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just previously. Now, using other examples, we indicate some other kinds of argument which it may be useful to apply to these situations.

CO-OPERATION

In certain ants, notably Lasius flavus and L. niger (Waloff, 1957), it is known that companies of several queens will cooperate in excavating the initial nest. Since these have just come to earth from a vast mating-flight they are un- likely to be close relatives. According to Waloff, the queens of L. flavus usually cohabit peacefully in the nest-chamber and even keep their eggs in a common pile, but about the time cocoons are first formed they tend to separate, some taking a portion of the brood (not necessarily a very fair one it seems) to a particular corner of the nest. There is evidence that the queens so separated tend to control distinct sectors in the developing nest, each having its own worker population; and whether by death of queens-by fighting or otherwise or by migration of a “sector”, most nests of L. flavus end up haplo- metrotic. In L. niger fighting between the queens is regular and generally only one survives in the initial nest chamber.

If we imagine a situation where, of the queens which succeed in co-opera- tively establishing an initial nest, only one is allowed to survive and use it, rather as happens with L. niger except that the survivor is chosen at random and not according to fighting prowess, we see that unrelated queens will evolve instincts to co-operate as a group of n if the chanceth at they succeed in establishing the chamber is more than n-times the chance that one would succeed if alone. When engaged in digging the queens are very helpless and it is not difficult to imagine that a team gets itself underground so much more quickly than an individual that this criterion is met. As to the continued amity once the chamber is made Waloff’s observations on experimental multi-queened initial nests showed that for some reason the queens survive better and rear their first workers sooner when in a group than when alone; if sufficiently marked in a state of nature such an effect could explain the continued amity. With the appearance of the first workers the queen and her brood tend to become more independent and we expect behaviour to change accordingly. It will be seen that in essentials this situation has much in common with that previously described concerning the fusion of sporelings of Gracillaria verrucosa.

In both cases we have a strong presumption that a stage in which selection very strongly favours the united group over the lone individual gives place to conditions where the individual would be better off in the absence of its close companions. According to our theory whether these new conditions will bring on an overt struggle or fighting will depend very largely on the

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degree of relationship in the group in question, or rather on the degree of relationship that has held on average in the multitude of similar situa- tions which have occurred during the evolutionary development of the behaviour.

FIGHTS

The argument to be applied to fights is merely another form of the argu- ment applied above to co-operation. If two evenly matched unrelated animals holding one unit of reproductive potential each are in a typical situation which holds out the prospect of a fight, and if their instincts have been nicely adjusted by natural selection to suit the average outcome, then they will fight only if the expectation of reproductive potential for the winner is more than one unit. If they are sibs they will fight only if the expectation of “winner’s r.p.loser’s r.p.” is greater than 1. Thus if one inevitably dies in the fight the winner must normally gain by more than 50% or the two will prefer to co- exist. In the case of a “hymenopteran full-sistership” they will not fight to the death unless the expected gain to the winner is more than 75%. But with the honeybee, with the amount of multiple-insemination discussed previously, about a 40% increase will be enough. In this case we may put it that unless the presence of an extra young queen can increase the growth of the colony by more than 40% the reigning young queen will prefer to do without her. Thus the mutual animosity of young queens is not very surprising. The “piping” by a still imprisoned queen incidentally would seem to have the characteristics of altruism. The females of various species of Hymenoptera (in Vespula Halictus, etc.) are said to fight in spring for the possession of the maternal nest in which they hibernated together. But in these cases we do not know about multiple-mating and anyway there is probably no question of a fight to the death, beaten females are usually expelled and presumably go off to discover or excavate other nest sites. It may be noted that the larvae of “gregarious” parasitoid Hymenoptera in whose case there is normally no question of “going off” do not fight even if overcrowded (Salt, 1961). “Gregarious” refers to species where the adult normally lays several eggs per host. In “solitary” species, which lay only one egg per host, the first instar larva is adapted for fighting and always attempts to kill any other larvae in the same host; normally there is only one survivor. The gregarious larvae in a host are not necessarily “hymenopteran full-sisters” however, even apart from the question of polyandrous insemination. In cases of polyembrony they will be clonal. The same would be true if the mother reproduces by thelytoky, and, as Dr. Salt has reminded me, this certainly occurs in some ichneumon- flies; and female-to-female parthenogenesis of one kind or another is wide-

46 W. D. HAMILTON spread throughout the parasitoidal Hymenoptera. In such cases the compari- son to the batch of females competing for the nest is still less valid, although in itself the difference in social behaviour between these two types of parasitoid according to relationship remains very striking. In the parasitoidal Diptera with normal sexual reproduction our theory predicts that the competition between gregarious larvae should be fiercer; whether this is observed I have been unable to ascertain, but gregarious cases are certainly much less com- mon in Diptera and this at least is what we expect. PARENTAL BEHAVIOUR TO MINIMIZE SIBLING COMPETITION Of course the above argument is of potentially much wider application. It may be applied to broods of insect larvae feeding under circumstances where the exigencies of competition are not so inflexible as with parasitoids, for example to broods feeding on plants. Competition within such broods should according to our theory be fiercest in species where the female is inseminated by many males. Fierce competition will waste the energies of the brood and the ovipositing behaviour of adult females should tend to evolve so as to minimize this wastage which spells a lowering of total surviving progeny. Hence over a range of species the habit of laying eggs in batches should correlate with monandrous insemination of females. The correlation should be stronger for cases where the larvae are also gregarious. This reminds us of Fisher’s suggestions concerning the evolution of distastefulness and warning-coloration and we note that he appears to have tacitly assumed that the broods he discusses would be of full sibs. Probably this is fair for his cases of Lepidoptera. But as regards the sawfly larvae which he also cites, we have all the diverse hymenopteran possibilities already mentioned, both those dependent on multiple mating and, for some species, those due to female-to-female parthenogenesis. Since we know polyandrous insemination to be a distinct possibility for the Hymenoptera it is of interest to note that D’Rozario (1940) found evidence for the gooseberry sawfly, Nematus ribesii, that though the males are readily polygynous the female ceases to be attractive after one mating. N. ribesii is a good Dzierzon-rule species and concerning the sex-ratio it is said that “females predominate” (Imms, Richard & Davies, 1957). If we assume equilibrium sex-ratio and equally costly males and females the average relationship is actually a little under one-halft. In accordance with Fisher’s suggested correlation the eggs are laid close together and the larvae are aposematic and fairly gregarious. However to the counter-instance admitted by Fisher-the butterfly Anosia †The equilibrium ratio assuming the cost of male and female to be equal is (3- √5): (5-1). Using the coefficients given in Fig. 2 we get the average relationship 1- √5/40-44.

47 plexippus which “scatters her eggs although she has solitary, inedible, conspicuous, larvae”-it will be fair to add another; the case of the moth Panaxia dominula which also scatters her eggs although her larvae are conspicuous and presumably distasteful. In the vegetation they tend to be found concentrated on the preferred food plants but are probably not truly gregarious. I have noticed in the wild that the female moth ceases to be attractive as soon as she enters copulation; thus females are probably only once mated, and the case is contrary to my suggested correlation as well as to Fisher’s. But of course, though these few instances help to outline the situation, they carry little weight for or against the hypothesis. When a brood is still under parental care the parent or parents involved will be concerned to minimize the wasteful effects of sibling competition.

Their disciplinary task will be easiest if the brood is of full-sibs. In the vast majority of cases it is so, either due to monogamy or to polygamy combined with parental care by the female alone. In the unusual cases of birds where polyandry is combined with male parental care it seems that the male is always mono- gynous and broods a clutch given him by a single female (Wynne-Edwards, 1962, pp. 237-8). But in some Ratites male parental care for polymaternal broods does seem to occur (Kendiegh, 1952); and in lekking birds there would seem to be a distinct possibility of polypaternal clutches. Doubtless many more exceptions could be found. The notable case of the polyandrous social insects has already been discussed; we merely note here that the method of rearing larvae in cells is ideal for preventing direct competition and where this method is not adopted, as in Bombus and the social xylocopine bees, we have added reason for expecting that the queens are effectively monandrous. Nevertheless larval competition seems to be severe in some species of Bombus (Free & Butler, 1959, pp. 16, 19-21). Although the cases where full-sibships are not the rule cannot amount to much numerically compared to the vast array of cases where they are, we do not intend to suggest that diminishment of sibling competition is the sole evolutionary raison d’etre of permanent mating ties and bi-parental broods. The cases where the tie continues, as in many birds, from brood to brood and even sometimes until one of the mates dies are sufficient to show that other factors must be operating as well. There are some rather puzzling cases where the parent seems deliberately to provoke competition in the brood, for example by associating more eggs with a food-supply than it could ever fully support. As just one example we have the case of Bombus just mentioned: in B. agrorom it has been found that only 30 to 40% of the eggs laid become eventual adults. Mortality is greatest in the late egg and early larval stages and cannibalism among the larvae is suggested (p. 16). However, the habit of many hawks of having one more nestling than it is normally possible to rear is fairly obviously a special

48 W. D. HAMILTON

strategy allowing for the chance that the breeding season will turn out a good one; and explanations of a like nature may appear for the other cases eventually.

The strong tendency of plants to produce seeds of standard sizes irrespec- tive of the size of the plant shows that how available food-reserves are apportioned between seeds is not a matter of indifference to the fitness of a plant. This is indeed just what we would expect provided the situations into which the seeds disperse are not too varied. Thus for one seed to expand selfishly at the expense of its neighbours may or may not be advantageous to the inclusive fitness of its genotype but it is almost certainly not in the interest of that of the parent plant. Wind-pollination will tend more to produce half- sibships among the seeds in an ovary than will insect-pollination. Hence according to our theory if seeds in general have genotypic control of their own growth, as they surely must to some extent, wind-pollinated plants will tend to have the more pressing difficulties in respect of uniform seed produc- tion. Hence it is rather to be expected that the situation which most lays itself open to this type of competition, the ovary with numerous closely placed ovules, will be uncommon in wind-pollinated plants. By comparison with entomophilous plants this is certainly the case, although there do seem to be a few anomalous genera, e.g. Populus and Juncus. In a great many anemo- philus genera carpels or gynoecia originally with two, three or four ovules end up, through more or less regular abortions, as one-seeded “fruits”. But sometimes the seeds may nevertheless be quite closely placed, as in the pine cone, the birch “catkin”, the maize cob, etc.

The remarks at the end of Section 3 of the previous paper apply to this case as well as to the above problems of animal parental care. We note again that the selfish genes for seed growth tend to waste their powers a little not only because of the assortation due to relationship but also because of the purely chance occurrence of extreme situations where gene-replicas are largely in competition with one another. But this extra effect can only be of importance when the number of seeds in the ovary is very small. A much more important contrary factor must be the tendency of wind-borne pollen grains to arrive one by one rather than all at once as with insect pollination, so exacerbating the disciplinary problem of the wind-users. But on this point, even more than on others in the above discussion, our ideas are as yet rather unclear.

7. Anomalies Here and there in the literature are found records of behaviour where relationship is conspicuously disregarded, or harms or benefits are dispensed apparently in contravention of our principles.

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However, in every case known to me it seems possible to claim either that the situation has been misinterpreted or that the observation concerns a biological error; that is, a rare occurrence in an unusual situation or something of the kind. The latter would seem to be the case for instance with the unusual cases of adult birds feeding the young of other species (e.g. Summers-Smith, 1963, p. 50). Where apparently gratuitous inter-species assistance is recorded more regularly, misinterpretation must be suspected. A non-apparent return benefit signifying a symbiosis, or some degree of positive deception signifying some sort of cuckoo-parasitism, are possibilities that should be borne in mind. For instance, it has been reported that different species of xylocopine bees of the genus Exoneura in Australia will sometimes pool their broods in a common nest (Rayment, quoted by Sakagami, 1960). The finding by Miche- ner (1961a) of a seemingly very similar situation in the related genus Allo- dapula, together with signs of adaptation to parasitism by one of the species, strongly suggests that the situations Rayment has observed contain at least some mild element of parasitism. And Michener’s (1961b) further finding of two species parasitic on Exoneura, clearly derived from the genus itself and hardly separable from it taxonomically, point the same way. These two species are not adapted for pollen-collecting and hence must be fully dependent, but at least one of the supposed parasites in Allodapula does collect pollen and so presumably does contribute something to the nest. Among birds the Cuculidae are a thoroughly anomalous family as regards parental care. We have already mentioned Guira and Crotophaga. Kendiegh (1952) gives a summary of knowledge of reproductive behaviour in other genera. Geococcyx californicus also seems to have many females laying in each nest. The two North American species of Coccyzus show a situation rather like that which Rayment has found in Exoneura. The species are reported sometimes to lay in each other’s nests. But both have brooding instincts and a case has been recorded where both species incubated on the same nest. At the level of single species we may instance the occasional exceptions to the rule that nesting Hymenoptera know their own nests and do not, even if they safely could, transfer to others. As regards the transference of workers, which seems to be not uncommon in some wasps, some cases are perhaps errors due to the powers of visual recognition not being equal to the situation. A strong basis of relationship between neighbour nests, which I believe is usual with the species of Polistes in which I have observed worker transference (canadensis and versicolor), would greatly reduce the selection against such errors. Then there may be situations in which transferral is

50 W. D. HAMILTON really in the interests of inclusive fitness, for example if a colony is dying out (Deleurance, 1955), or happens to find itself with more workers than can use- fully be employed on it, or if a wasp brings in food when all the larvae on its own nest are completely sated. This last explanation may perhaps apply to the cases of cross-provisioning by solitary wasps in a dense nest aggregation observed by Tsuneki (quoted by Sakagami, 1960), and to the cases which Deleurance (1952) has observed in Polistes in the wild where a worker pays visits to two nests. In birds there is a parallel of a sort in a practice of nesting guillemots and razorbills (Fisher & Lockley, 1954, p. 283). It seems that parent birds will sometimes feed the hungriest chicks in the dense nest aggre- gation rather than their own. As regards the already mentioned fostering passion shown by Emperor Penguins that have lost their chicks, some doubt as to whether the observa- tions have been correctly interpreted would seem to remain (Kendiegh, 1952). But taking the statements at their face value we might suggest for instance, that it has something to do with heat-conservation. Perhaps the parent penguin is so closely adapted to living with its offspring that it is, at the stage in ques- tion, at a positive disadvantage without a chick nestling in the brood-pouch. But such a situation would hardly come into being unless there were strong general relationship within the flock. We seem to need to postulate this in any case to explain some other social behaviour of penguins, for example, the way Adelie Penguins parents are said to leave their young in the care of only a few adults while they go off on long fishing expeditions. On the other hand, some apparently social behaviour such as the formation of the crêche in severe weather is easily interpretable as being almost entirely selfish.