severely epileptogenic EEG patterns are related to the poor seizure outcome, poor intellectual capabilities and autistic behavior. Higher tubers numbers is associated with poor seizure outcome and autistic behavior. Left-sided tuber burden is associated with poor intellect, while frontal location is more encountered in ASD [autism spectrum disorders]. So, close follow up for the mental development and early control of seizures are recommended in a trial to reduce the risk factors of poor outcome. Also early diagnosis of autism will allow for earlier treatment and the potential for better outcome for children with TSC." [33]

Leading causes of death include renal disease, brain tumour, lymphangioleiomyomatosis of the lung, and status epilepticus or bronchopneumonia in those with severe mental handicap. [34] Cardiac failure due to rhabdomyomas is a risk in the fetus or neonate but is rarely a problem subsequently. Kidney complications such as angiomyolipoma and cysts are common and more frequent in females than males and in TSC2 than TSC1. Renal cell carcinoma is uncommon. Lymphangioleiomyomatosis is only a risk for females with angiomyolipomas. [35] In the brain, the subependymal nodules occasionally degenerate to subependymal giant cell astrocytomas. These may block the circulation of cerebrospinal fluid around the brain, leading to hydrocephalus. [ citation needed ]

Detection of the disease should be followed by genetic counselling. It is also important to realise that though the disease does not have a cure, symptoms can be treated symptomatically. Hence, awareness regarding different organ manifestations of TSC is important. [ citation needed ]

TSC occurs in all races and ethnic groups, and in both genders. The live-birth prevalence is estimated to be between 10 and 16 cases per 100,000. A 1998 study [1] estimated total population prevalence between about 7 and 12 cases per 100,000, with more than half of these cases undetected. Prior to the invention of CT scanning to identify the nodules and tubers in the brain, the prevalence was thought to be much lower, and the disease associated with those people diagnosed clinically with learning disability, seizures and facial angiofibroma. Whilst still regarded as a rare disease, TSC is common when compared to many other genetic diseases, with at least 1 million individuals affected worldwide. [13]

TSC first came to medical attention when dermatologists described the distinctive facial rash (1835 and 1850). A more complete case was presented by von Recklinghausen (1862), who identified heart and brain tumours in a newborn who had only briefly lived. However, Bourneville (1880) is credited with having first characterized the disease, coining the name "tuberous sclerosis", thus earning the eponym Bourneville's disease. The neurologist Vogt (1908) established a diagnostic triad of epilepsy, idiocy, and adenoma sebaceum (an obsolete term for facial angiofibroma). [36]

Symptoms were periodically added to the clinical picture. The disease as presently understood was first fully described by Gomez (1979). The invention of medical ultrasound, CT and MRI has allowed physicians to examine the internal organs of live patients and greatly improved diagnostic ability. [ citation needed ]

In 2002, treatment with rapamycin was found to be effective at shrinking tumours in animals. This has led to human trials of rapamycin as a drug to treat several of the tumors associated with TSC. [37]

Tracing the Path From Inflamed Skin to Heart Disease

IRP researcher Nehal Mehta established a link between the skin disease psoriasis, pictured above, and an elevated risk of cardiovascular disease.

Most Americans know someone who has been affected by heart disease. Despite its status as the leading cause of death in the U.S. today, rates of heart disease have actually been steadily falling since they hit their peak in 1968. In fact, between 1970 and 2005, the life expectancy of the average American increased over 70 percent due in part to reductions in heart disease-related deaths.

Research conducted by IRP scientists has played a key role in curbing the heart disease epidemic by helping identify now well-known risk factors for heart disease, such as high blood pressure, obesity, and physical inactivity. However, not all risk factors are so commonly known. A 2017 study by IRP Lasker Clinical Research Scholar Nehal Mehta, M.D., M.S.C.E., revealed that untreated psoriasis — a chronic, relapsing, inflammatory skin disease — is linked to an elevated risk for premature coronary artery disease. Dr. Mehta’s research demonstrated a strong link between psoriasis-induced skin inflammation and and inflammation of the blood vessels, a precursor to heart disease. Through this study, the largest ongoing study of individuals with psoriasis to-date, Dr. Mehta’s team has concluded that controlling psoriasis-associated skin disease could be an important means of reducing cardiac risk in this population.

In recognition of August as National Psoriasis Awareness Month, I spoke with Dr. Mehta to discuss how he discovered the link between psoriasis and cardiac risk, his continued investigation of that relationship, and his motivation to study the cardiovascular system in the first place.

Did something personal or societal prompt you to start performing cardiology research?

“It was a societal issue that prompted me to study this topic. Before coming to the NIH, I worked in Philadelphia as a cardiologist at the University of Pennsylvania. During that time, I noticed that around 75 percent of my patients who were having heart attacks were obese, so I became interested in understanding how fat itself drives heart attacks. We found that the connection may be in part through elevated inflammation driven by the fat itself.

“The second piece of why I became interested in this topic is that society is getting older and more obese, and as a result there is more inflammation within the body as it ages, leading to an increased risk for heart disease.”

How has your work linking psoriasis and heart disease affected advancements in heart healthcare?

“In 2015, our whole-body scans showed that the effects of psoriasis reach far beyond the skin. The data from our first positron emission tomography (PET) study showed that individuals with psoriasis also have inflammation scattered throughout the body. These data in part led the Word Health Organization to redefine psoriasis as a serious autoimmune disease.

“The next major impact occurred in 2018 when the 2018 American College of Cardiology/American Heart Association (ACC/AHA) Multisociety Guideline on the Management of Blood Cholesterol identified psoriasis as a high-risk condition for developing heart disease, thereby qualifying this population for early initiation of statin therapy. That was an exciting development because it prompted cardiologists to begin identifying psoriasis as a high-risk condition and educating those with psoriasis about their future risks of heart disease.”

What was the most challenging aspect of this study?

“The challenge of starting any large cohort study is getting the ‘set-up’ correct. In each patient, we examine blood for advanced cholesterol testing, degree of inflammation, diabetes risk, and then get images of the body with computed tomography (CT), magnetic resonance imaging (MRI), and PET scans. These tests have advanced our understanding of heart disease progression in states of chronic inflammation. Therefore, we spend considerable time on our infrastructure and workflow, since managing follow up for hundreds of patients at exact time intervals over multiple years requires organization.

“Second, our colleagues in dermatology and rheumatology refer many patients to our study, and despite the time investment required from patients (a two-day initial visit), the unique results available to both patients and providers balance out this time investment. Patients themselves enjoy contributing knowledge to our scientific understanding.

“I would also say that keeping up with modern science has been a challenge. We wrote the protocol for this study in 2012, and recently I’ve spent most of my time making sure that our study remains a contemporary cardiovascular study. This is a tough thing to do because one can get very complacent and simply stop progressing forward, and we don’t want that. Rather, staying contemporary is a challenge we spend an immense amount of time on as I visit programs domestically and internationally to extend our observations. For example, recently we realized that we needed to modify some of the blood tubes we use for our study because newer blood tubes facilitate the cutting-edge research we are able to do in 2019.

“It is important to stay contemporary, but also to stay true to the original research question. It’s definitely a fine balance.”

What particular tools or collaborations were important in conducting this research?

“Our research has been sped up by the fact that we’re at this amazing place, the NIH, which has allowed me to conduct advanced cardiac imaging and characterization of blood vessels before clinical disease to help predict a person’s risk for cardiovascular disease. When I moved my program to the NIH, I was able to have one of few combined PET-MRI scanners in the world, as well as advanced coronary computed tomography angiogram (CTA) scanner platforms not available outside of research. I believe that having access to these tools accelerated my discoveries. The availability of high-grade imaging at the NIH Clinical Center and the NIH’s commitment to me have been extremely helpful.

“I now have a flow cytometry lab where I’m conducting advanced immune phenotyping and vascular imaging, through which we have been able to view arterial plaque and the immune cells that influence it, which is pretty powerful.

“I think that being at the NIH, and the opportunities that it’s given me, have been the best things that could’ve happened to me in my career. Being here allows me to have awesome collaborations with people who otherwise wouldn’t be so quick to share their expertise, knowledge, and intellectual property. The spirit of the Intramural Research Program, along with people trusting the NIH, has been truly incredible.”

How have you continued to study this topic, and what are your plans to study it in the future?

“In 2019, we published a paper that showed treating skin disease in psoriasis reduces heart disease. Our next steps are to understand other factors that might mitigate coronary risk. The idea that one has the ability to mitigate heart disease by treating an inflammatory condition affecting a distant part of the body is really cool to me.

“Right now, the billion-dollar question in cardiology is, ‘Why are people still having heart attacks without having classic risk factors for heart attack?’ In fact, we currently only understand factors that explain roughly 64 percent of heart attacks, so there is still about a 36 percent risk for heart attack that we don’t understand. We’re looking to understand how to define and address risk due to inflammation that we could treat. Through this research, I’m hoping to inform the field about discovering novel pathways so that those in drug development can start targeting them.

“Overall, we need to reduce the risk of heart attacks. I recently read that the highest rates of acute heart attack are happening in younger, obese people between the ages of 35 and 45. We clearly have an inflammatory epidemic driving vascular risk, and we need to understand it. It’s for that reason that my next steps are to dig deep during my tenure at the NIH and finish what I started. I wanted to start my research with a clinical program that defined the link between heart disease and inflammation. Now I have to figure out why that link exists.”

Head over to our Accomplishments page for more information on Dr. Mehta’s research, or listen to his interview on our Speaking of Science podcast. You can also subscribe to our weekly newsletter to stay up-to-date on the latest breakthroughs in the NIH Intramural Research Program.

Calculate joint and last survivor life expectancy - actuarial

I've been able to figure out how a basic life table works.

But I would like to know how to extend it to calculate the life expectancy of the last survivor of a married couple.

(I understand there are some complexities from the fact that deaths of married couples may not be independent, but I can ignore that here. )

With a simple life table, you have a column of values named $m_x$ , which represent the mortality rate at age x. (I'm using unisex mortality rates, so I don't need to worry about the sex of the person.)

You also have a column of values named $l_x$ , which is the number of persons alive at age x (where $l_0$ starts at 100,000). So, $l_x = l_(1 - m_)$

$d_x$ contains the number of persons who died in the interval (x, x+1), which is $l_xm_x$

$L_x$ contains the total number of person-years lived by the cohort in the interval (x, x+1), which is the equal to $l_ + 0.5d_x$ . (Each person who lives to x+1 contributes one year, and each person who dies in x contributes half a year, on average.)

$T_x$ contains the total number of person-years lived by the cohort from age x until all members of the cohort have died. I.e., the sum of $L_x$ through $L_n$ (where n is the total number of rows).

Finally, $e_x$ contains the life expectancy of a person at age x, computed as $e_x = frac$ .

This all makes sense to me.

But, how would I use this approach to calculate the "joint and survivor" life expectancy of two people (e.g., a married couple) assuming their deaths are independent? I.e., how long would you expect at least one of those two people to still be alive?

(Also, for the sake of simplicity, I'm using a single unisex mortality rate, so I don't need to worry about the sex of each person.

How was the cama's life expectancy computed? - Biology

Paper Information

Journal Information

International Journal of Statistics and Applications

p-ISSN: 2168-5193 e-ISSN: 2168-5215

Expected Life Time at Birth in Kerala

Statistical Investigator, Taluk Statistical Office Tirur, Department of Economics and Statistics, Malappuram, Kerala, India

Correspondence to: Saheeda C. O., Statistical Investigator, Taluk Statistical Office Tirur, Department of Economics and Statistics, Malappuram, Kerala, India.


Copyright © 2019 The Author(s). Published by Scientific & Academic Publishing.

This work is licensed under the Creative Commons Attribution International License (CC BY).

Life expectancy at birth is the average number of years a new born is expected to live given current conditions. Life Expectancy is one of the major indicators in human development that shows how long a person can expect to live on average given prevailing mortality rates. Technically it is the average number of years of life remaining to a person at a specified age, assuming current age–specific mortality rates continue during the person’s lifetime. Life-expectancy is the standard measure of the length of people’s life. Life expectancy can be computed at birth and at various ages. This study covers the period from 2006 to 2015. The life expectancy will be determined in this period. For this I took it 10 years death rate in Kerala for calculating probability of dying. That means through this I have been able to do 10 years time series. I am including in this paper Expected life time at birth in Kerala 2006-2015. Here life expectancy viewed with a life table for 10 years. Using this we can distinguish differences. Mainly life expectancy was found using the death rate.

ASJC Scopus subject areas

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Handbook of Statistics. Elsevier B.V., 2020. (Handbook of Statistics).

Research output : Chapter in Book/Report/Conference proceeding › Chapter

T1 - Human life expectancy is computed from an incomplete sets of data

T2 - Modeling and analysis

AU - Srinivasa Rao, Arni S.R.

N1 - Funding Information: Dr. Cynthia Harper (Oxford) and Ms. Claire Edward (Kent) have helped to correct and revise several sentences. Our sincere gratitude to all. Publisher Copyright: © 2020 Elsevier B.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

N2 - Estimating the human longevity and computing of life expectancy are central to the population dynamics. These aspects were studied seriously by scientists since 15th century, including renowned astronomer Edmund Halley. From basic principles of population dynamics, we propose a method to compute life expectancy from incomplete data.

AB - Estimating the human longevity and computing of life expectancy are central to the population dynamics. These aspects were studied seriously by scientists since 15th century, including renowned astronomer Edmund Halley. From basic principles of population dynamics, we propose a method to compute life expectancy from incomplete data.

Female and male life tables for seven wild primate species

We provide male and female census count data, age-specific survivorship, and female age-specific fertility estimates for populations of seven wild primates that have been continuously monitored for at least 29 years: sifaka (Propithecus verreauxi) in Madagascar muriqui (Brachyteles hypoxanthus) in Brazil capuchin (Cebus capucinus) in Costa Rica baboon (Papio cynocephalus) and blue monkey (Cercopithecus mitis) in Kenya chimpanzee (Pan troglodytes) in Tanzania and gorilla (Gorilla beringei) in Rwanda. Using one-year age-class intervals, we computed point estimates of age-specific survival for both sexes. In all species, our survival estimates for the dispersing sex are affected by heavy censoring. We also calculated reproductive value, life expectancy, and mortality hazards for females. We used bootstrapping to place confidence intervals on life-table summary metrics (R0, the net reproductive rate λ, the population growth rate and G, the generation time). These data have high potential for reuse they derive from continuous population monitoring of long-lived organisms and will be invaluable for addressing questions about comparative demography, primate conservation and human evolution.

Conflict of interest statement

The authors declare no competing financial interests.


Figure 1. Sex ratio (proportion female) for…

Figure 1. Sex ratio (proportion female) for individuals born into each study population whose sex…

Figure 2. Age-specific probability of producing a…

Figure 2. Age-specific probability of producing a son (blue) versus a daughter (red).

Figure 3. Age-specific survival ( l x…

Figure 3. Age-specific survival ( l x ), fertility ( m x ), and reproductive…

Figure 4. Distribution of female age (yr)…

Figure 4. Distribution of female age (yr) of first reproduction.

In this box-and-whiskers plot, red…

Figure 5. Female Life expectancy at age…

Figure 5. Female Life expectancy at age x ( e x ) versus x (in…

Watch the video: Calculations for Life Expectancy using a Hypothetical Life Table. (July 2022).


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