Contradictory findings in studies of sex ratio variation in roe deer (Capreolus capreolus)

Patterns of sex ratio variation and maternal investment reported in the literature are often inconsistent. This could be due to intra- and inter-specific variation in social systems, but may also be a result of the a posteriori nature of much of this type of analysis or the testing of models which are inappropriate. Two recent papers reported directly opposed results concerning variation in offspring sex ratios in relation to maternal condition in roe deer, interpreting the results as support for the Trivers and Willard model and for the local resource competition hypothesis, respectively. In this paper, we present data on offspring sex ratios and early juvenile body weight from two long-term studies of this species to test predictions arising from these two models concerning sex biases in litter composition and maternal care. First, we observed no consistent pattern of sex differences in an index of weaning weight or body weight at 1 month old in either population, indicating a lack of sex bias in maternal care. However, in one population, higher maternal body weight was associated with higher juvenile body weight of daughters, but not of sons. Secondly, we found a negative, but not statistically significant, relationship between maternal body weight and litter sex ratio such that heavier females tended to produce more daughters and lighter females to produce more sons. These results indicate that roe females which have additional investment potential available do not invest it in sons, as predicted by the Trivers and Willard model. Our results may provide some support that roe deer are subject to local resource competition acting at the level of the individual mother; however, the fact that particular trends in sex ratio data can be explained in functional terms provides no indication that they are actually adaptive. Received: 9 December 1997 / Accepted after revision: 11 November 1998     

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.     

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     

Maternal effects on post-weaning physical and social development in juvenile mountain goats (Oreamnos americanus)

Little is known about maternal effects on post-weaning development, yet they may be important because maternal care could have long-term consequences only evident when offspring approach adulthood. We have assessed the effects of maternal age, current reproduction (presence of a kid of the year) and social rank on the body mass, horn length and social rank of 1- and 2-year-old mountain goats (Oreamnos americanus). Maternal reproductive status and social rank did not affect the mass or horn length of either yearlings or 2-year-olds. Maternal age was positively correlated with yearling body mass for males but not females. We could not detect any maternal age effects on body mass of 2-year-olds. Maternal age and spring forage quality were positively correlated with horn length of yearlings of both sexes, but not of 2-year-olds. Juvenile females showed compensatory growth in mass between 1 and 2 years of age, but males did not. Neither sex showed compensatory growth in horn length. None of the maternal characteristics we examined directly affected the social rank of juveniles, which increased with body mass. Social rank in female mountain goats seems to be established early in life and maintained to adulthood. By affecting yearling development, maternal age could affect the reproductive success of males.     

Fighting and assessment in the yellow-rumped cacique (Cacicus cela)

Summary I tested the prediction derived from game theory models that the intensity of aggressive interactions should reflect the value of the resource being contested and the disparity in fighting ability of the contestants. Females of the yellow-rumped cacique compete for nest sites and the material to build nests. Females competing for established nest sites engage in higher intensity interactions than those competing for sites in which building has not begun and against females robbing nest material (Fig. 1). For males, access to females is determined by dominance, which is positively correlated with weight. Comparably-sized males (Fig. 2) and those of similar rank (Fig. 3) engage in significantly more intense interactions than males that differ widely in size or rank.     

Food abundance and parental care in yellow warblers (Dendroica petechia)

Emlen and Oring (1977) suggested that monogamy in birds is maintained because of the need for strict biparental care. A corollary of their suggestion is that paternal care should decrease under conditions of high food abundance. An alternative is that paternal care would increase if males take advantage of the higher food abundance by trying to reduce the length of the nestling feeding period. We tested these two ideas using yellow warblers (Dendroica petechia) by providing some pairs with supplemental food, thereby reducing the importance of biparental care. However, the extra food did not decrease paternal effort, nor did it increase it (Fig. 2). Early in the nestling period experimental females brooded more but visited their nestlings less than did control females, but later, when brooding times decreased, experimental females fed their nestlings more than did control females (Fig. 3). There were no significant differences in nestling survival (Fig. 5), but nestlings in the control treatment were larger and heavier up to 6 days old (Fig. 6). The main effect of supplemental food was on maternal, not paternal behaviour. Models of biparental care assume interdependence between the parental effort of both parents. In this species, however, males and females provide for their brood independently from each other.     

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

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

Status,reproductive success and fitness in Cape mountain zebra (Equus zebra zebra)

Summary Demographic data relating to herd size and stability are given for a population of Cape mountain zebra (Equus zebra zebra) under longterm observation. Temporal dispersion patterns of male and female offspring differed and were independent of the mother's status. Dispersion in females appeared to be related to physiological state, and dispersion in both sexes was related to age rather than changes in parental behaviour. Reproductive success of dominant and subordinate mares was equal and independent of age and social and reproductive variables. Fitness of dominant mares, however, was significantly higher than that of subordinates, the latter having a higher foal mortality, part of which could be attributable to dominants' aggression. The fitness of all males born was 1.6:1 compared with all females. Dominant mares produced significantly more daughters than sons. This trend was not found for subordinates. Mother's status was positively correlated with dominant status in her female offspring but not related to the subsequent status of her sons. Daughters had a more than twice as great a chance of breeding than sons. For maximum fitness gains, therefore, dominant mares should produce more daughters, since a high proportion of these would also have high status and fitness. This tendency is reflected in the sex ratio skewed towards females found for dominant mares.     

Philopatry,reproductive success of females,and maternal investment in the red-necked wallaby

Summary Female red-necked wallabies settle within their mothers' home ranges, apparently for life, while males disperse at about two years of age. However, sons spend much more time with their mothers before dispersing than do daughters of similar ages. Females who associate regularly with their subadult offspring are less likely to reproduce successfully at their next breeding attempt than are females who spend little time with their subadults, and sons therefore impose greater short-term reproductive costs on their mothers than do daughters. Females who are generally gregarious also suffer reduced reproductive success, even though reproductive success is independent of local density. It is suggested that the reproductive costs to females of associating with their subadult offspring, and other relatives, are incurred through tolerance of ecological competition from those kin, and therefore reflect a form of prolonged maternal investment, which is initially heaviest in sons but is sustained for longer periods in daughters. Females produce equal numbers of male and female offspring, and spend equal amounts of time suckling them in infancy.     

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.     

Determinants of parental effort: a behavioural study in the Eurasian kestrel,Falco tinnunculus

We recorded behaviour of kestrels (Falco tinnunculus) in western Finland during the courtship (1988–1992), incubation (1989–1991), early nestling (age of young 1–2 weeks, 1989–1992) and late nestling stages (3–4 weeks, 1989–1991) to examine determinants of their parental effort (PE). In males, PE was estimated as the hunting effort (the proportion of budget time spent in flight-hunting) and in females as the food provisioning rate (number of prey items delivered to the nest per hour). The following predictions derived from the parental investment theory were examined. (1) Parents rearing large clutches and broods should invest more in breeding than do parents rearing small clutches and broods. The hunting effort of parents did not increase with clutch or brood size, but males tending large broods had a higher prey delivery rate than males tending small broods (Figs 1–2). (2) PE of parents should increase in the course of the breeding season. In males, this was true only between the incubation and early nestling phases (Fig. 3). (3) The early pairs should invest more in breeding than late ones. This tended to be true during the early (for males) and late nestling phases (for females) (Fig. 4). (4) There should be a negative correlation between PE of mates within pairs, but no evidence for such adjustment was found (Fig. 5). (5) Females mated with bright-coloured attractive males should show higher PE than females mated with dull-coloured males but our results were inconsistent with this prediction. We conclude that PE decisions of kestrels are mainly based on cost-benefit estimates of residual reproductive value, rather than on current investment indicators, like clutch or brood size. This might be beneficial in environments with highly variable survival prospects of offspring caused by pronounced among-year variation in abundance of the main food (microtine rodents). The results also show that hypotheses explaining variation in PE in the short term are not necessarily valid for long-term PE, e.g. tending clutches or broods, which also reflects the demands of female and young.     

Sensory ecology of a semi-aquatic spider (Dolomedes triton)

Summary Preferred ambush sites of fishing spiders Dolomedes triton (Pisauridae) were investigated, primarily with respect to aquatic vegetation and wave action, at five locations differing in these variables along the shore of Dow Lake (near Athens, Ohio). The linear density of spiders correlated positively with the presence of aquatic vegetation. D. triton most often stood at a distance from shore proportional to the width of the zone of floating and emergent vegetation (Fig. 2). Usually they positioned their bodies in the horizontal plane on floating living or dead plant parts. Spider density was negatively correlated with the amplitude of wind-generated waves (Fig. 4). The maximum energy of these waves measured on breezy days was at a frequency of 1.4 Hz, with no components exceeding 10 Hz (Fig. 5). Spiders could discriminate high-amplitude (up to 40 mm) wind waves from prey waves, probably since the latter have substantially higher frequencies (Figs. 3, 5).     

Resource allocation,brood production and cannibalism during colony founding in the fire ant,Solenopsis invicta

Summary The colony founding characteristics of newly mated fire ant queens from monogyne colonies were studied in the field and in the laboratory under haplo- and pleometrotic conditions. Initial queen weight (live) was not correlated with subsequent progeny production. During founding, queens lost a mean of 54% of their lean weight, 73% of their fat weight and 67% of their energy content. The percentage of fat decreased from 44% to 33%. Queens lost weight or energy in relation to the amount of progeny they produced (Figs. 1, 2). The efficiency of the conversion of queen to progeny increased as more progeny were produced, leading to a decline in the unit cost of progeny (Fig. 3). The more minims a queen produced, the lower the mean weight of these minims and the faster they developed (Fig. 4). In a field experiment on pleometrotic founding, total brood increased with queen number, peaked between four and seven queens and declined with 10 queens (Fig. 5). Brood developed faster at the sunny, warmer site, but total production and queen survival was higher at the shady site. As queen density increased, production per queen decreased as a negative exponential in which the exponent estimated sensitivity of brood production to queen-crowding and the constant estimated the production by solo queens (Fig. 9). These effects of queen number were confirmed in laboratory experiments. The decrease of production per queen was small and not always detectable during the egg-laying phase, but brood attrition was always strong during the larval period and increased with queen number (Figs. 8, 10). While airborne factors may have contributed to this inhibition, most of the brood reduction was due to other causes, probably cannibalism. For a given number of minims, increased queen number increased the mean weight of these minims, an effect that resulted both from a lower minim production per queen and from cannibalism of dead queens by survivors (Fig. 11). Cannibal queens lost much less weight to produce a given number of minims than unfed control queens, and these minims were heavier (Fig. 12).     

Evidence of equal maternal investment in the sexes in the polygynous and sexually dimorphic grey seal (Halichoerus grypus)

In polygynous and sexually dimorphic mammals, parents may be expected to bias their investment towards sons because variation in reproductive success is usually higher among males than among females. Moreover, male reproductive success often depends on adult body size, which, in turn, may depend on the level of parental investment. We therefore predicted that in the grey seal (Halichoerus grypus), a polygynous and sexually dimorphic phocid seal, females should invest more in individual sons than in individual daughters. We found that male pups were born heavier than female pups, but that the growth rates and suckling behaviour were similar for the two sexes. The growth rates and the birth weights were not correlated for the pups of either sex. Mothers did not behave differentially towards offspring of the two sexes, except that mothers of male pups spent more time in visual contact with their pups. Male and female pups had similar activity levels and begged at similar rates. We argue that reports of equal expenditure on the two sexes can be accepted as evidence of equal investment, provided that three assumptions are fulfilled. First, parental care must be costly to the parent. Second, energy expenditure must be the most important component of parental investment. Third, there must be no negative correlation between maternal body condition and the ratio of sons to daughters produced. We argue that these assumptions are met in our study, and that our results provide evidence of equal maternal investment in the sexes in grey seals.     

Agonistic relationships between female mountain gorillas (Gorilla gorilla beringei)

Females in some mountain gorilla groups can be ranked on the basis of decided, non-aggressive approach-retreat interactions. However, data on four gorilla groups show that females do not form clear agonistic dominance hierarchies. Most aggressive interactions between females were undecided, and most dyads had undecided dominance relationships (Fig. 2). Females ignored aggression or responded to it aggressively more often than they responded submissively (Fig. 3). Moreover, directional inconsistency in aggression (including escalated contests) was high, and in some groups females showed significant bidirectionality in initiation of aggression (i.e., the more often they received aggression from partners, the more often they directed aggression at those partners; Fig. 4). Assigning ranks on the basis of aggressive interactions has limited power to explain variation in rates of initiating aggression and in responses and outcomes to aggression. Aggression was most common during feeding, but usually did not interrupt feeding bouts. It was proportionately more common in contexts that seem to involve competition for access to males (Figs 5, 6). This is consistent with the argument that females depend crucially on male services. As predicted by current models of female primate social relationships, agonistic relationships between gorilla females are unlike those typical in cercopithecine primates. They resemble those of some other primates and some equids in which contest competition for food is relatively unimportant and ecological costs of female transfer are low.     

Copulation duration and sperm competition in white-faced dragonflies (Leucorrhinia intacta; Odonata: Libellulidae)

Summary In many odonates, females mate with more than one male while laying a single clutch of eggs. We studied paternity of eggs laid by remated females of Leucorrhinia intacta, a small libellulid dragonfly, at a pond near Syracuse, NY, USA. The probability of a female remating is a function of male density on the pond. The length of copulations differs considerably among males active on the study pond at the same time. Much of this variation was correlated with differences in mating tactics of the males; copulations by males that stayed on their territories during copulation were shorter than those by other males (Fig. 2). Eggs collected from females mated to irradiated, sterile males and to free-living, fertile males indicated that the average paternity expectation was higher for long than for short copulations, and that the variance in paternity expectation was lower for long than for short copulations. Some possible causes of the high variation in paternity at low copulation durations and possible reasons for differences in copulation duration between male mating tactics are discussed.     

Conditional lekking in ruff (Philomachus pugnax)

Summary In our study of ruff, a lekking shorebird, we found that the lek ratio — the proportion of the total population of males occurring on leks was low, averaging 12% over the breeding season (Fig. 1D). Off-lek males spent approximately the same proportion of time as lek males in displaying to females (Fig. 4). We defined three spacing tacties that male ruffs use to position themselves to court females: Following — directly pursuing females, and two types of lekking behavior, Intercepting — waiting for females at resource-rich sites, and True Lekking — waiting for females at places without any resources other than the males themselves. Males switched among these tactics, causing the lek ratio to vary over the season (Fig. 1 D). Lek ratio increased when the number of females present in the study area plummeted at the end of May, and was positively correlated throughout the season with the copulation rate of the preceding day, suggesting that males were tracking the behavior, as well as the number, of females available (Table 1, Fig. 1). Early in the season, males off leks spent most of their time feeding (Fig. 4), and lek ratio was positively correlated with temperature (Table 1), suggesting that some males may have been unable to lek during cold weather. Males on leks mated at significantly higher rates than Followers (Table 4). On average, males at our interception lek were less site faithful and less peristent than males at true leks, and the interception lek itself disappeared after females stopped coming to use its adjacent resource (Table 2, Fig. 5). The most successful individuals in our population were the True Lekking males, rather than the Interceptors.In addition to the conditinal lekking tactics described here, ruff display a dimorphism in behaviorat leks. Independent males defend small courts on leks, while Satellite males share courts and mutually display with independents Both independents and satellites may use all three conditional tactics. We propose that satellites evolved as specialized. Followers, adept at tracking the movements of females among leks.     

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     

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.     

Effects of predator visibility on prey encounter: a case study on aerial web weaving spiders

Summary Perhaps the most important factor affecting predator-prey interactions is their encounter probability. Predators must either locate sites where prey are active or attract prey to them, and prey must be able to recognize potential predators and flee before capture. In this study we manipulate and describe three components of the foraging system of predatory, web-weaving spiders, the presence of viscid droplets, silk brightness (achromatic surface reflectance), and visibility of the orb pattern, to determine their effect on insect attraction, recognition, and web avoidance. We found that webs with viscid droplets were more visible to prey at close range, but at greater distances the sparkling droplets lured insects to the web area and hence increased insect capture probability. Although the size of viscid droplets and silk brightness are closely correlated (Table 2, Fig. 3), the relationships among droplet size, spider size, and the visual environments in which webs are found are more complicated (Fig. 2, Tables 2, 3). In environments with predictable light exposure, droplet size and hence silk visibility correlate with spider size, and spiders that forage at night produce relatively more visible silks then spiders that forage during the day (Table 3, Fig. 4). In habitats in which light levels are not predictable, silk surface reflectance and spider size are not closely correlated, suggesting that the complexity of the light environment, as well as the visual and foraging behaviors of insects found there, has played an important role in the evolution of spider-insect interactions.Offprint requests to: C.L. Craig