Polydomy and sexual allocation ratios in the ant Myrmica punctiventris

Summary Colony structure and reproductive investment were studied in a population of Myrmica punctiventris. This species undergoes a seasonal cycle of polydomy. A colony overwinters in entirety but fractionates into two or more nest sites during the active season and then coalesces in the fall. Colony boundaries were determined by integrating data on spatial pattern, behavioral compatability, and genetic relatedness as revealed by protein electrophoresis. Colonies contained at most one queen. Consequently, a colony consisted of one queenright nest and one or more queenless nests. Furthermore, estimates of relatedness were fully consistent, with queens being single mated. M. punctiventris therefore has a colony genetic structure that conforms to the classical explanation of the maintenance of worker sterility by kin selection. Kin selection theory predicts that workers would favor a female-biased allocation ratio while selection on queens would favor equal investment in males and females. We predicted that in polydomous populations, queenless nests would rear more female reproductives from diploid larvae than queenright nests. There was a significant difference between queenright and queenless nests in sexual allocation; queenless nests allocated energy to reproductive females whereas queenright nests did not. At neither the nest nor colony levels did worker number limit sexual production. We also found that nests tended to rear either males or females but when colony reproduction was summed over nests, the sexes were more equally represented. The difference in allocation ratios between queenless and queenright nests was attributed solely to queen presence/absence. Our work shows that polydomy provides an opportunity for workers to evade queen control and thereby to sexualize brood.Offprint requests to: L.E. Snyder at the current address     

Sex allocation and queen-worker conflict in polygynous ants

Summary Sex allocation theory is developed for polygynous eusocial Hymenoptera in which nests recruit their own daughters as new reproductive queens. Such restricted dispersal of females leads to the expectation of male-biased investment ratios. The expectation depends on the parameter q telling what proportion of the total contribution in the gene pool by all new queens is due to those dispersing. Under queen control the expected sex allocation, expressed as the proportion of resources invested in males, is IM =1/(1 + q). Under worker control, IM depends on the relatedness of old queens, on the number of males they have mated with, and on the proportion of males produced by workers. With single mating and no worker reproduction, the approximate predictions for IM are 1/(1 + q) when the nests have many highly related queens, 1/(1 + 2 q) when the old queens are as related as average worker nest mates, and 1/(1 + 3q) when the old queens are not related to each other at all. The observed investment ratios in polygynous ants would, on average, match values of the parameter q between 0.4 and 0.5. Values of q have not been estimated in nature. If q is smaller than 0.4, which may well be true, the observed sex allocation in polygynous ants is in fact more female-biased than predicted by the theory. This indicates that the female bias found in monogynous ants may not be exceptional and could be due to factors other than worker control of sex allocation. Because the value of q is likely to vary among species, testing the predictions of the theory requires thorough single-species studies.     

Alternative reproductive tactics and the impact of local competition on sex ratios in the ant Hypoponera opacior

The ant Hypoponera opacior exhibits alternative reproductive morphs of males and females associated with distinct sexual behaviours. Our long-term study reports strong seasonality in sexual production with a mating season in early and one in late summer. Winged (alate) reproductives emerge in June, swarm during the monsoon season and establish new colonies independently. In contrast, wingless worker-like (ergatoid) reproductives that appear in late August mate within their natal or adjacent nests and either do not disperse or establish new nests close by. These divergent dispersal patterns allowed us to analyse the impact of local factors on investment strategies by comparing sex allocation between and within the two reproductive events. The optimal sex ratio for ergatoid reproductives should be influenced both by competition for matings between brothers (local mate competition) and rivalry among young locally dispersing queens for workers, nest sites or food (local resource competition). The greater importance of local resource competition was demonstrated both by a male-biased sex ratio for wingless sexuals and a stronger increase in the number of males with total sexual production than for the number of queens. Microsatellite analysis revealed that inter-nest variation in relatedness asymmetry cannot explain split sex ratios in the August generation. Instead, nests with related ergatoid males raised a male-biased sex ratio contrary to the expectations under local mate competition. In conclusion, male bias in wingless H. opacior indicates that local mate competition is less strong than local resource competition among ergatoid queens over the help of workers during nest foundation.     

Genetic relatedness and evolution of insect sociality

Summary Genetic relatedness is a vital concept in the study of the evolution of social behaviour because it can be used to predict gene transmission into future generations. Any models using genetic relatedness to predict the course of social evolution have to take into account that this relatedness, when defined as genotypic regression, is affected by selection and that the evolution also depends on specific assumptions concerning the cost/benefit ratios. In this paper these problems are shown to exist in recent studies examining the evolution of worker behaviour in insects; these studies are reanalysed using allele frequency models, and the results compared with those from other models.It is shown that cyclic inbreeding (alternating outbred and inbred generations) can favour worker evolution in diploid populations but is a necessary condition only within a very limited range of the cost/benefit ratio.Male-haploid models show that both female and male workers evolve more easily if they can manipulate the brood produced by the queen by biassing the brood sex ratio in favour of females (the optimal proportion of females is ca. 0.75). The threshold for female workers to evolve is also lowered if they are allowed to produce some of the colony's male offspring (which arise from unfertilized eggs), in which case the optimal brood sex ratio becomes closer to 1:1. It is apparent that the two factors — sex-ratio bias and worker-produced males — are also important in the comparison of worker evolution in male-haploid and diploid insects.     

Colony level sex allocation in a polygynous and polydomous ant

The colony-level sex allocation pattern of eusocial Hymenoptera has attracted much attention in recent studies of evolutionary biology. We conducted a theoretical and empirical study on this subject using the dolichoderine ant Technomyrmex albipes. This ant is unusual in having a dispersal polymorphism in both males and females. New colonies are founded by an alate female after mating with one or more alate males in the nuptial flight. In mature colonies, the reproductive role of the foundress queen is taken over by wingless offspring (supplementary reproductives). Mature colonies are extremely polygynous, with many wingless queens reproducing through intea-colonial mating with wingless males (inbreeding), and producing both alate and wingless sexuals. The population sex ratio of wingless sexuals was found to be extremely female-biased, while the population allocation ratio of alates was almost 1:1. This result suggests that there is local mate competition among wingless sexuals. A specific model for this extraordinary life cycle predicted that the asymmetry of regression relatedness (b _f/b _m) will disappear during the first few generations of wingless reproductives after the foundress dies. If colonies begin to produce alates after several wingless generations, this undermines the hypotheses for intercolonial sex ratio variation based on the relatedness asymmetry. We compared the magnitude of variation in sex ratios and other characteristics between two levels (within-colony-inter-nest and between-colony). Although there was considerable within-colony variation in all the examined characteristics, between-colony variances were always larger. This means that allocation is important at the whole-colony level, not that of the nest. There was no apparent correlation between the sex ratio of alates and colony size. Furthermore, partial correlation analysis indicated that neither the number of workers nor investment in alates explained the variation in the sex ratio of alates. The only factor which was significantly correlated with the sex ratio of alates was the sex ratio of wingless sexuals (a positive correlation). We conclude that both the alate and wingless sex ratios may be influenced by a common primary sex ratio at the egg stage, the variance of which may have genetic components. In the wingless sexuals, partial correlation analysis indicated that colony size and the number of workers explained the sex allocation ratio. The number of wingless females was strongly (positively) correlated with the total investment in wingless sexuals, while the number of males showed no such correlation. There is, however, no convincing explanation for the variation in sex allocation ratio of wingless sexuals, because the estimates of investment in wingless males may have a large sampling error. Correspondence to: K. Tsuji     

Support for maternal manipulation of developmental nutrition in a facultatively eusocial bee, <Emphasis Type="Italic">Megalopta genalis</Emphasis> (Halictidae)

Developmental maternal effects are a potentially important source of phenotypic variation, but they can be difficult to distinguish from other environmental factors. This is an important distinction within the context of social evolution, because if variation in offspring helping behavior is due to maternal manipulation, social selection may act on maternal phenotypes, as well as those of offspring. Factors correlated with social castes have been linked to variation in developmental nutrition, which might provide opportunity for females to manipulate the social behavior of their offspring. Megalopta genalis is a mass-provisioning facultatively eusocial sweat bee for which production of males and females in social and solitary nests is concurrent and asynchronous. Female offspring may become either gynes (reproductive dispersers) or workers (non-reproductive helpers). We predicted that if maternal manipulation plays a role in M. genalis caste determination, investment in daughters should vary more than for sons. The mass and protein content of pollen stores provided to female offspring varied significantly more than those of males, but volume and sugar content did not. Sugar content varied more among female eggs in social nests than in solitary nests. Provisions were larger, with higher nutrient content, for female eggs and in social nests. Adult females and males show different patterns of allometry, and their investment ratio ranged from 1.23 to 1.69. Adult body weight varied more for females than males, possibly reflecting increased variation in maternal investment in female offspring. These differences are consistent with a role for maternal manipulation in the social plasticity observed in M. genalis.     

Operational sex ratios and behavioural sex differences in a pipefish population

In the pipefish Syngnathus typhle, only males brood embryos in specially developed brood pouches, supplying oxygen and nutrients. Laboratory studies have shown that this elaborate paternal care has led to sex-role reversal in this species: males limit female reproductive rate, females are the primary competitors for mates and males exercise greater selectivity in accepting mates. In the first field study of this pipefish, we describe mating behaviour in the wild and test the hypothesis that temporal variations in the operational sex ratio (OSR) determine sex differences in mating behaviour. Our study comprised two reproductive seasons of two sequential mating periods each, the latter separated by a lengthy interval of male brooding. During mating periods, females displayed to all males without wandering and males moved about searching for females, without reacting to all females. The OSR was least female-biased (or even male-biased) at the onset of the breeding season, when most pipefish were simultaneously available to mate, but became strikingly female-biased as males' pouches were filled. The OSR remained substantially female-biased during the second mating period, because few males became available to remate at any one time. As hypothesised, female-biased OSRs resulted in more female-female meetings. As well, females were above the eelgrass more often than brooding males, thus exposing themselves to conspecifics and/ or predators. In the second year, males arrived earlier than females on the breeding site and male pregnancies were shorter, because of higher water temperatures, so rematings occurred earlier. Males met more often during that year than the previous one, but male competitive interactions were still not observed. The field results support laboratory studies and demonstrate that behaviours associated with female-female competition are more prominent when the OSR is more female-biased. Correspondence to: A. Vincent     

Intraspecific parasitism and split sex ratios in a monogynous and monandrous ant (Leptothorax nylanderi)

Sex ratios were bimodally distributed in a population of the monogynous and monandrous ant Leptothorax nylanderi during each of 3 study years. The population-wide investment ratios suggested worker control of sex allocation. Nest-level variation in the proportional investment in virgin queens was not affected by the presence or absence of a queen and only slightly by collecting year, but was correlated with nest size, total sexual investment and, unexpectedly, with differences in nestmate relatedness: small, low-investment nests and nests with several worker lineages produced male-biased sex ratios. Colonies containing several worker lineages arise from usurpation of mature colonies by unrelated founding queens and the fusion of unrelated colonies under strong nest site limitation. In contrast to facultatively polygynous and polyandrous species of social insects, where workers can maximize their inclusive fitness by adjusting sex ratios according to the degree of relatedness asymmetry, workers in mixed colonies of L. nylanderi do not benefit from manipulating sex allocation, as here relatedness asymmetries appear to be the same as in homogeneous colonies. Received: 7 December 1999 / Received in revised form: 29 February 2000 / Accepted: 13 March 2000     

Foundress polyphenism and the origins of eusociality in a facultatively eusocial sweat bee, Megalopta genalis (Halictidae)

The reproductive (queen) and nonreproductive (worker) castes of eusocial insect colonies are a classic example of insect polyphenism. A complementary polyphenism may also exist entirely among females in the reproductive caste. Although less studied, reproductive females may vary in behavior based on size-associated attributes leading to the production of daughter workers. We studied a bee with flexible social behavior, Megalopta genalis, to better understand the potential of this polyphenism to shape the social organization of bee colonies and, by extension, its role in the evolution of eusociality. Our experimental design reduced variation among nest foundresses in life history variables that could influence reproductive decisions, such as nesting quality and early adulthood experience. Within our study population, approximately one third of M. genalis nests were eusocial and the remaining nests never produced workers. Though they do not differ in survival, nest-founding females who do not attempt to produce workers (which we refer to as the solitary phenotype) are significantly smaller and become reproductive later than females who attempt to recruit workers (the social phenotype). Females with the social phenotype are more likely to produce additional broods but at a cost of having some of their first offspring become nonreproductive workers. The likelihood of eusocial organization varies with body size across females of the social phenotype. Thus, fitness consequences associated with size-based plasticity in foundress behavior has colony level effects on eusociality. The potential for size-based polyphenisms among reproductive females may be an important factor to consider in the evolutionary origins of eusociality.     

Solitary and eusocial nests in a population of Augochlorella striata (Provancher) (Hymenoptera; Halictidae) at the northern edge of its range

Summary Augochlorella striata was studied at the northern limit of its range. The study population contained a mixture of solitary and social nest foundresses. Eusocial foundresses produced 1 or 2 workers before switching to a male biased brood. Solitary foundresses produced males first. Cells vacated by eclosed offspring were reused late in summer. A female biased brood resulted from cell reuse in both solitary and eusocial nests. Workers were slightly smaller than their mothers and were sterile although most of them mated. In comparison to published data from a Kansas population of this species, the Nova Scotia population had i) a lower proportion of multiple foundress nests, ii) a smaller worker brood and iii) a briefer period of foraging activity but iv) comparable overall nest productivity.     

The biology of a subtropical population of Halictus ligatus Say (Hymenoptera: Halictidae)

Summary A large population of Halictus ligatus was studied in the subtropical climate of Knights Key, Monroe County, Florida. The dissection of 858 female bees caught on flowers and 420 bees from completely excavated nests gives the following picture of phenology, colony development and social organisation. In the Florida keys, H. ligatus is continuously brooded and multivoltine. However, towards the coldest time of year young gynes may rest in their natal nests rather than found a new colony. This may result in a partial synchronisation of nest initiation when warm weather returns after a particularly cold spell. Most nests are started by a single foundress that usually survives until near the end of the production of reproductives. The first brood is very variable in size and males average 11% of the bees produced at this stage. This figure increases to 56% when the first brood workers begin provisioning. Queens are produced some time after the rise in male production and colony longevity is extended by the presence of some worker brood during this phase. Queens average 16% larger than their workers but appear to exert little inhibition of worker reproductivity: 57% of worker bees mate and 68% show ovarian development. This population is unique amongst social halictines in being continuously brooded, multivoltine and in having such weak physiological caste differentiation. It seems to represent an intermediate stage between the primitively eusocial colonies of H. ligatus found in temperate regions and the communal-like ones of the tropics.     

Sociogenetic organization of the red ant Myrmica rubra

Knowledge of the sociogenetic organization determining the kin structure of social insect colonies is the basis for understanding the evolution of insect sociality. Kin structure is determined by the number and relatedness of queens and males reproducing in the colonies, and partitioning of reproduction among them. This study shows extreme flexibility in these traits in the facultatively polygynous red ant Myrmica rubra. Relatedness among worker nestmates varied from 0 to 0.82. The most important reason for this variation was the extensive variation in the queen number among populations. Most populations were moderately or highly polygynous resulting in low relatedness among worker nestmates, but effectively monogynous populations were also found. Polygynous populations also often tend to be polydomous, which is another reason for low relatedness. Coexisting queens were positively related in two populations out of five and relatedness was usually similar among workers in the same colonies. Due to the polydomous colony organization and short life span of queens, it was not possible to conclusively determine the importance of unequal reproduction among coexisting queens, but it did not seem to be important in determining the relatedness among worker nestmates. The estimates of the mating frequency by queens remained ambiguous, which may be due to variation among populations. In some populations relatedness among worker nestmates was high, suggesting monogyny and single mating by queens, but in single-queen laboratory nests relatedness among the worker offspring was lower, suggesting that multiple mating was common. The data on males were sparse, but indicated sperm precedence and no relatedness among males breeding in the same colony. A comparison of social organizations and habitat requirements of M. rubra and closely related M. ruginodis suggested that habitat longevity and patchiness may be important ecological factors promoting polygyny in Myrmica. Received: 15 May 1995/Accepted after revision: 17 October 1995     

Intra-colony relatedness and sociality in the allodapine bee Exoneura bicolor

Summary Overwintered and newly co-founded nests of Exoneura bicolor exhibit different grades of sociality. Intra-colony relatedness was estimated for adults and female brood in both nest types using allozyme data and a multiallelic estimator. The higher relatedness among female brood from overwintered nests compared to newly-founded nests is consistent with the difference in sociality between these colony types (semisocial versus quasisocial). However, intra-colony relatedness among adults is higher in cofounded nests than in overwintered nests, suggesting that differences in sociality are determined by benefit/cost ratios associated with non-reproductive strategies, rather than relatedness between interactants. Rapid egg-production in newly founded nests allows eggs to be stockpiled. This reduceds the tasks available to non-reproductives in early phases of colony development and limits the payoffs available for reproductive altruism. It is suggested that the social flexibility characteristic of allodapines is a consequence of communal progressive rearing which allows many benefits from cooperative nesting to be gained without worker sterility.     

Biased sperm use by polyandrous queens of the ant<Emphasis Type="Italic"> Proformica longiseta</Emphasis>

The occurrence and genetic effects of polyandry were studied in the ant Proformica longiseta using three microsatellite markers. The average queen mating frequency (QMF) estimated from the sperm dissected from the spermathecae of 61 queens was 2.4 with 69% of the queens being multiply mated. QMF estimated from worker offspring in a subsample of eight monogynous colonies was 3.5, but the effective paternity (m_e,p) was only 1.23. The difference between these values reflected unequal sperm use by the queens. Most colonies of P. longiseta were polygynous and the average relatedness among workers was 0.35. Polyandry thus added only marginally to the genetic diversity of colonies, and our results gave little support to the genetic-variability hypothesis for explaining polyandry. Diploid male load was low, as only 1% of males were diploid. A large majority (92%) of nests produced one sex only, with males produced in colonies that had higher than average worker relatedness. This contradicted the predictions derived from worker control of sex ratios. Males produced enough sperm to fill the spermathecae of several queens. Thus, the results indicated that diploid male load, sperm limitation and sex ratio conflict are also unlikely explanations of polyandry. Plausible hypotheses for polyandry include mating by convenience, as the sex ratio is male biased and the mating costs to a female can be low because the females are wingless and have no mating flight. The observed unequal sperm use furthermore points to sperm choice and sperm competition as important factors in the evolution of polyandry.     

Sex ratio and maternal rank in wild spider monkeys: when daughters disperse

Summary Data from a long-term field study of the spider monkey, Ateles paniscus, in Peru indicate that a strongly female-biased sex ratio exists from birth in this population. Of 46 infants born between July 1981 and June 1986, 12 were male, 32 were female and 2 were of undetermined sex. This effect is consistent between years as well, with more females than males born in each year of the study (Table 1). This bias is driven by the fact that low-ranking females produce daughters almost exclusively, while high-ranking females bias their investment somewhat less strongly towards sons (Table 2). The unusual pattern of female-biased maternal investment observed in this population of Ateles probably occurs for a combination of the following reasons: (1) maternal investment in individual male offspring is somewhat greater than in individual female offspring; (2) males remain with their natal groups, and the sons of high-ranking females are likely to be competitively superior to the sons of low-ranking females; (3) males compete for mates, and only the one or two most dominant males within a community are likely to achieve significant reproductive success. Two possible mechanisms of sex-ratio adjustment and the evidence for each are discussed.     

Dual mechanism of queen influence over sex ratio in the ant Pheidole pallidula

Social Hymenoptera are general models for the study of parent-offspring conflict over sex ratio, because queens and workers frequently have different reproductive optima. The ant Pheidole pallidula shows a split distribution of sex ratios with most of the colonies producing reproductives of a single sex. Sex ratio specialization is tightly associated with the breeding system, with single-queen (monogynous) colonies producing male-biased brood and multiple-queen (polygynous) colonies female-biased brood. Here, we show that this sex specialization is primarily determined by the queens influence over colony sex ratio. Queens from monogynous colonies produce a significantly more male-biased primary sex ratio than queens from polygynous colonies. Moreover, queens from monogynous colonies produce a significantly lower proportion of diploid eggs that develop into queens and this is associated with lower rate of juvenile hormone (JH) production compared to queens from polygynous colonies. These results indicate that queens regulate colony sex ratio in two complementary ways: by determining the proportion of female eggs laid and by hormonally biasing the development of female eggs into either a worker or reproductive form. This is the first time that such a dual system of queen influence over colony sex ratio is identified in an ant.     

Brood sex ratios, female harem status and resources for nestling provisioning in the great reed warbler (Acrocephalus arundinaceus)

The theory of parental investment and brood sex ratio manipulation predicts that parents should invest in the more costly sex during conditions when resources are abundant. In the polygynous great reed warbler, Acrocephalus arundinaceus, females of primary harem status have more resources for nestling provisioning than secondary females, because polygynous males predominantly assist the primary female whereas the secondary female has to feed her young alone. Sons weigh significantly more than daughters, and are hence likely to be the more costly sex. In the present study, we measured the brood sex ratio when the chicks were 9 days old, i.e. the fledging sex ratio. As expected from theory, we found that female great reed warblers of primary status had a higher proportion of sons in their broods than females of lower (secondary) harem status. This pattern is in accordance with the results from two other species of marsh-nesting polygynous birds, the oriental reed warbler, Acrocephalus orientalis, and the yellow-headed blackbird Xanthocephalus xanthocephalus. As in the oriental reed warbler, we found that great reed warbler males increased their share of parental care as the proportion of sons in the brood increased. We did not find any difference in fitness of sons and daughters raised in primary and secondary nests. The occurrence of adaptive sex ratio manipulations in birds has been questioned, and it is therefore important that three studies of polygynous bird species, including our own, have demonstrated the same pattern of a male-biased offspring sex ratio in primary compared with secondary nests. Received: 1 June 1999 / Received in revised form: 10 January 2000 / Accepted: 12 February 2000     

On the evolution of male workers in the Hymenoptera

Summary The effects of brood sex-ratio (investment ratio) and the presence of laying workers on relatedness in the Hymenoptera are analyzed. It is shown that the conditions of brood composition that generate degrees of relatedness favorable to the evolution of eusocial type helping behavior among females will select against such helping behavior among males, and vice versa (see Fig. 1). Thus, societies in the Hymenoptera can be expected to have male workers or female workers, but not both. It is argued that the conditions leading to degrees of relatedness favorable to male helping are quite restrictive and unlikely to be met in haplodiploid species.The presence of laying workers is shown to lead to biasses in relatedness such that females may be selected to be workers even when the sex-ratio is male-biassed. This result sheds new light on a possible pathway to eusociality in the Hymenoptera. It is argued that offspring parasitism of the natal nest may have been important in the evolution of eusociality.     

Synergism between sib-rearing and sex ratio in Hymenoptera

Summary In many bees and wasps, solitary females produce offspring without help from other females. The transition from lone mothers producing offspring to situations in which females often help to rear siblings is an important step in the origins of complex sociality and nonreproductive castes. Recent work on Hymenoptera has stressed the role of sex ratio variation in this transition; when a mother's brood is more female biased than average, older daughters are favored to help rear their younger siblings because they are more closely related to sisters than to their own offspring. Here the direction of causality is from biased sex ratios, which arise by some extrinsic mechanism, to the origins of sib-rearing (eusociality). We present a model in which there is a synergism between sib-rearing and female-biased sex ratios, which may either complement the sex ratio variation idea by increasing the rate at which helping spreads or be an alternative hypothesis about the origins of eusociality. The synergism in our model depends on three conditions. 1) Daughters that help cause more food to be provisioned per offspring, which in turn causes larger offspring. 2) Females gain more than males by being large, which favors mothers with helpers to produce a higher proportion of daughters. 3) A helper's inclusive fitness rises as her mother's brood becomes increasingly female biased because a female helper is more closely related to her sisters than to her brothers. A female helper may also be more closely related to her sisters than to her own offspring, but this particular sibling-offspring relatedness asymmetry is not required by the synergism model. These three conditions create a synergism which favors a rapid transition from solitary (subsocial) to eusocial. Demographic and ecological factors that facilitate the evolution of eusociality reduce the stringency of the relatedness asymmetry condition (3) required by our idea. The synergism model therefore complements factors other than relatedness that may have been important during the evolution of eusociality.     

Absence of sex-differential brood raising by workers in Diacamma sp. from Japan

To optimally allocate resources between workers, reproductive females, and males, ant workers have to be able to identify the sex of larvae and raise them differently. The ability of workers to discriminate between the sexes in the brood was tested in colonies of queenless ponerine ants, Diacamma sp., from Japan. The ratio of male eggs in the egg pile was increased experimentally. This manipulation resulted in a corresponding increase in the ratio of adult males, suggesting that Diacamma workers do not raise the sexes differently. Received: 4 November 1997 / Accepted after revision: 14 March 1998