Seasonal variation of reproductive success under female philopatry and male-biased dispersal in a common vole population

Variation of reproductive success, an important determinant of the opportunity for sexual selection, is an outcome of competition within one sex for mating with members of the other sex. In promiscuous species, males typically compete for access to females, and their reproductive strategies are strongly related to the spatial distribution of females. I used 10 microsatellite loci and the mtDNA control region to determine seasonal differences in the reproductive success of males and females of the common vole (Microtus arvalis), one of the most numerous mammals in Europe. The sex-related spatial structure and bias in dispersal between genders were also assessed. Standardized variance of the reproductive success of females did not vary seasonally due to the continuity of female philopatry throughout the breeding season and to the constancy of the number of females reproducing successfully in each season. The males are the dispersing sex, undergoing both natal and breeding dispersal. Their standardized variance of reproductive success was significantly higher than that for females in July, when only two males monopolized 80% of the females in the population and when variance of male reproductive success was highest (I_m = 7.70). The seasonally varying and high standardized variance of male reproductive success may be explained by male-male competition for matings, coupled with seasonal changes in the age structure of the population.     

Territorial behavior of the plethodontid salamander Plethodon kentucki: influence of habitat structure and population density

To investigate the possible influence of variation in ecological and demographic factors on the spatial organization of the terrestrial plethodontid salamander Plethodon kentucki, I conducted a 3-year capture-recapture study and determined home-range characteristics and spatial relationships of individuals at two field sites that differed in predominant cover type and population density. Home ranges of adults were fixed and the home ranges of same-sex adult neighbors were mostly exclusive. The spatial arrangement of adult home ranges exhibited overall regularity or regularity within aggregations, whereas the distribution of juvenile home ranges was usually random. Analysis of nearest-neighbor sex indicated a positive intersexual association of adult home ranges. Removal studies provided evidence for defense of adult home ranges only at the high-density site. The distribution of home ranges was influenced by the presence of cover objects, but there was no significant relationship between adult body size and percent of home-range area with cover. Males overlapped the home ranges of gravid females significantly more often than those of non-gravid females, indicating that the distribution of gravid females had a strong influence on the distribution of male home ranges. In laboratory tests, increased male-male aggression during the breeding season suggests that males may compete for access to mates. At the high-density site, larger males may have benefited by having greater reproductive success than smaller males because they were more dominant and their home ranges overlapped a greater number of gravid-female home ranges. My results indicate that habitat structure and population density may influence the spatial organization and mating system of P. kentucki. Received: 26 May 1997 / Accepted: 9 October 1997     

Sex‐related spatial patterns of Poa ligularis in relation to shrub patch occurrence in northern Patagonia

Abstract. Poa ligularis is a dioecious species and a valuable forage plant which is widespread in the arid steppe of northern Patagonia (Argentina). The vegetation in these areas consists of a system of perennial plant patches alternating with bare soil areas defining contrasting micro‐environments. We hypothesized that (1) male and female individuals of P. ligularis are spatially segregated in different micro‐environments, (2) the intensity of spatial segregation of sexes depends on plant structure and (3) spatial segregation of sexes is enhanced by competitive interactions between the sexes within the vegetation patches. We analysed the spatial distribution of female and male individuals in relation to the spatial pattern of vegetation in two areas differing in their vegetation structure. The location of P. ligularis within patches where either male, female or both sexes occurred was also analysed. The results indicate that different patterns of spatial distribution of sexes of P. ligularis may be found at the community level depending on the dominant life forms and geometric structure of plant patches. Where patches are of a lower height, with a high internal patch cover, individuals of both sexes are concentrated within patch canopies. In sites characterized by large, tall patches and less internal patch cover suitable microsites for female and male P. ligularis occur both within and outside the patch with males located at further distances from the patch edge. Where the patch is large and tall enough to allow the establishment of males and females at relatively high numbers, males occupy the patch periphery or even colonize the interpatch bare soil. These spatial patterns are consistent with selective traits in which females better tolerate intraspecific competition than males, while males tolerate wider fluctuations in the physical environment (soil moisture, nitrogen availability, wind intensity, etc.).     

Seasonal Variation in Mate Choice of Photinus ignitus Fireflies

Mate choice by either sex may vary with changes in the associated costs and benefits, determined by factors such as the availability of potential mates and variation in mate quality. We examined seasonal variation in operational sex ratio, courtship behavior, spermatophore mass, egg count, and the relationship between morphological traits and mating success in Photinus ignitus fireflies to determine if mate choice in either sex varied with the availability and relative reproductive investment of fertilizable females and sexually active males. Successfully mating males had larger lanterns than unsuccessful males when the operational sex ratio was male‐biased. In addition, female responsiveness to male signals increased as the number of courting males decreased, and male spermatophore mass decreased with body size across the mating season. Successfully mating females had larger body mass than unsuccessful females. Female body mass predicted egg count and female rejection by males increased as the season progressed and female size decreased. These results suggest that both male and female P. ignitus exhibit mate choice, and that such choice is influenced by seasonal variation in the abundance and quality of potential mates.     

A SEX DIFFERENCE IN THE PROPENSITY TO ENTER DIRECT/DIAPAUSE DEVELOPMENT: A RESULT OF SELECTION FOR PROTANDRY

In monandrous mating systems with discrete nonoverlapping generations males should maximize the expected number of matings by starting to emerge before females. This is known as protandry. Moreover, Evolutionarily Stable Strategies (ESS) models show that the male emergence curve should be abruptly truncated before female emergence has ceased. In temperate areas where many insects have partial second generations, we accordingly predict that males should enter diapause development at an earlier date than should females, as a result of late-emerging males being penalized in terms of fewer mating opportunities. The decision to diapause or to develop directly is usually mediated by response to environmental stimuli of which day length is the most important. Hence we predict that the mechanism by which males enter diapause at an earlier date than females will be that of the male reaction norm for diapause development being shifted towards longer day lengths when compared to that of females. As a result of the greater tendency of males to enter diapause development, partial second generations that develop directly should be female biased. As a corollary, first generations should be male biased because some males of the first generation are from the previous year. The prediction that males should enter diapause development earlier in the season, i.e., at longer day lengths, as compared to females was corroborated by rearing Pieris napi under a variety of critical day length regimes producing mixed broods of directly developing and diapausing individuals, and by outdoor rearings of cohorts of larvae of P. napi and P. rapae initiated throughout the season. The prediction that partial second generations should be female biased was corroborated by laboratory rearings at constant temperature of P. napi (Pieridae), Polygonia c-album (Nymphalidae), and Pararge aegeria (Satyridae) under critical day length conditions, producing female-biased sex ratio under direct, and male-biased sex ratio under diapause development.     

Sexual Selection and Dynamics of Jaw Muscle in Tupinambis Lizards

Sexual dimorphism patterns provide an opportunity to increase our understanding of trait evolution. Because selective forces may vary throughout the reproductive period, measuring dimorphism seasonally may be an interesting approach. An increased male head size may be important in intersexual and intrasexual interactions. In Tupinambis lizards, a big head is attributed in part to a large adductor muscle mass. Competition for mating can differ in species with different sex ratio and different degrees of sexual size dimorphism. We examined sexual differences in mass of the pterygoideus muscle, its temporal variation throughout the reproductive period and the relationship between muscle and reproductive condition in Tupinambis merianae and T. rufescens. We characterized sexual size dimorphism and sex ratio in both species. Mature males had larger jaw muscles than mature females in both species, mainly during the reproductive season. The dimorphism in jaw muscle was due to an increase in muscle mass in sexually active males. Seasonal increases in muscle mass and variation between immature and mature individuals suggest that the jaw muscle might be a secondary sexual character. We propose that the pterygoideus muscle may act as a signal of reproductive condition of males because it is associated with testis size and sperm presence. The patterns of sexual dimorphism in jaw muscle in both species were similar; however, the comparison shows how sexual characters remain dimorphic in different competition contexts and in species with different degrees of body size dimorphism. Our results suggest that jaw muscle as sexual character could be influenced by inter- and intrasexual selective pressures.     

Sex‐specific differences in spatial behaviour in the flesh fly Sarcophaga crassipalpis

Abstract Territoriality in the flesh fly Sarcophaga crassipalpis (Diptera: Sarcophagidae) is studied in the laboratory. In rectangular enclosures, male flies exhibit a lower tolerance (occupation of the same physical space) of same‐sex conspecifics than do females. In circular arenas, male flies show significantly higher levels of spatial separation among themselves (as determined from nearest neighbour analyses) than do females: males show a slight tendency towards a uniform distribution, whereas females exhibit a slight tendency towards clustering. The male spatial behaviour occurs during the photophase but not the scotophase, suggesting that visual cues are required for maintenance of inter‐individual spacing. No significant differences in male spacing behaviour occur between subjective day and subjective night in either constant dark or constant light conditions, suggesting that spatial patterning is not driven by a circadian rhythm.     

Male‐skewed adult sex ratio,survival, mating opportunity and annual productivity in the Snowy Plover Charadrius alexandrinus

Sex differences in adult mortality may be responsible for male‐skewed adult sex ratios and male‐skewed parental care in some birds. Because a surplus of breeding males has been reported in serially polyandrous populations of Snowy Plover Charadrius alexandrinus, we examined sex ratio, early‐season nesting opportunities, adult survival and annual reproductive success of a Snowy Plover population at Monterey Bay, California. We tested the hypotheses that male adult survival was greater than female survival and that a sex difference in adult survival led to a skewed adult sex ratio, different mating opportunities and different annual productivity between the sexes. Virtually all females left chicks from their first broods to the care of the male and re‐nested with a new mate. As a result, females had time to parent three successful nesting attempts during the lengthy breeding season, whereas males had time for only two successful attempts. Among years, the median population of nesting Plovers was 96 males and 84 females (median difference = 9), resulting in one extra male per eight pairs. The number of potential breeders without mates during the early nesting period each year was higher in males than in females. Adult male survival (0.734 ± 0.028 se) was higher than female survival (0.693 ± 0.030 se) in top‐ranked models. Annually, females parented more successful clutches and fledged more chicks than their first mates of the season. Our results suggest that in C. alexandrinus a sex difference in adult survival results in a male‐skewed sex ratio, which creates more nesting opportunities and greater annual productivity for females than for males.     

同种雄性竞争对手的存在对星豹蛛雄蛛求偶和交配行为的影响

越来越多的研究发现,雄性产生精子(精液)也需付出代价。雄性除了依据配偶质量和竞争对手的竞争强度适应性调整生殖投入外,雄性在求偶和交配行为上也相应产生适应性反应,求偶和交配行为具有可塑性。目前雄性求偶和交配行为可塑性研究主要集中于雌性多次交配的类群中,在雌性单次交配的类群中研究甚少。以雌蛛一生只交配一次而雄蛛可多次交配的星豹蛛为研究对象,比较:(1)前一雄性拖丝上信息物质对后续雄蛛求偶和交配行为的影响,(2)雌雄不同性比对雄蛛求偶和交配行为的影响。研究结果表明,星豹蛛前一雄蛛拖丝上的信息物质对后续雄蛛求偶潜伏期、求偶持续时间和交配持续时间都没有显著影响,但前一雄蛛拖丝上的信息物质对后续雄蛛求偶强度有显著抑制作用。同时,性比对星豹蛛雄蛛求偶和交配行为都没有显著影响。可见,星豹蛛雄蛛对同种雄性拖丝上的化学信息可产生求偶行为的适应性调整,而对性比不产生适应性反应。     

Age‐ and sex‐related differences in the spatial ecology of a dichromatic tropical python (Morelia viridis)

Abstract: Despite outnumbering their temperate counterparts, tropical snake species have been poorly studied. Yet, the few tropical species that have been studied show a variety of behavioural traits beyond those described in temperate species. Here we reveal both age and sexual differences in the movements of tropical green pythons (Morelia viridis: Pythonidae). We radio‐tracked 27 individuals (17 females and 10 males) for up to 18 months, locating individuals during both the day and night. The home range size for adult females (mean ± SE of 6.21 ± 1.85 ha) was correlated with snout–vent length. Neither adult males nor juveniles had a stable home range. Adult females had stable home ranges that overlapped considerably with those of other females and yellow individuals. Multiple radio‐tracked adult males passed through the territory of radio‐tracked adult females during the study. Females of all sizes were more likely to change position each day than males. There were no differences between the sexes or size categories in the distances moved in most months, although the variation in movement distances was higher in the dry season than during the wet season. In the wet season (January–March) movement distances increased and these were size‐ and sex‐related. This increased activity may be associated with mate searching. Males of M. viridis may maximize their rate of encountering mature females by roaming rather than maintaining a home range. Juvenile green pythons moved distances equal to adult snakes in most months despite their comparatively small size.     

Spatial sex segregation in the dioecious grass Poa ligularis in northern Patagonia: the role of environmental patchiness

We examined the effect of environmental patchiness on the spatial segregation of the sexes in the dioecious anemophilus grass Poa ligularis. Because the species is sensitive to grazing, a better understanding of environmental factors that control its spatial distribution and abundance could improve conservation efforts. We hypothesized that (i) males and females are spatially segregated in the microenvironments created by plant patches as the result of sexual specialization in habitat and/or resources use, (ii) sexual specialization is related to different tolerance to competition and reproductive costs of males and females, and (iii) changes in patch structure affect the microenvironment and the intensity of spatial segregation of the sexes. We analyzed the spatial distribution of sexes at three sites with different plant and micro-environmental patchiness and performed a controlled competition experiment with different substitution of males and females. Our results showed that large plant patches created larger sheltered soil fertility islands than small patches. As patch size and their area of influence increased, the density and the spatial segregation of the sexes of P. ligularis also increased, resulting in biased habitat-specific sex ratios. In accordance with their higher reproductive costs, females were more frequent in sheltered (low air evaporative demand) and nitrogen-rich areas inside patch perimeters than males. Females were also better able to tolerate inter-sexual competition than males. In contrast, males tolerated low nitrogen concentration in soil and low sheltering, probably gaining advantage in pollen dispersal. Inter- and intra-sexual competition, however, affected the reproductive output of both sexes. From the point of view of conservation, environmental patchiness is important to the status of P. ligularis populations. The reduction of patch size limits the available microsites, biases the sex ratio towards males inside patches, increases inter- and intra-sexual competition, and it might be expected to decrease overall seed and pollen production and consequently potential recruitment.     

Mate-Guarding as a Male Reproductive Tactic in <Emphasis Type="Italic">Propithecus verreauxi</Emphasis>

Sexual selection theory predicts that in group-living mammals, male reproductive tactics can lead to high reproductive skew in favor of dominant individuals. In sifakas (Propithecus verreauxi), a group-living primate with extremely seasonal reproduction, male reproductive success is highly skewed because dominant males sire almost all offspring despite a tendency toward an even adult group sex ratio. To understand the underlying behavioral mechanism resulting in this rank-related reproductive skew in male sifakas, we studied mate-guarding as a potential reproductive tactic. Behavioral observations of dominant males and adult females in combination with hormonal determination of timing of female receptivity in 9 groups at Kirindy Forest revealed that dominant males spent more time in proximity to females when they were receptive and were responsible for the maintenance of this proximity. Results also indicated that monopolization of receptive females was facilitated by both estrous asynchrony within groups and by the ability of dominant males to obtain olfactory cues as to the timing of female receptivity. Although dominant males engaging in mate-guarding are expected to experience various costs, there was no evidence for decreased foraging behavior and only a trend toward increased aggression between dominant and subordinate non-natal males within groups. Our results are in accordance with the hypothesis that dominant males use mate-guarding to monopolize receptive females and that it is one proximate mechanism that contributes to the high reproductive skew observed within the population of male sifakas at Kirindy.     

No differential consequences of reproduction according to sex in Juniperus communis var. depressa (Cupressaceae)

In dioecious plant species, males and females are thought to have dissimilar allocation patterns. Females are believed to invest more in reproduction and less in growth and maintenance than males. This differential investment between sexes could result in distinct growth patterns and contrasting survival rates, thereby affecting the sex ratio of a population and the age and size distribution of males and females, possibly leading to habitat segregation according to sex. These effects might become more apparent under particularly limiting conditions, such as in nutrient-deficient soils or in climatically stressed environments. To verify these predictions, growth patterns, microsite characteristics, and age and size distribution of male and female individuals were compared, and population sex ratio was determined in three populations of the dioecious shrub Juniperus communis var. depressa (Cupressaceae, Pinophyta) along a short latitudinal gradient on the eastern coast of Hudson Bay (Northern Québec, Canada). We found that the northernmost population had a male-biased sex ratio, but that the southernmost one had a higher proportion of females. Our results failed to reveal any significant differences in radial growth patterns, mean sensitivity, annual elongation of the main axis, and size and age frequency distribution between males and females in any population. Furthermore, there was no evidence of microhabitat segregation according to sex as indicated by the lack of differences in the physicochemical characteristics of the substrate under males and females. Clearly, the expected ecological consequences of a presumed greater investment of females in reproduction were not apparent even under the very stressful conditions prevailing on subarctic dunes. Many factors could reduce differences in the cost of reproduction between males and females, such as the number and quality of reproductive structures produced annually by individuals of each sex, the possible photosynthetic activity of the immature female cones, and the complexity of the source/sink relationship within individuals. Alternatively, there may be no differences between sexes in their reproductive investment.     

Breeding biology, resource partitioning and reproductive effort of a dioecious shrub, Clutia pulchella L. (Euphorbiaceae)

 The flowering of Clutia pulchella was studied in a coastal scarp forest community in southern KwaZulu-Natal, South Africa. Sex dependent differences in the frequency and magnitude of floral output were recorded, with male individuals producing 4.32 times more flowers per leaf axis than females. Increased node production, as a manifestation of significantly increased branching, allowed for prolific flower production in males. Energy investment per flower was marginally greater in females (0.045 J/mg), despite copious pollen production and glandular secretion in males (0.035 J/mg). Differential flower production, reproductive organ dry mass and an unbalanced branching ratio revealed that “per plant” expenditure towards flowering was more pronounced in males (♀ flowering × 5.04). The elevated cost of fruit production (♀ flowering × 5.5), inclusive of imperfect fruit set, resulted in overall reproductive expense being slightly higher for females. Such sex-dependent reproductive investment was shown to have minimal influence on the population sex ratio, with sex frequencies and nearest neighbor distances yielding a non-significant male bias of 1.16. No evidence of spatial asymmetry was found. Received December 1, 1999 Accepted September 27, 2000     

Sex ratio and gender-dependent neighboring effects in <Emphasis Type="Italic">Podocarpus nagi</Emphasis>, a dioecious tree

We analyzed sex ratio, growth rates, and spacing among individuals of Podocarpus nagi, a dioecious tree, on Mt. Mikasa, Nara City, Japan. The sex ratio of reproductive trees ≥ 5 cm in stem diameter at breast height (dbh, 130 cm above ground level) was significantly male-biased. The sex ratio was male-biased in the < 20 cm and ≥ 50 cm size classes, while it did not depart from 1:1 in the 20 ≤ dbh < 50 cm class. Growth rate varied with tree size in males but not in females. The precocity and vigor of males suggests that differences in reproductive costs between sexes induce the biased sex ratio. Random labeling tests on the positions of reproductive trees showed that in the < 30 cm class, males and females were distributed randomly and independently from each other. In the ≥ 30 cm class, males were significantly clumped, whereas females were randomly distributed. Males and females showed significant repulsion, i.e., a spatial segregation of sexes. Both intra- and intersexual effects on the growth rate of crowding by neighbors were significant for females, but not for males. Maximum competitive interference was observed at a distance of 5 m, which corresponded approximately to the radius of clumps of large males and to the significant repulsive distance between large males and females. These results suggest that sexual differences in sensitivity to local crowding are related to the formation of gender-dependent spatial patterns. Formation of female-repulsive male clumps and a male-biased sex ratio may intensify the decreased probability of regeneration near males, as suggested by the limited seed-dispersal range of this species, thereby promoting coexistence with other species.     

Reproductive behaviour of the white-tailed zygaenid moth,Elcysma westwoodii (Lepidoptera,Zygaenidae) I. Mating sequence

The mating behaviour of the white-tailed zygaenid moth,Elcysma westwoodii, was observed. During the morning in the breeding season, males fly in search of females. It seems that females release sex pheromone and that olfaction is important in the search, although the moth is diurnal. In mating behaviour, males often gather to a female. Some factors which cause male gathering are considered: 1) high density of male moths, 2) males' tendency to be attracted by other fluttering males, and 3) females' tendency to refuse males.     

Defence of Females by Dominant Males of Artibeus jamaicensis (Chiroptera: Phyllostomidae)

Defence of females by dominant males of the Jamaican fruit‐eating bat Artibeus jamaicensis was observed in two natural colonies over 2 yr. A log‐linear model was used to evaluate the frequency distribution of visits to harems by sex, season and agonistic interaction of dominant males. Harem group size varied from four to 18 females, with one adult male in the small and medium‐sized groups and two males in the large groups (> 14 females). A highly significant interaction was noted between the age and sex of the visitor and the response of the dominant male. Male visitors were attacked more often than female and juvenile visitors. Aggressive defence increased during the reproductive seasons, with dominant males showing more agonistic responses towards male visitors. An increase in the frequency of visits by male visitors was noted in harem groups that ranged in size from four to 12 females, but the frequency of male visits declined in harem groups that contained more than 14 females.     

Interference of asexual and sexual reproduction in the green hydra

The green hydra, Hydra viridissima, has three sexes: hermaphrodite, male, and female. I investigated the reproductive strategies of the green hydra and the relationship between asexual budding and sexual reproduction. The proportion of mature individuals in the asexually reproducing population increased with increasing temperature. Sexual reproduction did not interrupt asexual budding in hermaphrodites or males; sexual reproduction did interrupt asexual budding in females. Sexual reproduction also resulted in exponential population growth during the reproductive season. The number of asexual buds on each parental individual was positively correlated with the parental individual size in asexual individuals and in males. The same positive correlation was found between the number of testicles and the size of males. These correlations reflect a common tendency in asexual and sexual reproduction: larger parental individuals have a greater number of propagules or gametes. No correlation was found between size and buds or size and gonads in hermaphrodites; hermaphrodites had at most one asexual bud and were significantly larger than males, females, and asexual individuals. The larger size of hermaphrodites supports the hypothesis that producing both female and male gonads is more energetically costly than producing only one type of gamete (gonochorism).     

Use of space by Necromys lasiurus (Rodentia,Sigmodontinae) in a grassland among Atlantic Forest fragments

The spatial patterns presented by the rodent Necromys lasiurus were studied through capture-mark-recapture in a grassland among Atlantic Coastal Forest fragments in Southeastern Brazil. Males moved farther than females. Males moved similar distances in the dry and wet seasons, whereas females moved significantly longer distances in the dry season. Home ranges sizes were estimated for 32 individuals, and varied from 0.02 to 0.52 ha. Males had larger home ranges than females when all data are pooled and in the wet season; in the dry season home ranges of both sexes were of similar sizes. Home range sizes did not vary significantly between seasons for either sex. Home ranges of males overlapped extensively among themselves and with females, whereas females showed mutually exclusive home ranges. The spatial patterns described here are consistent with the results found for this species in different habitats and they suggest that N. lasiurus has a promiscuous mating system.     

SEX-RATIO AND REPRODUCTIVE VARIATION IN THE MISTLETOE PHORADENDRON JUNIPERINUM (VISCACEAE)

Despite the fact that many parasitic and hemiparasitic plant species such as mistletoes are dioecious and occur in both the new and the old world, few data exist on variation in the sex ratio and allocation to reproduction in these taxa. We investigated 1) the sex-ratio of the xylem-tapping mistletoe Phoradendron juniperinum in relation to its age and position within the canopy of its host tree Juniperus osteosperma, and 2) reproductive effort in relation to the gender and age of mistletoe plants. Our surveys showed that P. juniperinum has a male-biased sex ratio. Despite this predominance of male individuals, females lived longer and had a greater reproductive effort than did males. A statistical analysis of the age distribution data indicated that the peak in the frequency of reproductively mature individuals was later in females than in males. These gender-specific distributions may have resulted 1) from sequential hermaphroditism (age-specific sex switching), or 2) because the average age of peak reproduction is later in female individuals. Because sex is genetically determined in a closely related genus of mistletoe and because we have no data to indicate sex switching in this species, we feel that our data support the interpretation that female individuals, on average, show a peak in reproductive vigor at an older age relative to males. While delayed reproduction in females may be favored because reproductive effort and success appear to be age-dependent in females of this species, both sexes can become reproductively mature relatively early in life. Further, because 1) allocation to reproduction as a function of age increases more rapidly for females of this species relative to males, and 2) because there may be a higher resource cost associated with reproduction in females, we hypothesized that female individuals would be more abundant in the best quality locations within the host tree so as to maximize the opportunity to meet those costs. In spite of the association between gender and some host characteristics, there was no indication that female plants were located in sites most favorable to either their carbon or water balance. We discuss reasons why this may be the case.