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

A weird psychadelic poster saying "Secure all classified material"

  • The NSA has released an archive of old security posters. (h/t Schneier on Security).
  • There is a unit of radiation called the banana equivalent dose (h/t The Prepared).
  • [I]f the chief executive officer of a public company commits sexual harassment, he is probably also guilty of insider trading“.
  • ‘Like my cat, I often simply do what I want to do.’ This was the opening sentence of Derek Parfit’s philosophical masterpiece, Reasons and Persons… However, there was a problem. Derek did not, in fact, own a cat. Nor did he wish to become a cat owner, as he would rather spend his time taking photographs and doing philosophy. On the other hand, the sentence would clearly be better if it was true. To resolve this problem Derek drew up a legal agreement with his sister, who did own a cat, to the effect that he would take legal possession of the cat while she would continue living with it.”
  • China’s Supreme People’s Court is not happy with Wuhan police for suppressing “rumours” of a pneumonia outbreak: “It … undermines the credibility and chips away at public support for the Communist Party. It could even be used by hostile overseas forces as an excuse to criticise us.”
  • Speaking of hostile overseas forces using this as an excuse to criticise China, Scott Sumner argues that authoritarian nationalism is bad for your health.
  • The robots are coming for your blood.
  • Grey seals clap underwater to show dominance (maybe).
  • Speaking of seals, did you know some fur seals in Antarctica have sex with penguins? Sometimes they eat the penguins afterwards, sometimes they don’t.
  • Gun owners aren’t happier, don’t sleep better at night.” No opinion on the research itself, but I love the headline.
  • Miami has issued a falling iguana warning. (h/t The Prepared)
  • Intimidation is the father of silence and the mother of lies.”
  • This building exists.
  • Which emoji scissors close?? “If you could file those parts down, you could close [these scissors] a lot more. But you couldn’t, because 📁 is the only file you can get in emoji”. (h/t The Prepared)

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.

Also posted on the EA Forum; see there for further critique and discussion.

The Weapon of Openness is an essay published by Arthur Kantrowitz and the Foresight Institute in 1989. In it, Kantrowitz argues that the long-term costs of secrecy in adversarial technology development outweigh the benefits, and that openness (defined as “public access to the information needed for the making of public decisions”) will therefore lead to better technology relative to adversaries and hence greater national security. As a result, more open societies will tend to outperform more secretive societies, and policymakers should tend strongly towards openness even in cases where secrecy is tempting in the short-term.

The Weapon of Openness presents itself as a narrow attack on secrecy in technological development. In the process, however, it makes many arguments which seem to generalise to other domains of societal decision-making, and can hence be viewed as a more general attack on certain kinds of secretiveness1. As such, it seems worth reviewing and reflecting on the arguments in the essay and how they might be integrated with a broader concern for information hazards and the long-term future.

The essay itself is fairly short and worth reading in its entirety, so I’ve tried to keep this fairly brief. Any unattributed blockquotes in the footnotes are from the original text.

Secrecy in technological development

The benefits of secrecy in adversarial technological development are obvious, at least in theory. Barring leaks, infiltration, or outright capture in war, the details of your technology remain opaque to outsiders. With these details obscured, it is much more difficult for adversaries to either copy your technology or design countermeasures against it. If you do really well at secrecy, even the relative power level of your technology remains obscured, which can be useful for game-theoretic reasons2.

The costs of secrecy are more subtle, and easier to miss, but potentially even greater than the benefits. This should sound alarm bells for anyone familiar with the failure modes of naïve consequentialist reasoning.

One major cost is cutting yourself off from the broader scientific and technological discourse, greatly restricting the ability of experts outside the project to either propose new suggestions or point out flaws in your current approach. This is bad enough by itself, but it also makes it much more difficult for project insiders to enlist outside expertise during internal disputes over the direction of the project. The result, says Kantrowitz, is that disputes within secret projects have a much greater tendency to be resolved politically, rather than on the technical merits. That means making decisions that flatter the decision-makers, those they favour and those they want to impress, and avoiding changes of approach that might embarrass those people. This might suffice for relatively simple projects that involve making only incremental improvements on existing technology, but when the project aims for an ambitious leap in capabilities (and hence is likely to involve several false starts and course corrections) it can be crippling3.

This claimed tendency of secret projects to make technical decisions on political grounds hints at Kantrowitz’s second major argument5: that secrecy greatly facilitates corruption. By screening not only the decisions but the decision-making progress from outside scrutiny, secrecy greatly reduces the incentive for decision-makers to make decisions that could be justified to outside scrutinisers. Given the well-known general tendency of humans to respond to selfish incentives, the result is unsurprising: greatly increased toleration of waste, delay and other inefficiencies, up to and including outright corruption in the narrow sense, when these inefficiencies make the lives of decision-makers or those they favour easier, or increase their status (e.g. by increasing their budget)4.

This incentive to corruption is progressive and corrosive, gradually but severely impairing general organisational effectiveness in ways that will obviously impair the effectiveness of the secret project. If the same organisation performs other secret projects in the future, the corrosion will be passed to these successor projects in the form of normalised deviance and generalised institutional decay. Since the corrupted institutions are the very ones responsible for identifying this corruption, and are screened from most or all external accountability, this problem can be very difficult to reverse.

Hence, says Kantrowitz, states that succumb to the temptations of secret technological development may reap some initial gains, but will gradually see these gains eaten away by impaired scientific/technological exchange and accumulating corruption until they are on net far less effective than if they’d stayed open the whole time. The implication of this seems to be that the US and its allies should be tend much more towards openness and less towards secrecy, at least in the technological domain in peacetime6.

Secrecy as a short-term weapon

Finally, Kantrowitz makes the interesting argument that secrecy can be a highly effective short-term weapon, even if it isn’t a viable long-term strategy.

When a normally-open society rapidly increases secrecy as a result of some emergency pressure (typically war) they initially retain the strong epistemic institutions and norms fostered by a culture of openness, and can thus continue to function effectively while reaping the adversarial advantages provided by secrecy. In addition, the pressures of the emergency can provide an initial incentive for good behaviour: “the behavior norms of the group recruited may not tolerate the abuse of secrecy for personal advancement or interagency rivalry.”

As such, groups that previously functioned well in the open can continue to function well (or even better) in secret, at least for some short time. If the emergency persists for a long time, however, or if the secret institutions persist past the emergency that created them, the corroding effects of secrecy – on efficacy and corruption – will begin to take root and grow, eventually and increasingly compromising the functionality of the organisation.

Secrecy may therefore be good tactics, but bad strategy. If true, this would explain how some organisations (most notably the Manhatten Project) produce such impressive achievements while remaining highly secretive, while also explaining why these are exceptions to the general rule.

Speculating about this myself, this seems like an ominous possibility: the gains from secrecy are clearly legible and acquired rapidly, while the costs accrue gradually and in a way difficult for an internal actor to spot. The initial successes justify the continuation of secrecy past the period where it provided the biggest gains, after which the accruing costs of declining institutional health make it increasingly difficult to undo. Those initial successes, if later made public, also serve to provide the organisation with a good reputation and public support, while the organisations declining performance in current events are kept secret. As a result, the organisation’s secrecy could retain both public and private support well past the time at which it begins to be a net impediment to efficacy7.

If this argument is true, it suggests that secrecy should be kept as a rare, short-term weapon in the policy toolbox. Rather than an indispensible tool of state policy, secrecy might then be regarded analogously to a powerful but addictive stimulant: to be used sparingly in emergencies and otherwise avoided as much as possible.

Final thoughts

The Weapon of Openness presents an important-seeming point in a convincing-seeming way. Its arguments jibe with my general understanding of human nature, incentives, and economics. If true, they seem to present an important counterpoint to concerns about info hazards and information security. At the same time, the piece is an essay, not a paper, and goes to relatively little effort to make itself convincing beyond laying out its central vision: Kantrowitz provides few concrete examples and cites even fewer sources. I am, in general, highly suspicious of compelling-seeming arguments presented without evidentiary accompaniment, and I think I should be even more so when those arguments are in support of my own (pro-academic, pro-openness) leanings. So I remain somewhat uncertain as to whether the key thesis of the article is true.

(One point against that thesis that immediately comes to mind is that a great deal of successful technological development in an open society is in fact conducted in secret. Monetised open-source software aside, private companies don’t seem to be in the habit of publicly sharing their product before or during product development. A fuller account of the weapon of openness would need to account for why private companies don’t fail in the way secret government projects are alleged to8.)

If the arguments given in the Weapon of Openness are true, how should those of us primarily concerned with value of the long-term future respond? Long-termists are often sceptical of the value of generalised scientific and technological progress, and in favour of slower, more judicious, differential technological development. The Weapon of Openness suggests this may be a much more difficult needle to thread than it initially seems. We may be sanguine about the slower pace of technological development9, but the corrosive effects of secrecy on norms and institutions would seem to bode poorly for the long-term preservation of good values required for the future to go well.

Insofar as this corrosion is inevitable, we may simply need to accept serious information hazards as part of our narrow path towards a flourishing future, mitigating them as best we can without resorting to secrecy. Insofar as it is not, exploring new ways10 to be secretive about certain things while preserving good institutions and norms might be a very important part of getting us to a good future.

  1. It was, for example, cited in Bostrom’s original information-hazards paper in discussion of reasons one might take a robust anti-secrecy stance. 

  2. Though uncertainty about your power can also be very harmful, if your adversaries conclude you are less powerful than you really are. 

  3. Impediments to the elimination of errors will determine the pace of progress in science as they do in many other matters. It is important here to distinguish between two types of error which I will call ordinary and cherished errors. Ordinary errors can be corrected without embarrassment to powerful people. The elimination of errors which are cherished by powerful people for prestige, political, or financial reasons is an adversary process. In open science this adversary process is conducted in open meetings or in scientific journals. In a secret project it almost inevitably becomes a political battle and the outcome depends on political strength, although the rhetoric will usually employ much scientific jargon.

  4. The other side of the coin is the weakness which secrecy fosters as an instrument of corruption. This is well illustrated in Reagan’s 1982 Executive Order #12356 on National Security (alarmingly tightening secrecy) which states {Sec. 1.6(a)}:

    “In no case shall information be classified in order to conceal violations of law, inefficiency, or administrative error; to prevent embarrassment to a person, organization or agency; to restrain competition; or to prevent or delay the release of information that does not require protection in the interest of national security.”

    This section orders criminals not to conceal their crimes and the inefficient not to conceal their inefficiency. But beyond that it provides an abbreviated guide to the crucial roles of secrecy in the processes whereby power corrupts and absolute power corrupts absolutely. Corruption by secrecy is an important clue to the strength of openness.

  5. As a third argument, Kantrowitz also claims that greater openness can reduce “divisiveness” and hence increase societal unity, further strengthening open societies relative to closed ones. I didn’t find this as well-explained or convincing as his other points so I haven’t discussed it in the main text here. 

  6. We can learn something about the efficiency of secret vs. open programs in peacetime from the objections raised by Adm. Bobby R. Inman, former director of the National Security Agency, to open programs in cryptography. NSA, which is a very large and very secret agency, claimed that open programs conducted by a handful of matheticians around the world, who had no access to NSA secrets, would reveal to other countries that their codes were insecure and that such research might lead to codes that even NSA could not break. These objections exhibit NSA’s assessment that the best secret efforts, that other countries could mount, would miss techniques which would be revealed by even a small open uncoupled program. If this is true for other countries is it not possible that it also applies to us?

  7. Kantrowitz expresses similar thoughts:

    The general belief that there is strength in secrecy rests partially on its short-term successes. If we had entered WWII with a well-developed secrecy system and the corruption which would have developed with time, I am convinced that the results would have been quite different.

  8. There are various possible answers to this I could imagine being true. The first is that private companies are in fact just as vulnerable to the corrosive effects of secrecy as governments are, and that technological progress is much lower than it would be if companies were more open. Assuming arguendo that this is not the case, there are several factors I could imagine being at play:

    • Competition (i.e. the standard answer). Private companies are engaged in much more ferocious competition over much shorter timescales than states are. This provides much stronger incentives for good behaviour even when a project is secret.
    • Selection. Even if private companies are just as vulnerable to the corrosive effects of secrecy as state agencies, the intense short-term competition private firms are exposed to means that those companies with better epistemics at any given time will outcompete those that do not and gain market share. Hence the market as a whole can continue to produce effective technology projects in secret, even as secrecy continuously corrodes individual actors within the market.
    • Short-termism. It’s plausible to me that, with rare exceptions, secret projects in firms are of much shorter duration than in state agencies. If this is the case, it might allow at least some private companies to continuously exploit the short-term benefits of secrecy while avoiding some or all of the long-term costs.
    • Differences in degrees of secrecy. If a government project is secret, it will tend to remain so even once completed, for national security reasons. Conversely, private companies may be less attached to total, indefinite secrecy, particulary given the pro-openness incentives provided by patents. It might also be easier to bring external experts into secret private projects, through NDAs and the like, than it is to get them clearance to consult on secret state ones.
    I don’t yet know enough economics or business studies to be confident in my guesses here, and hopefully someone who knows more can tell me which of these are plausible and which are wrong. 

  9. How true this is depends on how much importance you place on certain kinds of adversarialism: how important you think it is that particular countries (or, more probably, particular kinds of ideologies) retain their competitive advantage over others. If you believe that the kinds of norms that tend to go with an open society (free, democratic, egalitarian, truth-seeking, etc) are important to the good quality of the long-term future you may be loath to surrender one of those societies’ most important competitive advantages. If you doubt the long-term importance of those norms, or their association with openness, this will presumably bother you less. 

  10. I suspect they really will need to be new ways, and not simply old ways with better people. But I as yet know very little about this, and am open to the possibility that solutions already exists about which I know nothing. 

Also posted on the EA Forum.

[Epistemic status: Quick discussion of a seemingly useful concept from a field I as yet know little about.]

I’ve recently started reading around the biosecurity literature, and one concept that seems to come up fairly frequently is the Web of Prevention (also variously called the Web of Deterrence, the Web of Protection, the Web of Reassurance…1). Basically, this is the idea that the distributed, ever-changing, and dual-use nature of potential biosecurity threats means that we can’t rely on any single strategy (e.g. traditional arms control) to prevent them. Instead, we must rely on a network of different approaches, each somewhat failure-prone, that together can provide robust protection.

For example, the original formulation of the “web of deterrence” identified the key elements of such a web as

comprehensive, verifiable and global chemical and biological arms control; broad export monitoring and controls; effective defensive and protective measures; and a range of determined and effective national and international responses to the acquisition and/or use of chemical and biological weapons2.

This later got expanded into a broader “web of protection” concept that included laboratory biosafety and biosecurity; biosecurity education and codes of conduct; and oversight of the life sciences. I’d probably break up the space of strategies somewhat differently, but I think the basic idea is clear enough.

The key concept here is that, though each component of the Web is a serious part of your security strategy, you don’t expect any one to be fully protective or rely on it too heavily. Rather than a simple radial web, a better metaphor might be a multilayered meshwork of protective layers, each of which catches some potential threats while inevitably letting some slip through. No layer is perfect, but enough layers stacked on top of one another can together prove highly effective at blocking attacks3.

This makes sense. Short of a totally repressive surveillance state, it seems infeasible to eliminate all dangerous technologies, all bad actors, or all opportunities to do harm. But if we make means, motive and opportunity each rare enough, we can prevent their confluence and so prevent catastrophe.

Such is the Web of Prevention. In some ways it’s a very obvious idea: don’t put all your eggs in one basket, don’t get tunnel vision, cover all the biosecurity bases. But there’s a few reasons I think it’s a useful concept to have explicitly in mind.

Firstly, I think the concept of the Web of Prevention is important because multilayer protective strategies like this are often quite illegible. One can easily focus too much on one strand of the web / one layer of the armour, and conclude that it’s far too weak to achieve effective protection. But if that layer is part of a system of layers, each of which catches some decent proportion of potential threats, we may be safer than we’d realise if we only focused on one layer at a time.

Secondly, this idea helps explain why so much important biosecurity work consists of dull, incremental improvements. Moderately improving biosafety or biosecurity at an important institution, or tweaking your biocontainment unit protocols to better handle an emergency, or changing policy to make it easier to test out new therapies during an outbreak…none of these is likely to single-handedly make the difference between safety and catastrophe, but each can contribute to strengthening one layer of the system.

Thirdly, and more speculatively, the presence of a web of interlocking protective strategies might mean we don’t always have to make each layer of protection maximally strong to keep ourselves safe. If you go overboard on surveillance of the life sciences, you’ll alienate researchers and shut down a lot of highly valuable research. If you insist on BSL-4 conditions for any infectious pathogens, you’ll burn a huge amount of resources (and goodwill, and researcher time) for not all that much benefit. And so on. Better to set the strength of each layer at a judicious level4, and rely on the interlocking web of other measures to make up for any shortfall.

Of course, none of this is to say that we’re actually well-prepared and can stop worrying. Not all strands of the web are equally important, and some may have obvious catastrophic flaws. And a web of prevention optimised for preventing traditional bioattacks may not be well-suited to coping with the biosecurity dangers posed by emerging technologies. Perhaps most importantly, a long-termist outlook may substantially change the Web’s ideal composition and strength. But in the end, I do think I expect something like the Web, and not a single ironclad mechanism, to be what protects us.

  1. Rappert, Brian, and Caitriona McLeish, eds. (2007) A web of prevention: biological weapons, life sciences and the governance of research. Link here

  2. Rappert & McLeish, p. 3 

  3. To some extent, this metaphor depends on the layers in the armour being somewhat independent of each other, such that holes in one are unlikely to correspond to holes in another. Even better would be an arrangement such that the gaps in each layer are anticorrelated with those in the next layer. If weaknesses in one layer are correlated with weaknesses in the next, though, there’s a much higher chance of an attack slipping through all of them. I don’t know to what extent this is a useful insight in biosecurity. 

  4. Of course, in many cases the judicious level might be “extremely strong”. We don’t want to be relaxed about state bioweapons programs. And we especially don’t want those responsible for safety at each layer to slack off because the other layers have it covered: whatever level of stringency each layer is set to, it’s important to make sure that level of stringency actually applies. But still, if something isn’t your sole line of defence, you can sometimes afford to weaken it slightly in exchange for other benefits. 

Follows from: Why We Age, Part 1; Evolution is Sampling Error; An addendum on effective population size

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

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

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. 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. 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.

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 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. Higher mortality results in a faster exponential decline in survivorship. 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.

The box plot from part 1 of this series, showing that bat species have much longer maximum lifespans than mice species. All data obtained from the AnAge database.

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). Bird species tend to have longer lifespans than mammal species of similar body weight. 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:

The box plot from part 1 of this series, showing that bat species have much longer maximum lifespans than mice species. All data obtained from the AnAge database. 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. 

Happy New Year! More links abound. As always, these are “new” only in the sense that I read them recently; some of them are actually quite old.

  • More on the Blackmail Paradox: David Henderson and Robin Hanson in favour of legalising blackmail, Tyler Cowen, Scott Sumner and Paul Christiano against. Hanson has written a lot on this; see the linked post for extra links if you want to go digging. Currently I feel the theoretical arguments probably support legalising blackmail, but this feels like one of those Secret-Of-Our-Success-y cases where tradition says blackmail should be illegal and we don’t have a compelling enough case to risk screwing around with it.
  • Given Aumann’s agreement theorem, should you persist in disagreeing with a painted rock? Should you double-crux with one?
  • However, it is unfortunate that for billions of people worldwide, the quadratic formula is also their first (and perhaps only) experience of a rather complicated formula which they must memorize. Countless mnemonic techniques abound, from stories of negative bees considering whether or not to go to a radical party, to songs set to the tune of Pop Goes the Weasel.”
  • I’m pretty confused about flossing and I think you should be too.
  • A classic in observer selection effects from Nick Bostrom: cars in the next lane really do go faster.
  • Rather than steal a load of cool links from another linkpost, here’s the post itself. I can’t vouch for their epistemic standards though.
  • There are at least 4,500 speakers of Kannada in Canada. All of whom are presumably delighted that you’ve brought up how funny that is.
  • Wikipedia has a dedicated talk page for arguing about the spelling of alumin(i)um. I don’t have strong feelings about it1, but it’s undeniably entertaining. See also Wikipedia’s list of lamest edit wars.
  • A university in Serbia is accused of plagiarising a research ethics code from another university. On the one hand, this is obviously pretty funny, but on the other if I’d produced a research ethics code I thought was good I think I’d want as many people as possible to copy it, with or without credit.
  • I’ve seen some bad websites in my time, but this one achieves the dubious feat of being genuinely physically painful to read. I’m not sure why I’m sharing this.
  • British naming habits have changed a lot in the last 30 years.
  • Andrew Gelman points out that the opposite of “black box” is not, in fact, white box.
  • I always vaguely assumed that “never send to know for whom the bell tolls; it tolls for thee” was some sort of memento mori thing, but it turns out I was totally wrong about this, as reading the whole poem makes clear. I might memorise this one. I also never realised before that “for whom the bell tolls” and “no man is an island” are quotes from the same poem, so TIL.

  1. This is a lie, but it’s one I endorse. 

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 \(N_e\)) 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 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. 

Here are some more links I read recently that I thought were cool. No guarantees any of them are actually new in an absolute sense; if it’s relevant, make sure to check the date before using them in an argument or something.

  • The blackmail paradox is my current favourite thing in common law – to the extent that I’m now very open to the possibility that blackmail shouldn’t be illegal, or perhaps even be considered a thing. (I mean, probably that’s a terrible idea, but I’m honestly not really sure why.)
  • This post by Robin Hanson both gives a nice counterargument to the Bostromian Vulnerable World thesis and illustrates what happens what the world would be like if Nick Bostrom were attacked by a swarm of rabid ellipses. And also quotes this bombshell tweet from Anders Sandberg in 2018, which I’m amazed hasn’t seen more play.
  • I really like Winograd schemas, a form of linguistic puzzle that humans find trivial but machines find challenging; in 2016 the best-performing system managed 58% accuracy.
  • I’ve been thinking about information hazards a lot lately; maybe I shouldn’t have told you that. Anyway, for countervailing views, check out Bruce Schneier’s interview with 80,000 Hours and this post on the EA forum.
  • Like first-past-the-post voting, pre-performance competition for public resources is an intuitively appealing idea that turns out to work horrendously badly — in this case, eating up vast amounts of time and money, most of which is wasted. That it also happens to be the way we allocate almost all of our scientific funding might therefore be considered something of a disaster. This Vox piece does a good job laying out the case for one of many much-better alternatives (grant lotteries), though it does kinda pivot away into weak-sauce objections at the end. (h/t Vlad Sitalo for the EconTalk link, which I was struggling to find in the archives.)
  • DNA can hold over 200 petabytes of data per gram. Why not use it for long-term storage?
  • I am a fan of Stephan Guyenet and am pretty strongly convinced by his scepticism of the “woo fats boo carbs” narrative that seems to have taken over in many circles these days. Here he is pointing out that, actually, fat seems to be at least as addictive as sugar. (NB: I think I might have actually got this one from an SSC linkpost.)
  • Harvard is setting up a research/teaching program called “Embedded EthiCS”: because it’s a collaboration between the philosophy and computer science departments GET IT? It’s probably a good thing that this exists, but I’m not sure how I feel about august institutions choosing their naming conventions based on puns.
  • Ada Lovelace’s reputation is somewhat fraught these days, caught between all those people who want to claim her as “the world’s first computer programmer” and splash her name everywhere, and people who think she’s badly overrated. Stephen Wolfram was also confused by this and decided to dig into it; he seems to rate her. I still think her story is more one of tragically wasted potential than actual lasting achievement, and we should maybe find some more women in computer science to name things after, but this and a couple of other things have definitely updated me regarding the depth and originality of her vision, and how great a tragedy her early death really was. (Content note: Stephen Wolfram’s primary fascination is always Stephen Wolfram, so as always he mentions himself more often than you might naïvely think would be necessary, were you not aware of how great Stephen Wolfram is.)
  • Finally, did you know that the Online Etymology Dictionary (one of my favourite websites) has a blog? It’s true! And it’s fascinating and grumpy and great. Highlights include my favourite ever discussion of autoantonyms, discussions of the knotty histories of “fast” and “gun”, and lots of very entertaining ranting about how, no, your favourite word is not a fucking acronym.

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:

Ten dots representing individuals, stacked vertically and coloured to represent their genotype: five red and five blue

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:

Two columns of ten dots, stacked vertically, with lines between the columns representing parentage. Some individuals produce no offspring, some one, and some more than one.

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:

Twenty columns of ten dots, stacked vertically, with lines between the columns representing parentage. The red allele reaches fixation at generation 14.

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:

A plot of the allele frequency distribution of a larger population, reaching fixation at roughly generation 350.

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:

Another twenty-column plot, this time in green and purple. The single initial purple individual produces no offspring, so the purple lineage dies out immediately.

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…

Another twenty-stage green-and-purple plot, this time representing two alleles with only a small difference in fitness. The less-fit purple allele persists until stage 18, then is lost.

…or even fix!

An independent run of the scenario from the previous figure. This time, the slightly-less-fit purple allele reaches fixation at stage 6.

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:

A plot of population size vs probability of fixation for two competing alleles, one of which is 10% fitter than the other. The fitter allele fixes at just over 50% when population size is very small, rising to 100% at population sizes of 100 or larger.

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.


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: A log-log plot of relative mean absolute difference vs sample size, showing a very linear-looking relationship 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: A plot of population size vs probability of fixation for two competing alleles, one of which is 1% fitter than the other. The fitter allele fixes at roughly 50% when population size is very small, rising to about 95% at a population size of 300. The rise in fixation rate is much slower than when the fitness difference was 10%. 

  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. 

Stuff from me

I put up two more pieces on the EA Forum that I didn’t think needed to be on this blog: a question about Bostrom’s “Disneyland without children” and a followup to my previous post about ageing-based welfare measures with some concrete suggestions for future progress in the area.

New stuff

Technically, much of this stuff is not actually new, but I only came across it recently and it’s my blog.

  • Lately I’ve been enjoying Jason Crawford’s blog Roots of Progress: “an intellectual project, which may take many years, to understand the nature and cause of human progress.” Highlights include his discussion of the fundamental artificiality of “natural resources” and his public boggling at the wonders of iron and cement.
  • The classic story of how blind auditions reduced discrimination against women in orchestras may not be real.
  • The Dutch have a special symbol called the flourish of approval.
  • A mole of moles is a lot of moles.
  • The UK is experimenting with new ways of paying for antibiotics.
  • Part of what makes us happy is the satisfaction of actually (or likely) helping people. Consequentialism can ask us to give up even this.”
  • Here’s an actually-quite-old post about Really Big Numbers. I still don’t really comprehend Graham’s Number, but at least I’m starting to get an inkling of how unimaginably vast it is.

Golden oldies

Here’s some older stuff that I read a while ago, but has been on my mind for one reason or another.