Why don't whales get more cancer? - Peto's Paradox
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- Опубліковано 12 чер 2024
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1st cited paper showing the algebraic model for estimating cancer probabilities by Calabrese and Shibata: bmccancer.biomedcentral.com/a...
2nd cited paper focusing on whales by Caulin et al: royalsocietypublishing.org/do...
Peto's paradox describes the phenomenon that despite whales having roughly 1000 times as many cells as humans and living a similar time span, they don't appear to have far more cancers than we do. Why not? In this video we explore a probabilistic formula that might give some insight into the kinds of numbers needed. It turns out, for instance, that with only a 3.2x decrease in mutation frequency you can equal the rates despite the 1000x increase in number of cells.
0:00 Peto's Pardox
0:59 Mutuations
3:24 Probability Review
4:40 Deriving the Probability Formula
7:42 Sample Calculations
11:13 Brilliant.org/TreforBazett
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This is easily one of the most challenging problems of biology. What's even more fantastic is how it is linked to mathematical concepts. How beautiful that mathematics can slither into almost everything. I remember Alan Turing gave some equations governing the strips and patterns in animals. Thanks Prof. Trefor for demonstrating time and again how profound and worth Mathematics really is.
Glad you enjoyed!
Trefor , I have watched most of your videos and I have learned a lot from them, so thank you. I'm glad to hear that you have been 10 years cancer-free. I had a tumour in the liver which was destroyed by microwave ablation more that 3.5 years ago with no recurrence. The doctors are pleased, and I feel lucky.
Glad to hear that!
@@DrTrefor 👍
I do computational biology and this is exactly the kind of stuff we do. Finding a simple model for a complex problem is always our main goal.
thanks for sharing!
Let's be brutal about this: NATURAL SELECTION.
As whales got bigger there cancer problem became more serious - so they would have been increasingly selected for lower cancer rates, either by better DNA copying or by improved repair or longer time between cell division or all four (I included a spare mechanism because nature does have a way of sidestepping problems in ways we don't anticipate).
interestingly we do see a higher risk of geting cancer for bigger individuals inside of the same species. Taller humans and bigger dog breeds have a higher chance of getting cancer.
@@mathiasrennochaves3533 Oh, interesting, I didn't know that - as a tall human that's relevant (slightly).
I'm intrigued by this, though I do shudder at the concept of *whale colonoscopies* that would be needed to verify the model.
Haha wouldn’t be fun!
You're my teacher and I found this channel without looking for it, it showed up in suggested
This is super cool, I’m always interested to see which problem you tackle next in your videos and am never disappointed !!
This was so much mind intriguing, loved the combination of math & bio problems
Perhaps whatever fitness advantage they have to cancer allowed them to grow larger. Without those advantage, they either would have stayed small or died out when they grew larger due to cancer.
I used to watch this channel as a great way to study, your charm, passion for education, and quality of your videos have somehow convinced me to watch your videos out of pure curiosity on winter break, thank you so much for being such a great educator!
I want to show this video to my Elementary Stats students next semester.
Love your videos Dr. Trefor. You are one of the sole reasons I made it through the math side of electrical engineering. Now I finally have time to sit back and enjoy some of your “not school-related” videos XD. Happy New Years, and I will continue putting my upcoming engineering friends onto your channel!
Sir please come up with a series on Numerical methods for ODE & PDE.
If whales have less cancer than humans, could this imply there is a "critical number of cells" for an organism... that an organism with this number of cells have the highest incidence of cancer?
Great content, as usual
Maybe you should take into account, that cancer cells are usually less cooperative than normal cells. Therefore they eliminate themselves before they can occupy a big volume. Maybe this limit size is too small compared to the big organs of whales to have any effect. So, maybe, whales have cancer all the time, new cancer appearing and vanishing all the time, but it never gets big enough to bother the big organs of the whale.
Physics style video loving it.
If we assume every cell in the whale can divide, to reach 100 times as many cells would take much fewer generations than if only a small population of cells can divide. For instance, it could be the case that most cells are made from a very large population of progenitor cells that divide seldomly, or most cells are made from a small but rapidly dividing population of cells and are made via in an order of magnitude more divisions, which could give a higher chance for mutations to accumulate.
great video
Thank you!
I LOOOOOOOVE Your videos
Thank you so much!
Is the reverse true, smaller creatures also have fewer cancers? is there an optimum size?
It's because they quit smoking 😅
congrats on beating cancer dude
How do you numerically evaluate a term like (1-mu)^d where mu is almost zero and d is 8e3 ?
I can imagine that on a regular computer, the (ahem) limited precision of a floating-point unit can lead to significant numerical error on the end-result.
Probably by expanding Taylor series until it converges
While it is small^large, the numbers here aren't so crazy that we can't get the computers to be able to do it, but maybe don't try it on your 4 function calculator ha!
@@DrTrefor That's the thing - had it been mu^d that would be fine - the "floating point" representation would take care of the exponent. But (1-mu) *isn't* small, and the 23-bit (or whatever) FPU-mantissa might miss this nuance.
Probably good ol' log tricks. While (1-mu)^d might be difficult to evaluate, d*log(1-mu) is likely not (and there are optimized routines for log(1 - x) for really small x). Then exponentiating the quantity you obtain will be more feasible
1-(1-\mu)^d is not the probability of one mutation has happened but the probability of nonzero amount of mutations have happened. So all subsequent calculations are wrong
I normally get notifications when you upload a video but this time there was nothing. Has anbody else the same problem?
Indohyus, my brother?
my man refuses to buy a mic