Posted by: Jeremy Fox | May 24, 2011

Ignorance is bliss (sometimes)

Ecologists (and lots of other people) often say that the world, or some feature of it, is ‘random’ or ‘stochastic’. But what exactly does that mean?

One view is that randomness is real; some features of the world are inherently probabilistic. Quantum mechanics is the paradigmatic example here, but that doesn’t mean there aren’t others. An alternative view is that calling something ‘random’ is shorthand for our ignorance. If we knew enough about the precise shape of a coin, the force with which it was flipped, the movement of the surrounding air, etc., we could accurately predict the outcome of any particular coin flip, which is deterministic. But we don’t have that information, so we pretend that coin flipping is a random process and make probabilistic statements about the expected aggregate outcome of many flips.

Does the distinction between these two views matter for ecologists? It’s tempting to say no. In practice there’s no possibility we’ll ever have enough information to predict the roll of a die, so we lose nothing by treating it as random. No less an authority than Sewell Wright was of this view. But I’m going to suggest that’s incorrect; I think ecologists do need to decide whether they think randomness is real, or merely determinism disguised by our ignorance. And I’ll further suggest that the appropriate choice can vary from case to case and is only sometimes dictated by empirical facts.

If apparent randomness is just ignorance of relevant information, then when we learn new information the apparent randomness of events should decline. This happens whenever you add an additional predictor variable to a statistical model, increasing explained (deterministic) variation and reducing unexplained (random) variation. A personal favorite example of mine is recent work on the ‘decision’ by a bacteriophage as to whether to lyse its bacterial host. This decision had been regarded as a paradigmatic example of a probabilistic biological process. But it turns out that the decision is actually quite (although perhaps not entirely) deterministic, and depends on the size of the host cell. Cell size varies, and phage decision making looks random if you don’t account for that variation. This is a specific example of a general principle: if some process (like the lysis decision) is not random with respect to some property or outcome of interest (like cell size), then it’s simply false to treat that process as random.

But is it always a good idea to try to minimize apparent randomness by incorporating all relevant information? In ecology, Jim Clark has argued as much (if I understand him correctly). But I’m not so sure I agree. If calling something random is merely to statistically summarize the net effects of various unknown deterministic processes, well, summaries are really useful. Think for instance of genetic drift, and its ecological equivalent, demographic stochasticity. Genetic drift and demographic stochasticity arise from random variation in the birth and death rates of individuals that is independent of their phenotypes and other properties, and so would occur even if all individuals were otherwise identical. I’m happy to stipulate that, if we knew enough, much or even all of this apparent randomness could be explained away. But why would we want to explain it away? What would we gain? I’d argue that we’d actually lose a lot. We’d be replacing the generally-applicable concepts of genetic drift and demographic stochasticity (and the associated well-developed, highly elegant, and well-tested mathematical theory) with a stamp collection of inherently case-specific, and hugely complex, deterministic causal stories. The complex deterministic causal factors generating apparently-random variation in the birth and death rates of, say, different E. coli genotypes in a laboratory culture have nothing to do with the complex deterministic causal factors generating apparently-random variation in the birth and death rates of, say, introduced rats on a marine island. The important thing is that deterministic causal factors in both cases have apparently-stochastic consequences described by models of genetic drift and demographic stochasticity. Laplace’s demon, which has perfect information about the position and movement of every particle of matter in a deterministic universe, would see no randomness—thereby making it completely ignorant about one of the most important and best-confirmed concepts in all of ecology and evolution (see here for more on this).

And while Laplace’s demon is a mere philosopher’s dream, even trying to emulate it has its pitfalls. In Do lemmings commit suicide? Beautiful hypotheses and ugly facts, population ecologist Dennis Chitty describes his career-long unsuccessful struggle to identify the causes of population cycles in small mammals. His lack of success is almost certainly attributable, at least in part, to his search for a deterministic sequence of causal events that always drives population cycles. Observations that a particular causal factor was apparently weak or absent in some cases (or even absent at one particular time for one particular population of one particular species) repeatedly caused him to modify or abandon his causal hypotheses. In contrast, modern stochastic dynamics has been quite useful for inferring the causes of population fluctuations (e.g., Henson et al. 2002 Oikos). See here for further discussion of the pitfalls of insisting on an overly-detailed ‘low-level’ description of one’s study system.

Bottom line: if randomness is ignorance, sometimes ignorance is bliss.

p.s. The distinction between real and merely apparent randomness crops up outside of science too, for instance in professional sports. Traditionally, events in sports—such as who wins and who loses—often are explained by appeal to specific details associated (or putatively associated) with the event. Perhaps the winning team exhibited a stronger ‘will to win’, or is ‘on a hot streak right now’, while the losers were ‘tired’ and ‘wilted under pressure’. For many traditionalists, much of the appeal of sports is in these explanatory stories. But such claims invariably are post hoc and so impossible to test—had the outcome been different, we’d have told a different story to explain it. Recently, statistically-minded observers (especially of baseball) have begun insisting that many events in sports really are random, or at least are best thought of as random because we are ignorant of their causes (although we may think we’re not). As another example, religious beliefs sometimes have been interpreted as a way for believers to see deterministic causality, order, and a purposeful plan in a universe that would otherwise appear random, uncontrollable, and purposeless.

UPDATE: xkcd hits the nail on the head, as usual.

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Responses

  1. Wonderful post, I agree that we don’t think about what it means to be stochastic often enough. I think there’s another way randomness enters that never goes away regardless of how much information we have. Often we consider things that only exist as statistical quantities, so they are random by definition. I think this happens whenever we consider different scales, (as we always do). A physical example would be temperature — it’s a real, meaningful, and measurable quantity, but it’s also a random quantity, the average kinetic energy of the molecules. Since there are usually lots of molecules, it just doesn’t vary that much. If we had very few molecules, we’d have a better description of this average as a stochastic quantity, coming from a distribution.

    I think we deal with these quantities all the time in ecology, such as any time we make a statement about “the species” or “the population.” For instance, we may wish to describe the growth rate of some juvenile fish. That’s a statistical quantity, like temperature, that emerges over having lots of ways to grow and lots of fish. It varies, and by representing it with the appropriate stochastic model, we get a better description of reality. I think most things that we measure and discuss don’t exist except in this sense; they are random because we define them that way.

  2. […] public [4] Wow, once again Jeremy really writes about some great stuff on Oikos blog. Just a read a piece after my own heart on the meaning of “random” in ecology. I think I need to cut back, I might be addicted. […]

  3. I used to work on phage lambda, and I think the randomness posited by the paper you cite is a straw man created by the authors to make their results seem more important. I worked with Allan Campbell, a lambda pioneer, and the events that led to lysis or lysogeny were always referred to as a ‘decision’ made by the phage. The phage was seen as assessing the physiological state of the cell by its effect on phage proteins and regulatory processes. This sensitivity of the lysis-lysogeny decision was viewed as an adaptation to optimize the phage’s choice of reproductive strategy.

    So maybe this is an example of a process that was originally seen as deterministic but that recently was presented as random?

    • Hi Rosie,

      Thank you for your insight. I don’t claim to be an expert on phage lambda and I’ll admit I’m only up on the literature from the last decade or so. I’m intrigued that the phage decision was once seen as very deterministic, came to be seen as somewhat random, and now is coming to be seen as quite deterministic again.

      Having said that (and now I’m going to drift off on to another topic), it is worth noting that even a random decision can be adaptive–think bet hedging. For instance, phage that have made the decision to go lysogenic subsequently will sometimes ‘spontaneously’ change their minds and decide to lyse the host cell in the absence of any apparent cue to do so. It’s my understanding that such spontaneous lysis is conventionally viewed as a mistake, and selection should minimize the rate at which it occurs (and indeed it does occur only rarely). Of course, one alternative possibility is that spontaneous lysis is a deterministic response to some cue of which we’re not aware. A second possibility is that it’s actually adaptive, for bet hedging reasons (e.g., because host cells face unpredictable mortality risks which aren’t preceded by any warning signals the phage can detect). One way to test the second possibility would be to try to select for a higher spontaneous lysis rate by imposing a higher rate of unpredictable, no-warning mortality on hosts (e.g., by chloroforming).

      This might be a crazy idea, as I say I’m not a phage expert. It’s just something that occurred to me a while back when I got interested in the evolution of bet hedging and was casting about for an experimental model system that would allow you to select for bet hedging. It was in the course of doing some background research on that idea that I got into the phage literature, and encountered the research referred to in the post.

  4. […] won in the replicates in which it initially had an advantage. The outcome was stochastic, or maybe effectively stochastic because highly sensitive to tiny differences in initial […]

  5. […] of the surprise hopefully can be identified. If your system is hugely complex and ‘noisy’ (which is often shorthand for ‘hugely complex’), it can be hard to tell if you’ve been surprised or not, because of the many factors that can […]

  6. […] Why ignorance is bliss (sometimes) […]

  7. […] Ignorance is bliss (sometimes) […]

  8. […] once again Jeremy really writes about some great stuff on Oikos blog. Just a read a piece after my own heart on the meaning of "random" in ecology. I think I need to cut back, I might be […]

  9. […] Ignorance is bliss by Jeremy Fox. On deterministic versus stochastic model formulation. Fusing theory and data a plea for help from Dan Bolnick by Dan Bolnick. Most of us agree that fusing theory and data is a worthy objective. How exactly to go about doing this is a topic that I wish received a bit more attention. 20 different stability concepts by Jeremy Fox. A compendium of ways to describe the properties of fixed points. On the use and care of mathematical models by Simon Levin (1975) as quoted by Jeremy Fox. […]

  10. […] statistically/phenomenologically. For some purposes that will be totally fine, even essential (see this old post for discussion), but for other purposes it’s tantamount to just throwing up your hands and […]

  11. […] statistical analysis. To give credit where credit is due, a recent post by Amy Hurford and an older one by Jeremy Fox inspired me to dive deeper into this […]


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