Brief Candle in the Dark Read online

  There’s an insect called Sphex ichneumoneus,

  Whose encounters are seldom harmonious.

  Twixt Enter or Dig

  They don’t care a fig,

  But to Join or Be Joined is erroneous.

  But how could we measure such benefits in order to compare them and test Model 2? We had to think carefully about the correct way to use Jane’s data to assess the benefits and costs accruing to each strategy. The evidence showed that individual wasps didn’t use the same strategy every time, so there was no point in totting up the benefits and costs to individual wasps. We had to do the totting up for strategies themselves, averaged across wasps. And to do this we recognized what we called decisions. The whole of a wasp’s adult life was a series of decisions, where each decision committed a wasp to a definite and measurable period of time associated with a particular burrow. Each period ended at the precise moment when the next decision was taken, initiating an association with a new burrow, whether dug or entered. Benefits and costs were credited to each decision. Then we could average the net benefit associated with decisions to dig versus decisions to enter.

  A successful decision was one which resulted in an egg being laid on katydids in the burrow. If the wasp laid two eggs in different chambers in the burrow, the decision was twice as successful. But could we refine our measure of benefit by taking account of the katydids on which each egg was laid? Presumably an egg laid on a single katydid constituted less of a success than an egg laid on three katydids, because the first larva would be less well nourished. Moreover, not all katydids were the same size, and a quirk of wasp behaviour enabled Jane to measure them.

  Remember my philosophical digression on ‘sphexishness’ and the wasp’s habit of leaving prey by the burrow’s entrance while she goes briefly inside and re-emerges? This gave Jane her chance. While the wasp was down in the burrow she would quickly measure the length of the katydid, taking care to replace it exactly where the wasp left it so as not to trigger any ‘sphexish’ repeats. Volume is a better measure of nutritional value than length, and we approximated volume as the length cubed. In the case of a shared burrow we credited the sum of the katydids to the benefit score of the wasp who ended up laying an egg on the joint cache – winner take all.

  This, then, was our measure of benefit: numbers of katydids (or estimated volume of katydid flesh) on which an egg was successfully laid. How about cost? In a stroke of insight that made a big impression on both Jane and me, Alan urged that time was the appropriate currency of cost. Time is a precious commodity to these wasps. The summer season is brief, they don’t live long; their genetic success will depend on how many times they manage to repeat the burrowing/nesting cycle before the season – and their life – ends. This, indeed, was our rationale for recognizing the concept of a ‘decision’: a commitment of time by a wasp to a particular burrow, for a period terminated by the next decision. Every minute of a wasp’s time, then, was accounted as a cost on the ledger of the decision to enter upon a strategy. The net benefit of Dig was measured as an average rate: the sum of the benefits from all digging decisions divided by the sum of the time costs. And we calculated the equivalent net benefit rate for Enter.

  Now this is where we start to ‘think ESS’. According to our ESS model, we should predict that Dig and Enter will coexist at a balanced frequency where their success rates are equal. If the frequency of Enter were to drift above this equilibrium, natural selection would start to favour Dig, because too many enterers would find themselves sharing a burrow and at risk of engaging in, and perhaps losing, a costly fight. And vice versa: if Enter drifts below the equilibrium, Enter is favoured because there are rich pickings among abandoned burrows. The observed frequency of Enter in the New Hampshire population was 41 per cent, and we conjectured that this might actually be the equilibrium frequency for the New Hampshire population. In that case the measured success rates of Dig and Enter should be equal. So we looked.

  The actual rates were not identical (0.96 versus 0.84 eggs per hundred hours, with a similar conclusion for the katydid volume scores) but there was no statistically significant difference between them, and they were close enough to encourage us to test the model further. Alan did some clever algebra which enabled him to deduce from the model four further predicted numbers, which we could then compare with the observed numbers. The numbers concerned were the proportions of wasps who fell into four categories, and the predictions were the proportions that ought to be observed if the population was at equilibrium according to our ESS model. The table below shows the results: these observed figures from New Hampshire failed to falsify the predictions of Model 2. This pleased us.

  Proportion of wasps who: Observed Predicted

  Dig then abandon 0.272 0.260

  Dig and do not abandon 0.316 0.303

  Enter and find themselves alone 0.243 0.260

  Enter and find themselves sharing 0.169 0.176

  Nevertheless, we were mindful of the principle that a model whose predictions are not falsified by the observed data is impressive only insofar as those predictions were vulnerable to falsification. If you use too much of the observed data in order to deduce your predictions, the predictions almost can’t help being right. We demonstrated by computer simulation (plugging in random hypothetically possible data instead of Jane’s real data) that this was far from the case with our Model 2 predictions. The model could very easily have been wrong, yet it wasn’t in fact. It had stuck its neck out and survived. Karl Popper would have loved it.

  Well, it survived in New Hampshire. As if to ram home the point that Model 2 could very easily have been wrong, it actually was wrong in the other population Jane studied, in Michigan. We were disappointed, but stimulated to think constructively about why this was. We came up with various suggestions, of which the most interesting was that the Michigan wasps were adapted to a different environment from the one in which Jane studied them. Perhaps the Michigan wasps were ‘out of date’, their genes having been adapted to some earlier set of conditions – somewhat as our human genes are adapted to a hunter-gatherer way of life in Africa, but we now find ourselves in cities, with shoes, cars, refined sugar and other food surpluses. The Michigan wasps were working in a large, raised flowerbed, which must have been pretty different from their normal environment, and indeed was different from the more natural-seeming environment of the New Hampshire wasps.

  In spite of its failure in Michigan, the success of our Dig/Enter model in New Hampshire was striking, and it remains one of only a few quantitative field tests of Maynard Smith’s elegant theory of the ‘mixed ESS’ (in this case the ‘mixture’ is between Dig and Enter). For me, it exemplified the joy of working in collaboration with compatible colleagues having complementary knowledge and skills.

  Consider her ways and be wise

  Our work on the ESS model came to an end and was sent off to the Journal of Theoretical Biology for publication, becoming ‘Brockmann, Grafen and Dawkins, 1979’ – the citation engendering, as always, a nice sense of accomplishment. Jane and I continued to work together on a larger paper called ‘Joint nesting in a digger wasp as an evolutionarily stable preadaptation to social life’. This paper presented, and substantiated statistically, many of the background facts that we had used in the ESS paper. And it had its own theoretical aim, which was to contribute to the controversial debate over how social behaviour in insects might have originated from solitary ancestors. Could the kind of uncooperative, inadvertent nest-sharing, which we had shown to be evolutionarily stable in solitary digger wasps, have been the forerunner of the massive cooperative colonies of wasps, ants and bees which are such a spectacular feature of life on Earth? The close genetic relatedness within social insect colonies is certainly an important factor, as my friend and colleague Bill Hamilton had so persuasively argued. But could there have been other pressures predisposing to social life, and could one of these other pressures have been foreshadowed by something like our ESS model in ancient wasp
ancestors? Jane and I worked hard on this paper, mostly in her lodgings in Oxford (tastes and smells are notoriously evocative, and I associate those happily productive times with the taste of Cinzano and a slice of lemon amid clinking ice cubes), and eventually we published it in the journal Behaviour.

  The organization of the paper was unusual, in a way that I am quite proud of and would like to see emulated. The standard plan for a scientific paper was, and still is, the one I had fought a losing battle against during my four years, from 1974 to 1978, as editor of the journal Animal Behaviour (assisted by the vivacious Jill McFarland, wife of my then boss and predecessor as editor, David McFarland): Introduction, Methods, Results, Discussion. This plan, although dull, makes sense for a certain kind of scientific study in which a single experiment is planned, executed and discussed. But what if a series of experiments is performed sequentially as each prompts the next? Pose a question, try to answer it with Experiment 1. The result of Experiment 1 raises a further question, answered by Experiment 2. Experiment 2 needs clarifying by Experiment 3; the result of Experiment 3 provokes Experiment 4. And so on. It seemed to me that the obvious plan for such a paper would be: Introduction; Question 1, Methods 1, Results 1, Discussion 1, leading to Question 2, Methods 2, Results 2, Discussion 2, leading to Question 3, Methods 3 . . . etc. But time after time, as editor, I received papers laid out like this: Introduction; Methods 1, Methods 2, Methods 3, Methods 4; Results 1, Results 2, Results 3, Results 4; Discussion. Seriously! What an utterly bonkers way to write a paper: tailor-made to destroy the narrative flow of a story, kill the interest, emaciate the relevance to the rest of the subject! I struggled as editor to persuade authors to abandon it, but old habits die hard.

  When Jane and I came to write our paper, we had a narrative flow to offer, even though it took the form of a series of observational measurements rather than experiments. Our conclusions constituted a series of factual statements about the wasps, each one needing statistical justification, and each one prompting a new question which led to the next factual statement in building up an argument about the possible origins of social life in insects. So we wrote out a summary of our paper consisting of thirty discrete factual propositions, every one of which we had substantiated with quantitative evidence. Each of those thirty propositions then became a heading in the paper itself. Underneath each heading, the text, tables, diagrams, statistical analyses etc. were directed at demonstrating the truth of the heading. You could get the gist of the paper simply by reading the headings. And indeed, since the journal required a Summary at the end of each paper, we simply reprinted all the headings in sequence as a single summary narrative. The same scheme was independently adopted by Jim Watson in his excellent textbook of molecular genetics. And I was to use a version of it again much later in the last chapter of The Greatest Show on Earth, where I took the famous final paragraph of Darwin’s Origin of Species and made each phrase, in sequence, a section heading of my last chapter. The body of each section was a meditation upon Darwin’s phrase.

  Here is the sequence of headings from Jane’s and my paper, which constitute a concise summary of the facts that we demonstrated. Bear in mind, if you read them, that each one is substantiated in the paper itself by the text, numbers and analyses that follow it.

  One suggested evolutionary origin of insect sociality is joint nesting by females of the same generation.

  Long before selection favoured joint nesting itself, it might have favoured some other incidental preadaptation such as the habit of ‘entering’ abandoned burrows, found in the usually solitary wasp Sphex ichneumoneus.

  We have comprehensive economic records of individually marked wasps.

  There is little evidence of consistent individual variation in nesting success.

  Wasps often abandon the nests they have dug, and other individuals adopt or ‘enter’ these empty burrows.

  ‘Dig/Enter’ is a good candidate for a mixed evolutionarily stable strategy.

  Digging and entering decisions are not characteristic of particular individuals.

  The probability of entering is not conditional upon whether it is early or late in the season.

  There is no correlation between an individual’s size and her tendency to dig or enter.

  There is no correlation between an individual’s egg-laying success and her tendency to dig or enter.

  Individuals do not choose to dig or enter on the basis of immediate past success.

  Individuals do not dig and enter in runs, nor do they alternate.

  Wasps do not choose to dig or enter on the basis of how long they have been searching.

  At one study site digging and entering decisions are roughly equally successful, but at another entering decisions are perhaps slightly more successful.

  Entering wasps seem not to distinguish empty, abandoned burrows from burrows that are still occupied.

  As a consequence of indiscriminate entering, two females sometimes co-occupy the same burrow.

  Co-occupation should not be called ‘communal’ because the wasps usually share the same brood cell, not just the same burrow.

  One might expect that wasps would gain some benefit from co-occupying, but they do not, for a number of reasons.

  Only one egg is laid in a shared cell, and obviously only one of the two wasps can lay it.

  Two wasps together do not fetch noticeably more food than one alone.

  Two wasps together are no quicker at provisioning a cell than one wasp alone.

  Wasps sometimes duplicate each others’ efforts when they co-occupy a nest.

  Co-occupying wasps often have costly fights.

  About all that can be said for joint nesting is that it may reduce parasitism.

  The risk of joint nesting is the price wasps pay for the advantages of taking over an already dug and abandoned burrow.

  A mathematical model assuming ‘dig/enter’ as a mixed evolutionarily stable strategy has some predictive success.

  If the parameters changed quantitatively, the Sphex model could come to predict selection in favour of joint nesting as such.

  The selection pressures would have to be very strong to overcome the demonstrated disadvantages of co-occupying.

  Variants of the Sphex model may be applicable to other species, and may help our understanding of the evolution of group living.

  The theory of evolutionarily stable strategies is relevant not just to the maintenance of behaviour but to its evolutionary change.

  Our conclusion was that the Dig/Enter model which fitted the New Hampshire population of Sphex ichneumoneus could, if named economic parameters were to change over evolutionary time, move into any of a number of ‘spaces’, including ‘social space’ (see graph opposite). We took our Model 2 and calculated what would happen if we systematically varied two of the terms in the algebra, namely B4, the benefit of joining, and B3, the benefit of being joined. Would the model yield a stable ESS at different values of these two benefits?

  The New Hampshire population of Sphex ichneumoneus is indicated by the star as being stable in ‘aggressive space’ (where the wasps are better off being alone). Our analysis showed that the model allows a smooth gradient, as the B values change (over evolutionary time), through ‘tolerant space’ (where wasps who are joined do better than lone wasps but joiners do worse) to ‘cooperative space’ (where joiners do better than lone wasps and wasps who are joined by enterers do best of all). All the way along this evolutionary gradient there are stable solutions such that both digging and entering would be favoured at the (changing) equilibrium frequency. Our analysis showed that, even without the strong kinship reasons which undoubtedly apply in many cases, social behaviour could evolve from a Sphex ichneumoneus type of ancestor. And of course close kinship only adds to the pressure to become social and stay social.

  Plan view of ‘economic landscape’ for the evolution of social insects based on our game theory model of digger wasps’ behaviour. The two economic variables, B3 and B4, a
re the benefits to a wasp of being joined, and of joining, respectively. The star represents Sphex ichneumoneus in ‘aggressive space’ (where a wasp is better off being solitary). The map shows that, if economic conditions change, there is a smooth trajectory from aggressive space all the way through ‘tolerant space’ to ‘cooperative space’ and ‘social space’. Source: H. J. Brockmann, R. Dawkins and A. Grafen, ‘Joint nesting in a digger wasp as an evolutionarily stable preadaptation to social life’, Behaviour 71 (3), 1979, pp. 203–44.

  Interlude in Florida

  In 1978 Jane’s year at Oxford came to an end, and we sadly relinquished her to the University of Florida in Gainesville. But we three musketeers were to be reunited. In 1979 I took a sabbatical leave in Jane’s Gainesville lab, and I arranged for Alan to join us towards the end of my time there. Jane was by then working on another species of solitary wasp, Trypoxylon politum. These ‘mud daubers’ are related to Sphex and have similar habits – but, instead of digging burrows underground, they build aerial ‘burrows’ up on walls, under bridges, on rock faces. The aerial burrows are tubes built of mud, carried dollop by dollop from streams. The tubes often are stacked side by side, hence the name ‘organ pipe mud dauber’. Having built its tube, the wasp then provisions it, like Sphex, except that Trypoxylon hunt spiders instead of katydids and they pack a succession of them into one tube, separated by mud partitions. Jane worked under a bridge on these wasps, recording the comings and goings of marked individuals just as she had with Sphex. Alan worked with her on the theory, and we both spent time under the bridge with Jane and some of her students, helping to observe the wasps – and dodging the cottonmouth snakes, which frightened me more than they frightened the natives.