A blog about biology, self-improvement, and the future

# Tag archive: Evolution

Peter Godfrey-Smith’s Other Minds, which is mostly a combination of a discussion on the evolution of intelligence/consciousness and a collection of fun cephalopod anecdotes, surprised me by having a very nice presentation of the core ideas of non-adaptive theories of ageing.

On mutation accumulation:

If we are thinking in evolutionary terms, it’s natural to wonder if there is some hidden benefit from aging itself. Because the onset of aging in our lives can seem so “programmed,” this is a tempting idea. Perhaps old individuals die off because this benefits the species as a whole, by saving resources for the young and vigorous? But this idea is question-begging as an explanation of aging; it assumes that the young are more vigorous. So far in the story, there’s no reason why they should be.

In addition, a situation of this kind is not likely to be stable. Suppose we had a population in which the old do graciously “pass the baton” at some appropriate time, but an individual appeared who did not sacrifice himself in this way, and just kept going. This one seems likely to have the chance to have a few extra offspring. If his refusal to sacrifice was also passed on in reproduction, it would spread, and the practice of sacrifice would be undermined. So even if aging did benefit the species as a whole, that would not be enough to keep it around. This argument is not the end of the line for a “hidden benefit” view, but the modern evolutionary theory of aging takes a different approach. […]

Start with an imaginary case. Assume there is a species of animal with no natural decay over time. These animals show no “senescence,” to use the word preferred by biologists. The animals start reproducing early in their life, and reproduction continues until the animal dies from some external cause—being eaten, famine, lightning strike. The risk of death from these events is assumed to be constant. In any given year, there is a (say) 5 percent chance of dying. This rate does not increase or decrease as you get older, but there is some number of years by which time some accident or other has almost certainly caught you. A newborn has less than a 1 percent chance of still being around at ninety years in this scenario, for example. But if that individual does make it to ninety, it will very probably make it to age ninety-one.

Next we need to look at biological mutations. […] Mutations often tend to affect particular stages in life. Some act earlier, others act later. Suppose a harmful mutation arises in our imaginary population which affects its carriers only when they have been around for many years. The individuals carrying this mutation do fine, for a while. They reproduce and pass it on. Most of the individuals carrying the mutation are never affected by it, because some other cause of death gets them before the mutation has any effect. Only someone who lives for an unusually long time will encounter its bad effects.

Because we are assuming that individuals can reproduce through all their long lives, there is some tendency for natural selection to act against this late-acting mutation. Among individuals who live for a very long time, those without the mutation are likely to have more offspring than those who have it. But hardly anyone lives long enough for this fact to make a difference. So the “selection pressure” against a late-acting harmful mutation is very slight. When molecular accidents put mutations into the population, as described above, the late-acting mutations will be cleaned out less efficiently than early-acting ones.

As a result, the gene pool of the population will come to contain a lot of mutations that have harmful effects on long-lived individuals. These mutations will each become more common, or be lost, mostly through sheer chance, and that makes it likely that some will become common. Everyone will carry some of these mutations. Then if some lucky individual evades its predators and other natural dangers and lives for an unusually long time, it will eventually find things starting to go wrong in its body, as the effects of these mutations kick in. It will appear to have been “programmed to decline,” because the effects of those lurking mutations will appear on a schedule. The population has begun to evolve aging.

On antagonistic pleiotropy:

Is it worth saving enough money so that you will live in luxury when you are 120? Perhaps it is, if you have unlimited money coming in. Maybe you will live that long. But if you don’t have unlimited money coming in, then all the money you save for a long retirement is money you can’t do something else with now. Rather than saving the extra amount needed, it might make more sense to spend it, given that you are not likely to make it to 120 anyway.

The same principle applies to mutations. A lot of mutations have more than one effect, and in some cases, a mutation might have one effect that is visible early in life and another effect that is visible later. If both effects are bad, it is easy to see what will happen—the mutation should be weeded out because of the bad effect it has early in life. It is also easy to see what will happen if both effects are good. But what if a mutation has a good effect now and a bad effect later? If “later” is far enough away that you will probably not make it to that stage anyway, due to ordinary day-to-day risks, then the bad effect is unimportant. What matters is the good effect now. So mutations with good effects early in life and bad effects late in life will accumulate; natural selection will favor them. Once many of these have arisen in the population, and all or nearly all individuals carry some of them, a decay late in life will come to seem preprogrammed. Decay will appear in each individual as if on a schedule, though each individual will show the effects a bit differently. This happens not because of some hidden evolutionary benefit of the breakdown itself, but because the breakdown is the cost paid for earlier gains.

[Mutation accumulation and antagonistic pleiotropy] work together. Once each process gets started, it reinforces itself and also magnifies the other. There is “positive feedback,” leading to more and more senescence. Once some mutations get established that lead to age-related decay, they make it even less likely that individuals will live past the age at which those mutations act. This means there is even less selection against mutations which have bad effects only at that advanced age. Once the wheel starts turning, it turns more and more quickly.

The book discusses various wrinkles in the theory as it applies to different kinds of organisms, then goes on to discuss the question of why most cephalopods are so short-lived. Recommended.

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 interest1. 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 survivorship2.

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)4. 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.

Survivorship, cumulative fecundity and cumulative reproductive output curves for a population of elves with 1% fecundity and 0.1% mortality per year.

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?

Three potential fatal mutations in the elven populations, and their effects on lifetime reproductive output.

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 5

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.

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 pleiotropy6. 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 pleiotropy7. 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.

Age-specific survivorship as a function of different levels of constant extrinsic mortality.

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):

Scatterplots of bird and mammal maximum lifespans vs adult body weight from the AnAge database, with central tendencies fit in R using local polynomial regression (LOESS).

In addition to body size and flight, you are also likely to have a longer lifespan if you are8:

• 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:

Mortality (red) and fertility (blue) curves from the desert tortoise, showing declining mortality with time. Adapted from Fig. 1 of Jones et al. 2014.

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.

1. 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.

2. Exponential in continuous time; geometric in discrete time.

3. The reproductive output $$r_a$$ at some age $$a$$ is therefore equal to $$f_a \cdot s_a$$, where $$f$$ is fecundity and $$s$$ is survivorship. Since survivorship is determined by mortality, reproductive output can also be expressed as $$r_a = f_a \cdot \int_0^a m_x \:\mathrm{d}x$$ (in continuous time) or $$r_a = f_a \cdot \prod_{k=0}^am_k$$ (in discrete time).

4. Lifetime reproductive output is equal to $$\int_0^\infty r_a \:\mathrm{d}a$$ (in continuous time) or $$\sum_{a=0}^\infty r_a$$ (in discrete time), where $$r_a$$ is the age-specific reproductive output at age $$a$$

5. Williams (1957) Evolution 11(4): 398-411.

6. 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.

7. 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.

8. 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.

Follows from: Evolution is Sampling Error

It seems a lot of people either missed my footnotes in the last post about effective population size, or noticed them, read them and were confused1. I think the second response is reasonable; for non-experts, the concept of effective population size is legitimately fairly confusing. So I thought I’d follow up with a quick addendum about what effective population size is and why we use it. Since I’m not a population geneticist by training this should also be a useful reminder for me.

The field of biology that deals with the evolutionary dynamics of populations — how mutations arise and spread, how allele frequencies shift over time through drift and selection, how alleles flow between partially-isolated populations — is population genetics. “PopGen” differs from most of biology in that its foundations are primarily hypothetico-deductive rather than empirical: one begins by proposing some simple model of how evolution works in a population, then derives the mathematical consequences of those initial assumptions. A very large and often very beautiful edifice of theory has been constructed from these initial axioms, often yielding surprising and interesting results.

Population geneticists can therefore say a great deal about the evolution of a population, provided it meets some simplifying assumptions. Unfortunately, real populations often violate these assumptions, often dramatically so. When this happens, the population becomes dramatically harder to model productively, and the maths becomes dramatically more complicated and messy. It would therefore be very useful if we could find a way to usefully model more complex real populations using the models developed for the simple cases.

Fortunately, just such a hack exists. Many important ways in which real populations deviate from ideal assumptions cause the population to behave roughly like an idealised population of a different (typically smaller) size. This being the case, we can try to estimate the size of the idealised population that would best approximate the behaviour of the real population, then model the behaviour of that (smaller, idealised) population instead. The size of the idealised population that causes it to best approximate the behaviour of the real population is that real population’s “effective” size.

There are various ways in which deviations from the ideal assumptions of population genetics can cause a population to act as though it were smaller – i.e. to have an effective size (often denoted $$N_e$$) that is smaller than its actual census size – but two of the most important are non-constant population size and, for sexual species, nonrandom mating. According to Gillespie (1998), who I’m using as my introductory source here, fluctuations in population size are often by far the most important factor.

In terms of some of the key equations of population genetics, a population whose size fluctuates between generations will behave like a population whose constant size is the harmonic mean of the fluctuating sizes. Since the harmonic mean is much more sensitive to small values than the arithmetic mean, this means a population that starts large, shrinks to a small size and then grows again will have a much smaller effective size than one that remains large2. Transient population bottlenecks can therefore have dramatic effects on the evolutionary behaviour of a population.

Many natural populations fluctuate wildly in size over time, both cyclically and as a result of one-off events, leading to effective population sizes much smaller than would be expected if population size were reasonably constant. In particular, the human population as a whole has been through multiple bottlenecks in its history, as well as many more local bottlenecks and founder effects occurring in particular human populations, and has recently undergone an extremely rapid surge in population size. It should therefore not be too surprising that the human $$N_e$$ is dramatically smaller than the census size; estimates vary pretty widely, but as I said in the footnotes to the last post, tend to be roughly on the order of $$10^4$$.

In sexual populations, skewed sex ratios and other forms of nonrandom mating will also tend to reduce the effective size of a population, though less dramatically3; I don’t want to go into too much detail here since I haven’t talked so much about sexual populations yet.

As a result of these and other factors, then, the effective sizes of natural populations is often much smaller than their actual census sizes. Since genetic drift is stronger in populations with smaller effective sizes, that means we should expect populations to be much more “drifty” than you would expect if you just looked at their census sizes. As a result, evolution is typically more dominated by drift, and less by selection, than would be the case for an idealised population of equivalent (census) size.

1. Lesson 1: Always read the footnotes. Lesson 2: Never assume people will read the footnotes.

2. As a simple example, imagine a population that begins at size 1000 for 4 generations, then is culled to size 10 for 1 generation, then returns to size 1000 for another 5 generations. The resulting effective population size will be:

$$N_e = \frac{10}{\frac{9}{1000} + \frac{1}{10}} \approx 91.4$$

A one-generation bottleneck therefore cuts the effective size of the population by an order of magnitude.

3. According to Gillespie again, In the most basic case of a population with two sexes, the effective population size is given by $$N_e = \left(\frac{4\alpha}{(1+\alpha)^2}\right)\times N$$, where alpha is the ratio of females to males in the population. A population with twice as many males as females (or vice-versa) will have an $$N_e$$ about 90% the size of its census population size; a tenfold difference between the sexes will result in an $$N_e$$ about a third the size of the census size. Humans have a fairly even sex ratio so this particular effect won’t be very important in our case, though other kinds of nonrandom mating might well be.

A common mistake people make about evolution is to think it’s all about natural selection and adaptation. In fact, random non-adaptive changes often dominate the evolutionary process.

Today I’m going to lay out a useful framework that I hope makes this fact more intuitive, which might in turn help non-experts build better intuitive models of evolutionary processes. This will come in handy when I try to explain non-adaptive theories of ageing later on.

## Sampling error and genetic drift

We can think of evolution as sampling error: deviation in the genetic composition of the offspring in a population relative to their parents. To illustrate this, let’s imagine a simple, asexual population, evenly divided between two gene variants (alleles) which produce no difference in fitness1:

These individuals will reproduce, giving rise to the next generation. Since all the individuals are genetically identical and have the same chance of reproducing, we can think of these offspring being randomly sampled, with replacement, from the previous generation:

Since there is a great deal of randomness involved in who reproduces successfully and whose offspring survive, not all individuals will produce the same number of offspring in the next generation, even though they all had the same probability of reproducing to begin with. As a result, even in the absence of selection effects, the allele distribution of the new generation is likely to differ from that of the previous generation; this random, unbiased change in allele distribution is known as genetic drift.

As a result of genetic drift, the allele distribution will fluctuate up and down stochastically; sooner or later, one or the other will be eliminated from the population, resulting in fixation:

The time to fixation depends on the population size2 and some other population parameters; here’s an example plot for a population with a carrying capacity of 200 instead of 10:

Fairly dramatic genetic changes, then, can accumulate in a population based purely on genetic drift; there’s not necessarily any need to invoke selection to explain why genetic differences between populations accumulate over time. That said, what happens when we add selection into the mix?

## Natural selection is sampling bias

Suppose that one of the starting alleles in the population is less fit than the other: individuals with that allele are less likely to produce reproductively-successful offspring. What happens now?

If one allele is much less fit than the other, the individuals bearing it will probably die without issue, producing a very boring plot:

So far, so trivial. The interesting cases occur when the fitness of one genotype is close to (either a bit higher or a bit lower than) the old one. In this case, thanks to genetic drift, the less-fit allele (here in purple) can persist in the population for a surprisingly long time…

…or even fix!

Overall, under these conditions (carrying capacity = 10, relative fitness ~ 0.9) the less-fit allele will reach fixation about a quarter of the time; more than enough for 100% the population to be bearing many deleterious alleles.

These results are a pretty trivial application of statistics, but they have very important implications for how we should view evolution. Thanks to genetic drift, beneficial mutations will often die out and deleterious ones reach fixation. How often this occurs depends on various factors, the most obvious of which is the magnitude of the mutation’s effect on fitness — the more dramatic the effect, the greater selection’s ability to overcome drift and eliminate the less-fit allele.

However, another crucial variable, underappreciated outside evolutionary biology, is population size.

## Evolution and the law of large numbers

According to the law of large numbers, the average of a sample converges in probability towards its expected value as sample size increases: the larger the sample, the smaller the expected relative mean absolute difference between the sample mean and the expected value3. If you flip a coin ten times, the chance of deviating from the expected value (five heads) by at least 20% is more than 75%, whereas it’s only 5% if you flip 100 times and virtually zero if you flip 1000 times. The larger the sample, the more likely you are to see roughly what you expect.

In our framework of evolution as sampling error, natural selection determines the expected value: the number of offspring of each genotype we expect to see in the next generation, given the distribution in the current generation. But the smaller the population, the more likely it is to deviate substantially from this expectation – that is, for random genetic drift to overwhelm the bias imposed by natural selection.

If you combine this sample-size-dependent variability with the absorbing nature of fixation and elimination (that is, once an allele has been eliminated, it isn’t coming back), you obtain the result that the larger the population, the more likely it is that the fitter allele is actually the one that gets fixed, all else equal. We can see this in our toy model from earlier, where the green allele is 10% fitter than the purple allele and both start with 50% prevalence in the population:

When population size is very small, the chance that the fitter (green) allele is the one that eventually fixes is close to 50%; as population size increases, this probability increases, until for sufficiently-large populations it is virtually certain. Smaller differences in fitness would require larger population sizes to consistently fix the fitter allele4.

Population size, then, is a crucial factor affecting the optimisation power of evolution: the larger the population size, the greater the capacity of natural selection to select for beneficial mutations and eliminate deleterious ones. This is why bottlenecks and founder effects are so important in evolution: by reducing the size of the population, they both increase the relative prevalence of rare mutations and decrease the relative strength of natural selection, resulting in very powerful drift. The results of this can be quite striking: on the tiny Micronesian island of Pingelap, for example, almost 10% of the population are completely colourblind, a condition that is extremely rare elsewhere5. This is believed to be the result of a typhoon in 1775 that left only 20 survivors, one of whom was a carrier of the condition6.

## Implications

What can we infer from all this? Firstly, when thinking about evolutionary processes it’s vital not to neglect genetic drift. Just because something spread throughout a population and reached fixation does not mean it is adaptive. Secondly, this is especially true when populations are small, and we should always pay careful attention to population size when thinking about how a population might evolve. In general, we should expect larger populations7 to be fitter than smaller ones, since (among other things) natural selection will be more effective at weeding out deleterious alleles and propagating beneficial ones.

Finally, it has not escaped my notice that this framework has obvious implications for thinking about analogous evolutionary processes that might occur outside of biology. More on this anon.

1. I’m also assuming non-overlapping generations and a constant carrying capacity; relaxing these assumptions makes the maths more complicated but shouldn’t alter the basic conclusion. Similarly, while new genetic variants are capable of spreading much more quickly through sexual populations, the same basic phenomena still apply.

2. Actually, the time to fixation (and many other aspects of the population’s behaviour) depend on its effective population size, which depends not only on its actual population size but also on various demographic and genetic factors. This is an absolutely crucial distinction that I am eliding here for the sake of brevity (in my defence, population geneticists seem to also do the same thing when speaking casually). Effective population sizes are often much smaller than actual (“census”) sizes; for example, the usual estimate that gets bandied about for global human effective population size is roughly 10,000.

3. In fact, the RMD looks like it might vary as a power law of sample size: I noticed this from simulations and haven’t bothered to tease out the underlying mathematics here, but still, kinda cool.

4. See e.g. this plot for a 1% difference in fitness:

5. According to Wikipedia, the proportion of Americans with the same condition is 0.003%.

6. It probably didn’t hurt that the suspected carrier was also the chief of the island.

7. Again, I’m actually talking about effective population size here, not census size.

At the LessWrong European Community Weekend 2018, I gave a talk explaining the intuition behind non-adaptive theories of the evolution of ageing. This blog post and its followup are adapted from that presentation.

When people find out that I did my PhD in the biology of ageing, they tend to ask one of two questions. First, they ask what they can do to live longer. Second, they ask why people age in the first place. My answer to the first question is unfortunately fairly boring at present — don’t smoke, eat well, get enough exercise, get enough sleep, et cetera — but when it comes to the second I think I have more of interest to say. To get this blog rolling (see what I did there), let’s dive into the important and fractious question of why we age.

## What is ageing?

It is a curious thing that there is no word in the English language that stands for the mere increase of years; that is, for ageing without its connotations of increasing deterioration and decay.

—Peter Medawar, “An Unsolved Problem in Biology”

When people talk about “ageing”, there are broadly speaking three different things they might mean1. Firstly, there is the simple process of getting older — of the amount of time since you were born inexorably increasing. Let’s call this process “temporal ageing”. Ageing in this way has a lot of benefits: more memories, more experience, and with luck more self-knowledge and more wisdom.

Unfortunately, the benefits conferred by temporal ageing are currently inextricably tied to the physical changes denoted by the second meaning of “ageing”: a generalised physiological deterioration, characterised by a wide range of unfortunate symptoms affecting almost every system of the body. As a result of this second kind of ageing, we become slower, more fragile, more prone to disease, and generally more likely to experience impaired health and wellbeing as we get older, eventually leading to death. As we as a civilisation have gradually eliminated more and more extrinsic forms of suffering and death, the depredations of ageing have gradually become the primary cause of ill health and death in developed countries by an overwhelming margin. This is the kind of ageing people mean when they worry about getting cancer or dementia, buy “anti-ageing” skin cream, or invest in real anti-ageing research; it’s the province of doctors, physiologists, and molecular biologists. Let’s call it “physiological ageing”.

Finally, the individual changes taking place due to physiological ageing give rise to a distinctive statistical pattern at the level of entire populations of humans or other animals: a progressive increase in mortality (probability of dying) and decrease in fecundity (expected number of offspring) in older age cohorts. This pattern is what gives rise to plots like the ones below, and it’s what demographers, actuaries and evolutionary biologists generally mean when they talk about “ageing”. From this perspective, the specific functional changes underlying these changes in survival and reproduction are less important than the high-level functional changes that result: changes in the rates of reproduction, illness, disability, and death. From an evolutionary perspective it is the first and last of these, reproduction and death rates, that are the most important. We can call this final meaning of the word ageing “demographic ageing”.

Logarithmic mortality curves for British and American populations at different points in the 20th century. The $$y$$-axes give the log-probability of dying for individuals in a given age-class in the year and country indicated. Source: US Office of Retirement and Disability Policy

These two phenomena, of physiological and demographic ageing, are tightly interlinked in any given population but are nevertheless conceptually distinct: two different species (an insect and a mammal, say) could undergo very different physiological ageing processes but exhibit very similar patterns of demographic ageing. Physiological and demographic ageing also give us very different perspectives on the question of why we age. From the perspective of physiological ageing, the question is generally asking about the specific genetic, molecular, histological or physiological mechanisms underlying the changes we observe: what particular aspect of our biology is causing our bodies to deteriorate with age in this or that particular way? From the perspective of demographic ageing, the relevant why question is simpler and more fundamental: given that ageing appears to be pretty deleterious to the survival and reproduction chances of any individual experiencing it, how could we have evolved to exhibit declining functionality with age at all?

In these posts, I’ll be focusing on the second kind of why question, discussing the evolutionary teleology of the ageing process. As we’ll see, from that perspective, ageing is frankly pretty weird.

## Three puzzles of ageing

When we look at nature, or at ourselves, we observe something surprising: animals get old. In many, many different species, old age is accompanied by a progressive decline in functionality, leading to higher rates of death2 and lower rates of reproduction. This pattern is seen almost everywhere you look in the animal kingdom, suggesting that it has either evolved again and again independently or been retained after inheritance from a common ancestor. Yet despite this commonality, there is profound variation in the details of the ageing process: even closely related species can differ dramatically in how quickly they age and how long they tend to live. And here and there, we see species that seem to have escaped the iron grip of ageing, exhibiting mortality that stays constant or even declines over time.

Distribution of lifespans across all mouse and bat species from the AnAge database (accessed 2018-09-01). Despite their relatively close relationship, similar size, and similar metabolic rates, bats live dramatically longer than mice.

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?

Any successful theory of the evolution of ageing must be able to convincingly answer all these questions. A number of attempts have been made over the years, none of which has managed to capture the consensus of the academic community. These attempted explanations can be broadly divided into two groups: those that propose with some reason why ageing, which seems so deleterious, is adaptive after all, and those that accept that ageing is deleterious and attempt to explain why it might evolve anyway. I’ll discuss the main representatives of each group in separate blog posts, but first I want to tackle one simple non-adaptive theory that doesn’t quite manage to do the job.

## Why ageing is not (just) wear and tear

The senescence of human organs consists not of their wearing out but of their lack of replacement when worn out.

George C. Williams, “Pleiotropy, Natural Selection, and the Evolution of Senescence”

One common folk theory of ageing is that it is simply wear and tear: like a car, the body is a machine, and like any machine it wears out over time. Exposure to the environment naturally leads to the accumulation of damage, which progressively impairs the function of the machine until it breaks down (i.e. we die). Any imperfection in the machine’s components will hasten this process, either by generating more damage or by becoming progressively more dysfunctional over time. This progressive degradation is inevitable: we can keep a car in working order with regular maintenance and repair, but we are not (yet) capable of doing this for the kinds of wear and tear that accumulate in the body. Hence, ageing.

This explanation of ageing is intuitive, and parts of it are true as far as they go. There are certainly various kinds of damage and dysregulation that accumulate in the body with age: genetic mutations, senescent cells, shortened telomeres, cross-linked chemical aggregates, degraded stem-cell niches, and on and on. If we could remove and correct some or all of these issues the way we can replace a dodgy spark plug, we’d go a long way towards addressing the problem of physiological ageing.

But as an explanation of why ageing exists in the first place, “wear and tear is inevitable” just doesn’t cut it, because a living body is not like a car. Where a car is dead matter shaped by external tools, a body is a dynamic, self-generating system with incredible powers of self-repair. These self-repair processes are awe-inspiringly good: of the tens of thousands of genetic mutations that occur per cell every day in the human body, virtually all are accurately repaired. Our bodies can repair wounds, fight off infections, kill and replace malfunctioning cells, partially regrow (some) organs, even remodel their bones to best respond to the forces they experience. Many of these regenerative processes decline as we age, but that decline is itself part of the ageing process: young children are amazingly good at healing without scarring, for example.

So while bodily damage is inevitable as part of the daily business of living, our bodies successfully repair almost all of it, especially when we’re young. Evolutionarily speaking, the question is not why the damage occurs, but why it is permitted to accumulate. It seems our bodies’ repair processes are not quite perfect, and allow damage and dysregulation to progressively accumulate over time. Why aren’t they better?

Could our bodies’ repair systems be better? They could certainly be worse: there are many, many mammal species with much shorter lifespans than humans’, even when kept in very safe conditions. These animals age faster than humans because they accumulate damage and dysregulation faster; for whatever reason, their monitoring and repair systems have evolved to be that much sloppier than ours3. Conversely, there are at least a few mammals (such as bowhead whales) that live longer than we do; clearly they have something going for them that we don’t, but why? And that’s without going into animals like green hydra or naked mole rats that don’t seem to age at all: if they can do it, why can’t we?

Because it’s not an evolutionary theory, wear-and-tear is incapable of addressing these questions. Yes, damage is inevitable, but why does this result in such different rates of ageing in different species? If one species can evolve to remove this damage so efficiently that it doesn’t age at all, what is preventing most other species from doing the same? The answers to these questions don’t lie in the eternal inevitability of molecular damage, but in the selective pressures each species is exposed to across evolutionary time. In the rest of this series, I’ll address theories of ageing that attempt to explain ageing in these terms.

1. Actually, there’s a fourth meaning that gets used in the media quite a lot: “population ageing”, by which is meant an increase in the median age of a population and the proportion of old people due to changes in social conditions. This is distinct from my “demographic ageing” in that the former is looking at the age composition of the whole population, while the latter is comparing different age groups within the population. I don’t plan on talking about population ageing here.

2. This increase in death rate is both intrinsic and extrinsic: older individuals are more likely to die from heart attack, stroke, cancer and so on, but are also more vulnerable to predation, starvation and disease.

3. I’ve left out an important consideration here, which is that rather than worse repair systems, these other mammals might be experiencing higher rates of damage, perhaps due to a higher metabolic rate. A repair system with the same stringency that is exposed to a higher level of damage will let more damage events through. Even if this is true, though, the question remains of why these animals haven’t evolved better repair mechanisms to cope with this higher rate of damage.

4. In addition to being longer-lived than humans, bowhead whales are also larger. This also raises the classic “why don’t all whales get cancer” problem: if cancer is a matter of mutations, mutations are a matter of chance, and whales have more cells in which the right mutations can accumulate, why don’t they all get horrible tumours? There are various theories about this problem, too, none of which I intend to discuss here.