Offspring sex ratio variation in the bridled nailtail wallaby, Onychogalea fraenata

The bridled nailtail wallaby is a sexually size dimorphic, promiscuous, solitary macropod. Sex ratios of pouch young were studied at two sites over 3 years, beginning with 14 months of severe drought. Females that were in better condition were more likely to have sons, and condition was dependent on body size. Females at one site were heavier, were consequently in better condition, and produced more sons than females at the other site. Females that declined in condition had more daughters during the most severe part of the drought than females that maintained condition, but endoparasite infection did not affect the pouch young sex ratio. Age also appeared to affect sex ratio adjustment, because weight was strongly influenced by age. Sex ratio bias was not caused by early offspring mortality, but occurred at conception. Mothers did not appear to bias energy expenditure on sons or daughters; males and females did not differ in condition at the end of pouch life. Pouch young sex ratio variation was most consistent with the Trivers-Willard hypothesis, but could also have been influenced by local resource competition, since sons dispersed further than daughters. Offspring condition was related to survival, and was correlated with maternal condition. Received: 14 April 1998 / Accepted after revision: 10 November 1998     

Birth sex ratios in toque macaques and other mammals: integrating the effects of maternal condition and competition

Mammalian life histories suggest that maternal body condition and social dominance (a measure of resource-holding potential) influence the physical and social development of offspring, and thereby their reproductive success. Predictably, a mother should produce that sex of offspring which contributes most to her fitness (as measured by the number of her grandchildren) and that she is best able to raise within the constraints imposed by her condition, social rank, and environment. Such combined effects were investigated by monitoring variations in body condition (weight) and behavior of female toque macaques, Macaca sinica of Sri Lanka, in a changing forest environment over 18 years. Maternal rank, by itself, had no influence on offspring sex, but did affect maternal body condition. The combined effects of rank and condition indicated the following: mothers in robust condition bore more sons, whereas those in moderate condition bore more daughters, but both effects were expressed most strongly among mothers of high rank. Where the consequences of low rank were felt most acutely, as shown by poor condition, mothers underproduced daughters. Environmental quality directly influenced rank and condition interactions, and thus sex ratios. These relationships, and data from other mammals suggest an empirically and theoretically consistent pattern of sex allocation in mammals. New predictions integrate effects, proposed by Trivers and Willard, that are rooted in male mate competition, which is universal among polygynous mammals, with those of local resource competition (and/or female reproductive competition), which are not universal and differ in intensity between the socioecologies and local environments of different species. Received: 30 May 1998 / Accepted after revision: 29 August 1998     

Parental investment and the secondary sex ratio in northern elephant seals

Summary Data on northern elephant seals, Mirounga angustirostris, bearing on sex ratio theory were collected at Año Nuevo, California, and other Californian and Mexican Islands, during the period 1967 to 1988. The mass of males exceeded that of females by 7–8% at birth and at weaning. The sex ratio was biased to males at birth (51.2%) and was near unity at weaning (49.6% males). The sex ratio did not vary as a function of maternal age or maternal mass except in 6-year-old females, who produced significantly more males. Although sons cost more to rear in energetic terms than daughters, and mothers were more successful weaning the latter, the sex of the pup reared exerted no significant effect on the mother's reproductive performance the following year or on her subsequent survival. These data suggest that parents invest equally in sons and daughters when investment is measured in terms of future reproduction (Fisher 1930) and provide no support for the theory of adaptive shifts in sex ratio (Trivers and Willard 1973). The small sex difference in mass due to maternal effort reflects the fact that females fast during lactation and all energy transferred is from limited body stores. Because of these circumstances, selection for superior condition at the end of the period of parental investment may act more strongly on pups, who have the opportunity to steal milk, than on their mothers.     

Do female roe deer in good condition produce more sons than daughters

In polygynous roe deer Capreolus capreolus, males are only slightly heavier than females and the overall sex ratio at birth is close to unity. We studied offspring sex ratio and litter size (range 1–4, n = 74) of culled females, in utero, which provided an opportunity to examine responses of sex ratio to maternal condition. Male embryos were heavier than their sisters, and male fawns (9 months old) heavier than female fawns, suggesting a higher growth rate in males. There was no evidence for differential mortality between the sexes from birth to 9 months old. Heavier adult females produced larger embryos than lighter, or primiparous females. The overall sex ratio of embryos did not differ from unity, but adult does had more male embryos (55%) than primiparous does (32%), and the proportion of male embryos in a litter increased with the mother's body mass. Litter size also tended to increase with maternal age and body mass. We argue that this pattern reflects adaptive variation in offspring sex ratio.     

Mixed sex allocation strategies in a polytocous mammal,the house mouse (<Emphasis Type="Italic">Mus musculus</Emphasis>)

The issue of adaptive adjustment of offspring sex ratio (proportion of male births) in polytocous mammals, producing several offspring per litter, is controversial because females of these species can maximize their fitness mainly by adjusting offspring number. To address this issue, we examined the effect of maternal condition at mating, experimentally decreased by pre-mating food restriction, on the sex ratio variation in 137 female mice. We tested two basic sex allocation hypotheses plausible for polytocous mammals: (1) the Myers hypothesis, predicting that cheaper sex should be favored in poor environmental conditions to maximize offspring number; and (2) the Williams hypothesis, predicting maximum fitness returns by adjusting size- and sex-specific composition of the litter according to the maternal condition. The food-restricted mothers produced larger litters with a higher proportion of cheaper daughters than the control mothers. By contrast, the control mothers optimized size and sex composition of the litter according to their weight at mating. In addition, the offspring of the food-restricted mothers suffered less from pre-weaning mortality than those of the control mothers. Therefore, when comparing the groups, the Myers hypothesis had a general significance while the Williams hypothesis was plausible only for the control mothers. Furthermore, some of the food-restricted mothers partly coped with the pre-mating food restriction and increased the proportion of sons in the litter with the increasing maternal weight loss (during the period of food restriction). The sex ratio variation was thus a result of three sex allocation strategies depending on the maternal condition at mating.     

Adaptive significance of sex ratio adjustment in semifree-ranging Barbary macaques (Macaca sylvanus) at Salem

Summary New data on the secondary sex ratio in semi-free-ranging Barbary macaques at Salem confirm the observation that the offspring of high-ranking females in this colony are biased towards sons while the offspring of low-ranking females are biased towards daughters. Analysis of interbirth intervals yielded no consistent differences in the relative costs of rearing male and female offspring for either high- or low-ranking females. Survivorship to adulthood of male and female offspring born to mothers of all rank classes was remarkably high, and there was no indication that juvenile females of low-ranking mothers face any greater risk. Daughters of high- and low-ranking mothers showed no substantial differences in reproductive success, while mating and probably reproductive success of sons seemed to be dependent on maternal rank, at least at the beginning of their reproductive career. The results suggest that variation in sex ratio does increase parental fitness. Offprint requests to: A. Paul     

Adaptive sex allocation by brood reduction in antechinuses

Antechinuses (Dasyuridae: Marsupialia) exhibit dramatic interpopulation variation in the sex ratio at birth, a pattern which has previously been interpreted in terms of both local resource competition and Trivers/Willard effects. However, Antechinus stuartii usually fail to wean all the young that attach to their teats. At least in captivity, this is because they often eat their young. In free-living populations, brood reduction affects sons and daughters differently. Mothers virtually always wean some daughters. The probability that a daughter will be weaned declines with the number of daughters in the pouch. The health or quality of the mother does not affect the number of daughters weaned. By contrast, mothers tend to wean all or none of their sons. A strong correlate of infanticide against sons is senescence. Old mothers rarely invest in sons, and produce low-quality daughters. Mothers suffer a direct cost (mortality during lace lactation) of male-biased litters. Coupled with data on prenatal sex allocation, these results support the conjoint influence of local resource competition and the Trivers-Willard effect. However, they suggest that in populations where females are largely semelparous, the population optimum generated by local resource competition may be unattainable, because of the importance of producing at least one daughter. These observations support recent theoretical claims that the sex ratio at the population level is not easily predicted, but suggest that the diversity of mammalian sex allocation tactics has been underestimated.     

Male-biased maternal expenditure and associated costs in fallow deer

This study tested whether fallow deer mothers, Dama dama, bias their investment towards sons and, thus, whether sons are more costly to produce than daughters. Young (2 years) and old (≥3 years) hinds were analysed separately. Old hinds who raised sons accumulated less body mass than those who raised daughters, during the period between late gestation and the end of lactation. This difference in body mass persisted to the following spring. Mothers who had raised sons gave birth later and their offspring's pre-winter mass was lower the following year than for mothers who had raised daughters. These results indicate higher expenditure for hinds who raise sons and support theories of male-biased maternal investment. However, young mothers with sons and those with daughters did not differ in reproductive performance the following year. One reason might be that young mothers are close to the maximum level of maternal expenditure, since they are still growing, and cannot invest any extra resources in sons. Received: 28 August 1997 / Accepted after revision: 5 April 1998     

Sex bias or equal opportunity? Patterns of maternal investment in bison

Summary In polygynous mammals, it may be adaptive for mothers to invest more in sons and/or to adjust the sex ratio of offspring in relation to body condition. Calving patterns were examined over an 8-year period (1982–1989) for a population of Bison bison in which barren females are not selectively culled. From these data, we tested predictions of the sex ratio adjustment hypothesis as well as two assumptions: (1) that offspring weight at the end of the period of parental investment (PI) is correlated with later condition, and (2) that maternal and offspring condition during the period of PI are correlated. In contrast to predictions, there was little evidence that mothers in better condition bear more sons. Short- and long-term measures of maternal condition (previous reproductive status, age, dominance status, pre-pubertal body weight, age at first reproduction, birth date, and the duration of the mother's own suckling period) were little related to offspring sex ratio, although the last calves of old females were nearly always female. Similarly, there was little evidence for sex-biased PI. Weights at about 7 months of age were greater for males than females; males also had somewhat later birth dates, suggesting either longer gestation or later conception. However, maternal reproductive costs, as measured by subsequent fecundity, weight loss, and interbirth intervals, did not vary with calf sex. Both assumptions of the model received some support. However, while maternal condition was correlated with offspring condition, there may be sex differences in investment patterns. Mothers appear better able to influence the condition of daughters than of sons. This sex difference may negate any benefit from male-biased investment.     

Mind the gap: the ratio of yolk androgens and antioxidants varies between sons and daughters dependent on paternal attractiveness

Females are expected to partition resources between offspring in a context-dependent way to maximise total fitness returns from a reproductive attempt. Female zebra finches (Taeniopygia guttata) vary the allocation of yolk androgens and antioxidants among offspring. Importantly, the balance between androgens and antioxidants in yolks may be more important than their independent absolute amounts in terms of fitness consequences for developing young. Therefore, we tested whether the relative allocation of these two resources in yolks varies according to either the Trivers–Willard, positive or compensatory maternal investment hypothesis. We manipulated male attractiveness using coloured leg bands (red-banded males appear attractive; green-banded males, unattractive) and measured yolk androgens and antioxidants in each egg, egg sex, clutch sex ratio and female condition. While female zebra finches manipulated the balance of androgens and antioxidants within and between clutches in response to mate attractiveness, offspring sex and their own condition, they did not do so in a way that consistently followed any of the hypotheses. Mothers paired with unattractive males allocated a larger antioxidant/androgen ratio to daughters than sons. This pattern was reversed when paired to an attractive male; sons received a larger antioxidant/androgen ratio than daughters. We also found offspring sex ratio decreased with increasing female condition for unattractive males, but not for attractive males. However, without knowing the fitness consequences of the balance of different egg constituents, it is difficult to interpret the patterns consistently in terms of the Trivers–Willard, compensatory and positive investment hypotheses.     

Androgen-dependent maternal effects on offspring fitness in zebra finches

There is accumulating evidence that maternal hormones may play a role in offspring sex adjustment, but little is known about the costs of such hormone-mediated mechanisms. Recent studies have reported sex-specific effects of hormones on offspring viability. Specifically, we previously found that elevating the plasma androgen level in mothers results in a male-biased offspring primary sex ratio, but it affects the viability of sons negatively and daughters positively in zebra finches (Taeniopygia guttata; Rutkowska and Cichoń, Anim Behav, 71:1283–1288, 2006). In this study, we studied further fitness consequences of exposure to elevated yolk androgen levels in zebra finches. We measured growth rate and cellular immune response of nestlings that hatched from eggs laid by females injected with testosterone during egg laying and nestlings of unaffected control females. We found that sons of testosterone-treated females grew slower in comparison to sons of control females. The significant interaction between experimental group and offspring sex indicates that sons of testosterone-treated mothers suffered impaired immune responsiveness while daughters seemed to benefit from elevated androgen level in terms of enhanced immune responsiveness. We found no effects of androgens on offspring performance at adulthood—neither fecundity of females nor attractiveness of males was affected. We conclude that the benefits of biasing sex ratio towards males by increasing androgen level in the yolk may be limited due to negative effects on male offspring performance early in life.     

Maternal investment in rhesus macaques (Macaca mulatta): reproductive costs and consequences of raising sons

Maternal investment in offspring is expected to vary according to offspring sex when the reproductive success of the progeny is a function of differential levels of parental expenditure. We conducted a longitudinal investigation of rhesus macaques to determine whether variation in male progeny production, measured with both DNA fingerprinting and short tandem repeat marker typing, could be traced back to patterns of maternal investment. Males weigh significantly more than females at birth, despite an absence of sex differences in gestation length. Size dimorphism increases during infancy, with maternal rank associated with son’s, but not daughter’s, weight at the end of the period of maternal investment. Son’s, but not daughter’s, weight at 1 year of age is significantly correlated with adult weight, and male, but not female, weight accounts for a portion of the variance in reproductive success. Variance in annual offspring output was three- to fourfold higher in males than in females. We suggest that energetic costs of rearing sons could be buffered by fetal delivery of testosterone to the mother, which is aromatized to estrogen and fosters fat accumulation during gestation. We conclude that maternal investment is only slightly greater in sons than in daughters, with mothers endowing sons with extra resources because son, but not daughter, mass has ramifications for offspring sirehood. However, male reproductive tactics supersede maternal investment patterns as fundamental regulators of male fitness. Received: 23 July 1999 / Received in revised form: 23 February 2000 / Accepted: 13 March 2000     

Proximate and ultimate explanations of mammalian sex allocation in a marsupial model

Offspring sex ratios in mammals vary in potentially adaptive yet unpredictable ways. An integrative approach that simultaneously examines proximate and ultimate explanations of mammalian sex ratios would greatly advance the field. We examined the importance of maternal glucose and stress hormones for offspring sex (male or female) as mechanisms associated with the Trivers–Willard and the local resource competition hypotheses of sex allocation. We tested this framework in a marsupial mammal, the tammar wallaby (Macropus eugenii). Mothers that were better able to maintain body condition over the driest part of the year, a presumptive proxy for local resource availability, were more likely to produce daughters (the philopatric sex), consistent with local resource competition. Maternal glucose was correlated with offspring sex, but in the opposite direction than we predicted—higher maternal glucose was associated with female pouch young. These patterns, however, were not consistent across the 2 years of our study. Maternal stress hormone metabolites measured from fecal samples did not predict glucose or offspring sex. A causative glucose mechanism may underlie an adaptive strategy for mothers with high local resources (high glucose) to produce philopatric daughters that will benefit from inheriting resource access. Examining species-specific relationships between glucose and offspring sex across mammals could provide crucial insight into the disparate ecological and selective pressures faced by mammals with respect to offspring sex ratio.     

Female-biased sex allocation of offspring by an <Emphasis Type="Italic">Apodemus</Emphasis> mouse in an unstable environment

We investigated the effects of population fluctuation on the offspring’s sex allocation by a weakly polygynous mouse, Apodemus argenteus, for 3 years. In acorn-poor seasons, heavier mothers invested more in sons, and lighter mothers invested more in daughters. In acorn-rich seasons, heavier mothers invested more in daughters, and lighter mothers invested more in sons. Maternal body condition and litter size affected the sex allocation. Furthermore, there was a maternal investment trade-off between a son’s birth mass and the number of daughters. Based upon the effect of population fluctuation on the lifetime reproductive success of each sex, we proposed the new “safe bet hypothesis”. This hypothesis predicts that frequent and unpredictable change in female distribution, which is often caused by abrupt fall in food condition, favors female-biased maternal investment to offspring by polygynous mammals and is applicable to many small mammals inhabiting in unstable environments.     

Offspring sex ratio response to host size in the parasitoid wasp Spalangia endius

The host size model, an adaptive model for maternal manipulation of offspring sex ratio, was examined for the parasitoid wasp Spalangia endius. In a Florida strain, as the model predicts, daughters emerged from larger hosts than sons, but only when mothers received both small and large hosts simultaneously. The pattern appeared to result from the mother's ovipositional choice and not from differential mortality of the sexes during development. If sex ratio manipulation is adaptive in the Florida strain, it appears to be through a benefit to daughters of developing on large hosts rather than through a benefit to sons of developing on small hosts. Both female and male parasitoids were larger when they developed on larger hosts. For females, developing on a larger host (1) increased offspring production, except for the largest hosts, (2) increased longevity, (3) lengthened development, and (4) had no effect on wing loading. For males, development on a larger host had no effect on any measure of male fitness – mating success, longevity, development duration, or wing loading. In contrast, a strain from India showed no difference in the size of hosts from which daughters versus sons emerged, although both female and male parasitoids were larger when they developed on larger hosts. These results together with previous studies of Spalangia reveal no consistent connection between host-size-dependent sex ratio and host-size-dependent parasitoid size among strains of S. endius or among species of Spalangia. Received: 28 October 1998 / Received in revised form: 20 May 1999 / Accepted: 30 May 1999     

Brood sex ratio is dependent on female mating status in polygynous great reed warblers

Females capable of adjusting the sex ratio of their offspring should be more fit than females lacking such an ability. In polygynous birds where breeding success in males is more strongly influenced by body size and/or attractiveness than in females, females might produce more sons when predicting good conditions or when mating with attractive males. Polygynous great reed warbler, Acrocephalusarundinaceus, males direct most of their feeding effort to the primary (first-hatching) nest and in these nests increase their feeding effort in relation to the brood sex ratio (proportion of sons). Therefore, with the expectation of well-nourished sons, we would predict that females which start breeding first within harems might produce more sons than those which start breeding later, and in anticipation of sons with good genes, that females mated to polygynous males might produce more sons than females mated to monogamous males. I took blood samples from hatchlings and determined the sex using DNA markers. The sex ratio of primary (monogamous and polygynous primary) broods is more male-biased (mean 0.58 males, n = 50) than that of secondary (polygynous secondary and tertiary) broods (mean 0.46, n = 25). Moreover, in the secondary broods with the largest clutch (five eggs), in which offspring are most likely to suffer food shortage, the sex ratio was distinctively female biased (mean 0.33, n = 10). In the primary broods, sex ratio was correlated to harem size. The results suggest that great reed warbler females modify the brood sex ratio to produce both well-nourished sons and sons with good genes, but the former effect is probably stronger than the latter factor. Received: 11 March 1998 / Accepted after revision: 23 May 1998     

Parental investment and its ecological consequences in the solitary wasp Sceliphron assimile (Dahlbom) (Sphecidae)

Summary The sphecid wasp Sceliphron assimile Dahlbom builds mud cells whose volumes are positively correlated to maternal length, the relationship being highly significant for daughters (Fig. 1). However, small females build cells longer and wider in relation to their own body length than large females do (Fig. 3). Cell volume closely regulates the total weight of prey stocked per cell (Figs. 4, 10). Maternal length is directly related to prey size and inversely related to the number of prey stocked (Fig. 5). Female length, above a threshold of 19 mm, probably does not influence her chance of starting a nest (Fig. 6) but is strongly positively correlated to achieved fecundity. Large females have larger offspring and a higher proportion of daughters than small females do (Fig. 7), but this is largely controlled by maternal behaviour rather than by genetical mechanisms (Fig. 10). The results are in general agreement with those of Trivers and Hare (1976) for solitary wasps, but large progeny are cheaper to produce per unit weight than small ones, and for a given weight sons are cheaper to produce than daughters.     

Sex ratio manipulation and decreased growth of male offspring of undernourished golden hamsters (Mesocricetus auratus)

Summary The theory that female mammals in poor condition may increase individual fitness by skewing the sex ratio of their offspring toward daughters and by investing more resources in daughters than in sons was tested in hamsters. Newly mated experimental females were food-restricted during pregnancy and lactation (RR) or during lactation only (AR). Controls received food ad libitum. Maternal body weights were assessed daily from mating to 25 days postpartum. Litter survival (% litters with at least one pup surviving on any day), litter size, offspring sex ratios (=% males), and pup weights were monitored daily from birth (Day 1) to Day 25. All control and AR dams gave birth 16 days after mating. Gestation was extended by 1–3 days for 35.4% of RR dams. RR dams weighed significantly less at parturition than controls and AR females. During lactation, AR females showed the greatest weight loss and control females the least. AR weight loss exceeded that of RR females, possibly because the former maintained larger litters. Survival was highest for controls, intermediate for AR, and lowest for RR litters. Mean sex ratio at birth was significantly less for RR (40.7%) than for control (49.6%) and AR (48.8%) litters. RR sex ratio did not change significantly postnatally. Sex ratios of control and AR litters never differed statistically from 50%. Control male pups were significantly heavier than their sisters throughout the experiment. No significant gender differences were observed for AR pup weights after Day 2 postpartum. RR female offspring weighed more than their brothers throughout the experiment, and this difference was statistically significant immediately prior to the time that pups began to feed independently (Days 14–17). RR female pup weights were similar to, and sometimes significantly greater than, weights of control daughters during the period of postnatal maternal investment. Control males were always heavier than males from the other treatments. Patterns of weight gain by AR and RR males varied with age. We conclude that underfed female hamsters are able to adjust the sex ratio of offspring prenatally and parental investment postnatally to favor daughters.     

Maternal quality and differences in milk production and composition for male and female Iberian red deer calves (Cervus elaphus hispanicus)

Several theories predict a sex-biased investment either through unbalanced sex ratios in offspring or through differences in provisioning. According to them, one would expect an optimisation in indirect fitness, or else a compensation for increased mortality of one sex. In addition, biases in provisioning may also arise as a consequence of weight-dependent non-adaptive nutrient demands by offspring. This study examines milk provisioning and sex biases in offspring sex ratio together with maternal quality variables. Mothers of higher quality (weight and age) showed greater milk provisioning ability (in terms of production) resulting in greater calf weight gain. Mothers of sons produced greater yields of milk, milk protein, fat and lactose than mothers of daughters, and increased percentage of protein after controlling for higher male birth weight. In contrast, mothers of males did not differ from mothers of females in age or any body weight variables related to maternal quality. These results suggest that differences in milk production and composition for sons and daughters are rather a mechanism to optimise indirect fitness than a mechanism to compensate for increased mortality in male calves, or a consequence of greater weight-dependent nutrient demands by heavier male calves. Results also suggest that biases in milk provisioning may occur without biases in offspring sex ratio, and furthermore, in contrast to the prediction that biases should be relative to the mean investment of the population, that milk provisioning biases might not be relative.Communicated by F. Trillmich     

Maternal investment in Antarctic fur seals: evidence for equality in the sexes?

Studies of the otariids (fur seals and sea lions), a highly sexually dimorphic group, have provided conflicting evidence of differential maternal expenditure in male and female offspring and, thus, suggestions that they conform to predictions of investment theory are equivocal. Since the mid-1970s, a diversity of research on Antarctic fur seals (Arctocephalus gazella) including studies of their reproductive ecology, lactation energetics, and foraging behaviour have been conducted at Bird Island, South Georgia that have resulted in one of the more complete and diverse data sets for any species of otariid. These long-term data were reviewed to determine whether there was any evidence to support that differential maternal expenditure occurred in Antarctic fur seals. Most of the data examined were collected during five consecutive austral summers from 1988 through 1992 and included years in which local food resources were abundant and scarce. We were unable to detect differences in the sex ratios of pups at birth or sex-biased differences in growth rates estimated from serial data, the number of foraging trips made, the duration of attendance ashore, diving behaviour, suckling behaviour, or milk consumption in any year and in the duration of foraging trips or age at weaning in 2 of 3 years. In addition, we found no evidence of greater reproductive costs between mothers with sons or daughters relative to their reproductive performance the following year. In contrast, sex-biased differences were only found in the duration of foraging trips in 1990, the age at weaning in 1988, and consistently in growth rates estimated from cross-sectional data. We suggest that differential maternal expenditure does not occur in Antarctic fur seals because male pups probably do not gain greater benefit from additional maternal expenditure than female pups. After weaning, males experience a period of rapid juvenile growth over 3–4 years during which time body mass nearly trebles. This growth will almost certainly be dependent upon available food resources then rather than on any maternal expenditure received over the first 4 months of life and, thus, the assumptions of the Trivers and Willard hypothesis are probably invalid for Antarctic fur seals. Received: 10 July 1996 / Accepted after revision: 3 March 1997