Cue-Based Hedging

Usually a contrast is made between bet hedging and adaptive plasticity. What makes adaptive plasticity different from hedging is that organisms respond adaptively to environmental cues. But what if organisms respond to environmental cues in ways that do not increase mean fitness, but do increase geometric mean fitness? In other words, what happens if bet hedging occurs in response to uninformative cues? This is explored in this paper accepted last month in the journal Evolution.

The study consists constructs and makes use of an artificial system in which organisms use an cue to generate a phenotype that enhances fitness in one environment, but decreases it in another. Critically the provision of the cue is orthogonal to the environment and is therefore not predictive of it. This trade-off is critical for the evolution of diversified bet hedging.

The Set-Up

The study uses Saccharomyces cerevisiae and makes use of the gene URA3 which codes for orotidine 5’- phosphate decarboxylase (Ura3p). Ura3p synthesises uracil from precursors, but if the pro-toxin 5-fluororotic acid (5-FOA) is present in the environment, it will convert this to the toxin 5-fluorouracil (5FU) killing the cell. The trade-off was generated via two phenotypes/genotypes:

  • P1: URA3+ yeast
  • P2: URA3– yeast

And these were grown on two environments:

  • E1: SC-ura: a media that lacks uracil
  • E2: SC+5-FOA: a media containing the pro-toxin

A strong trade-off was demonstrated via a concave fitness function with P1 strongly favoured on E1 and P2, on E2. In order to create bet hedging based on a cue, the authors chose estradiol. Estradiol doesn’t regulate any genes in S. cerevisiae, but they constructed a new phenotype/genotype where it does:

  • plastic yeast: URA3 under the control of the transcription factor (TF) Z4EV

When estradiol is added, the TF, usually excluded from the nucleus, is able to enter and bring about expression of URA3. Spotting estradiol at the centre of E1 plates resulted in plastic yeast having high fitness at the centre, while spotting onto E2 plates gave the highest fitness at the periphery.

Main Experiment

The authors constructed an varying environment by growing the different yeasts  on alternating E1 and E2 plates spotted with estradiol. Between plates, yeast cells were collected using glass beads rolled on the plate (often used as a neat method for spreading plates). GFP-labelled (green) P1 or P2 was competed against mCherry-labelled (red) plastic yeast. (Label swaps were also used in the study).

The authors found that the plastic yeast could rapidly outcompete the P1 and P2 yeast in this regime, presumably owing to the near zero fitness of P1 on E2 (and P2 and E1). Having zero in a series brings the geometric mean of the series to zero. To show the other requirement for bet hedging: that there is a fitness cost, they looked at the selection coefficients of plastic versus the other strains in their best environments. Against P2 on E2 plastic yeast were significantly less fit. Against P1 on E1, they were also less fit although this didn’t reach significance.

 Tweaking Hedging

When it evolves, diversified bet hedging should have phenotype frequencies correlated with the probability of (or proportion of time spent in) each environment and the fitness of the phenotypes in each. The authors manipulated the response to estradiol with a third phenotype/genotype:

  • plastic ∆/∆ yeast: deleted ABC transporters PDR5 and SNQ2

These transporters remove estradiol from the cell and their deletion is expected to increase intracellular estradiol concentration. As a result of this change, URA3 expression at a given [estradiol] should be dialled up in plastic ∆/∆ yeast. As expected, these yeast occupied more space on E1 plates, and less on E2 plates, than the original plastic yeast.

Ceteris paribus

This is an interesting study although clearly it is limited by being an artificial system. The authors refer to it as “constructive proof”of cue-based hedging and its tune-ability. In particular they consider the implications of environmentally cued bet hedging for the detection of bet hedging. Detecting hedging is already a difficult task because a fitness trade-off between phenotypes in different environments and a matching frequency of environments must be demonstrated. With cue-based hedging we have the added difficulty that the usual experimental practice is to hold everything else constant (e.g., in a chemostat) except the variable of interest. Bet hedging may disappear in this case.

The Origins of Sensing

As the authors indicate, it is usually assumed that molecular stochasticity within the cell is exploited to generate bet hedging. Sensing the environment is a costly, and therefore disfavoured, addition. However, estimating costs is difficult and once sensing emerges it might be co-opted to generate diversity if doing so has small or no costs. Sensing can be quite rudimentary – depending on protein conformation alone for example.

If you can “wire” sensing to responding even with uninformative cues this has implications for the evolution of sensing and responding. Adaptive phenotypic plasticity is usually considered as the context for this, but it may not be.

Posted in bet hedging, experimental evolution | Leave a comment

Adaptive Tracking and Rare Alleles

  1. In my lab we are experimenting with evolution at high mutation rates and examining populations as they respond to alternating environments.
  2. I/we need to read more and more deeply.
  3. This blog exists and can be a commitment device.

Today I will start with the task of providing summaries of relevant literature by discussing Dean et al. (2017) Fluctuating Selection in the Moran (published one month ago in Genomics).

When thinking about changing environments a lot of the evolutionary fun would appear to be related to various flavours of bet hedging. The less exciting possibility is adaptive tracking in which populations respond to changing contingencies with changing allele frequencies. The conditions under which balancing selection maintains diversity are thought to be quite restricted, essentially frequency-dependent selection in haploids + heterozygote advantage in diploids. Without frequency-dependent selection, haploid organisms bearing alleles with lower fitness would be driven to extinction. (Recall that bet hedging is the interesting corner in which an allele with a lower arithmetic mean fitness, but a higher geometric mean fitness, across environments, is favoured.) This paper shows that frequency dependence can occur in a dynamic system in a manner that permits the persistence of alleles over time and this results in quite a radical conclusion about how polymorphism is affected by fluctuating selection.

The authors begin by making the interesting point that when populations are growing towards a carrying capacity this implicitly favours rare alleles. In a simple two allele model, when the fitter allele is rare, the population takes longer to reach the carrying capacity so a large time slice is available for the rare allele to increase in frequency. If the fitter allele is more common (and the rare allele is less fit) the population will grow faster and the time slice, during which the rare allele reduces in frequency, is shorter. This can increase the residence time of rare alleles and favour their persistence if the selective contingencies reverse when carrying capacity is reached. The authors show that this is empirically supported by serial transfer experiments. The key point here is that there is a kind of frequency dependence, but it is time not growth rate that varies. (This point is subtle and reminds me of the distinction between Allen Orr’s argument about risk aversion (owing the inherent payoff asymmetries in relative fitness) versus the specific adaptations implied by conservative bet hedging.)

The rest of the paper takes this into more dynamic territory. Working with continuous, time-overlapping models they look at what happens in a chemostat in which organisms remain at a starving quasi-steady state. The analogous point applies. The growth rates of organisms slows to match the wash out rate as they become dominant in a population. Again it is not the intrinsic growth rate (unconstrained by resources) associated with an allele that varies with its frequency, but there is a frequency dependence in their realised growth. Doublings increase for all genotypes when fit alleles are rare (helping them on the way up), and decrease when less fit alleles are rare (slowing down their exit from the population). And so far we haven’t changed the environment.

Now the authors allow changes in the environment during which intrinsic (resource-independent) growth rates can vary more or less and may correlate (between alleles) more or less. Unsurprisingly, tightly correlated and invariant rates result in loss of polymorphism as alleles that are less fit overall are driven to extinction. However if you dial up the frequency of environmental shifts you can rescue those rare alleles. Using a mixture of simulations and analytical results, they show, among other things, that overlapping fitness distributions allow an allele with lower fitness overall (averaging across environments) to persist.

The Moran of the title comes in when they look at models with finite population size, something expected to disfavour rare alleles as they are stochastically lost. Similarly to the carrying capacity and steady-state models above, birth and death events are paired. They begin with strict symmetrical fitness between alleles in two types of environment. In this model the persistence times of rare alleles can be hugely increased by modest frequencies of switching. This is actually favoured by Goldilocks level of selection against the (temporarily) less fit allele. Too high and it gets nixed in one period, too low and drift will kick it out. With varying durations between switching events, the presence of a single long period will drive out polymorphism. Similar conclusions also apply to the equilibrium condition (eventual loss/fixation).

Of course real evolution includes mutation adding new alleles into the population. So how does fluctuating selection affect our expectations here? It drives up polymorphism, but, intriguingly, a high mutation rate is an opposing force owing to clonal interference between alleles. Strong selection also promotes polymorphism – again perhaps surprisingly, and perhaps because it enhances the time slice asymmetries discussed above and allows recent deleterious mutations to stick around for a bit.

Finally the authors allow neutral alleles and here the conclusions become very interesting. Fluctuating selection, because it introduces frequent bottlenecks, has the interesting property of purging neutral variation. Given the ubiquity of seasonal and weather-based fluctuations this certainly changes the expectations for wild populations!

This is an interesting paper and has me thinking about (dynamic) equilibria and the striking complexity introduced when you add even the most basic bits of ecology into the evolutionary mix. Now let’s see if we can add an evolving distribution of fitness effects into their models!

Posted in evolutionary theory | Leave a comment

How not to be a sucker

I’ve just finished reading Nassim Nicholas Taleb’s (NNT’s) recent book “Antifragile” (UK link, US link). A brief and organised summary of some of the key ideas is here on the Edge website. The book is disorganised and chock-a-block with interesting ideas and judgemental corollaries.

NNT describes a triad of properties. First: fragility. A fragile object is one that is liable to break. He defines this according to a second order property mapping its response to variability. This derivative function is called convexity. An object is fragile if application of major force damages it more than a series of minor shocks. This is true even when the cumulative force applied through minor shocks equals that from the major shock. So if we relate variation in applied forces to harm we have a convex function. The kind of fragility in which harm is a linear function of force is probably quite rare NNT asserts (and this seems correct given the degrees of freedom in any real system).

Second: robustness. Here you expect that increases in force do not cause increases in harm: one is simply not a function of the other. Third: anti-fragility, and this term is NNT’s. Here there is “positive convexity” as harm decreases with increasing force. An anti-fragile object benefits from mishandling. If you are graphically minded see here or buy his whole book which has the interesting innovation of a graphical tour in one of its appendices.

NNT points out that in many situations convexity will be both positive and negative across different ranges. An organism, for example, may be anti-fragile to physical exertion up to some point and fragile beyond this. What exercises NNT is the fact that people do not attend to convexity. This is because he sees the same logic in epistemology. Errors in models are not distributed linearly. For example, a naively estimated low probability is more likely to be under- than over-estimated (maybe a Bayesian can tell me something here?).

The epistemic point generalises. NNT emphasises the opacity of the tails of distributions and notes that in fragile/anti-fragile systems the consequences of this inevitable ignorance are inauspicious/propitious. It therefore stands to reason that statistically acquired knowledge is inferior to hedging. It makes more sense to reshape your responses to maximize potential benefits and minimize potential losses – or to seek optionality. The action should be in modifying the second order responses, not predicting the first order behaviour from partial information. This point is well made and even leads to some sassy advice (summarized here – recommend speed read) which might be well attended to by researchers (a species hated by NNT – especially when in receipt of public funds). It also constitutes a fascinating defence of sceptical empiricism against rationalism.

My response to an empiricism v. rationalism conflict is to firmly sit on the fence – which is what I think we should do as scientists and what we do in fact do as a moderately intelligent species. The problem with NNT’s argument is that it argues for the unknowability of a primary (and fat-tailed) distribution, while presuming that the second order function (e.g., harm caused) can be estimated more easily (this is most clearly illustrated in the Edge summary). This is silly because scepticism cuts deeper than this – you can never be sure that you have hedged correctly. For example, perhaps you take out insurance on your household, but have you factored in the risks of political revolution? Science achieves its success partly because it tempers rationalism with empiricism and empiricism with theory. NNT believes in “aggressive tinkering” and “convex bricolage”, as do I (sounds so cool), but seems to believe that this activity is somehow sui generis. If he was listening to episode one of Lisa Jardine’s latest history of science radio programme, I suspect he’d say that Robert Hooke was a genius and Isaac Newton an imbecile. The trick is obviously to be sceptical about theory, but not dismissive.

I am also unhappy with many of NNT’s statements about biology. Partly this is because he seems to think researchers are monomaniacal theorizers (something I object to as an experimental evolutionist). On first reading I became irritated as several statements appeared to invoke group selection. I will not adumbrate this debate because it is both subtle and tedious, but also because I think his conceptual error is more circuitous.

NNT invokes the anti-fragility of nature supposedly imparted by its long exposure to variability, but is subtle enough to note that fragility manifests itself at extreme values. He supposes the (undirected) solution to this is hierarchical structures in which fragile units (e.g., organisms) impart anti-fragility up the scale. While it may have some validity, I suspect this is a new sort of scala naturae. Unreferenced are the limits of natural selection attributable to population size or to the power of individual-level selection (both of which can lead to decreases in population mean fitness, e.g., under mutation load or Fisherian sex ratio selection). Also absent is the point that soft selection is common and can favour individual bet hedging (or even, God forbid, cognition). Simply put nature is more messy than this. I like fractals, but trees also have galls and hacked-off branches.

In summary, I think NNT has done us a great service by warning us not to be suckers to “knowledge”. Many of his points about tail opacity and illegitimate inference might apply to certain areas of genomics as much as to the world of economics (which is famously fond of formalisms). I believe his arguments have greatest heft whenever complex systems are modelled in complex ways (although I have yet to figure out how or if they apply to agent-based modelling or Bayesian inference). His iconoclasm is also helpful – sometimes you should trash the textbook, but I recommend first reading it. His health advice is good in parts (e.g., don’t smoke), but potty in others (randomly do tonnes of exercise). The danger, a new kind of sucker’s game (!), is to forgo the benefits of domain-specific knowledge in favour of generalised scepticism and heuristics based on dodgy general intuitions.

Posted in Uncategorized | Leave a comment

Repulsive or attractive?

PNAS Early Edition has a paper that phage enthusiasts should read. I was alerted to it by this Economist piece. Symbioses are widespread and the focal paper adds animal mucosa to the list of ecosystems where they play a critical role. The paper convinces me that lytic phage are actively recruited by metazoan cells to reduce the colonization of mucous layers by pathogenic bacteria. All the relevant steps in reasoning are there: the relative enrichment of bacteriophage in mucous layers (relative to the ~10:1 ratio found in adjacent microenvironments or in the marine environment), the mechanism of attachment (immunoglobulin-like protein domains expressed on the capsid of phage T4 – their model – attach to mucin glycoproteins) and the lysis-mediated reduction in bacterial numbers. The authors used a number of clever methods in their assays including a modified phage overlay assay to quantify reductions in colonization in vitro, and an amber mutant phage to confirm that lysis conferred the protective effect.

The paper ends by considering the role that lysogenic phage may play in protecting commensal bacteria. This reminds me of an argument made here and elsewhere that resistance to potential parasites and tolerance of them (by for example repairing the damage they do) have divergent ecological and evolutionary consequences that can feedback on the expected prevalence of these mechanisms. Loosely speaking, the argument is that resistance to invaders (by definition) imposes costs on them. Selection occurs for immune evasion (virulence) in the invader population, in turn selecting for a variant host resistance allele in an arms race. Resistance alleles are therefore not subject to sustained positive selection in the host, but instead show transient or frequency-dependent selection dynamics. Tolerance, on the other hand, permits populations of the invader to persist and, in its purest form, imposes no costs on them. Therefore host tolerance alleles experience sustained positive selection and an elevated geometric mean fitness (which seems to be what selection “likes”).

The focal paper plays into this argument in two ways that I can see. First, the presence of an adaptive immune system or an adaptive component of the innate response mediated by phage may bolster the efficacy of what might be termed “meta-resistance” alleles in the host. In this case, meta-resistance alleles are those that modify/form glycoproteins to support phage attachment. Second, and on the side of tolerance, it is possible that lysogenic phage could be recruited to modify the virulence of the pool of invading micro-organisms either indirectly, through ecological interactions, or directly, through modification of bacterial genomes. Of course, the distinction between resistance and tolerance is a false dichotomy, but I find it useful to keep in mind. Since vertical transmission is a relevant factor for the explanatory utility of the Red Queen, it would also be interesting to know whether phage communities themselves are stable over longer periods and between animal generations.

After reading and enjoying Forest Rohwer’s very accessible book on coral reef ecology and noting his authorship in the focal paper, I anticipate a future book of mucosal musings…

Posted in ecology, evolutionary theory | Leave a comment


Does it make sense to separate ecology and evolution? Conceptually yes, but practically no. This week let me draw your attention to this recent paper in Ecology Letters which has been covered by the BBC. You have to love ANOVAs (and related methods) to make friends with this paper – but so you should because understanding variance and covariance is at the heart of understanding evolution. For an experimental evolutionist this paper also makes for a refreshing read because it uses soil mites as a model system.

By growing lineages of mites in conditions of limited resource and under different harvesting regimes, the authors conclude that life history parameters that influence ecology undergo significant responses to selection during the course of the experiment. In particular limited food leads to prolonged development which, in turn, leads to greater fecundity and evolutionary rescue (R0, the basic reproductive ratio, goes from < 1 to > 1). Harvesting modulates this by shortening development (when juveniles are harvested) or lengthening it (when adults are harvested), but with a smaller effect size than the main effect attributed to diminished food availability. These manipulations affect ecological responses to fluctuations in food supply throughout the experiment (with adult harvesting potentiating shifts in population size).

This obviously has practical implications for how we understand conservation, but I’d like also to alert you to the conceptual distinction between ecology and evolution or what Andrew McColl of Nottingham University, UK calls the ecological causes of evolution. The key point here is that ecology plays a mediating role between phenotype and fitness. It does this for all traits because the fitness of (to use one of McColl’s examples) a finch’s beak depends on the availability of seeds of difference hardnesses, which in turn depends on abiotic factors such as the climate. (McColl’s point is that we ought to pay attention to this more often and more rigorously as have the Galapagos finch folk).

Ecological dependence gets serious with phenomena such as frequency- or density-dependent selection for which a model must account for fitness relative to other members of the population. The old idea of soft selection (introduced to deal with the problem of mutation load) captures this concept well I think (contrasted with hard selection on viability), but so too does the idea of relative fitness (which differs from mutation load in considering fitness relative to the mean fitness rather than to some ideal). I recently re-read this short paper by Allen Orr describing how simply moving from absolute to relative fitness influences our expectations about how selection behaves. I’ll write more on bet hedging soon, but the conclusion is that, when the fitness of others matters, selection becomes conservative and acts to decrease the variance in (absolute) fitness as well as to increase the mean.

So a lot of what we think of as evolutionary theory entails ecology, but being precise about the distinction (and about concepts like fitness and selection) is necessary to avoid confusion.

Posted in ecology, evolutionary theory, experimental evolution | Leave a comment


It’s not as if TED needs any additional advertising, but this seems relevant to my recent posts. Nor am I casting around for reasons to be sceptical – it seems self-evidently cool to me – team-wise and in terms of the goal.

PostScript: This recent perspective piece in PLoS Biology explores the future uses of synthetic biology in conservation.

Video | Posted on by | Leave a comment

Biology Letters’ February Experimental Evolution Special

Link | Posted on by | Tagged | Leave a comment