Inbreeding avoidance in a poeciliid fish (Heterandria formosa)

Polyandry is hypothesized to give females an opportunity to avoid inbreeding through postcopulatory selection mechanisms if precopulatory inbreeding avoidance is not possible, for example, because of forced matings. Here, we report a postcopulatory, prefertilization, inbreeding avoidance mechanism in the least killifish, Heterandria formosa, a species in which males can force matings. Females had 50% less sperm in their oviducts and ovarian cavities after mating with a sibling compared to a mating with a nonsibling male. Neither sex showed inbreeding avoidance in a dichotomous precopulatory mate choice test or during mating trials. Females in this species invest substantially in each offspring after fertilization (matrotrophy), whereas males invest little more than sperm. Based on theory, females should therefore be more likely than males to avoid inbreeding in this species. We suggest that females do this by reducing the amount of sibling sperm in their reproductive system. However, the possibility that males invested more sperm to nonsiblings could not be ruled out. In a fertilization success experiment, the first male to mate with a female sired all the offspring in most cases, even if it was a sibling. However, large females were more likely to carry offspring of multiple males. Possibly female sperm storage sites were filled by the first male, and only large females had space for the second male's sperm.     

Paternal investment in Poecilimon veluchianus bushcrickets: beneficial effects of nuptial feeding on offspring viability

In most bushcrickets, males transfer a large spermatophore during copulation that is afterwards consumed by the female. In some species this nuptial gift enhances offspring fitness and is therefore believed to function as paternal investment. To determine whether this is the case, I examined whether a male's own offspring benefit from spermatophore consumption in the bushcricket Poecilimon veluchianus. Females that consumed a spermatophore produced offspring with increased residuals of dry weight compared to females that were prevented from feeding on the spermatophore. This beneficial effect of spermatophore consumption occurred within the first 4 days after copulation. An increased dry weight indicates higher energy reserves because offspring dry weight correlates significantly with the lifespan of starved larvae and because spermatophore consumption increased the lifespan of starved offspring. During egg-laying, females apply a liquid substance to the soil that hardens and probably serves as protection for the egg clutch. The amount of this substance correlated with the number of eggs laid but did not differ between spermatophore treatments. In P. veluchianus, females mate frequently and there is last-male sperm precedence. The spermatophore thus only constitutes paternal investment when offspring produced before female remating benefit from spermatophore consumption. The dry weight of offspring increased during the first 4 days after spermatophore consumption and thus within the natural remating interval. This shows that the spermatophore has a paternal investment function in addition to its already known sperm protection function. Received: 15 May 1998 / Accepted after revision: 11 October 1998     

Female choice in the opportunistic mating of wild chimpanzees (Pan troglodytes schweinfurthii) at Mahale

For female chimpanzees (Pan troglodytes schweinfurthii) in the Mahale Mountains National Park, Tanzania, the most common mating pattern is opportunistic. In such opportunistic matings, females copulated promiscuously but not randomly. This study describes female mate choice during 1-year observation of six females who exhibited regular genital-swelling cycles. During the study period, 169 opportunistic matings and four restrictive matings were recorded over the course of 51 days. As female estrus progressed, mating frequency and the number of adult male mating partners increased, although the number of potential mating partners did not change. Criteria of female choice examined were the direction and consent/rejection of courtship, proximity maintenance, and female grooming. Adult-male courtships were successful more often than those of adolescent males. During the earlier phase of estrus, females copulated rather promiscuously with many males. But during the later phase of estrus when the likelihood of conception is expected to be highest, they copulated repeatedly with high-ranking adult males. There was a positive correlation between female grooming frequency and mating frequency when the likelihood of conception was greatest. Female chimpanzees are thought to choose high-ranking males as fathers of their offspring. Moreover, female chimpanzees may adopt one or both of two mating strategies, i.e., a many-male strategy and a best-male strategy. Received: 23 November 1998 / Received in revised form: 12 April 1999 / Accepted: 26 April 1999     

The effect of male sodium diet and mating history on female reproduction in the puddling squinting bush brown<Emphasis Type="Italic"> Bicyclus anynana</Emphasis> (Lepidoptera)

The males of butterflies transfer a spermatophore to the female during mating that can contain nutrients enhancing the reproductive potential of their partners. The nutrients transferred by males can be derived from both larval and adult feeding. These nutrients may be depleted by multiple matings. An apparent difference in adult feeding behaviour between the sexes is puddling on mud, dung and carrion, which in most butterfly species is exclusively a male behaviour. A possible explanation for this division in feeding behaviour is that nutrients derived from puddling by males are transferred to the female during mating. Here, we test this hypothesis in the African fruit-feeding butterfly Bicyclus anynana. We varied the male nuptial gift by (1) feeding males either a diet with or without sodium, and (2) varying the number of previous successful copulations by remating males up to five times on consecutive days. The results show both a strong effect of order of mating on the mating duration, and an individual effect with some males typically copulating for a shorter time than others. The effects on female reproduction were, however, minimal. The total number of eggs per female and the sodium content of the eggs did not differ significantly between diets, nor were they affected by the mating histories of the males. Eggs showed a non-significant lower hatching for females partnered by a male who had already mated several times. There was an indication of an interaction with male diet: the sodium treatment showing a decline in egg hatchability with order number of male mating, whilst the control treatment showed a constant hatchability. The results are discussed in relation to determinants of male gift-giving strategy and to other potential explanations for a restriction of puddling to males in butterflies.Communicated by M.A. Elgar     

Mate choice in the face of both inbreeding and outbreeding depression in the intertidal copepod Tigriopus californicus

 In species vulnerable to both inbreeding and outbreeding depression, individuals might be expected to choose mates at intermediate levels of genetic relatedness. Previous work on the intertidal copepod Tigriopus californicus has repeatedly shown that crosses between populations result in either no effect or hybrid vigor in the first generation, and hybrid breakdown in the second generation. Previous work also shows that mating between full siblings results in inbreeding depression. The present study again found inbreeding depression, with full sibling mating causing significant fitness declines in two of the three populations assayed. In the mate choice assays, a single female was combined with two males. Despite the costs of both inbreeding and outbreeding, mate choice showed clear inbreeding avoidance but no clear pattern of outbreeding avoidance. This lack of outbreeding avoidance may be attributed either to the temporary increase in fitness in the F₁ generation or to the absence of selection for premating isolation in wholly allopatric populations with infrequent migration. If this inability to avoid unwise matings is common to other taxa, it may contribute to the problem of outbreeding depression when allopatric populations are mixed together. Received: 18 May 1999 / Accepted: 25 January 2000     

Copulation duration,but not paternity share,potentially mediates inbreeding avoidance in Drosophila montana

Studying the incidence of inbreeding avoidance is important for understanding the evolution of mating systems, especially in the context of mate choice for genetic compatibility. We investigated whether inbreeding avoidance mechanisms have evolved in the malt fly, Drosophila montana, by measuring mating latency (a measure of male attractiveness), copulation duration, days to remating, offspring production, and the proportion of offspring sired by the first (P₁) and second (P₂) male to mate in full-sibling and unrelated pairs. SNP markers were used for paternity analysis and for calculating pairwise relatedness values (genotype sharing) between mating pairs. We found 18 % inbreeding depression in egg-to-adult viability, suggesting that mating with close relatives is costly. Copulation duration was shorter between previously mated females and their brothers than with unrelated males. Based on an earlier study, shorter copulation is likely to decrease the number of inbred progeny by decreasing female remating time. However, shorter copulations did not lead to lower paternity (P₂) of full-sibling males. Progeny production of double-mated females was lower when the second male was a full-sibling as compared to an unrelated male, but we could not distinguish between inbreeding depression and lower female reproductive effort after mating with a relative. Relatedness estimates based on 34 SNPs did not detect any quantitative effect of relatedness variation on copulation duration and progeny production. We suggest that inbreeding depression has been strong enough to select for inbreeding avoidance mechanisms in our Finnish D. montana population.     

A field test of the effects of familiarity and relatedness on social associations and reproduction in prairie voles

Inbreeding depression is a well-documented phenomenon. In animals, one means of avoiding the costs of inbreeding is through the recognition and avoidance of kin as mates. Prairie voles (Microtus ochrogaster) are short-lived, socially monogamous rodents that demonstrate inbreeding depression in the laboratory. Field data indicate that pair formation in nature is opportunistic but pairing among close relatives seems uncommon. We examined the role of relatedness and familiarity on prairie vole social associations and reproduction by placing adult voles into 0.1-ha enclosures with familiar siblings, unfamiliar siblings, and unrelated, unfamiliar conspecifics. Live-trapping data indicated that indices of social pair bonding were random with respect to relatedness and familiarity. Among females whose litters were sired by a single male, litters were significantly more likely to be sired by unfamiliar than familiar males, but the number of litters sired by males that were unrelated to their partner was not different from the number of litters sired by males that were related to their partner. Additionally, females that produced offspring with familiar siblings were significantly more likely to have litters with multiple paternity than females not producing offspring with familiar siblings. However, multiple paternity was not influenced by relatedness of sires. Finally, older individuals were more likely to produce offspring with each other than with younger individuals. Our findings suggest that prior association is a more important mechanism of inbreeding avoidance than phenotype matching for prairie voles mating under ecologically relevant conditions.     

Polyandry and enhanced reproductive success in the harlequin-beetle-riding pseudoscorpion

The growing molecular evidence that females of many species mate with several males calls for a critical reassessment of the selective forces which act to shape female mating tactics. In natural populations of the harlequin-beetle-riding pseudoscorpion, Cordylochernes scorpioides, females are polyandrous and typically produce mixed-paternity broods. Laboratory behavioral analyses and breeding experiments indicate that polyandry in this pseudoscorpion is an active strategy which increases female reproductive success. Females restricted to mating with a single male experienced a higher rate of embryo failure and produced significantly fewer offspring than either females mated to more than one male in the laboratory or females naturally inseminated in the field. Forced copulation, insufficient sperm from a single mating, male nutrient donations and variation in inherent male genetic quality cannot explain the greater number of nymphs hatched by polyandrous females in this study. Evidence suggests that, by mating with several males, C. scorpioides females may exploit postcopulatory mechanisms for reducing the risk and/or cost of embryo failure resulting from fertilization by genetically incompatible sperm. Received: 5 May 1996 / Accepted after revision: 16 October 1996     

Inbreeding level does not induce female discrimination between sibs and unrelated males in guppies

Significant empirical evidence has demonstrated the importance of discriminative mate choice as a mechanism to avoid inbreeding. Incestuous mating can be avoided by recognition of kin. The guppy, Poecilia reticulata, is a livebearer with a polygamous mating system and active female choice. Despite potential inbreeding costs in the guppy, Viken et al. (Ethology 112:716–723, 2006) and Pitcher et al. (Genetica 134:137–146, 2008) have found that females do not discriminate between sibs and unrelated males. However, populations experiencing different inbreeding histories can have different levels of inbreeding avoidance, and it is possible that the lack of inbreeding avoidance observed in guppies is a consequence of using outbred fish only. Here we tested the preference of female guppies with different inbreeding coefficients, for olfactory cues of males that were either unrelated but had the same inbreeding coefficient, or were related (i.e. brother) with the same inbreeding coefficient. We found no evidence that female guppies preferred unrelated males with the same inbreeding coefficient. Moreover, inbreeding level did not influence female preference for unrelated males, suggesting that inbreeding history in a population has no influence on female discrimination of unrelated males in guppies.     

The effects of age and relatedness on mating patterns in thornbug treehoppers: inbreeding avoidance or inbreeding tolerance?

The social environment of many species includes synchronous maturation of siblings in family groups, followed by limited dispersal of adults from their natal site. Under these conditions, females may experience high encounter rates with same-age siblings during mate searching, increasing their risk of inbreeding. If inbreeding depression occurs, mating with a sibling is often considered maladaptive; however, in some contexts, the inclusive fitness benefits of inbreeding may outweigh the costs, favoring females that tolerate some level of inbreeding depression. We evaluated mating patterns in the treehopper Umbonia crassicornis, a semelparous species in which females encounter same-age siblings during mate searching. A female U. crassicornis that mates with a brother suffers from inbreeding depression. We used a free-choice mating design that offered females simultaneous mating opportunities with three groups of males: siblings, same-age nonsiblings, and older nonsiblings. These groups represent the types of males typically encountered by females during mate searching. Our goal was to assess whether mating patterns were influenced by inbreeding avoidance by evaluating two hypotheses: kin discrimination and age-based mating (older males cannot be siblings in this species). There was no difference in the proportions of females mating with siblings vs nonsiblings, suggesting an absence of kin discrimination. However, females mated with a greater proportion of older vs younger males. Given that females do not avoid siblings as mates despite a cost to inbreeding, our results provide a possible example of inbreeding tolerance. We also discuss some factors that may have contributed to the mating advantage of older males.     

Fallow deer polyandry is related to fertilization insurance

Polyandry is widespread, but its adaptive significance is not fully understood. The hypotheses used to explain its persistence have rarely been tested in the wild and particularly for large, long-lived mammals. We investigated polyandry in fallow deer, using female mating and reproduction data gathered over 10 years. Females of this species produce a single offspring (monotocous) and can live to 23 years old. Overall, polyandry was evident in 12 % of females and the long-term, consistent proportion of polyandrous females observed, suggests that monandry and polyandry represent alternative mating strategies. Females were more likely to be polyandrous when their first mate had previously achieved high numbers of matings during the rut or was relatively old. However, polyandry was not related to the following factors: female age, the stage of the rut, the dominance ranks of mates, or the number of daily matings achieved by males. Polyandrous and monandrous multiple-mating females were not more likely than single-mating females to be observed with an offspring during the following year, and there were no significant differences in offspring size between these females. These results provide support for a fertility insurance hypothesis, with females remating if fertilization from the first mating was uncertain due to possible sperm depletion. The potential for different female mating strategies among large, polygynous mammals has generally been overlooked. Our findings highlight the complexity of female reproductive strategies and the possible trade-offs between fertilization success, preferences for high-quality males, and potential costs of polyandry, particularly for monotocous species.     

Effects of size and nuptial gifts on butterfly reproduction: can females compensate for a smaller size through male-derived nutrients?

In butterflies and other insects, fecundity generally increases with female adult weight. Hence, most butterflies are essentially "capital breeders", because nutrients acquired during the larval stage are stored and subsequently used for egg production during the adult stage. However, in some species, males transfer a large nutritious ejaculate to the female at mating. These females can partly be characterized as "income breeders", and female mass can potentially be decoupled from fecundity to some extent. In the gift-giving green-veined white butterfly Pieris napi, it has been shown that female fecundity and longevity increase with number of matings and also that females mature at smaller size under poor food conditions compared to males. So it has been suggested that females can compensate for their smaller size through nuptial feeding. Here we test this hypothesis in P. napi by assessing female fecundity and longevity in relation to female mass and polyandry. The results showed no support for the hypothesis. Smaller females were not capable of increasing their mating rate to compensate for a low weight at eclosion. Instead, larger females remated sooner. Also, smaller females suffered from both a reduced daily and total fecundity compared to larger females and this decrease in fecundity was independent of female mating status, i.e. females allowed to mate only once and multiply mated females suffered to the same extent from their smaller size.     

Indirect genetic benefits of polyandry in a spider with direct costs of mating

The search for the evolutionary explanation of polyandry is increasingly focused on direct and indirect selection on female resistance. In a polyandrous spider Stegodyphus lineatus, males do not provide material benefits and females are resistant to remating. Nevertheless, polyandrous females may obtain indirect genetic benefits that offset the costs associated with multiple mating. We manipulated the opportunity for females to select between different partners and examined the effect of female mating history (mated once, mated twice, or rejected the second male) on offspring body mass, size, condition, and survival under high- and low-food rearing regimens. We found that multiple mating, not female choice, results in increased female offspring body mass and condition. However, these effects were present only in low-food regimen. We did not find any effects of female mating history on male offspring variables. Thus, the benefits of polyandry depend not only on sex, but also on offspring environment. Furthermore, the observed patterns suggest that indirect genetic benefits cannot explain the evolution of female resistance in this system.     

Fitness benefits of multiple mating versus female mate choice in the cellar spider (Pholcus phalangioides)

Recent studies have demonstrated that mating with multiple males can be beneficial for females and her offspring even if males contribute nothing but sperm. This was mainly established for species in which sperm from several males mix in the reproductive tract of the female, thus allowing sperm competition and/or female sperm choice. However, in species with last male sperm precedence, female re-mating decides against the previous male by strongly limiting his reproductive success. We tested the effect of female re-mating behaviour using the cellar spider Pholcus phalangioides, which shows strong last males sperm precedence and moderate levels of polyandry under natural situations. We predicted that females prevented from remating even though they are receptive would show reduced reproductive success compared to females that accept two copulations and females that reject a second male, since the latter two treatments were allowed to behave according to their decisions. However, if the number of matings per se had an effect on oviposition or on offspring performance, double-mated females should perform better compared to both treatments of once-mated females. We measured female fecundity and fertility over a period of 140 days, comparable to the species' natural reproductive peak season. Two thousand one hundred and fifty-two offspring from 67 first egg sacs were reared under two feeding levels. We registered development time and survival, and measured offspring adult size and mass. We found a positive effect of double mating, as in this treatment, oviposition probability was higher compared to the other treatments. Interestingly, adult female offspring of the DM treatment that were raised under low food level had a higher condition index compared to those from FS and RM, but development time, size and mass at adulthood were not affected by mating treatment. Female choice only seemed to affect hatching latency of the offspring. Overall, the main predictor of female reproductive output and success was female body size.     

Should he stay or should he go: male influence on offspring sex ratio via postcopulatory attendance

In species without nuptial gifts or parental care, postcopulatory attendance of females by males has generally been interpreted as males guarding against sperm competition. Guarding benefits may be concurrent with attendance (the guarding-now hypothesis), or male behavior during attendance may make the female unreceptive (the guarding in absentia hypothesis). However, in addition to guarding functions, attendance may provide the male with an opportunity to influence the female's use of sperm. In haplodiploids such as hymenopterans, doing so may be beneficial because only daughters and not sons are produced sexually and so influence male reproductive success (the sex ratio hypothesis). In the parasitoid wasp Urolepis rufipes, postcopulatory attendance involved the male remaining mounted after copulation and resuming courtship. Support for the guarding-now hypothesis was limited. A male's presence on a female did not reduce the probability, or quickness, of another male mounting, and second-mounted males frequently copulated. The guarding in absentia hypothesis was not supported. Females became unreceptive soon after mating even when copulation and postcopulatory attendance were experimentally prevented. The sex ratio hypothesis was supported. Postcopulatory attendance caused females to produce more daughters. They also produced more total offspring. Thus, a male should stay and should not go even in the absence of other males, at least when opportunities for other matings are absent as in the present study. Although most studies of offspring sex ratios have focused on maternal control, this study provides an example of apparently adaptive male influence on sex ratio.     

Prior encounters with the opposite sex affect male and female mating behavior in a wolf spider (Araneae,Lycosidae)

Mate availability can vary widely in nature depending upon population density and sex ratio and can affect the ability of individuals to be selective in mate choice. We tested the effects of prior encounters with the opposite sex (i.e., exposure to the opposite sex either with or without mating) on subsequent mating behavior in two experiments that manipulated mate availability for both males and females in the wolf spider, Hogna helluo. The probability of mating in the experimental trial depended upon whether the prior encounter involved mating or not, and males and females responded in opposite directions. Exposure without mating resulted in a higher subsequent frequency of mating for females and a lower subsequent frequency of mating for males, while prior mating experience resulted in a lower frequency of female remating and a higher frequency of male remating. Prior exposure without mating did not affect female aggression. However, mated females engaged in precopulatory cannibalism more frequently than virgins. Mated males escaped postcopulatory cannibalism more frequently than virgins. Our results show that males respond to exposure without mating in the expected manner. However, prior mating (1 week earlier) had unexpected effects on males, which may be due to mated males being of higher quality. There were little or no effects of the size of the prior exposure individual or mate on subsequent mating behaviors. Further research is needed to determine why different species use different degrees of prior information in mate choice.     

Sex-biased dispersal in a long-lived polygynous reptile (Crocodylus johnstoni )

We compared natal dispersals of freshwater crocodiles (Crocodylus johnstoni) against the prediction of male dispersal bias for a polygynous mating system. The crocodiles inhabited a linear series of pools and we calculated the net distances from natal pools to recapture locations some 12–18 years later, at maturity. Philopatry was assessed in terms of adult social distances. A female social distance was 0.46 pools and a male social distance was 1.0 pool. By these criteria, both sexes showed low levels of philopatry (7–12%). However, individuals of both sexes dispersed from the natal site long before they were sexually mature. Divergence in dispersal patterns by sex occurred after the maturity threshold, as males dispersed two to three times farther than females. Intrasexual competition by males is resolved by a size-based hierarchy. The displacement of small males from local mating access is a probable cause of the longer dispersals undertaken by males. Competition, rather than inbreeding avoidance, is driving dispersal in this population of freshwater crocodiles. Received: 8 May 1998 / Accepted after revision: 26 June 1998     

Sex-specific reproductive behaviours and paternity in free-ranging Barbary macaques (Macaca sylvanus)

In a wide variety of species, male reproductive success is determined by contest for access to females. Among multi-male primate groups, however, factors in addition to male competitive ability may also influence paternity outcome, although their exact nature and force is still largely unclear. Here, we have investigated in a group of free-ranging Barbary macaques whether paternity is determined on the pre- or postcopulatory level and how male competitive ability and female direct mate choice during the female fertile phase are related to male reproductive success. Behavioural observations were combined with faecal hormone analysis for timing of the fertile phase (13 cycles, 8 females) and genetic paternity analysis (n = 12). During the fertile phase, complete monopolisation of females did not occur. Females were consorted for only 49% of observation time, and all females had ejaculatory copulations with several males. Thus, in all cases, paternity was determined on the postcopulatory level. More than 80% of infants were sired by high-ranking males, and this reproductive skew was related to both, male competitive ability and female direct mate choice as high-ranking males spent more time in consort with females than low-ranking males, and females solicited copulations mainly from dominant males. As most ejaculatory copulations were female-initiated, female direct mate choice appeared to have the highest impact on male reproductive success. However, female preference was not directly translated into paternity, as fathers were not preferred over non-fathers in terms of solicitation, consortship and mating behaviour. Collectively, our data show that in the Barbary macaque, both sexes significantly influence male mating success, but that sperm of several males generally compete within the female reproductive tract and that therefore paternity is determined by mechanisms operating at the postcopulatory level.     

Sperm precedence and sperm storage in multiply mated red flour beetles

In insects, the last male to mate with a female often gains access to a disproportionate number of subsequent fertilizations. This study examined last-male sperm precedence patterns in doubly and triply mated Tribolium castaneum females. Sperm storage processes were investigated by measuring the quantity of sperm stored within the female spermatheca following single, double, and triple matings. Both doubly mated and triply mated females exhibited high last-male sperm precedence for progeny produced during the first 48 h following the last mating, with females in both groups exhibiting parallel declines in sperm precedence 1 and 2 weeks later. The number of sperm stored by females increased by 33% between singly mated and doubly mated females, indicating that the spermatheca is filled to only two-thirds capacity following insemination by the first male. Based on the proportion of stored sperm from first and second matings, we tested predictions about sperm precedence values based on models of random sperm mixing. High initial last-male sperm precedence strongly supports stratification of last-male sperm. By 1–2 weeks after double matings, sperm precedence declined to levels indistinguishable from values expected under random mixing. These results provide insight into mechanisms of sperm storage and utilization in this species. Received: 20 August 1997 / Accepted after revision: 24 May 1998     

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