Mihlbachler 495 LINKING SEXUAL DIMORPHISM AND SOCIALITY IN RHINOCEROSES: INSIGHTS FROM TELEOCERAS PROTERUM AND APHELOPS MALACORHINUS FROM THE LATE MIOCENE OF FLORIDA Matthew C. Mihlbachler1,2 A strong relationship between sexual dimorphism and the degree of polygyny (i.e., the degree to which males compete for mates) is not apparent in living perissodactyls. For instance, in both monomorphic and dimorphic species of rhinos, about half of male mortality is attributable to tusk and horn mediated combat. Males of the North American Miocene rhinoceros Teleoceras had delayed tusk (i2) eruption, prolonged tusk root growth, and highly sharpened tusk facets maintained by honing on the upper incisor, thus predicting high levels of intermale aggression similar to living rhinos. The sex biases and elevated male mortality rates found in Teleoceras assemblages from Nebraska and Florida seem to confirm this prediction. However, the degree of body size dimorphism in these assemblages varies. Therefore, the intensity of intermale competition seems unrelated to the magnitude of body size dimorphism in Teleoceras. Male individuals of Aphelops, a sympatric rhino, experienced more finite tusk growth and tusks were blunted with age due to the ancestral loss of the upper honing incisor, thus predicting lower levels of intermale competition. The Aphelops fossil assemblage from the Love Bone Bed of Florida is not sex-biased, shows more balanced sex-specific mortality rates, and seems to confirm the prediction of reduced intermale competition, thus suggesting a type of sociality that is different from both Teleoceras and modern rhinos. However, the same assemblage exhibits a degree of sexual dimorphism in tusk and body size that are is not demonstrably different from Teleoceras. Thus, we are left with a perplexing relationship between dimorphism and sociality for rhinos, where levels of intermale competition seem uncorrelated to the degree of sexual dimorphism in both living and extinct species. Key Words: Teleoceras; Aphelops; Miocene; rhinoceros; sexual dimorphism; sociality INTRODUCTION SEXUAL DIMORPHISM AND SOCIALITY IN PERISSODACTYLS Sexual dimorphism in mammals is best understood as a result of sexual selection in polygynous species where males invest large amounts of energy into competing with other males to monopolize access to females (Alexander et al. 1979; Jarman 1983, 2000; Clutton- Brock et al. 1988; Andersson 1994; Berger & Cunningham 1994a). Mature males commonly possess enlarged body size or enlarged weapon-like structures (e.g., horns, tusks, or antlers) that are used to compete for mates either directly through combat, or more indi- rectly through complex behaviors (e.g., ritualized dis- plays). The identification and quantification of sexual dimorphism in fossils is potentially informative of the degree of polygyny in extinct species (Plavcan 2000). The relationship of sexual dimorphism with sociality is most clear among ruminant artiodactyls where increas- ingly larger species tend be extremely dimorphic and form large, herd-like social groups that enable males to monopolize large numbers of mates (Jarman 1983; Geist & Bayer 1988; Loison et al 1999). Extant perissodac- tyls are unusual in the sense that, although all living spe- cies appear to be polygynous, sexual dimorphism is not prominent and there is no clear-cut relationship between sexual dimorphism and sociality. Tapirs and horses are both monomorphic in body size, yet tapirs tend to be solitary while most horse species form year-round har- ems (Berger 1986; Rubenstein 1986; Nowak 1999). Rhinos are the only living perissodactyls that posses con- spicuous weapon-like structures in the forms of horns and tusks; therefore we might expect to find among rhi- nos a stronger relationship between dimorphism and so- ciality. The degree of sexual dimorphism in living rhinos varies from species to species and there are both mono- 1 New York College of Osteopathic Medicine, Department of Anatomy, Northern Boulevard, Old Westbury, NY 11568-8000. 2 American Museum of Natural History, Division of Paleontol- ogy, Central Park West at 79th Street, New York, NY 10024 Bull. Fla. Mus. Nat. Hist. (2005) 45(4):495-520 496 CENOZOIC VERTEBRATES: Papers to Honor S. David Webb morphic (Diceros bicornis) and moderately dimorphic forms (Ceratotherium simum, Rhinoceros unicornis) (Groves 1982; Owen-Smith 1988; Dinerstein 1991, 1993; Berger 1994; Rachlow & Berger 1995). Despite some variability in the degree of dimorphism, all living rhinos are typically solitary. They rarely form small, tempo- rary aggregations, and these appear to result from the chance clustering of critical food or water resources. Social bonding is minimal among adults, even among the most dimorphic species (Laurie 1982; Owen-Smith 1988; Dinerstein 2003). Despite the absence of coherent groups, intermale competition among rhinos is intense and they are among the most violent and aggressive of mammals. In the most well-studied populations of Af- rica and Asia, aggressive confrontations among males account for up to half of male mortality in both mono- morphic (D. bicornis) and dimorphic species (C. simum and R. unicornis) (Hitchins & Anderson 1983; Owen- Smith 1988; Dinerstein & Price 1991; Berger 1994; Berger & Cunningham 1994b; Dinerstein 2003). Males are also aggressive towards females. For instance, R. unicornis males ram females to subdue them (Dinerstein 1991). Sexual dimorphism is commonly reported for ex- tinct perissodactyls, suggesting that sexual dimorphism was more prominent in the past. Dimorphism has been identified in an early “equoid” (Gingerich 1981), various ceratomorphs, including Homogalax, Isectolophus (Radinsky 1963), Hyrachyus (Radinsky 1967), Indricotherium transouralicum (Fortelius & Kappelman 1993), and the chalicothere Moropus (Coombs 1975). Horned species of the extinct family Brontotheriidae show high levels of intraspecific varia- tion in horn size and zygomatic thickness, suggesting a degree of sexual dimorphism similar to modern rumi- nants (Osborn 1929; Mihlbachler et al. 2004a). Dimor- phism has been recognized among many extinct mem- bers of the Rhinocerotidae. Osborn (1898a) reported dimorphism in the mandibular incisor and nasal horn bosses of Oligocene rhinos Subhyracodon occidentalis and Diceratherium tridactylum. The early Miocene Menoceras arikarense shows a degree of dimorphism in its horn bosses that is comparable to the level of di- morphism found in modern ruminants (Peterson 1920; Mihlbachler unpublished data). Osborn (1898b) recog- nized sexual dimorphism in the tusks of Teleoceras fossiger from the late Miocene Long Island Rhino Quarry, Kansas. Mead (2000) further quantified sexual dimorphism in tusk size and body size in Teleoceras from the Ashfall site, Nebraska. Voorhies and Stover (1978) found fetal bones within the abdominal regions of skel- etons of small-tusked individuals from the Ashfall site, confirming that the small-tusked individuals were fe- males. Matthew (1932) and Lambert (1994) found that lower tusks of Aphelops mutilus from Coffee Ranch, Texas and Moss Acres, Florida could be easily divided into male and female groups based on size. Borsuk- Bialynicka (1973) discovered that several cranial dimen- sions of Coelodonta antiquitatis, the Pleistocene woolly rhino of Europe, were bimodal. Finally, Deng (2001, 2005) attributed intraspecific variation in the cranial os- teologies of Chilotherium wimani and Iranotherium morgani to sexual dimorphism. Frequent sexual dimorphism among fossil perisso- dactyls and less pronounced dimorphism among modern species resembles Wright’s (1993) findings on peccar- ies; sexual dimorphism is not prominent among the few living species although pronounced dimorphism is found in extinct species. Perissodactyls were more diverse in the past, and extinction over the last several million years has resulted in drastic reductions in taxonomic diversity. Additionally, population sizes of most extant species have been greatly diminished in recent times. Population bottlenecking, geographic range restriction, artificial population management, and phenotypic alteration (e.g., dehorning of rhinos) can have dramatic effects on eco- logical relationships and social behaviors of large mam- mals (Berger 1994; Berger & Cunningham 1994a, 1994b). Consequently, recent perissodactyls might not serve as good models for the first ~99.9% of perisso- dactyl evolutionary history. For instance, sociality and sexual dimorphism might have been more strongly cor- related in the past, during a time when anthropogenic effects were absent or minimal. Among the three surviving families of perissodac- tyls (Tapiridae, Equidae, Rhinocerotidae), sexual dimor- phism appears to have been most pronounced in rhinos. The family Rhinocerotidae is cladistically defined by a honing relationship between a chisel-like upper incisor (I1) and a dimorphic tusk-like mandibular incisor (i2) (Prothero 2005). The living Asian rhinos (Rhinoceros unicornis, Rhinoceros sondaicus, and Dicerorhinus sumatrensis) possess both tusks and horns. Surpris- ingly, the enlarged tusks, rather than the horns, are used to establish dominance hierarchies among Asian rhinos. In R. unicornis, incisor size is strongly related to male dominance and tusk mediated combat commonly results in mortal wounding (Laurie 1982; Dinerstein & Price 497 2001; Dinerstein 2003). African rhinos (Diceros bicornis and Ceratotherium simum) have secondarily lost their incisors and intermale aggression is mediated by the horn, which results in similarly high levels of mor- tal wounding (Owen-Smith 1988; Berger 1994). Age- and sex-specific mortality patterns in modern rhinoc- eros populations are strongly imprinted by tusk and horn mediated social behaviors. In populations of the three well-studied species of living rhinos, C. simum, D. bicornis, and R. unicornis, 50% or more of male deaths are directly related to tusk and horn mediated aggres- sion (Hitchins & Anderson 1983; Owen-Smith 1988; Dinerstein & Price 1991; Berger 1994; Berger & Cunningham 1994b; Dinerstein 2003). Socially medi- ated mortality is more frequent in rhinos than other large mammals and is most heavily concentrated among young adult males during the life-history interval between the years of sexual maturity and the age of first reproduc- tion. OBJECTIVES Rhinos are good cases for linking sexual dimor- phism with paleosociality. Studies of rhino populations consistently indicate high rates of death among males due to horn and tusk mediated combat. Likewise, re- cent and fossil skeletal assemblages of rhinos contain clear evidence of elevated mortality rates for young adult males, whereas most other large mammal populations do not (Mihlbachler 2003). Because tusk and horn me- diated behavior strongly influences the mortality patterns of modern rhinos in a predictable way, and similar pat- terns are discernable in fossil rhino assemblages, it is possible to approximate the levels of intermale competi- tion by examining mortality patterns among fossil rhi- nos. Therefore, it is possible to compare sexual dimor- phism in fossil rhinos with aspects of sociality relating to intermale competition. In this paper, sexual dimorphism is quantified in the tusks (i2) and limb bones of late Mi- ocene assemblages of Teleoceras proterum and Aphelops malacorhinus from the Love Bone Bed (LBB), Florida, and Teleoceras proterum from Mixson’s Bone Bed (MBB), Florida. Secondly, the ontogeny and sex-specific use wear patterns of the tusks are described. Thirdly, postcranial body size dimorphism in the Florida rhino assemblages is compared to body size dimorphism in an assemblage of Teleoceras major from Ashfall, Nebraska, previously described by Mead (2000). The ensuing discussion on the sexual dimorphism, mortality, and sociality of these rhinos draws from the results of this paper as well as results reported in Mihlbachler (2003) on the age- and sex-specific demographics of these fos- sil assemblages. MATERIALS AND METHODS Mixson’s Bone Bed (MBB) and Love Bone Bed (LBB) contain large assemblages of Miocene rhinos. Early MBB collections are at the Smithsonian Institution, Wash- ington, D.C. (UNSM), while the bulk of the collection is housed at the American Museum of Natural History, New York (FAM). The LBB collection is housed in the Florida Museum of Natural History, Gainesville (UF). The taphonomic backgrounds of LBB and MBB are summarized elsewhere (Webb et al. 1981; Hulbert 1982; Mihlbachler 2003). LBB was dated biostratigraphically to the latest Clarendonian land mammal “age”, or about 8.5 to 10 million years old (Webb et al. 1981). The MBB is biostratigraphically placed in the early Hemphillian land mammal “age”, about seven million years old (MacFadden & Webb 1982). Aphelops malacorhinus and Teleoceras proterum are found at both localities, although the Mixson’s Aphelops sample is too small for statistical analysis of sexual dimorphism. The taxonomy used in this paper follows Prothero (2005). Skulls from these localities are mostly fragmented and severely crushed (Fig. 1), limiting interpretation of sexual dimor- phism to teeth and postcranial elements. I did not mea- sure cheekteeth because these elements are usually not dimorphic, even among dimorphic species. Based on the relative frequencies of tusks, both the LBB and MBB Teleoceras assemblages contain superabundant num- bers of adolescent or young adult males. The LBB as- semblage is 77% male and the MBB assemblage is 72% male. The LBB Aphelops assemblage is not signifi- cantly age- or sex-biased (Mihlbachler, 2003). Although the dimensions of Teleoceras and Aphelops tusks over- lap, they can be readily differentiated. Teleoceras tusks are more curved with a teardrop-shaped cross-section. The female tusk crown is short and somewhat triangu- lar and in both sexes the enamel crown is notably wider than the root. Male tusks have longer crowns, but they are often worn extensively with well-developed honing facets. Aphelops tusks are less curved and have a more rounded cross-section. The diameter of the crown is not much greater than the root diameter. Aphelops male tusks lack the well-developed honing facet seen in Teleoceras males. Aphelops female tusks have a nar- rower and more elongate crown than those of Teleoceras females. Virtually every postcranial element of MIHLBACHLER: Sexual Dimorphism and Sociality in Miocene Rhinoceroses 498 CENOZOIC VERTEBRATES: Papers to Honor S. David Webb Teleoceras and Aphelops can be differentiated. Teleoceras is smaller and has extremely shortened limb elements. Aphelops is larger and proportioned more like living rhinos (e.g., Diceros bicornis). To quantify size dimorphism, a series of measure- ments were taken on the tusk (i2) and on major weight- bearing limb elements including humerus, radius, third metacarpal (MC3), femur, tibia, and third metatarsal (MT3). All tusks with a fully formed crown and at least partial root formation were measured. Only adult bones with fully fused epiphyses were measured. Linear mea- surements up to 15 cm were taken with digital calipers, while longer measurements and diameter measurements were taken with a cloth tape measure accurate to the mm. For cross sectional area measurements, the cross sections of limb bones were replicated with polyvinvyl siloxane and scanned on a flatbed scanner. Area was calculated with ImageJ v1.33. Humeri and femora were not measured for the LBB assemblages because those elements were mostly crushed or incomplete. Mead’s (2000) study of Teleoceras major from Ashfall, Nebraska is the most rigorous analysis of sexual dimorphism for fossil rhinos to date; however my initial data on the Florida assemblages, described in Mihlbachler (2001a), was taken before Mead’s (2000) analysis was published. The measurements of the LBB assemblages are similar to those of Mead (2000), but not all of them are homologous. The landmarks are slightly different in some cases, and limb bone circum- ferences were measured rather than cross-sectional areas. However, I have since been able to make a more extensive set of measurements on the MBB Teleoceras assemblage, including measurements that are homolo- gous to those of Mead (2000), so that dimorphism in the MBB and Ashfall assemblages can be more directly compared. Because of the articulated nature of the Ashfall material, Mead (2000) was able to determine the sex of the skeletons apriori due to their association with the extremely dimorphic mandibular tusk. This enabled him to simply compare the mean values of male and female data with Student’s t-tests. Because of the disarticu- lated nature of the Florida assemblages, sex could not be determined in any element other than the dimorphic tusks. Therefore, it was necessary to adopt different methods. Rather than comparing means of males and females, it was necessary to test for patterns of bimo- dality in the sex-combined assemblage of bones against the null expectation of a unimodal normal distribution. To facilitate a more direct comparison of the Ashfall assemblage with the Florida assemblages, the raw data on the Teleoceras Ashfall assemblage (Mead 1999a) were used to calculate sex-combined statistics like those calculated for the Florida assemblages. A highly dimorphic species will be distinguished from a monomorphic one by a bimodal distribution. A Shapiro-Wilk test of normality (W) was used to test for deviation from a unimodal normal distribution. Signifi- cant results indicate deviation from normality. The rec- ommended alpha level for this test is p < 0.1 (Sall & Figure 1. Male skulls and mandibles of late Miocene rhinos from Florida: (top) Teleoceras proterum (Love Bone Bed, UF 40253) and (bottom) Aphelops mutilus (Moss Acres, UF 69944). These skulls demonstrate the shape difference in the heads of these genera corresponding to the presence of a honing rela- tionship among the incisors of Teleoceras and the lack of such a honing relationship in Aphelops. Although the Aphelops skull is laterally flattened, it is complete and the shape of the lateral profile is preserved. The following struc- tures are labeled to aid orientation: (N) nasal, (O) orbit, (T) mandibular tusk, (LM) left mandible, and (RM) bottom of the right mandible. 499 Lehman 1996). Because a large number of variables were tested simultaneously, statistical error is a concern. The chance of statistical error increases with the num- ber of tests, turning the analysis into a ‘fishing expedi- tion.’ A significant result is bound to eventually come about due to the sheer number of tests. There is no simple solution to the inevitability of statistical error. A Bonferroni correction (Rohlf & Sokal 1994) is one means of diminishing the chance of type one errors (falsely rejecting the null hypothesis, monomorphism). A Bonferroni correction can be calculated by dividing the alpha level of the test by the number of tests. This cor- rection raises the standard for what is accepted as sig- nificant, thus eliminating the ‘fishing expedition’ aspect of the analysis. However, the Bonferroni correction has the adverse effect of greatly magnifying the chance of type 2 error (falsely accepting the null hypothesis, mono- morphism), particularly for the relatively small sizes ana- lyzed in this paper. Indeed, the Bonferroni corrections on the Ashfall Teleoceras data (see below) seemed to result in what appear to be numerous type 2 errors. Therefore, the Bonferroni corrected results are reported for their heuristic value in evaluating the strength of the Shapiro-Wilk tests, but the uncorrected results were found to be more precise in terms of identifying sexual dimorphism, despite the likelihood of some type 1 er- rors. A second means of evaluating dimorphism is the coefficient of bimodality (b): where m 3 is skewness and m 4 is kurtosis. A value of b greater than 0.555 usually indicates a bimodal or polymodal distribution (SAS Institute Inc. 1985; Bryant 1991). RESULTS TELEOCERAS TUSK LIFE-HISTORY The life history patterns of the tusks are reported in terms of three basic ontogenetic processes, (1) for- mation of the crown and initial eruption, (2) growth of the root, and (3) use-wear. Among Teleoceras tusks, clear sex-specific differences are evident in all three of these processes. The age of tusk eruption was appar- ently delayed in males. A male mandible from LBB (UF 24221) with cheekteeth wear equivalent to a five- or six-year-old rhino (Hitchins 1978) contains an unerupted enamel tusk crown. Two female mandibles from MBB (FAM 141392 and FAM 141393) with a simi- lar degree of cheekteeth wear have fully erupted tusks. The root of male tusks continued to lengthen and erupt until very old age, while female tusks were fully formed in just a few years. Growth increments similar to the annual and subannual growth increments observed in the dentin of mammoth tusks (Fisher 1996) are clearly visible on the root surfaces of many of the male Teleoceras tusks (Fig. 2). The most conspicuous incre- ments are traceable to light and dark bands that are vis- ible in polished longitudinal sections and most likely rep- resent annual increments like those found in the incisors of other mammals (Fig. 4; Klevazal & Kleinberg 1969). A detailed study of these growth increments is beyond Figure 2. A pair of male and female Teleoceras proterum i2s (male: UF 41256; female: UF 41339) from the Love Bone Bed, Florida. MIHLBACHLER: Sexual Dimorphism and Sociality in Miocene Rhinoceroses 500 CENOZOIC VERTEBRATES: Papers to Honor S. David Webb the aim this paper. However, the increments on the root surface make it possible to preliminarily quantify the rate of tusk eruption by measuring the distance of the incre- ments that I have interpreted as most likely annual from the base of the enamel crown. Figure 5A shows the rate of eruption of male (UF 41256) and female (UF 41339) Teleoceras tusks. The tusks of both sexes ap- pear to have increased in length at an initially rapid rate. Lengthwise growth in the female tusk slowed after three years, followed by two more years of minor lengthwise growth, after which the pulp cavity was closed off at the proximal end, terminating lengthwise growth. In the male tusk, lengthwise growth was initially fast and gradu- ally slowed to a nearly continuous rate after a few years and continued for 16 more years until the death of the animal. In this particular specimen, the pulp cavity flares open at the proximal end of the tusk, indicating that erup- tion was still occurring at the time of death. I have observed hundreds of Teleoceras tusks, but have found only a few male tusks from very old-aged individuals in which the proximal opening of the pulp cavity was completely closed off, indicating that length- wise growth does eventually cease, but not until very old age. One tusk in the LBB sample, belonging to the individual with the most advanced cheekteeth wear in the sample (UF 24258), has a solid root and has 22 promi- nent rings visible on the root surface. From MBB, the oldest male tusk (USNM 3277a) has 19 or 20 growth increments visible on the outer surface of the tusk. The Figure 3. A pair of male and female Aphelops malacorhinus i2s (male: UF 41311; female: UF 41326) from the Love Bone Bed, Florida. Figure 4. Polished longitudinal section of a broken male Teleoceras proterum tusk (UF 41319) showing annual growth bands. Increments on the scale are millimeters. 501 proximal tip is broken off but the root is completely solid indicating lengthwise growth had ceased sometime af- ter 19 or 20 years. Because tusk growth ceased prior to death, it is impossible to determine the maximum age of these individuals, however they lived a minimum of 20- 22 years. If the subadult years prior to the formation of the tusk root are added, these individuals must have lived more than 25 years. In the wild, modern rhinos live a maximum of 30 to 40 years (Owen-Smith 1988) and it seems that the potential lifespan in Teleoceras was simi- lar or possibly somewhat shorter. For males, the extensive incisor honing results in a progressive volumetric loss of material at the distal end of the tusk. The crown is initially about 10 cm tall, but in old individuals the tusk is worn beyond the crown. Both UF 41256 (Fig. 2) and UF 41256 (Fig. 6A), are nearly worn to this stage. Male tusks maintain a sharp edge at the distolingual margin (Fig. 6A). The wear facet typi- cally exhibits coarse parallel striations that match stria- tions on the I1 (Fig. 7A). Continuous growth and erup- tion of the root coupled with the continuous honing of the crown seems to have allowed males to maintain sharpened tusks but without a progressive loss of total Figure 5. Years of lengthwise tusk growth in (A) Teleoceras proterum and (B) Aphelops malacorhinus based on measure- ments of the distance of presumably annual growth lines on the outer surface of the root from the base of the enamel crown. The resulting curves document the sex-specific length- wise growth history of tusks. An arrow signifies the presence of a pulp cavity and continued lengthwise root growth while an X signifies a solid root and discontinued growth. Figure 6. Distal ends of tusks exhibiting different types of wear: (A) right Teleoceras proterum male, UF 41256, with hon- ing facet; (B) left Teleoceras proterum female, UF 41337, with light polished wear; (C) right Aphelops malacorhinus young male UF 14229, with light wear and shallow lingual grooves; (D) left Aphelops malacorhinus old male (UF 41328) with oblit- erated tusk crown; (E) right Aphelops female, UF 41357, with light polished wear. MIHLBACHLER: Sexual Dimorphism and Sociality in Miocene Rhinoceroses 502 CENOZOIC VERTEBRATES: Papers to Honor S. David Webb tusk length. In older adults, the tusks are often worn beyond the original enamel crown, although because of the additional years of root growth, the tusk is similar in length to the tusk of a younger adult. Many female tusks show some evidence of honing, but it is not exten- sive and does not result in the loss of significant amounts of dental material. APHELOPS TUSK LIFE-HISTORY I was not able to determine the relative timing of male and female tusk eruption in Aphelops because I have never encountered a female mandible of the right age. However, many of the ontogenetic and functional morphology aspects of Aphelops tusks differ from Teleoceras in ways that are wedded to the loss of the upper honing incisor. The tusks are straighter (Fig. 3) and they tend to extend more horizontally from the man- dible, rather than curve upward to meet the upper inci- sors, as in Teleoceras (Fig. 2). The crown does not experience gradual lengthwise reduction due to honing wear. The crowns of male Aphelops tusks initially form a sharp distal point and sharp lingual blade. As life progresses, these initially sharpened edges become blunted and rounded (Fig. 6C-6D). Male tusks lack regu- lar wear facets. Gross wear patterns range from light polishing to severe rounding and splintering, to breakage of the distal end. In female tusks, wear is mainly re- stricted to a slight lingual or distal polishing (Fig. 6E). Microwear features are sporadically distributed across wear surfaces and consist primarily of scratches of vari- ous widths, lengths, and orientations (Fig. 7B). While many growth increments (> 100) appear on the outer surface of most male Aphelops tusks, a clear annual growth pattern is not discernable in most speci- mens. A small set of more prominent lines appear at intervals of some specimens that I preliminarily inter- pret as annual growth increments. This interpretation suggests that male and female Aphelops tusks formed over a finite period of time (Fig. 5B). A female tusk (UF 41326) grew rapidly for one year. Lengthwise growth ceased after four years. The first three years of growth in a male tusk (UF 41311) were rapid, followed by about five years of minor increase in tusk length, after which the pulp cavity was sealed off at the proxi- mal end, terminating lengthwise root growth. Tusk growth in Aphelops appears to have been initially rapid and without the prolonged period of root growth seen among Teleoceras males. This seemingly rapid and finite in- terval of root growth in Aphelops is functionally consis- tent with the lack of honing wear; continuous root growth Figure 7. Scanning electron microscope close-ups of the wear surfaces of male rhinoceros mandibular tusks. Teleoceras wear facets (A) frequently show coarse parallel striations that correspond to similar striations in the upper incisor. Aphelops wear facets (B) are smoother and show fewer numbers of wear striations of variable widths and orientations. Both photos were taken at the same magnification. 503 is not needed to replenish dental material lost to exten- sive honing. TUSK DIMORPHISM Statistical results on tusk dimorphism are summa- rized in Tables 1-3. Most of the male tusks are broken at one or both ends or they are extensively worn, thus limiting the number of available length measurements (CL and RL). Diameter measurements of the crown (WBC) and root (RD) are more commonly available and show no overlap between males and females. Length (CL) and width (WBC) data for complete crowns clearly contain size clusters (Figs. 8A, 9A, 10A). The ratios (M/F) calculated from the average propor- tions of male and female Teleoceras tusks range from 1.6-2.7. In all groups, the length of the enamel crown (CL) was the most dimorphic character (M/F = 2.7 at LBB and 2.5 at MBB). The ratios of enamel crown width (WBC), and root diameter (RD) ranged from 1.6- 1.8. This level of dimorphism is similar to the “tusk di- ameter” ratio of 1.53 reported for the Ashfall Teleoceras assemblage (Mead 2000). Aphelops tusk dimorphism is generally the same with M/F ratios ranging from 1.6- 2.4. Large samples of modern rhinos are not available to calculate a ratio of mean male and female values, but I calculated similar ratios for WBC (M/F = 1.7) and RD (M/F = 1.6) from a male (AMNH 81892) and a female (AMNH 54763) of Dicerorhinus sumatrensis. A male (AMNH 35759) and female (AMNH 54456) of Rhi- noceros unicornis yielded lower ratios of WBC (M/F = 1.4) and RD (1.1). Based on the Shapiro-Wilk test for normality (W), none of the sex-specific tusk data deviated significantly from normality in the MBB Teleoceras assemblage (Table 1). When the sexes were combined, the diam- eter measurements, WBC and RD, were highly bimodal (p < 0.1). The length variables, CL and RL, did not deviate significantly from normality. The tusk length measurements are more difficult to evaluate because of smaller sample sizes (most of the tusks are broken and are not measurable for length). Moreover, most of the male tusks are from young individuals with poorly formed tusk roots. However, it is clear that older males achieve much longer tusk roots than females. Likewise, most of the older males have tusks that are worn almost to the base of the crown, or in some cases, past the crown. These factors introduce overlap in the ranges of male and female tusk length variables in the MBB sample. Nonetheless, unworn male tusk crowns are far longer than unworn female tusk crowns. The coefficients of bimodality (b) confirm that most of the data are more strongly bimodal when the sexes are combined. The sex-combined data for WBC, CL, and RD are strongly bimodal (b > 0.55). Only RL yielded a coefficient sug- gesting unimodality (b = 0.31), but, as noted above, this result is related to the number of young males with poorly developed roots. Variable Sex Mean SD Min Max N CV Skew Kurt b Pr. 0.10 97.0 6.2 88.6 111.7 12 6.41 1.07 1.89 0.44 0.38 MT3PW 0.05 40.7 2.7 37.3 47.5 12 6.60 1.39 3.37 0.46 0.07 MT3DW 0.05 44.1 2.0 41.6 48.6 12 4.45 0.87 1.35 0.41 0.37 MT3D >0.10 19.1 1.2 17.6 22.1 12 6.51 1.42 2.16 0.58 0.07 Table 4. Statistics for the Teleoceras major assemblage from Ashfall, Nebraska, calculated from raw data in Mead (1999a). Column t includes the p-values of Mead’s (2000) Student’s t-tests used to compare male and female averages. See Table 5 for abbrevia- tions. Mead (2000) where male and female averages were compared using Student’s t-tests. Using t-tests, Mead (2000) found significant differences between male and female averages in 69% (18 out of 26) of the postcra- nial variables of the Ashfall Teleoceras assemblage (Table 4). The Bonferroni corrected alpha value for Mead’s original t-tests is 0.002 (alpha level of 0.05 di- vided by 26). Even with this correction, 46% of the original t-tests (12 out of 26) are still significant, thus maintaining a very strong signal for dimorphism in the Ashfall sample. The Shapiro-Wilk test for normality (W) identified ten (38%) variables that differed significantly from normality (p < 0.1). The Bonferroni corrected alpha value of the Shapiro-Wilk tests is 0.004 (alpha value of 0.1 divided by 26). This correction completely neu- ters the Shapiro-Wilk tests of all significance. There- fore, because we know this sample to be dimorphic, based on the t-tests, type 2 errors (wrongly accepting the null hypothesis, monomorphism, when the sample is actually dimorphic) are clearly made when the correction is ap- plied to the Shapiro-Wilk tests. Although there is no easy solution to discriminating real significant results from statistical error, out of the ten uncorrected significant results of the Shapiro-Wilk tests, six of these were also identified as dimorphic by the original t-tests. The un- corrected Shapiro-Wilk tests seem to have captured the signal for dimorphism, though not as strongly as the origi- nal t-tests. The coefficients of bimodality also seem to capture a signal of dimorphism. Nine of the 26 vari- ables (35%) yielded coefficients of bimodality higher than 0.55 (Fig. 11). Out of these nine, seven were charac- ters identified as dimorphic by Mead (2000). The Shapiro- Wilk test of normality and the coefficient of bimodality flagged six common variables; four of these are in com- mon with the results of Mead’s (2000) original t-tests. To summarize, the analysis of the sex-combined data 509 identified a little more than half as many variables as Mead’s (2000) analysis of sex-segregated data. It can be concluded that the Shapiro-Wilk test and coefficient of bimodality were less effective than the original t-tests at identifying dimorphism in the Ashfall sample. How- ever, these analyses flagged several of the variables iden- tified as dimorphic by the original t-tests, and it indicated some other variables as potentially dimorphic. This sug- gests that the analysis of sex-combined data was effec- tive at identifying size dimorphism, albeit not as effec- tively or thoroughly as the original t-tests. A total of 38 variables were measured for the MBB Teleoceras sample (Table 5), including the 26 variables used by Mead (2000). Of these 26 variables, only six (23%) deviated significantly from a normal distribution, based on the Shapiro-Wilk test for normality. Only three (12%) of the 26 variables used by Mead (2000) have bimodality coefficients above the 0.55 threshold. Out of all 38 variables, only 8% yielded coefficients of bimo- dality above 0.55 (Fig. 11) and only 18% yielded signifi- cant Shapiro-Wilk tests. The Bonferroni correction strips the Shapiro-Wilk tests of all significance; however, be- cause of the probability of type 2 error in the corrected results, complete monomorphism is unlikely. At any rate, a fewer number of variables were flagged as being po- tentially dimorphic, suggesting a lesser degree of dimor- phism in comparison to the Ashfall sample. Bivariate plots of selected variables of the MBB Teleoceras as- semblage seem to confirm some size dimorphism by suggesting two size clusters, particularly for the radius and MC3 (Fig. 8B, D). In both plots there are more specimens in the larger cluster. This pattern is consis- tent with the numerical domination of members of the larger sex in the sample based on counts of tusks (72% male) (Mihlbachler 2003). Similar size clusters are evi- dent in the plots of tibia and MT3 data (Fig. 8C, E), but Figure 11. The distributions of coefficients of bimodality (b) for limb bone measurements of Teleoceras and Aphelops fossil assemblages. Abbreviations are as follows: ASHT = Ashfall Teleoceras major; MBBT = Mixson’s Bone Bed Teleoceras proterum; LBBT = Love Bone Bed Teleoceras proterum; LBBA = Love Bone Bed Aphelops malacorhinus. MIHLBACHLER: Sexual Dimorphism and Sociality in Miocene Rhinoceroses 510 CENOZOIC VERTEBRATES: Papers to Honor S. David Webb Variable Mean SD Min Max N CV Skew Kurt b Pr. 0.5). Five of these variables were also identified by the uncorrected Shapiro-Wilk test, so these two sets of results may indicate moderate dimor- phism. However, in comparison to the Ashfall sample, body size dimorphism seems diminished in the LBB Teleoceras assemblage. Bivariate plots do not reveal any obvious size clustering (Fig. 9B-E). The results of the LBB Aphelops assemblage are more perplexing. Eleven out of 30 variables (37%) pro- duced coefficients of bimodality exceeding 0.55 (Fig. 11). This suggests a level of dimorphism approaching that of the Ashfall Teleoceras assemblage. But only two (7%) of these variables yielded a significant result for the Shapiro-Wilk test for normality. Of course, the Bonferroni correction strips these results of their signifi- cance. Bivariate plots do not reveal any obvious size clustering in the Aphelops assemblage (Fig. 10B-E). The coefficient of bimodality strongly suggests sexual dimorphism for Aphelops, but other analyses give in- conclusive results. DISCUSSION TELEOCERAS, HERDS, AND HIPPO MYTHS Because of its conspicuous abundance at many Miocene localities and its distinctive short-legged, broad- torsoed appearance, Teleoceras is one of the most in- Variable Mean SD Min Max N CV Skew Kurt b Pr.