Although they are called solitary because they don’t live in huge colonies with armies of sterile workers, these wasps are in another sense not solitary. They dig their burrows close to where they themselves hatched, so ‘traditional’ nesting areas naturally grow up. This generates a kind of village atmosphere in a particular patch of ground, with dozens of female wasps going about their separate business, largely oblivious of each other but occasionally clashing. This closeness enabled Jane to sit in one place with her notebook and watch all the wasps in the area, each of whom she had marked using a system of colour-coded paint spots. She knew every wasp by its code name (Red Red Yellow, Blue Green Red etc.) and she mapped where each wasp’s burrow was, then her next burrow and her next and so on. Among much else, Jane had observed that if a female comes across a burrow that another wasp has dug, she may save herself the trouble of digging her own and use the already existing burrow. And thereby hangs the tale we went on to tell.
Others, by the way, have told different tales. Charles Darwin was appalled by the cruelty of stinging a prey to paralyse it, keeping the meat fresh for larval consumption, rather than killing it outright. If the prey were killed it would decay and wouldn’t be so good for the larva to eat. We have no way of knowing whether the prey feels pain as its tissues are slowly devoured from within while it is paralysed and unable to move a muscle to prevent it. I devoutly hope not, but the possibility gave Darwin the horrors. According to the great French naturalist, Darwin’s contemporary Jean-Henri Fabre, there’s something clinically ruthless about digger wasps’ precise manner of stinging. Fabre said that they carefully aim their sting, targeting one by one the nerve ganglia strung out along the ventral side of the prey – presumably achieving paralysis with an economic minimum of venom.
Philosophers, too, have used Sphex to construct a narrative of their own, stimulated by some classic experiments, again begun by Fabre and repeated by others since. When a hunting wasp returns to her burrow with prey she doesn’t immediately drag it underground. Instead, she parks it near the entrance, then goes into the burrow empty-handed, re-emerges and only then drags the prey down. This has been described as a burrow ‘inspection’, the idea presumably being to check that there are no obstructions in the hole before she pulls the prey in. It is a well-replicated finding that, if the experimenter moves the prey a few inches while the wasp is down doing her ‘inspection’, when the wasp re-emerges she searches for the prey. Having found it, instead of dragging it straight down the hole she does another ‘inspection’. Experimenters have repeated this tease several dozens of times in succession. Every time, the ‘stupid’ wasp fails to ‘remember’ that she has only just ‘inspected’ the burrow and therefore there is no need to do it again. It appears to be a kind of robotic behaviour, akin to setting a washing machine back to an earlier part of its cycle, say back to ‘wash’ when it is about to start ‘final rinse’. No matter how many times you do it, the silly machine doesn’t ‘remember’ that it has already washed the clothes! Sphex has even conferred its name, in philosophical jargon, on this kind of mindless automatism – ‘sphexish behaviour’ or ‘sphexishness’. Jane is one of those wasp-watchers who is sceptical of this interpretation. She suspects that the wasp isn’t being ‘sphexish’ at all. The misunderstanding arises from the human assumption that it is ‘inspecting’ the burrow. Jane and others believe it needs to approach the prey coming out of the burrow, so that when it reverses back into the burrow dragging the prey, its abdomen is aimed in the right direction. So it goes down head first, turns round inside, and emerges head first so its abdomen is pointing down the burrow when it seizes the prey to drag it down. It’s just a way of taking aim, not an ‘inspection’ at all.
Exploring evolutionarily stable strategies
At the time of Jane’s arrival in Oxford, The Selfish Gene had only just been published, and my mind was dominated by one of its central ideas, the evolutionary game-theoretic ideas of John Maynard Smith: the ‘ESS’ or evolutionarily stable strategy. I was working on a lecture, ‘Good strategy or evolutionarily stable strategy’, to be delivered at a conference on sociobiology in Washington the following year (see page 95). Whenever I heard a story about animal behaviour – such as the stories Jane told me about her wasps – my mind at that time immediately leapt, with almost unseemly zeal, to translate it into ESS terms.
We need ESS theory whenever it happens that the best strategy for an animal depends on which strategy most other animals in the population have adopted. ‘Strategy’ doesn’t imply conscious deliberation; it is simply a rule for action, like a computer applet or a clockwork mechanism. It might be something like: ‘Attack first. If opponent retaliates, run away, otherwise continue the attack.’ Or: ‘Begin with a peaceful gesture. If opponent attacks, retaliate, otherwise continue peaceful.’ Sometimes there is simply a best strategy, in an absolute sense, regardless of what other strategies prevail in the population, and then natural selection will simply favour it. But often there is no single best strategy: it depends upon what other strategies dominate the population. A strategy is said to be evolutionarily stable if it is the best thing to do given that everybody is doing it. Why should it matter what ‘everybody is doing’? Because if something else was better than what ‘everybody is doing’ natural selection would favour that something. So, after a few generations of natural selection, it would no longer be true that ‘everybody is doing it’ – that is, the original behaviour. It would not be evolutionarily stable. It would be evolutionarily unstable, in the sense that the population would be invaded, evolutionarily speaking, by an alternative strategy, the ‘something else’ that I mentioned.
Some birds have a habit (Jane Brockmann herself later, with a colleague, reviewed the scientific literature on it) called ‘kleptoparasitism’: piratical stealing of food from other birds. Frigatebirds make a living by pirating fish from other species (as I later witnessed in Galápagos, and with Jane herself in Florida), but kleptoparasitism also happens within species, for example some gulls. Is piracy an evolutionarily stable strategy? We answer that by imagining a hypothetical population of gulls in which almost everybody is a pirate and hardly anybody is doing any fishing. Would it be stable? No. Pirates would starve because there’d be no fish to steal. Imagine you’re the sole honest fisher in a population of pirates. Even though you’d stand to lose a fair number of fish to the ubiquitous pirates, you’d still eat better than any one pirate. So a population of 100 per cent pirates would be ‘invaded’, over evolutionary time, by the honest fisher strategy. Natural selection would favour honest fishing and the frequency of honest fishers would increase. But it would increase only up to the point where piracy just starts to pay better.
So, piracy is not an evolutionarily stable strategy. Is honest fishing an ESS? Now we postulate a population consisting entirely of honest fishers. Would it be invaded, evolutionarily speaking, by pirates? Yes, it might well. If you were the only pirate in a population of honest fishers, there’d be rich pickings for you. So natural selection would favour piracy, and the frequency of pirates would increase.
But again, it would increase only to the point where it no longer pays compared to the alternative. So we end up with a balance between pirates and honest fishers, balanced at some critical frequency such as 10 per cent pirates, 90 per cent fishers. At the balance point, the benefits of piracy and honesty are exactly equal. If the ratio in the population should chance to swing away from the balance point, natural selection restores it by favouring whichever ‘strategy’ is temporarily at an advantage because it is rarer than the critical frequency.
It’s an important part of the theory that the frequencies we are talking about are frequencies of strategies. This doesn’t have to coincide with frequencies of individual strategists, although that is the way I chose, for simplicity, to express it. ‘Ten per cent pirates’ could mean that every individual gull spends a random 10 per cent of its time pirating and 90 per cent fishing. Or it could mean that 10 per cent
of individuals spend all their time pirating. It could apply to any combination that achieves the 10 per cent frequency of the pirating strategy in the population. The mathematics works out the same, regardless of how the ratio is achieved. By the way, there’s nothing magical about ‘10 per cent’. I chose that number just for a simple example. The actual critical percentage would depend on economic factors that would be hard to measure – indeed, would take a gull-loving equivalent of Jane Brockmann to measure.
Such matters, to be discussed in my Washington conference lecture, were buzzing around in my prepared mind when Jane Brockmann breezed into my Oxford room and we sat down and talked of her wasps. Sometimes they dig, sometimes they exploit the digging efforts of others, and perhaps also the others’ haul of katydids. You can just imagine the excitement in my ESS-primed brain when I heard this. Pirates and Honest Diggers! Is ‘digger’ an ESS? If the majority of the population dig, would the digging strategy be invaded by a rival strategy called ‘parasitize the digging efforts of others’? And is ‘parasitize’ an ESS? Probably not, because if nobody is digging there’ll be no burrows to hijack. Could there be a critical ratio, at which diggers and pirates are equally successful? What excited me is that Jane evidently had mountains of hard, quantitative data. Maybe we could use her data to actually measure the economic benefits and costs of the two strategies. Unlike the bird pirates and fishers of my draft Washington talk, for whom nobody had any real data, Jane Brockmann’s voluminous recordings of the timed behaviour of individually marked wasps had the tantalizing potential to turn into the first real field trial of mixed ESS theory.
Jane and I decided to work together on the project, but we needed more theoretical expertise, more mathematical wizardry than either of us could muster. It was time to call in the big guns, and the biggest gun in my world was my student Alan Grafen. It might seem strange to say that my guru and mentor was my own student, but it is true. He was that sort of student. He shared my enthusiasm for ESS theory, and helped me to understand its finer points and many other aspects of evolutionary biology. He taught me some of the intuitions and instincts of a mathematician, even if I couldn’t follow him through the thickets of symbol manipulation. There are mathematicians and physicists who sashay into biology, thinking they can clean up its act in a week. They can’t: they lack the intuitions and knowledge of a biologist. Alan is an exception. He has a rare combination of mathematical and biological intuition (shared, I believe, with his hero R. A. Fisher) which enables him to smell out the right answer to a problem almost instantaneously – and, like Fisher but unlike me, he can then go on to do the algebra if asked to do so, to prove he was right. He is now my colleague at Oxford, Professor of Theoretical Biology and a well-deserved Fellow of the Royal Society.
I first encountered Alan in 1975, when he was an undergraduate and I was tutor in Zoology at New College and in the middle of writing The Selfish Gene. A tutor from another college had recommended a young man from Scotland as something way out of the ordinary, and I agreed to take him on for tutorials in animal behaviour. In those days, the custom was for undergraduates to read their essays aloud in the first part of the tutorial, and we’d then discuss them. I’ve forgotten what Alan’s first essay was about, but I vividly remember the goosepimpling awe with which I listened to it. ‘Out of the ordinary’ had been an understatement.
Alan’s undergraduate degree was in psychology (his course had an animal behaviour option, which was why it was appropriate to send him to me for tutorials). I hoped he would go on to do a doctorate with me, but he decided to take the hard option of an Oxford master’s degree in mathematical economics, supervised by Jim (later the Nobel Prize-winning Sir James) Mirrlees, a fellow Scot and one of the world’s leading mathematical economists. Economics is increasingly important in evolutionary theory, so this would be a good choice for Alan whether he came back into biology or made his career as an economist. In the event, he did come back into biology and did his DPhil with me. But when Jane Brockmann came into our lives he was still studying mathematical economics, and he was to make good use of it in the wasp research which the three of us undertook together.
First things first, however. The day following Jane’s arrival, as she remembers (but I had forgotten), was the occasion of the Great Annual Punt Race. Less serious than the Oxford vs Cambridge boat race and probably a lot more fun, its competing teams were those of our Animal Behaviour Research Group (ABRG) and the Edward Grey Institute of Field Ornithology (EGI). The EGI is another sub-department of Zoology, named after the former Foreign Secretary and keen ornithologist Lord Grey (who, on the eve of the First World War, had intoned the unforgettable lament: ‘The lamps are going out all over Europe; we shall not see them lit again in our lifetime’). Both teams deployed an anarchically variable number of punts (flat-bottomed boats propelled by a pole thrust against – and all too often stuck in – the river bed). The name of the game was not just speed but sabotage, and Jane’s abiding memory is of John Krebs (later Sir John, now Lord Krebs FRS and one of Britain’s most distinguished biologists) showing up as especially ruthless on the EGI side. Did Alan, perhaps, see scope for a little ESS modelling: the Honest Punter strategy versus the Piratical Saboteur? Probably not; he has more sense and was too busy honestly poling his punt along.
Then it was down to the serious business of wasps. In her two different field sites, the main one in New Hampshire and a subsidiary one in Michigan, Jane had spent more than 1,500 hours meticulously recording the behaviour of individually colour-marked female digger wasps. She had an almost complete record of the histories of 410 burrows and of the nest-related activities that dominated 68 complete wasp lifetimes. As I said, she had originally used these records for an entirely different purpose, which she had already written up for her PhD thesis at the University of Wisconsin. Together with Alan, we now decided to use the same raw data again, to put real, measured economic values on the costs and benefits involved in ESS theory.
In my room in the Department of Zoology, with its view overlooking Matthew Arnold’s dreaming spires, Jane and I worked together every day at my PDP-8 computer, typing in the numbers from her voluminous wasp records, and pushing them through numerous statistical analyses. Alan swung by every few days for a visit, casting his swift and expert eye over our statistics and patiently teaching Jane and me how to think like mathematical economists. We all three worked together on plugging his economic ideas into formal ESS models. It was a magical time, one of the most constructive periods of my working life. There was so much to learn, and I learned from both my colleagues. I like to think that I am a natural collaborator, and one of the regrets of my life is that I haven’t done more of it.
The first model we tested – colourfully named Model 1 – turned out to be wrong; but, in textbook philosophy-of-science fashion, its disproof gave us the clue to inventing the much more successful Model 2. When we first proposed Model 1, we regarded ‘Join’ as a piratical strategy, cashing in on the digging and katydid-collecting efforts of Honest Diggers. All the predictions of Model 1 turned out to be wrong, so we went back to the drawing board and came up with Model 2. Model 2 postulated two strategies called Dig and Enter. ‘Dig’ speaks for itself. ‘Enter’ means ‘Enter an already dug burrow and use it exactly as though you had dug it yourself.’ This is not the same as the piratical ‘Join’ of Model 1, for an interesting reason.
That reason stems from an additional fact about the wasps: they quite often abandon the burrow they are working on. Why they do this is not always clear, and indeed the reasons seem to vary. Perhaps there is a temporary problem like an invasion by ants or a centipede; or maybe a wasp died while away from her nest. What this means is that an Enterer might find a burrow untenanted and assume sole ownership. Or, if the previous owner had not abandoned it, the two would continue to work on the nest, each ignoring the other – except that if they happened to meet in the nest at the same time (which was quite rare because they spent most of their time out hunting)
they would fight.
Model 2 suggests that Dig and Enter should be equally successful at a balanced frequency. When lots of digging is going on, entering becomes more successful, because there’s a good supply of abandoned burrows. But if the frequency of Enter rises too high, not enough burrows are being dug, therefore there aren’t enough abandoned burrows for the Enter strategy to prosper. Now, here’s an interesting complication. A wasp may abandon her nest at any time, even when she has already stowed katydids in it. So an Enterer might stand to gain not only a ready-dug burrow but a ready-caught cache of katydids too. The model assumes – with justification from Jane’s measurements, as she and I showed in a separate paper – that an Enterer has no way of telling whether a burrow has really been abandoned, or whether the owner is just temporarily out hunting. And we showed in yet another separate paper that each wasp behaves as if she knows how many katydids she herself has caught, but is blind to the number that another wasp might have put in the burrow.
If a wasp is the sole incumbent of a burrow – whether or not she dug it in the first place – there is a risk that she will be joined by an Enterer. And an Enterer runs the risk that the burrow she has chosen to enter is still occupied by its original owner. Both these outcomes are less favourable than being in sole possession. This is in spite of the fact that (as the discarded Model 1 emphasized) a shared nest is likely to contain more katydids (two wasps to hunt them), and there is a ‘winner take all’ benefit to the wasp who ends up laying an egg to take advantage of the shared cache. To use informal, personifying language: a wasp may dig a new burrow and ‘hope’ not to be joined by another wasp; or she may enter an existing burrow, ‘hoping’ it has been abandoned by its previous owner. In Model 1, Join was a strategic decision. In Model 2, both Join and Is Joined were undesirable accidents, unfortunate outcomes of a decision to Enter. Dig and Enter, by contrast, were alternative strategic decisions: at equilibrium wasps should be indifferent between the two of them. Model 2, if correct, could be summed up in a limerick:
Brief Candle in the Dark Page 6