Follows from: Why We Age, Part 1; Evolution is Sampling Error; An addendum on effective population size
Partially redundant with Highlights of Comparative and Evolutionary Aging.
Last time, I introduced three puzzles in the evolution of ageing:
This, then, is the threefold puzzle of ageing. Why should a process that appears to be so deleterious to the individuals experiencing it have evolved to be so widespread in nature? Given this ubiquity, which implies there is some compelling evolutionary reason for ageing to exist, why do different animals vary so much in their lifespans? And how, when ageing has either evolved or been retained in so many different lineages, have some animals evolved to escape it?
I divided existing theories of the evolution of ageing into two groups, adaptive and nonadaptive, and discussed why one commonly believed nonadaptive theory – namely, simple wear and tear – could not adequately answer these questions.
In this post I’ll discuss other, more sophisticated non-adaptive theories. These theories are characterised by their assertion that ageing provides no fitness benefit to organisms, but rather evolves despite being deleterious to reproductive success. Despite the apparent paradoxicality of this notion, these theories are probably the most widely-believed family of explanations for the evolution of ageing among academics in the field; they’re also the group of theories I personally put the most credence in at present.
How can this be? How can something non-adaptive – even deleterious – have evolved and persisted in so many species across the animal kingdom? To answer this question, we need to understand a few important concepts from evolutionary biology, including genetic drift, relaxed purifying selection, and pleiotropy. First, though, we need to clarify some important terminology.
Mortality, survivorship, and fecundity
For the purposes of this post, a cohort is a group of individuals from the same population who were all born at the same time, i.e. they are of the same age. The survivorship of a cohort at a given age is the percentage of individuals surviving to that age, or equivalently the probability of any given individual surviving at least that long. Conversely, the mortality of a cohort at a given age is the probability of an individual from that cohort dying at that age, and not before or after.
Survivorship and mortality are therefore related, but distinct: survivorship is the result of accumulating mortality at all ages from birth to the age of interest[1]. As a result, the mortality and survivorship curves of a cohort will almost always look very different; in particular, while mortality can increase, decrease or stay the same as age increases, survivorship must always decrease. As one important example, constant mortality will give rise to an exponential decline in survivorship[2].
Four hypothetical mortality curves and their corresponding survivorship curves.
In evolutionary terms, survival is only important insofar as it leads to reproduction. The age-specific fecundity of a cohort is the average number of offspring produced by an individual of that cohort at that age. Crucially, though, you need to survive to reproduce, so the actual number of offspring you are expected to produce at a given age needs to be downweighted in proportion to your probability of dying beforehand. This survival-weighted fecundity (let’s call it your age-specific reproductive output) can be found by multiplying the age-specific fecundity by the corresponding age-specific survivorship. Since this depends on survivorship, not mortality, it will tend to decline with age: a population with constant mortality and constant fecundity (i.e. no demographic ageing) will show reproductive output that declines exponentially along with survivorship.
Two hypothetical mortality/fecundity curves and their corresponding reproductive outputs.
The fitness of an individual is determined by their lifetime reproductive output (i.e. the total number of offspring they produce over their entire lifespan)[3]. Mutations that significantly decrease lifetime reproductive output will therefore be strongly opposed by natural selection. It seems mutations leading to ageing (i.e. an increase in mortality and decrease in fecundity with time) should be in that category. So why does ageing evolve?
What good is immortality?
Imagine a race of beautiful, immortal, ageless beings—let’s call them elves. Unlike we frail humans, elves don’t age: they exhibit constant mortality and constant fecundity. As a result, their age-specific survivorship and reproductive output both fall off exponentially with increasing age—far more slowly, in other words, than occurs in humans.
Under the parameters I’ve used here (1% fecundity, 0.1% mortality), an elf has about a 50% chance of making it to 700 years old and a 10% chance of living to the spry old age of 2,300. An elf that makes it that far will have an average of 23 children over its life; 7 if it only makes it to the median lifespan of 700.
Since fecundity and mortality are constant, an elf that makes it to 3,000 will be just as fit and healthy then as they were as a mere stripling of 500, and will most likely still have a long and bright future ahead of them. Nevertheless, the chance of any given newborn elf making it that far is small (about 5%). This means that, even though an old elf could in principle have as many children as a much younger individual elf, the actual offspring in the population are mainly produced by younger individuals. Just over 50% of the lifetime expected reproductive output of a newborn elf is concentrated into its first 700 years; even though it could in principle live for millennia, producing children at the same rate all the while, its odds of reproducing are best early in life. You can, after all, only breed when you’re living.
This fact—that reproductive output is concentrated in early life even in the absence of ageing—has one very important consequence: natural selection cares much more about you when you’re young.
Natural selection is ageist
No genome is totally stable—mutations always occur. Let’s imagine that three mutations arise in our elven population. Each is fatal to its bearer, but with a time delay, analogous to Huntington’s disease or some other congenital diseases in humans. Each mutation has a different delay, taking effect respectively at 100, 1000, and 10000 years of age. What effect will these mutations have on their bearers’ fitness, and how well will they spread in the population?
Although all three mutations have similar impacts on an individual who lives long enough to experience them, from a fitness perspective they are very different. The first mutation is disastrous: almost 90% of wild-type individuals (those without the mutation) live past age 100, and a guaranteed death at that age would eliminate almost 90% of your expected lifetime reproductive output. The second mutation is still pretty bad, but less so: a bit over a third of wild-type individuals live to age 1000, and dying at that age would eliminate a similar proportion of your expected lifetime reproductive output. The third mutation, by contrast, has almost no expected effect: less than 0.005% of individuals make it to that age, and the effect on expected lifetime reproductive output is close to zero. In terms of fitness, the first mutation would be strenuously opposed by natural selection; the second would be at a significant disadvantage; and the third would be virtually neutral.
This extreme example illustrates a general principle:
The impact of a mutation on the fitness of an organism depends on both the magnitude of its effect and the proportion of total reproductive output affected.
— Williams 1957 [4]
Mutations that take effect later in life affect a smaller proportion of total expected reproductive output and so have a smaller selective impact, even if the size of the effect when they do take effect is just as strong. The same principle applies to mutations with less dramatic effects: those that affect early-life survival and reproduction have a big effect on fitness and will be strongly selected for or against, while those that take effect later will have progressively less effect on fitness and will thus be exposed to correspondingly weaker selection pressure. Put in technical language, the selection coefficient of a mutation depends upon the age at which it takes effect, with mutations affecting later life having coefficients closer to zero.
Evolution is sampling error, and selection is sampling bias. When the selection coefficient is close to zero, this bias is weak, and the mutation’s behaviour isn’t much different from that of a neutral mutation. As such, mutations principally affecting later-life fitness will act more like neutral mutations, and increase and decrease in frequency in the population with little regard for their effects on those individuals that do live long enough to experience them. As a result, while mutations affecting early life will be purged from the population by selection, those affecting late life will be allowed to accumulate through genetic drift. Since the great majority of mutations are negative, this will result in deteriorating functionality at older ages.
So our elves are sadly doomed to lose their immortality, unless something very weird is happening to cause them to keep it. Mutations impairing survival and reproduction early in life will be strenuously removed by natural selection, but those causing impairments later in life will accumulate, leading to a progressive increase in mortality and decline in fecundity. This might seem bad enough, but unfortunately there is more bad news on the horizon—because this isn’t the only way that nonadaptive ageing can evolve.
Perverse trade-offs
Imagine now that instead of a purely negative, Huntingdon-like mutation arising in our ageless elf population, a mutation arose that provided some fitness benefit early in life at the cost of some impairment later; perhaps promoting more investment in rapid growth and less in self-repair, or disposing the bearer more towards risky fights for mates. How would this new mutation behave in the population?
The answer depends on the magnitude of the early-life benefit granted by the mutation, as well as of its later-life cost. However, we already saw that in weighing this trade-off natural selection cares far more about fitness in early life than in later life; as such, even a mutation whose late-life cost far exceeded its early-life benefit in magnitude could be good for overall lifetime fitness, and hence have an increased chance of spreading and becoming fixed in the population. Over time, the accumulation of mutations like this could lead to ever-more-severe ageing in the population, even as the overall fitness of individuals in the population continues to increase.
This second scenario, in which the same mutation provides a benefit at one point in life and a cost at another, is known as antagonistic pleiotropy[5]. It differs from the mutation accumulation theory of ageing outlined above in that, while in the former case ageing arises primarily through genetic drift acting on late-life-affecting deleterious mutations, the latter proposes that ageing arises as a non-adaptive side effect of a fitness-increasing process. Both theories are “non-adaptive” in that the ageing that results is not in itself good for fitness, and both depend on the same basic insight: due to inevitably declining survivorship with age, the fitness effect of a change in survival or reproduction tends to decline as the age at which it takes effect increases.
Mutation accumulation and antagonistic pleiotropy have historically represented the two big camps of ageing theorists, and the theories have traditionally been regarded as being in opposition to each other. I’ve never really understood why, though: the basic insight required to understand both theories is the same, and conditions that gave rise to ageing via mutation accumulation could easily also give rise to additional ageing via antagonistic pleiotropy[6]. Importantly, both theories give the same kinds of answers to the other two key questions of ageing I discussed last time: why do lifespans differ between species, and why do some animals escape ageing altogether?
It’s the mortality, stupid
As explanations of ageing, both mutation accumulation and antagonistic pleiotropy depend on extrinsic mortality; that is, probability of death arising from environmental factors like predation or starvation. As long as extrinsic mortality is nonzero, survivorship will decline monotonically with age, resulting (all else equal) in weaker and weaker selection agains deleterious mutations affecting later ages. The higher the extrinsic mortality, the faster the decline in survivorship with age, and the more rapid the corresponding decline in selection strength.
As a result, lower extrinsic mortality will generally result in slower ageing: your chance of surviving to a given age is higher, so greater functionality at that age is more valuable, resulting in a stronger selection pressure to maintain that functionality.
This is the basic explanation for why bats live so much longer than mice despite being so similar: they can fly, which protects them from predators, which reduces their extrinsic mortality.
You can see something similar if you compare all birds and all mammals, controlling for body size (being larger also makes it harder to eat you):
In addition to body size and flight, you are also likely to have a longer lifespan if you are[7]:
Arboreal
Burrowing
Poisonous
Armoured
Spiky
Social
All of these factors share the property of making it harder to predate you, reducing extrinsic mortality. In many species, females live longer than males even in captivity: males are more likely to (a) be brightly coloured or otherwise ostentatious, increasing predation, and (b) engage in fights and other risky behaviour that increases the risk of injury. I’d predict that other factors that reduce extrinsic mortality in the wild (e.g. better immune systems, better wound healing) would similarly correlate with longer lifespans in safe captivity.
This, then, is the primary explanation non-adaptive ageing theories give for differences in rates of ageing between species: differences in extrinsic mortality. Mortality can’t explain everything, though: in particular, since mortality is always positive, resulting in strictly decreasing survivorship with increasing age, it can’t explain species that don’t age at all, or even age in reverse (with lower intrinsic mortality at higher ages).
It’s difficult to come up with a general theory for non-ageing species, many of which have quite ideosyncratic biology; one might say that all ageing species are alike, but every non-ageing species is non-ageing in its own way. But one way to get some of the way there is to notice that mortality/survivorship isn’t the only thing affecting age-specific reproductive output; age-specific fecundity also plays a crucial role. If fecundity increases in later ages, this can counterbalance, or even occasionally outweigh, the decline in survivorship and maintain the selective value of later life.
Mammals and birds tend to grow, reach maturity, and stop growing. Conversely, many reptile and fish species keep growing throughout their lives. As you get bigger, you can not only defend yourself better (reducing your extrinsic mortality), but also lay more eggs. As a result, fecundity in these species increases over time, resulting – sometimes – in delayed or even nonexistent ageing:
So that’s one way a species could achieve minimal/negative senescence under non-adaptive theories of ageing: ramp up your fecundity to counteract the drop in survivorship. Another way would be to be under some independent selection pressure to develop systems (like really good tissue regeneration) that incidentally also counteract the ageing process. Overall, though, it seems to be hard to luck yourself into a situation that avoids the inexorable decline in selective value imposed by falling survivorship, and non-ageing animal species are correspondingly rare.
Next time in this series, we’ll talk about the other major group of theories of ageing: adaptive ageing theories. This post will probably be quite a long time coming since I don’t know anything about adaptive theories right now and will have to actually do some research. So expect a few other posts on different topics before I get around to talking about the more heterodox side of the theoretical biology of ageing.
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In discrete time, the survivorship function of a cohort will be the product of instantaneous survival over all preceding time stages; in continuous time, it is the product integral of instantaneous survival up to the age of interest. Instantaneous survival is the probability of surviving at a given age, and thus is equal to 1 minus the mortality at that age.
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Exponential in continuous time; geometric in discrete time.
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Lifetime reproductive output is equal to (in continuous time) or (in discrete time), where is the age-specific reproductive output at age .
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Williams (1957) Evolution 11(4): 398-411.
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“Pleiotropy” is the phenomenon whereby a gene or mutation exerts effects of multiple different aspects of biology simultaneously: different genetic pathways, developmental stages, organ systems, et cetera. Antagonistic pleiotropy is pleiotropy that imposes competing fitness effects, increasing fitness in one way while decreasing it in another.
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Which of the two is likely to predominate depends on factors like the relative strength of selection and drift (which is heavily dependent on effective population size) and the commonness of mutations that cause effects of the kind proposed by antagonistic pleiotropy.
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My source for this is personal communication with Linda Partridge, one of the directors at my institute and one of the most eminent ageing scientists in the world. I’m happy to see any of these points contested if people think they have better evidence than an argument from authority.
love all the graphs that help calibrate the relevant intuitions.
Antagonistic pleiotropy is certainly plausible in the abstract, but it’s not obvious how it would work in humans. Something like tissue repair, for instance, is obviously beneficial in old age but it’s hard to see how it would be harmful early on. From googling a little bit, I found some info suggesting:
The adaptive immune system (because it “runs out of capacity” late in life; see also the discussion here)
Genes associated with coronary artery disease that appear to be under positive selection (but it doesn’t say why)
A gene that causes premature cell senescence if you have multiple copies, but is useful for repairing UV-induced DNA damage
I’m curious if anybody knows of other examples of how this mechanism actually works out physiologically.
Also, it seems like this kind of explanation suggests we should be fairly pessimistic about finding a “cure” for aging, since there are likely many different unrelated causes. On the other hand, maybe it should make us optimistic about being able to gradually invent solutions to many of those causes individually, if they are created by selection rather than being fundamental/unavoidable consequences of our cellular metabolism or something.
Are you suggesting antagonistic pleiotropy is particularly non-obvious in humans (vs other animals), or that it’s non-obvious generally but you particularly care about humans? This isn’t directly related to your question, I’m just curious.
This sentence confuses me. Why would you expect it to be harmful early on? Antagonistic pleiotropy predicts mutations that are beneficial in early life and harmful later. Is this a typo (switching old and young)?
Yeah, I think this is basically right. In general my impression is that most experts don’t believe ageing is “one thing” – a single underlying cause we could neatly target. On the other hand it also doesn’t seem to be, like, a million things: there is an enumerable list of key causes, on the order of ten items long, which together account for most of the physiological ageing we see in mammals. It’s not obvious to me what to make of this theoretically.
(Of course, there are still plenty of people who like to claim they’ve found the single mechanism underlying all ageing, usually fortuitously closely related to the thing they study.)
As far as proof that it can happen in general, I found the example of animals that live just long enough to reproduce pretty convincing. Salmon don’t live more than about four years, but it’s quite clear how they gain a fitness advantage from dying after they spawn. But that sort of thing is pretty rare, so the claim that it happens in a particular species with no such obvious mechanism (or indeed in practically all animals) is a little harder to swallow.
I guess I put this sort of backwards. I meant that I would expect a mutation that causes tissue repair function to degrade with age to decrease fitness (slightly) overall, since there’s no obvious connection to some beneficial effect earlier in life. Same with heart disease, sarcopenia, etc.
I think it’s important that the AP theory holds even if the early-life gain is very small and the late-life cost is very large; that should broaden the list of potential ways to achieve that trade-off.
More generally, the idea of antagonistic pleiotropy as a general phenomenon doesn’t seem that surprising to me: trade-offs are everywhere in biology, and if one side of a trade-off is underweighted by selection then it’ll get shafted. It’s basically just overfitting: it would be surprising if the optimal set-up for growing, surviving and reproducing over a span of (say) 20 years were also the optimal set-up for doing the same over (say) 100 years, and natural selection is almost entirely optimising for the former.
One potential response to this is that this is systems thinking rather than genes thinking. Many genes do lots of things across lots of systems, so you could see a mutation that improves functionality in a way that’s relevant to one system early in life, at a cost to another system in late life.
(I’m personally more of a fan of relaxed purifying selection, which seems like the more general and less contingent theory, but I do think antagonistic pleiotropy theory is solid enough that finding more concrete examples of it wouldn’t surprise me.)
It seems to me unclear why loss of neurons and muscle cells which both are not much newly generated in human adults are not on that list. It would surprise me if the same wouldn’t be true for a bunch of other cell types as well.
Cells don’t just die of nothing. Their deaths have causes: causes like telomere attrition, genomic instability, cellular senescence, mitochondrial dysfunction, or loss of proteostasis.
The paper is not trying to enumerate every thing that changes for the worse with age (it doesn’t include immunosenescence, for example, even though that’s among the most important systemic changes you see with age). It’s trying to distill down to a list of things that cannot be adequately reduced to other processes.
You don’t need an increased amount of cell deaths for the cell deaths to become an issue without regeneration.
I would expect that some cells regularly die to all kinds of injury.
Consider telomeres. The body’s inability to repair telomeres can be considered as an adaptive mechanism protecting from tumor formation in early life.
A little thought experiment:
When you’re a unicellular organism, you want to make as many copies of yourself as possible to maximize fitness. When you evolve into a multicellular organism, this strategy ain’t working anymore. A multicellular organism with telomerase expressed in every cell of the body will eventually get a mutation in one of the cell division regulatory cascades which causes it to divide infinitely and kill the whole organism.
For this reason, telomere repair should be disabled in non-reproductive cells so that renegade mutant cells would run out of reproductive capacity and stop dividing. The only way large tumors would occur is due to 2 independent mutations: one for cell division and one for telomerase expression. This is vastly more unlikely. The downside is that lack of telomere repair would lead to gene deregulation and eventual aging.
But longer-lived animals get cancer less, not more. I’ve heard this theory before but I don’t quite understand it. It seems to predict that age would be bounded by a trade-off against child cancers. But in fact selection seems to make animals longer-lived pretty easily (e.g. humans vs homo erectus). Naked mole rats barely get cancer at all, afaik. Do baby bats get cancer more than baby mice?
I’ve also seen this in some literature, but a Google Scholar search for “mutation accumulation antagonistic pleiotropy” is popping up papers framing them as complementary. Mostly, I see three angles: simply accepting that both are well-supported, asking which is most important, or challenging the evidence for one or the other. But I don’t see papers in this convenience sample framing them as mutually exclusive.
Antagonistic pleiotropy and mutation accumulation influence human senescence and disease
Antagonistic pleiotropy and mutation accumulation contribute to age-related decline in stress response
Antagonistic pleiotropy, mutation accumulation, and human genetic disease
This one from 1993, and points out that (at least at that time):
Retesting the influences of mutation accumulation and antagonistic pleiotropy on human senescence and disease
Note that this paper rejects the finding of the first paper I linked above, based on a reanalysis (“their findings seem idiosyncratic and their evidence for the MA hypothesis is not robust.”).
Is antagonistic pleiotropy ubiquitous in aging biology?
This paper asks which model, MA or AP, is most important, rather than viewing them as mutually exclusive.
Antagonistic Pleiotropy in Human Disease
For the next post on cases where aging is adaptive, I think the octopus would make a great case study since they are well known for “self-destructing” after reproducing, theorized possibly to prevent them from competing with their offspring or eating them, i.e. octopuses that die after reproducing so they don’t outcompete their offspring and drive the species extinct through a cycle of falling survival to reproduction rates.
Interestingly, Other Minds (a recent popular science book about cephalopods) seems to mostly put credence in non-adaptive theories, and indeed has a very nice general exposition of these theories (the section of the book after the passages I quote in that link talks at length about octopus semelparity).
I think your elf example is even more extreme than you make it out to be, at least when population size is increasing, since the offspring an individual produces early in life can produce their own descendants exponentially while the original is limited to constant fecundity. 50% of an elf’s expected direct reproductive output comes in the first 700 years (5.03 expected offspring). But the total number of descendants is exp((fecundity—mortality)*age) − 1, or about 544 expected descendants at 700 years. It’s clear that (in this extreme case where fecundity is an order of magnitude higher than mortality) the death of the original at this point would make effectively no difference to the number of descendants going forward.
This effect should also apply to oscillating population sizes even if there’s no net increase over time (probably a more typical situation in practice). However, it does not account for the infertile period at the beginning of an organism’s life.
To be slightly more realistic, by the time aging seriously limits the ability to reproduce in humans (say age 40) a human could easily have multiple offspring old enough to reproduce. So even if extrinsic mortality is zero, a mutation that causes death or infertility at age 40 is reducing marginal reproductive output only by a fairly small fraction, which could be easily outweighed if it also increases fertility when young.
I’m not sure about this. I have to think about it.
So, clearly, we must have the same for humans. If we became progressively larger, women could carry twins and n-tuplets more easily. Plus, our brains would get larger, too, which could allow for a gradual increase in intelligence during our whole lifetimes.
Ha ha, just kidding: presumably intelligence is proportional to brain size/body size, which would remain constant, or might even decrease...
A Russian study (https://sites.kowsarpub.com/jjnpp/articles/83494.html) showed a geroprotective effect in rats from deuterium depleted water. This implies that aging could be simply caused by deuterium and evolutionary explanations would then be a red herring.
I don’t believe it.
The Jundishapur Journal of Natural Pharmaceutical Products doesn’t exactly scream “credible source” to me. My honest inclination is to ignore this paper and wait to see if the theory pops up somewhere more reputable. I somewhat doubt it, since this paper gives off pretty strong crank vibes.
Even if we ignore the credibility signals, the paper doesn’t show any effect of DDW on lifespan. The fact that they make claims about geroprotective effects without looking at lifespan is a big red flag. The paper is also just pretty bad and unconvincing in general (e.g. it appears to contain absolutely no statistics).
Even if DDW did increase lifespan, there are lots of other things that increase lifespan in mice. There’s no particular reason to just ignore all that and attribute everything to deuterium.
Even if DDW was as effective in mice as all other ageing treatments combined (which would be a huge finding), it still wouldn’t tell you why mice live so much shorter than naked mole rats (or humans).
So unless there’s solid evidence that DDW makes mice immortal, as opposed to making their coats (maybe, subjectively) a bit glossier, saying that “aging could be simply caused by deuterium and evolutionary explanations would then be a red herring” is flagrant hyperbole, verging on making stuff up.
Look at how declining NAD+ levels in age shut down the cellular innate immunity system… it automatically kills off the old during epidemics.
And yes, this is another attempt by me to get you to pay attention to the recent developments in NAD+ boosting vs. coronavirus… there’s finally a human trial on this in Denmark. Everyone please try to live long enough to worry about aging ;)
https://clinicaltrials.gov/ct2/history/NCT04407390?V_1=View#StudyPageTop
An even more interesting question is “Why are juveniles smaller than their parents?” It was raised by Ellistrand in a 1983 paper.
It isn’t clear that aging is something under evolutionary pressure. This may be what evolutionary theorists call a “spandrel” situation. It’s more about structure and mechanism, that is the shape of the landscape, than optimization in that landscape.
Isn’t it fairly obvious why juveniles are smaller? They have to fit inside the mother, or inside an egg which had to fit inside the mother. Even if the egg could potentially grow, you’re limited by the energy reserves you started with until you hatch and find more. Staying in the egg also seems very dangerous (can’t hide or run away from predators, can’t move away if temperature/water/etc levels aren’t good, etc).
I can’t tell whether or not your second paragraph is disagreeing with anything I said in my post.
Perhaps I’m missing the point, but doesn’t “because the juvenile needs to fit inside at least one parent” mostly suffice as an answer?