LITTER SIZES AND MAMMARY NUMBERS OF NAKED MOLE-RATS: BREAKING THE ONE-HALF RULE

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1 LITTER SIZES AND MAMMARY NUMBERS OF NAKED MOLE-RATS: BREAKING THE ONE-HALF RULE PAUL W. SHERMAN, STANTON BRAUDE, AND JENNIFER U. M. JARVIS Department of Neurobiology and Behavior, Cornell University, Ithaca, NY (PWS) International Center for Tropical Ecology and Washington University, St. Louis, MO (SB) Zoology Department, University of Cape Town, Rondebosch 7700, South Africa (fumf) Among mammals generally and rodents particularly mean litter sizes usually are about onehalf the number of mammae, and maximum litter sizes approximate mammary numbers. Naked mole-rats (Heterocephalus glaber: Bathyergidae) are exceptions to both generalizations. Field-caught litters averaged 11.3 young ± 6.2 SD (n = 82), and captive-born litters averaged 11.4 ± 5.6 young (n = 190). Similarly, numbers of mammae on breeding females averaged 11.6 ±. 1.1 (n = 43) in the field and 11.5 ± 2.0 (n = 29) in captivity. Maximum litter sizes were 28 in the field and 27 in captivity, whereas the maximum number of mammae was 15. More than one-half of field-caught and captive males and females had different numbers of mammae on the two sides of their body. Neither total numbers of mammae nor fluctuating asymmetries in mammary numbers differed significantly between males and females, nor between breeders and nonbreeders. There was no relationship between litter sizes and numbers of mammae or fluctuating asymmetries in mammary numbers. Breeding female naked mole-rats can bear and successfully rear litters that are far more numerous than their mammae because, on a proximate level, young take turns nursing from the same mammary and, on an ultimate level, breeding females are fed and protected by colony mates, enabling them to concentrate their reproductive efforts on gestation and lactation. Key words: Heterocephalus glaber, naked mole-rat, litter size, mammary formula, eusociality, one-half rule, fluctuating asymmetry Variations in litter sizes and numbers of mammae are striking features of mammalian diversity. Eighty-six years ago, Pearl (1913a) reported that these two traits are correlated. He found a significant positive relationship between numbers of mammae and litter sizes for 90 species of wild and domesticated mammals, representing all orders. This relationship was described by the equation L = 0.56 M , where L = litter size and M = number of mammae. Seventy-three years later, Gilbert (1986) rediscovered the significant positive relationship between mean numbers of mammae and mean litter sizes among 266 species of rodents, mainly in the families Muridae, Cricetidae, and Sciuridae. This relationship was described as L = 0.46 M Gilbert characterized his result as the "one-half rule" because mean litter size was about one-half of the mean number of mammae. Gilbert (1986:4829) also found that maximum litter 'sizes in rodents were approximately equal to the number of mammae, suggesting that "natural selection has favored mammary numbers adequate for the occasional extreme rather than the more frequent typical litter size." In mammals with an obligate teat-attachment phase of development, such as marsupials, litter size obviously cannot exceed the number of mammae (Eisenberg, 1988). Gilbert (1986) did not attempt to test his generalizations within species. Indeed, he argued (1986:4828) that "with few exceptions, mammary number in rodents is a species-typical invariant trait." Seventy years previously, Harris (1916) also considered Journal (!f Mammalogy, 80(3): ,

2 August 1999 SHERMAN ET AL.-LITTER SIZE IN NAKED MOLE-RATS 721 this issue. He saw "no reason to suppose" that selection would produce a correlation within a species between numbers of mammae and litter sizes. In support, Harris (1916) cited Pearl (1913b), who had found no correlation (r = 0.20) between numbers of mammae and litter sizes among female Duroc Jersey pigs. However, at about the same time, Alexander Graham Bell (1912) published results of breeding experiments which indicated that selecting for increased numbers of mammae in domestic sheep resulted in more twin and triplet births. For theoretical reasons, another anatomical correlate, namely the symmetry of mammary placement, recently has become of considerable interest. In some species, morphologically symmetric individuals grow faster, live longer, and have greater mating success and higher fecundity than asymmetric individuals (Mpller and Thornhill, 1998; Watson and Thornhill, 1994). Those authors hypothesized that such effects related to developmental stability of symmetric individuals. If the same genes control development of both sides of the body, phenotypic asymmetries indicate disrupted development due to genetic (e.g., mutations or inbreeding) or environmental factors (e.g., pollution, pathogens, and plant toxins). Symmetry thus indicates the extent to which an individual's development is buffered (canalized) because of either resistance to developmental disruptors or minimal exposure to them (Mpller and Swaddle, 1997). Naked mole-rats (Heterocephalus glaber) exhibit considerable variability in litter sizes and mammary numbers (Braude, 1991a; Brett, 1991a; Jarvis, 1991a; Lacey and Sherman, 1991). We investigated if their mean number of mammae is double their mean litter size and approximates maximum litter size, as in other rodents. We also looked for a relationship between numbers of mammae and litter sizes. Naked mole-rats will inbreed in captivity, and molecular genetic analyses indicate inbreeding in wild populations (Faulkes et ai., 1990, 1997; Honeycutt et ai., 1991b; Reeve et ai., 1990), so the animals frequently are exposed to a potential genetic disruptor of development. If symmetric individuals are more viable as embryos and healthier as adults, they should be overrepresented among breeders (compared to nonbreeders). We therefore tested if there are fluctuating asymmetries in numbers of mammae, if asymmetries differ between breeders and nonbreeders of either sex, and if symmetric females bear larger litters than asymmetric females. MATERIALS AND METHODS Study animals.-naked mole-rats are subterranean rodents that inhabit arid regions of Kenya, Ethiopia, and Somalia in northeastern Africa (Honeycutt et ai., 1991a). They are highly colonial; a single burrow system contains individuals on average, with a range of <10- >295 (Lacey and Sherman, 1997). Coloniality apparently is an evolutionary response to ecological constraints on solitary foraging and dispersal caused by extremely hard, sun-baked lateritic soil that cannot be efficiently excavated by an individual mole-rat (Lovegrove, 1989, 1991), and advantages of cooperative defense against predators and competitors (Alexander et al., 1991; Jarvis et ai., 1994). The social system of H. glaber is complex and fulfills the three traditional criteria for eusociality in insects (Jarvis, 1981; Sherman et ai., 1995): 1) colonies are extended family groups (Jarvis, 1991a; Lacey and Sherman, 1991, 1997); 2) most colonies contain only one reproductive female who mates with 1-3 breeding males (Sherman et ai., 1992), and other colony members are reproductively suppressed although not physiologically sterile (Faulkes and Abbott, 1997; Jarvis, 1991a); and 3) nonbreeders construct, maintain, and defend the colony's vast burrow system (sometimes 2-3 km long-brett, 1991b) and feed and protect the breeding female and her young (Lacey and Sherman, 1991, 1997). Field data.-most of our information on litters sizes was gathered during May-August from 41 different colonies that were located in the Meru National Park in northern Kenya (0005'N, 38 15'E). Colonies were living in native Acacia grasslands between the Mulika

3 722 JOURNAL OF MAMMALOGY Vol. 80, No.3 and Bwatherongi Rivers in the northeastern part of the Park at elevations of m above mean sea level. Mole-rats were captured by opening one or more burrows and inserting a plastic tunnel trap baited with sweet potato (Braude, 1991a). Entire colonies, including small young, usually were captured in :51 week. Individuals were weighed on a 100-g hanging scale or an electronic balance. They were marked permanently by clipping a unique combination of toes or by implanting a small transponder chip (Braude and Ciszek, 1998). Breeding females were identified by their large size and elongate shape, swollen and raised genital area, presence of well-developed mammaries, and their pink dorsal coloration, which is gray on nonbreeders. Minimum sizes of litters were inferred from numbers of young whose weights at capture clustered within ±: 3 g of each other. Mean weights of young ranged from 3 to 17 g, and up to three recent litters were identifiable per colony. We could not confidently assign juveniles to specific litters when their mass was >20 g because by the time they reached that size individual differences in growth rates blurred distinctions between litters (Jarvis et ai., 1991). Our data yield conservative estimates of litter sizes because some young may have died before their colony was captured and some living young may have evaded traps. However, evasion seemed unlikely because annual recaptures of 19 colonies never revealed any unmarked juveniles. Additional information on litter sizes was obtained in from 17 colonies living in and around Tsavo West National Park and the nearby village of Kathekani in southern Kenya (2045'S, 38 07'E). Most colonies were located in native grasslands, but a few were in agricultural areas (Brett, 1991a, 1991b). Colonies were captured throughout the year, either by excavating parts of burrow systems or opening a tunnel and trapping individuals that investigated the break by blocking off the burrow behind them (Jarvis, 1991b). Complete colonies seldom were captured. Recent litters were counted when nests were excavated. Litter sizes were inferred from the number of juveniles (i.e., individuals < 22 g) whose weights clustered within ±:3 g. Those were minimum estimates of litter sizes because some young may have died before their colony was excavated and some living young may have escaped. Laboratory data.-we recorded information on sizes of litters born in to 54 colonies that were maintained at Cornell University and the University of Cape Town. Colony members or their ancestors were captured near Tsavo West National Park or around the village of Lerata in northern Kenya (1030'N, 38 30'E). Colonies were housed in artificial tunnel systems in warm (28-30 C), humid (50-65%) rooms, and fed a variety of fresh tubers, vegetables, and fruits ad lib. Details of husbandry and breeding histories of many of those colonies are provided by Jarrow and Sherman (1996), Jarvis (1991a, 1991b), and Lacey and Sherman (1991, 1997). Captive-born litters always were counted in :524 h of birth (usually in :512 h). Newborns in the same litter weighed 1-3 g (1.9 g ±: 0.2 SD, n = 208-Jarvis 1991a). We analyzed information from all litters that were enumerated completely. Our data yield conservative estimates of litter sizes because we did not include eight very large litters (> 18 young) that we were unable to accurately count within 24 h of birth (i.e., before any young that were stillborn or otherwise nonviable were consumed by colony mates). Fluctuating asymmetry.-fluctuating asymmetry is "random deviation from perfect bilateral symmetry in a morphological trait for which differences between the left and right sides have a mean of zero and are normally distributed" (Watson and Thornhill, 1994:21). We counted mammae on the left and right sides of breeding females from 39 wild colonies, and breeding females and males (identified by observing mating) from 25 captive colonies. We also counted mammae on nonbreedin'g females and males in 13 of those captive colonies. The latter counts were made late in the gestation period of each colony's breeding female, when mammae of nonbreeders reached their peak of enlargement (Jarvis, 1991a). We did not count mammae that were obviously deformed or shriveled ("pin teats"). However, we did not know if all the mammae we counted on breeding females were viable; mammae on non breeding females and males certainly were not functional (Lacey and Sherman, 1991). Data analysis.-litter sizes, numbers of mammae, and asymmetries in mammary numbers are reported as means ±: 1 SD, and twotailed t-tests were used to analyze differences between them. Relationships between numbers

4 August 1999 SHERMAN ET AL.-LITTER SIZE IN NAKED MOLE-RATS :10. (I.) J -0 r::: ;; 0.10 b) :10. 0 C- O : c Litter Size Field Caught (n=82) Captive Born (n=190) FIG. I.-Frequencies of sizes of litters of naked mole-rats that were a) captured in the field (Kenya) and b) born in captivity. Mean litter sizes are indicated by arrows. of mammae and litter sizes were analyzed with linear regressions. Sexual dimorphisms in numbers of mammae and fluctuating asymmetries in their placement were. explored for breeders and nonbreeders using chi-squared tests, t-tests, and analysis of variance. All statistical analyses were conducted using Statview 4.5@> (Abacus Concepts, 1992). RESULTS Litter sizes.-field-caught litters of naked mole-rats (n = 82) contained up to 28 young (11.3 ± 6.2; Fig. 1a), and litters born in captivity (n = 190) contained up to 27 young (11.4 ± 5.6; Fig. 1b). Sizes of captive and wild litters did not differ significantly (t = 0.32, df = 270, P = 0.75). The distribution of field-caught litters was slightly more kurtotic (peaked) than that of captive-born litters (-0.46 versus -0.09); distribution of captive-born litters was more skewed (asymmetric) than that of fieldcaught litters (0.71 versus 0.18). However, only skewness among captive-born litters differed significantly from normality (t = 2.63, P < 0.01). 30 Among the wild litters, those captured at Meru (n = 61) were much larger than those (n = 21) unearthed near Tsavo West, which is ca. 300 km to the south (13.6 ± 5.6 versus 6.2 ± 4.0 young, t = -5.70, P < 0.001). That difference was probably due to the greater efficiency and thoroughness of capture techniques employed at Meru, although we cannot rule out variations in fecundity between sites; Meru is considerably more mesic than Tsavo West. Numbers of mammae.-the 249 female naked mole-rats we sampled had 9-15 mammae (11.9 ± 1.2). Field-caught breeding females had mammae (11.6 ± 1.1; Fig. 2a), captive breeding females had mammae (11.5 ± 2.0; Fig. 2b), and captive nonbreeding females had 9-15 mammae (12.0 ± 1.26; Fig. 2c). Numbers of mammae did not differ between wild and captive breeding females (t = -0.98, df = 70, P = 0.33), or between breeding and nonbreeding females (t = -1.55, df = 247, P = 0.12). Numbers of mammae usually did not change during an individuals' lifetime. Among 36 wild and captive breeding females whose mammae were counted twice, with ~2 yr between counts, 34 (94%) had the same number of mammae. Of the two females whose mammary number changed, one had one more teat and the other one less at the second count. The 206 captive males we sampled had 9-15 mammae (11.9 ± 1.2). Breeding males had mammae (11.8 ± 1.2; Fig. 2d), and nonbreeding males had 9-15 mammae (11.9 ± 1.1; Fig. 2e). Numbers of mammae did not differ between breeding and nonbreeding males (t = -0.93, df = 204, P = 0.35). Males and females had equivalent numbers of mammae (t = -0.07, d.! = 453, P = 0.94). Thus mammary numbers did not vary significantly depending on an individual's sex, breeding status, or whether it was wild-caught or captive (F = 0.89, df = 4,450; P = 0.47). Litter sizes versus numbers of mammae.-among all the naked mole-rats we

5 724 JOURNAL OF MAMMALOGY Vol. 80, No.3 U) - 0.4] b) Captive Breeding Females ~ I I 0.3 (n=29) "C 0.2 i ~:::, I.- ~~r:~;t ' 'lreedinlg Females o. - ~ ~ ;::: 0.41 d) Captive Breeding Males o I I I 0.3 (n=23) ::: a. 0.2 I... I 0.4ie) Captive Non-Breeding Males '" 1,,"'''' ::, I Number of Mammae FIG. 2.-Total numbers of mammae on naked mole-rats separated according to individuals' sex, breeding status, and if they were a) wildcaught or b--e) captive (most were born in captivity). sampled, the mean litter size was 11.4 ± 5.8 young (n = 272; Fig. 1) and the mean number of mammae was 11.9 ± 1.2 (n = 249; Fig. 2). Litter sizes and mammary numbers thus were indistinguishable statistically (t = 1.18, d.f = 519, P = 0.24). Information was available on numbers of mammae and sizes of litters borne by 60 individual females (29 captive, 31 wildcaught), 30 of which (14 wild-caught, 16 captive) had 2-6 litters each during our study. We analyzed only the mean size of those females' litters to avoid pseudoreplication (Fig. 3). Relationships between num- 30 a) Field Breeding Females (n=31 ) I I (1) N.- 5 I tn 0 J.. (1) 30 b) Captive Breeding Females... (n=29) J I I Number of Mammae FIG. 3.-Relationships between total numbers of mammae and mean litter sizes of breeding female naked mole-rats that were a) captured in the field and b) born in captivity. bers of mammae and litter sizes were not significant for either wild (F = 0.43, d.f = 1,29; r = 0.12, P = 0.52) or captive females (F = 1.02, d.f = 1,27; r = 0.19, P = 0.32). Regression equations relating litter size (L) and mammary number (M) were L = M (wild females) and L = 0.02 M (captive females). Fluctuating asymmetries.-most naked mole-rats did not have equal numbers of mammae on the two sides of their body. Among the 249 females we sampled, mammary asymmetries (number on the left minus number on the right) ranged from -3 to +3 (Figs. 4a-c). More females were asymmetric (59%) than symmetric (X 2 = 7.7, P = 0.005). However, mean asymmetry (-0.03 ± 0.98) did not differ from zero (t = -0.45, d.f = 248, P = 0.65) and the distribution of asymmetries did not differ from normality (Z = 0.44, P = 0.33). Mammary numbers therefore represented a fiuc-

6 August 1999 SHERMAN ET AL.-LITTER SIZE IN NAKED MOLE-RATS a) Field Breeding 0.4 (n=43) !!1 CO ::l 'tj :~ 'tj 0.6 c) Captive Non-Breeding Females s::: (n=177) -o 0.2 s::: o :e 0.6 o d) Captive Breeding Males Co 0.4 (n=23) o ~ 0.2 c.. O.O..L-,--"""""'I- 0.6 e) Captive Non-Breeding Males 0.4 (n=183) 0.2 O.O.L-, r>l >r Asymmetry in Mammary Numbers FIG. 4.-Fluctuating asymmetries in numbers of mammae on naked mole-rats (number on left minus number on right) separated according to individuals' sex, breeding status, and if they were a) wild-caught or b-e) captive. tuating asymmetry in female H. glaber (Mszmer and Swaddle, 1997; Watson and Thornhill, 1994). Among field-caught breeding females (n = 43), asymmetries in mammary numbers ranged from -2 to +3 (0.47 ± 0.99); of those females, 21 (49%) were symmetric, and 22 (51 %) were asymmetric (Fig. 4a). Among captive breeding females (n = 29) asymmetries ranged from -2 to +2 (0.10 ± 0.90); of those females, 12 (41 %) were symmetric, and 17 (59%) were asymmetric (Fig. 4b). Mammae of captive breeding females were slightly but not significantly more asymmetric than those of wild breeding females (X 2 = 2.4, P = 0.12). Among captive nonbreeding females (n = 177) asymmetries in mammary numbers ranged from -3 to +2 (0.07 ±.0.99); of those females, 69 (39%) were symmetric and 108 (61 %) were asymmetric (Fig. 4c). Asymmetries in mammary numbers did not differ between breeding and nonbreeding females (t = 1.01, d.f = 247, P = 0.32). Among the 206 captive males we sampled, asymmetries in numbers of mammae ranged from -2 to +3 (Figs. 4d-e).More males were asymmetric (63%) than symmetric (X 2 = 14.1, P = ). However, mean asymmetry (0.02 ± 1.08) did not differ from zero (t = 0.32, d.f = 205, P = 0.75) and the distribution did not differ from normality (Z = 0.38, P = 0.35), so mammary numbers of male H. glaber also represented a fluctuating asymmetry. Among breeding males (n = 23) asymmetries ranged from -2 to +2 (-0.17 ± 0.98); of those males, 10 (43%) were symmetric, and 13 (59%) were asymmetric (Fig. 4d). Among nonbreeding males (n = 183) asymmetries ranged from -2 to +3 (0.05 ± 1.10); of those males, 66 (36%) were symmetric and 117 (64%) were asymmetric (Fig. 4e). Mammae of nonbreeding males were slightly but not significantly more asymmetric than those of breeding males (X 2 = 1.91, P = 0.17). In our entire sample, mammary numbers varied from 9 to 15, and 277 of 455 individuals (61%) had different numbers of mammae on the left and right sides of their body. Males and females exhibited similar fluctuating asymmetries in numbers of mammae (t = -0.54, d.f = 453, P = 0.59). Fluctuating asymmetries in mammary numbers did not vary depending on an individual's sex, breeding status, or if it was wildcaught or captive (F = 0.56, d.f = 4,450; P = 0.70). Litters borne by symmetric females (at Meru) were slightly smaller than litters borne by asymmetric females. Wild-caught litters of symmetric females (n = 18) contained 11.2 ± 4.5 young, whereas wildcaught litters of asymmetric females (n = 13) contained 14.2 ± 5.0 young (t = 1.76,

7 726 JOURNAL OF MAMMALOGY Vol. 80, No.3 dj = 29, P = 0.09). Symmetric captive females (n = 13) bore 13.5 ± 3.8 young! litter, and asymmetric captive females (n = 16) bore 13.7 ± 5.1 youngllitter (t = -0.13, dj = 27, P = 0.89). Combining data from wild and captive breeders, 31 symmetric females bore 12.2 ± 4.3 youngllitter and 29 asymmetric females bore 13.9 ± 5.0 young/ litter (t = -1.49, dj = 58, P = 0.14). DISCUSSION Our data reveal a number of morphological and life-history traits of naked molerats that are unusual among mammals generally and rodents particularly. First, mean litter sizes (Fig. 1) and numbers of mammae (Fig. 2) were equal in H. glaber, whereas in most other mammals (Pearl, 1913a), especially rodents (Gilbert, 1986), average litter sizes are about one-half of mean mammary numbers. Second, maximum litter size in H. glaber (28) was nearly double the maximum number of mammae (15), whereas in most other mammals maximum litter size is equivalent to mean mammary number (Eisenberg, 1988; Gilbert, 1986; Hayssen et ai., 1993). Third, total numbers of mammae and fluctuating asymmetries in numbers of mammae on each side in H. glaber were variable (Figs. 2 and 4), rather than being "species-typical, invariant traits" (Gilbert, 1986:4828; Weir, 1974). Fourth, there was no intraspecific relationship between mammary numbers and litter sizes in H. glaber (Fig. 3), as reportedly occurs in sheep (Bell, 1912) but not pigs (Lagreca et ai., 1992; Parker and Bullard, 1913; Pearl, 1913b). Finally, male and female H. glaber had equal numbers of mammae (Fig. 2). Mammary numbers also are not sexually dimorphic in primates, but males in many other taxa typically have fewer mammae than females (e.g., pigs Seo et ai., 1996) or no mammae at all (e.g., mice-raynaud, 1961; rats-imperato McGinley et ai., 1986; horses-tucker, 1985). One of our most intriguing findings was that naked mole-rats do not conform to the one-half rule of Pearl (1913a) and Gilbert (1986). We suggest that they are exceptional due to their cooperative social system. In general, assistance of helpers at the burrow, den, or nest should reduce dangers to preand post-parturient females, and the time and energy that they must spend gathering food and protecting themselves and their neonatal young (Lewis and Pusey, 1997; Waser et ai., 1995). Helpers thus should enable breeding females to concentrate their reproductive efforts on gestation and lactation, and spend more time with neonatal young. If so, it should be reflected in morphological and life-history characteristics of breeding females in cooperatively breeding mammals. Limited information is available on litter sizes and mammary numbers of other cooperative breeders. Among the social canids, female wild dogs (Lycaon pictus) bear 10.1 youngllitter on average, with a range of 1-16 young (Geffen et ai., 1996; Moehlman, 1986), and they have mammae (van Heerden and Kuhn, 1985); female dholes (Cuon alpinus) bear 7.7 young/litter on average, with a range of 1-15 young, and they have mammae (Hays sen et ai., 1993); and female wolves (Canis lupus) bear 6.0 youngllitter on average, with a range of 1-14 young, and they have 8-10 mammae (Hayssen et ai., 1993). Among social herpestids (Rood, 1986), dwarf mongooses (Helogale pa'rvula), meerkats (Suricata suricata), and banded mongooses (Mungos mungo) bear 3-4 youngllitter on average, with a range of 2-8 young, and they have 4-6 mammae (Hayssen et ai., 1993). Thus, like naked mole-rats, those cooperative breeders do not strictly conform to either the one-half rule or the generalization that maximum litter sizes equal mammary numbers. However, group-living canids and herpestids do not deviate from either generalization as far as H. glaber, probably because they are not as eusocial (Sherman et ai., 1995). In a typical colony of naked mole-rats, small (generally young) animals perform

8 August 1999 SHERMAN ET AL.-LITTER SIZE IN NAKED MOLE-RATS 727 maintenance activities such as finding food (widely and unpredictably distributed tubers and patches of bulbs), cleaning tunnels, constructing nests, and clearing caveins, whereas larger colony mates defend the burrow system against snakes, driver ants, and foreign colonies, kick soil loosened during burrowing out onto the surface, and plug damaged burrows (Braude, 1991b; Jarvis, 1981; Judd and Sherman, 1996; Lacey and Sherman, 1991, 1997). When young are born, nonbreeders groom and clean them, huddle with them in the nest, and carry them to safety if a disturbance occurs. Nonbreeders also bring small bulbs and tubers to the nest chamber for the breeding female and her young, and supply them with partially digested fecal pellets (caecotrophes) that are laden with nutrients and endosymbionts (Jarvis, 1981; Lacey and Sherman, 1991, 1997). This assistance enables breeding females to specialize on reproduction. After a female becomes a breeder, her body shape changes, becoming dorsoventrally deep and noticeably elongated due to lengthening of individual vertebrae (Jarvis et ai., 1991). This increases the size of the breeder's body cavity, enabling her to gestate extremely large litters. During pregnancy, breeding females increase massively in girth-so much that they sometimes are unable to pass through narrow burrows. However, restricted mobility does not necessarily jeopardize their survival because pregnant females probably are seldom forced to flee from predators, living as they do in a subterranean fortress surrounded by large, aggressive soldiers (Jarrow and Sherman, 1996; Sherman et ai., 1992). Breeding female naked mole-rats certainly are safer than pregnant females in solitary, surface-dwelling small rodents. Moreover, the breeding female is usually one of the last colony members to visit a site of potential danger such as a tunnel break or predatory disturbance (Braude, 1991a; Brett, 1991a). Female naked mole-rats also are exceptions to the general rule that the number of mammae must be equal to the maximum litter size (Eisenberg, 1988; Gilbert, 1986). On a proximate (immediate cause) level of analysis (Sherman, 1988; Alcock and Sherman, 1994), this is because breeding females have an adequate milk supply for even the largest litters and spend enough time in the nest to nurse them to satiation. Young rotate between teats (i.e., they take turns) rather than aggressively defending one (Jarvis, 1991a), as do young of domesticated pigs (McBride et al., 1964). In hundreds of hours of observations of dozens of litters we have never seen neonatal naked mole-rats fight over access to milk. H. glaber young have low metabolic and growth rates relative to other rodents (Bennett et al., 1991; Jarvis, 1991a). This implies that they have lower daily food requirements, which would ease the per capita lactational burden on their mother. Young begin feeding on caecotrophes when they are only ca. 2 weeks old. Colony mates thus begin early to supplement energy requirements of young, further easing the lactational burden on their mother and facilitating the transition of young to independent foraging. On an ultimate (evolutionary) level of analysis, the low ratio of mammae to maximum litter size suggests that larger numbers of mammae incur increased costs (e.g., due to infections [mastitis] and mammary cancer). When there is sufficient milk and adequate time to nurse, young should readily share mammae, so the absolute number of mammae can be considerably lower than the maximum litter size. Naked mole-rats have the largest mean and maximum litter sizes and mammary numbers of any nondomesticated species in the order Rodentia (Hayssen et al., 1993; Weir, 1974), including the 12 species in the family Bathyergidae (Jarvis and Bennett, 1991). Most other bathyergids have 2-3 young/litter and 6 mammae (e.g., species of Bathyergus, Cryptomys, and Heliophobius-Bennett, 1989; Hayssen et al., 1993; Jarvis and Bennett, 1991, 1993) except Georychus capensis (mean = 5.9 young/lit-

9 728 JOURNAL OF MAMMALOGY Vol. 80, No.3 ter, range = 3-10 young, 6 mammae-bennett and Jarvis, 1988). G. capensis is solitary but Cryptomys damarensis is highly social (Jarvis and Bennett, 1991, 1993). These two species indicate that sociality is not the only factor affecting the ratio of litter sizes to numbers of mammae in bathyergids. Extreme and variable litter sizes in naked mole-rats (Fig. 1) may, on a proximate level, relate to female body size, because new or young breeders are not as large or elongate as old, experienced breeders. On an ultimate level, extreme and variable litter sizes probably are related to unpredictable food availability. To find their widely and irregularly spaced food plants, colonies excavate extensive tunnel labyrinths. In the baked lateritic soil of the Kenyan deserts, burrowing is energetically feasible only after rainfall (Brett, 1991b; Lovegrove, 1989). Timing and amount of rainfall are unpredictable within and between years, and colonies take advantage of even brief rains by digging furiously (Brett, 1991b; Jarvis et ai., 1994; Jarvis and Sale, 1971). The potential to bear large litters under optimal conditions enables breeding females to capitalize on the reproductive opportunities offered by moist soil and abundant food. Under suboptimal conditions, smaller litters reduce effort expended on young that are unlikely to be reared due to food scarcity. Similar arguments have linked fluctuations in abundance of food to variations in litter sizes in other less social mammals (cotton rats, Sigmodon hispidus-cameron and McClure, 1988; muskrats, Ondatra zibethicus-boyce, 1978; mammals generally-boyce, 1988; Eisenberg, 1981) and birds (Ashmole, 1963). Among all mammals, only Tenrec ecaudatus occasionally bear litters that are larger than those of naked mole-rats (up to 32 young in captivity). In the field, their litters usually are smaller, averaging 15 young on Madagascar (range = 10-32) and 11 young (range = 3-18) on the Seychelles (Nicoll and Racey, 1985). Female T. ecaudatus nest solitarily and they have mammae (Louwman, 1973; Nicoll, 1983). Thus, wild tenrecs conform to the one-half rule and their maximum litter sizes approximate mammary numbers, as expected given their solitary lifestyle. Domesticated swine and wild mice (Peromyscus) from northern latitudes are similar to naked mole-rats in having equivalent mammary numbers and litter sizes, and maximum litter sizes that are nearly double the greatest number of mammae. Female pigs typically bear young/litter (depending on their age) with a range of 2-22 young (Clark et ai., 1988; Krider et ai., 1982), and they usually have 12 mammae (Parker and Bullard, 1913). However, extreme fecundity has been selected artificially in swine (Hill and Webb, 1982; Lamberson et ai., 1991), and young fight viciously for access to favored teats, using sharp canine teeth (McBride et ai., 1964, 1965). Feral pigs bear 6-8 youngllitter, with a range of 1-9 young (Hays sen et ai., 1993; Herre, 1986), and they have mammae. Thus, they are more in conformity with the one-half rule and the generalization that maximum litter sizes approximate mammary numbers than naked mole-rats. At latitudes :::::: 45 N, female Peromyscus Zeucopus and P. manicuzatus bear 5-6 young/litter (Millar, 1989) with a range of 2-9 young (Fleming and Rauscher, 1978; Myers and Master, 1983) or 2"':'12 young (Hayssen et ai., 1993), and they usually have 6 mammae (Hayssen et ai., 1993). Increased fecundity at high latitudes has been linked to various ecological (Boyce, 1988; Lord, 1960) and demographic factors (Fleming and Rauscher, 1978), especially resource abundance (Millar, 1989). Comparative information on fluctuating asymmetries in mammary numbers among nondomesticated mammal species is virtually nonexistent. We do not know if this is because locations of mammae in pairs and their numerical symmetry is so stereotyped within species that investigators rarely feel compelled to quantify them, or because

10 August 1999 SHERMAN ET AL.-LITTER SIZE IN NAKED MOLE-RATS 729 only recently has theoretical interest focused attention on fluctuating asymmetries. We located (limited) information on mammary numbers of female foxes (Vulpes fulva). They ranged from 7 to 9, and 2 of 31 females examined (6%) had an odd number of mammae (Turner, 1939). In four families of bats (Craseonycteridae, Megadermatidae, Rhinolophidae, and Rhinopomatidae), occasional individuals in all species have "pubic" teats in addition to the thoracic pair (Simmons, 1993). The incidence of polythelia (supernumerary teats) is 1-2% in guinea pigs (Cavia porcellus-turner and Gomez, 1933), black bears (Ursus americanus-erickson, 1960), polar bears (u. maritimus-derocher, 1990), some primates (e.g., rhesus macaques, Macaca mulatta-hartman, 1927), and humans (Homo sapiens-anderson, 1978). Among domesticated mammals, functional supernumerary mammae occur more frequently. For example, 30-40% of domestic cows have at least one (Hammond, 1927; Turner, 1952). In pigs, numbers of functional mammae range from 8 to 18, and in one sample 1,166 of 2,946 females and 1,159 of 3,024 males had odd numbers of mammae (Harris, 1916; Parker and Bullard, 1913). This means that ;:::39% of those pigs were asymmetric. In domestic dogs, numbers of functional mammae range from 6 to 10, and 13 of 69 females examined had an odd mammary number (Turner, 1939; Wakuri, 1966). Thus, ;:::19% of those females were asymmetric. Finally, numbers of mammae in rats (Rattus norvegicus) range from 10 to 14, and 12 of 60 females examined had an odd number of mammae (Turner, 1939). So, ;:::20% of those females were asymmetric. No one has attempted to relate numerical asymmetries in numbers of mammae to reproductive performance in any mammal, as we have done for naked mole-rats. Indeed, the only remotely similar studies are those of Mfijller et ai. (1995) and Singh (1995) who reported that female humans with symmetrically shaped breasts are more likely to have children and likely to bear more children than women with asymmetric breasts. Naked mole-rats will inbreed in captivity, and wild populations that have been examined with molecular markers were extremely homozygous (i.e., inbred-faulkes et ai., 1990, 1997; Honeycutt et ai., 1991b; Reeve et ai., 1990). This implies that H. glaber is frequently exposed to a potential genetic disruptor of development. If symmetric individuals are more viable (i.e., more resistant to developmental disruption), breeders should have exhibited less fluctuating asymmetry than nonbreeders (Mfijller and Thornhill, 1998). However, there were no differences in left versus right asymmetries in numbers of mammae between breeding and nonbreeding males or females, either in wild-caught or captive colonies (Fig. 4). Also contrary to expectation, asymmetric breeding females bore slightly larger litters than symmetric females. Body size may be a better, more integrative indicator of relative phenotypic quality in naked mole-rats than fluctuating asymmetries in morphological characters such as mammary numbers. When a breeding vacancy occurs in a colony, the largest females vigorously compete for it. Aggression often continues until one female triumphs, sometimes by severely injuring or killing her rivals. Size among females indicates a pattern of dominance (O'Riain and Jarvis, 1998; Shieffelin and Sherman, 1995), success in competition for food, fighting abilities (Jarvis et ai., 1991; Lacey and Sherman, 1991), and low levels of stress from attacks by the current breeding female (Clarke and Faulkes, 1997; Faulkes and Abbott, 1997). Whereas fluctuating asymmetries probably are determined during embryogenesis, differences in body size develop over a much longer period, often an individual's entire lifetime (Lacey and Sherman, 1991, 1997; O'Riain and Jarvis, 1998). Differences in body size probably indicate a consistent history of over- (or under-) achievement more reliably than fluc-

11 730 JOURNAL OF MAMMALOGY Vol. 80, No.3 tuating asymmetries in numbers of mammae. In summary, naked mole-rats are exceptions to the one-half rule and the generalization that maximum litter sizes equal mammary numbers; they offer no support for the fluctuating asymmetry hypothesis. Ecological factors and eusociality help explain the adaptive significance of these unusual characteristics of H. glaber. ACKNOWLEDGMENTS For helpful suggestions we thank A. N. Gilbert, N. C. Bennett, L. C. Drickamer, T. A. Gavin, M. E. Hauber, E. A. Lacey, J. M. Mateo, and participants in the Animal Behavior Lunch Bunch at Cornell University. The National Science Foundation, Cornell University, the Alfred Sloan Foundation, and the South African Research Council kindly provided financial support. We thank N. Mathuku and N. Chondo for assistance in the field. For assistance with molerat husbandry and litter-size counts we thank N. C. Bennett, J. N. Davis, D. C. Gilley, E. A. Lacey, J. L. Nickerson, M. J. 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