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Peto’s Paradox (wikipedia.org)
142 points by Vigier on Nov 7, 2022 | hide | past | favorite | 68 comments



This article doesn't quite spell it out, but the current thinking is that the apparent paradox is explained by:

1. Bigger animals have larger cells, so the number of cells does not scale linearly with the mass of the animal.

2. Cells from larger animals are more resistant to cancer development in various ways (eg more copies of TP53, more propensity to die after DNA damage).

3. Large animals have non-linear metabolic scaling. So a cell in an elephant sees fewer metabolic cycles per unit time than a cell in a mouse. Some of this is due to the greater thermal efficiency of large animals.

Now that we have more detailed data on animals, I think this paradox is a bit less interesting, albeit generally true. For example, there are some animals that just don't seem to get cancer (eg the blackbuck and the Patagonian mara, from several hundred autopsies each) [1]. Cancer is also very rare in Zebras. This is fundamentally interesting because it shows that being free from cancer is possible in an otherwise normal looking mammal. In theory therefore, we could consider engineering humans to be cancer free. To me, given the high incidence of cancer, the progressively increasing incidence in an ageing population and the incredible amount of misery it causes, this is the most ethically palatable reason to consider widespread genetic modification of humans. I think all anti-ageing efforts will ultimately bump up against cancer as the limiting factor. The technology to safely genetically engineer humans is nowhere near ready for prime time.

The association between height and cancer is not thought to be due to 'more cells'. It only applies to some types of cancer and not others. It is believed to be due to growth factor signalling eg growth hormone and insulin-like growth factors.

[1] https://www.nature.com/articles/s41586-021-04224-5


> 1. Bigger animals have larger cells, so the number of cells does not scale linearly with the mass of the animal.

Where is this coming from? If I google "do larger animals have larger cells", it says the opposite.


The wikipedia article has a section on it.

But just consider nerve cells that control limbs. A nerve cell consists of a neuronal body and a long axon. If you have a longer limb, you will need a longer axon, and therefore a larger neuronal body to maintain it.


I've always been curious that old dogs often get cancer, despite "old" for a dog only being the early teens as well as dogs being smaller.


I asked a doctor about this once. He said that as any animal ages, the protective mechanisms they have eventually break down, and either work less well or stop working. In dogs, they break down sooner than in humans.

For example, the ends of chromosomes have telomeres[0]. When chromosomes are copied they can’t copy the full length of the chromosome, so every copy has fewer of these telomeres. When they eventually run out of telomeres, cell division stops happening. (I don’t know whether dog chromosomes have fewer telomeres or if it’s some other mechanism, but telomeres are an example of a cellular mechanism that has a limited lifetime.)

[0] https://en.wikipedia.org/wiki/Telomere


What I never understood is that, for the most part, a 30-something year old male and female can create a pristine new being from their already-slightly-knackered cells. I know it breaks down somewhat with age.

So... we can create pristine new life with biological clock reset at 0, but not do so for our own bodies.


Women are born with their supply of eggs, so they are more ‘pristine’ than any other cell. Sperm are generated continuously throughout life, and there is evidence sperm quality decreases over time. Some diseases associate with increasing age of the father (autism, schizophrenia). The effect takes hold mainly after paternal age 40. Having said that, I recall there is some work showing sperm generating cells are kinda special in that they don’t develop as much mutational damage as other cells. Does make you worry though that progressive generations of older and older fathers may lead to some kind of problem. With rates of assisted fertility increasing, perhaps 16 yo boys should bank sperm for the future.


Its by design, you are meant to pass on the genes and die. Thats how nature works.

Thats the best mechanism nature have to make sure we are evolving - more precisely mixing genes.

What people forget is that our enemies are constantly evolving and trying to kill us, bacteria, viruses, fungi etc. Passing on you dna and eventually dying frees up resources for your offspring to do the same, creating new combination of genes increasing odds of more optimal defense for current threats.

If lions didn't age. They would compete for same patch of land and given all are at the peak of their development roughly 50% of old genes would win resources. Slowing down gene mixing and genetic diversity.

Actually speaking of big cats. Look up cheetah and what happens when you don't mix genes often enough (for natural or unnatural reason)

"Cheetahs retain only 0.1–4% of overall genetic variation seen in most living species, much lower than other well-known examples of genetic impoverishment including"


That's why we have babies at all instead of just budding new copies of ourselves. Compressing everything down to gametes is a powerful form of error correction because it reduces degrees of freedom so heavily.


Sounds like a feature, not a bug. Unqualified speculation incoming, but I suspect that lifespans for different species approach the optimal replacement cadence for maximum fitness.


Women are born with all their eggs, which do deteriorate. The vast majority won't make it all the way through puberty even (lots will be gone by the time they're actually born). That's why there's a drop-off in fertility over time.


I guess having individuals with unbounded lifespans would slow down a species' evolutionary rate (less pressure to procreate), that would be a disadvantage.


Having just gone through it, what I found surprising was that cats one one hand are less likely to develop cancer than dogs, but also to develop types that are harder to treat and develop much more aggressively.. all of which leads to it being seen as practically untreatable in most cases.


I'd imagine r/K selection theory explains a bit of this. Haven't looked it up but I'd expect cancer to be a much more prominent cause of death in r strategists than in K-strategists (assuming otherwise equivalent levels of care etc.) since rs are optimised to live fast, die young leaving a ton of babies, compared with Ks' more measured approach.


> we could consider engineering humans to be cancer free

following until you get to that.. there are multiple mechanisms in the body that can result in "cancer" .. its an end result, not the cause. The jump to "we can engineer this out" is exactly what a reader would expect from an investment-and-profit medical company.

There are untold numbers of small poisons and behavioral habits that are known to increase cancer inducement in humans.. all of which could be addressed, but there is little profit in prevention.

Overall, I am taking the time to write this because a rush to genetic engineering is something that might behave like cancer itself over time.


>> a rush to genetic engineering is something that might behave like cancer itself over time.

Can you elaborate on this? To me, it seems perfectly reasonable that a directed and intentional process of man-made engineering could blow the random process of evolution out of the water, both in timescale and in effectiveness. For example, there's not really an evolutionary advantage to eliminating geriatric cancer: kids have been made, genes have been passed, in all likelihood multiple generations down by the time old-age related illnesses develop. Yet, we want to live longer, and live better lives during that time, so we can take the reigns and address what evolution couldn't.


What's the quote, "in their speed to find a solution, they never slowed down to think if they should"?

There are plenty of examples of humans rushing to market something they think works one way but upon a much longer study, the results are something much worse than if we had not instead. Heavy use of asbestos, heavy use of lead in fuel, paint, etc.

Genetically modifying anything just sounds like the most obvious of things that should be studied for much much longer than whatever the first company looking to profit is wanting.


Frankly, no. People are dying right now. Like, everyone, of one thing or another. The situation is an emergency, even if all we've ever managed is ten millennia of triage. That is the default, that is the background. Weigh the risks, sure, but don't act like choosing to do nothing is without cost. We should study genetic engineering just as much as we need to, as best as we can tell, and no more.

Less morbid, there are many more substances we "rushed to market" and worked out fine. Should antibiotics still be unavailable, banned even, to complete longitudinal trials? Chemotherapy and radiation "sound like the most obvious of things that should be studied for much longer". Thank God that didn't prevent us from using them to save hundreds of thousands of lives. Hell, asbestos was used for way longer than any of that stuff, didn't make it any safer.


Frankly, no. Buildings are burning with people dying inside right now. The situation is an emergency, even if all we've ever managed is ten millennia of triage. That is the default, that is the background. Weigh the risks, sure, but don't act like choosing to do nothing is without cost. We should study asbestos just as much as we need to, as best as we can tell, and no more. In the meantime we need to fireproof all buildings with asbestos.

Edit: /s (If that wasn't obvious.)


We did weigh the risks. We did study asbestos. And we as a society made an informed decision that the risk of asbestos outweighed the risk of buildings catching on fire.

I don't understand the point you were trying to make here. Why shouldn't we invest effort to research a technology that might mitigate the 2nd leading cause of death in the developed world?


People are talking about prevention vs treatment of cancer, yet, asbestos was a cause of cancer, so by eliminating it, we eliminated a vector of cancer. That's preventative. We as humans, have become so "smart" with all of the things we can create that while not truly understanding the long term effects. We know we've screwed ourselves in the past (even fairly recently) with our cleverness, yet we continue to be surprised when it happens again.

Modifying the source code of humans is like the new hire thinking they can make the code so much faster because they don't know how the section code they are working on is used by the larger system as a whole. All they see is that there's an apparent bug in the section they are viewing now. Never mind the sections of code that have programmed workarounds for that specific bug, and will now break downstream because the buggy returns are no longer present. So how do we know if these kinds of workarounds in the human genome are also not present?


> Modifying the source code of humans is like the new hire thinking they can make the code so much faster because they don't know how the section code they are working on is used by the larger system as a whole. All they see is that there's an apparent bug in the section they are viewing now. Never mind the sections of code that have programmed workarounds for that specific bug, and will now break downstream because the buggy returns are no longer present. So how do we know if these kinds of workarounds in the human genome are also not present?

We know for a fact the current code base is full of bugs and convoluted workarounds due to the original coder having no idea what they were doing. While we may not yet know the best way to refactor the code, it undoubtedly needs to be refactored.


> There are plenty of examples of humans rushing to market something they think works one way but upon a much longer study, the results are something much worse than if we had not instead. Heavy use of asbestos, heavy use of lead in fuel, paint, etc.

All this just means is that progress of science and technology has some qualities similar to natural evolution: namely, there's a bit of trial and error. It's not, however, a condemnation - not unless you can propose a way humanity could do even better.

All the cases you listed is something we've developed, discovered problems with, overcome and mastered in scope of couple generations. Were natural evolution to guide humans through their interactions with lead and asbestos, we'd still be dying in pain from exposure a thousand years from now, because evolution takes time and doesn't care that you're conscious.

> What's the quote, "in their speed to find a solution, they never slowed down to think if they should"?

Sure, but it's neither here or there. If you saw someone running away from a lion, would you throw this line towards them? Perhaps they should slow down and consider if they're not better off being eaten?


Agree, this is something that would take centuries probably. The most plausible way to do it would be including extra copies of TP53 under appropriate regulation. This has been done in mice and they seem fine. Unfortunately, it would need to be done in larger animals progressively to show safety, which would take 20 - 30 years for a full lifecourse study in primates (unfortunate because we are experimenting on primates). Even longer if their lifespan is increased.

After that, we would be left with a conundrum, which is the ethics of modifying the germline of an embryo. I don't know what the solution is there. Maybe it could be justified in families with an elevated risk of cancer, or Mars colonists for whom any sort of cancer will be a death sentence. Another option would be an as yet uninvented way to edit the genome, but provide an 'Undo' function to reverse the edit, say by giving some small molecule.


I grant you that this is a seemingly extreme opinion. It is however my conclusion form thinking about this problem for a long time. I work inside this field, and see people suffering terribly from cancer every day, both physically and psychologically. I think we are overly focused on treating established disease, and not focused enough on preventing cancer. The end game, in my opinion, is making ourselves more resistant to cancer.

The most difficult version of this is modifying the germline. There could be other less extreme versions, for example giving young adults a long lived population of genetically modified immune cells that persist and eliminate pre-neoplastic or neoplastic disease. A more advanced version of this would be introducing a new type of cell lineage that exceeds the limitations of immune cells (for example specific modes of recognition, and restriction to certain anatomical compartments), and delivering it as a therapeutic. But modifying the germline is the only way to really get the incidence approaching zero, I think.

I hope however there is some easier, quicker way... for example if we discover unknown viruses actually cause a lot more cancer than we thought.


> I think we are overly focused on treating established disease, and not focused enough on preventing cancer.

You should see the warnings we put on cigarettes.


Warning Label: "May cause birth defects"

Bill Hicks: "I found my brand!"

In this case, not sure of the label's use in this conversation.


I think you're confusing the warning California requires on products with traces of lead on them with the warnings that are required in every state on cigarettes.


I think you may be confused on who Bill Hicks was.


Living healthily is very important, but unfortunately can only help to a certain extent. Humans just get cancer.

Screw this disease and screw nature; the misery it causes is just too much. There is a way to get rid of cancer, and the sooner this is achieved, the better. There are protocols to help proceed carefully and ethically.


> In October 2015, two independent studies showed that elephants have 20 copies of tumor suppressor gene TP53 in their genome, where humans and other mammals have only one.[17] Additional research showed 14 copies of the gene present in the DNA of preserved mammoths, but only one copy of the gene in the DNA of manatees and hyraxes, the elephant's closest living relatives.[18] The results suggest an evolutionary relationship between animal size and tumor suppression, as Peto had theorized.

Is it possible that the evolutionary relationship arises from the size relationship? Basically: if elephants' ancestors grew in size and started dying much more quickly and commonly from cancer, nature would select for individuals who just so happened (via their increased risk of mutation) to have more copies of genes like TP53.


> The results suggest an evolutionary relationship between animal size and tumor suppression

My napkin formula would be p_tumor_body=(V_body/V_cell)*p_tumor_cell, so your statment makes intuitive sense, I'd say. The more cells you have, the more tumor suppression you need to make it a secondary cause of death over your expected life span.


That expression leads to something that isn't a probability. Try 1-(1-p_tumor_cell)^(V_body/V_cell).


I shouldn't comment on HN from bed after an evening out. Of course the rule of proportion is the wrong approach here. Even though the dimensional analysis seems to work out, it's still wrong. Bad case of thoroughly addled brain, this is supremely embarassing, and too late to delete now. I should be able to do this in my sleep, but I clearly wasn't. Seems there's not enough probabilities in my day-to-day, I will make a point of adding a few to fix my intuitions.


I read this recently - https://www.newyorker.com/science/elements/how-food-powers-y...

Seems potentially related - it discussed this idea in part of it:

> Maybe it’s both, but Lane suspects we pay too little attention to the latter possibility. He argues that it might explain the outsized correlation between cancer and aging. From age twenty-four to fifty, your risk of cancer increases ninety-fold, and it continues to grow exponentially from there. A popular hypothesis holds that the root cause of this mounting risk is the accumulation of genetic mutations. But some scientists have argued that the rate of accumulation isn’t nearly fast enough to explain the extraordinary trajectory that cancer risk takes over a lifetime. Nor does the gene’s-eye view explain why some tumors stop growing when moved into a different environment. For Lane, these facts suggest that cancer is best thought of as a derangement of metabolism.


Kurzgesagt had a video about the topic: https://m.youtube.com/watch?v=1AElONvi9WQ


> Peto's paradox is an observation that at the species level, the incidence of cancer does not appear to correlate with the number of cells in an organism.[1] For example, the incidence of cancer in humans is much higher than the incidence of cancer in whales,[2] despite whales having more cells than humans. If the probability of carcinogenesis were constant across cells, one would expect whales to have a higher incidence of cancer than humans. Peto's paradox is named after English statistician and epidemiologist Richard Peto, who first observed the connection.


Seems conceivable that the evolutionary pressure would push cancer rates down to some sort a similar level across species, a sort of cost-benefit equilibrium.


Cancer, mathematically, all things being equal, shouldn't simply scale with number of cells, but rather with number of cell divisions.

This differs by species, along with other cell mechanisms that could inhibit cancer that only certain species have evolved.


I just figured that with enough cells and enough time, any probability of cancer distinguishable from 0 becomes indistinguishable from 1, so large animals either learn to totally prevent cancer or die young.


Same goes for us though, no? Seems like you just need to push the expected time until onset past death by other issues, or at least reproduction


Staying Cancer free has a cost, in terms of DNA repair (proteins) and their optimization, immune system and probably more elements. If a species reaches a point at which it can reproduce without incurring too many germ line DNA errors, there is no need to optimize further.

I.e., if there was enough evolutionary pressure, our cancer incidence would also still be able to go down. However, the current incidence is not affecting natural selection at a significant magnitude. Same for mice and whales I would guess.


Side note, but it bothers me when people call a phenomenon a paradox. A paradox isn't just something you wouldn't expect to be true, it's something that causes itself to not be true. For example saying "This statement is false", or time travel shenanigans.

This is simply a phenomenon.


I know about it from this blog post (warning: it's about politics, not biology) https://slatestarcodex.com/2014/06/14/living-by-the-sword/


The salient part is that it's hypothetised that whale cancers can't grow big enough to threaten a whale before they themselves get cancer and either stabilize into a benign equilibrium or wither away. Fairly hilarious if true.


I thought cancer is not about the number of cells, but the number of cells that constantly die and have to be recreated (each time a cell is created, it has a chance to be a cancerous one). Maybe whales don't lose as many cells as humans, probably they sit less in the sun...


I always assumed that's because with people reproductive age precedes cancer age by a long shot, so cancer is not an evolutionary consideration. Blue whales mate till they die, but orcas don't, So I'd expect orcas to have a higher cancer incidence.


Sounds like the environment of humans is the explanation. If you were to put a whale in a human city, eating and working there, maybe the whale would have the same rate of cancerous cells


The effect isn't due to humans being an outlier, it can be seen across a range of species.

> A 2015 study, the San Diego Zoo, surveyed results from 36 different mammalian species, ranging in size from the 51-gram striped grass mouse to the 4,800-kilogram elephant, nearly 100,000 times larger. The study found no relationship between body size and cancer incidence, offering empirical support for Peto's initial observation.[8]


Side note that seems relevant: Cancers almost never metastasize to muscle tissue, even though muscle makes up 65 percent of the human body.


What about shorter and lighter humans vs taller heavier but both have similar good bmi?


Taller gets cancer more. See link


How long would whale lifespans be if whales had the same level of medical care as humans? Humans today regular live well beyond our natural lifespans, if we were all dying at 30 cancer probably wouldn’t be much of an issue


>Humans today regular live well beyond our natural lifespans

Is this really so? My understanding is that humans in antiquity who survived childhood typically lived to what we would now consider retirement age.


You're correct; GP is wrong. Human normal lifespan is and has been about 70 years, once you account for early demise, especially from infant mortality -- https://www.sapiens.org/biology/human-lifespan-history/


A useful corrective, but perhaps also misleading. Humans didn't peacefully keel over at 60, let alone 30, that's true. And death before 20 was indeed so horrifyingly common that it couldn't help but bias the average hard. But mortality was higher at every age, be it from disease, injury, or childbirth. A person of the past would have understood a death at 40 or 50 to be young, but not all that unusual. Most people would know quite a few who died in that range.


Yup. Unfortunately “mean age of death” is most commonly known, but in reality many children died at birth, hence lower mean.


I think traditionally actuarial tables have always been based on given achieving the age of 5 years.


    Our days may come to seventy years,
    or eighty, if our strength endures;
    yet the best of them are but trouble and sorrow
    for they quickly pass, and we fly away
Psalm 90:10 (probably from about 1000 BC)


Pre-industrial societies have much higher infant mortality but for those who live to adulthood their lifespans are not that much shorter than ours. If you survived early childhood, your odds of getting into your 60s would be pretty good, and plenty of people made it into their 70s.

And many whales die of what we would consider old age - typically they get weaker and weaker as they grow old until they reach a point where they are unable to consistently swim to the surface for air, and thus drown. Pretty much what you'd expect if you flooded a nursing home.


Do you think that you've come up with this simple explanation but the brightest people in the field have glossed it over?


At this point it's pretty safe to say that behavior has a big influence. I've never seen a whale smoke a cigarette, drink alcohol, or inhale exhaust fumes while sitting in traffic.


Maybe you hang out with the most boring of whales


Whales tend to be pretty straight-edge.

Dolphins, however... well lemme tell ya, those dudes know how to party.


I dunno, man. I hung out with some dolphins who loved getting high on pufferfish every day, and they’re still living in their parents’ sea floor.


> Peto noted that, on a cell-for-cell basis, humans were much less susceptible to cancer than mice.

Probably not explicable by cigarettes or alcohol, and we've dumped quite a bit of pollution into the whales' living environments.


as much as we've dumped in ours?


I thought regenerative ability vs cancer incidence was a problem for evolution to optimize per species rather than some statistical certainty per cell.




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