Estimating sexual size dimorphism in fossil species from posterior probability densities

Accurate characterization of sexual dimorphism is crucial in evolutionary biology because of its significance in understanding present and past adaptations involving reproductive and resource use strategies of species. However, inferring dimorphism in fossil assemblages is difficult, particularly with relatively low dimorphism. Commonly used methods of estimating dimorphism levels in fossils include the mean method, the binomial dimorphism index, and the coefficient of variation method. These methods have been reported to overestimate low levels of dimorphism, which is problematic when investigating issues such as canine size dimorphism in primates and its relation to reproductive strategies. Here, we introduce the posterior density peak (pdPeak) method that utilizes the Bayesian inference to provide posterior probability densities of dimorphism levels and within-sex variance. The highest posterior density point is termed the pdPeak. We investigated performance of the pdPeak method and made comparisons with the above-mentioned conventional methods via 1) computer-generated samples simulating a range of conditions and 2) application to canine crown-diameter datasets of extant known-sex anthropoids. Results showed that the pdPeak method is capable of unbiased estimates in a broader range of dimorphism levels than the other methods and uniquely provides reliable interval estimates. Although attention is required to its underestimation tendency when some of the distributional assumptions are violated, we demonstrate that the pdPeak method enables a more accurate dimorphism estimate at lower dimorphism levels than previously possible, which is important to illuminating human evolution.

Sexual dimorphism across primates and in humans has been investigated to elucidate its evolutionary significance. Particular attention has been paid to body, skeletal, and canine size dimorphism. This is because of suggested relationships of these dimorphisms with ecological and sociobehavioral variables, especially in relation to reproductive behavior, and also because these parameters can be assessed in fossil assemblages (see refs. 1–3 for relatively recent overviews). Following the influential work of Clutton-Brock et al. (4), the ratio between male and female mean sizes (or its logarithm) (5, 6) has been the predominant parameter used in quantifying sexual size dimorphism, a simple, but fundamental, parameter in assessing adaptive strategies. In this paper, we refer to this measure as the “m/f ratio.” Although this ratio is straightforwardly determinable in extant species and populations, this is not the case in fossils because the sex of a specimen is generally unknown.In estimating the m/f ratio from fossil assemblages with no sex information, a commonly applied method is the “mean method” (here abbreviated the “MM”) (7), which splits the sample into two subgroups, one above and the other below the sample mean. The ratio between the two subgroup means is considered the m/f ratio. In other words, the assumption is made that all specimens larger than the sample mean are males, and vice versa for females. This assumption would be reasonable only when the distributions of the two sexes overlap minimally, which is not necessarily the case in many features or taxa of interest. In estimating overall skeletal size dimorphism, a multivariate version of the MM has also been suggested (6). In this method, the m/f ratio is calculated as the geometric mean of the m/f ratios of multiple skeletal elements, thereby enabling dimorphism estimates from larger fossil sample sizes. However, caution is needed when partial skeletons are included in the analysis, because the dimorphism estimate can be weighted by relatively few individuals. This may result in a highly biased estimate, as in the case of the Australopithecus afarensis skeletal size dimorphism (6, 8).Rather than accepting the assumption that the two sexes segregate at the mean, Lovejoy et al. (9) proposed a method that takes into account the unknown sex status of the specimens. Supposing a sample of N specimens, there are N − 1 possible splitting points between males and females and an equal number of possible m/f ratio values. Then, assuming equal chance of the two sexes being represented in the fossil sample, the m/f ratio is calculated by weighing the N − 1 presumed male-to-female ratios with their binomial probabilities. This method was later termed the binomial dimorphism index (here, the “BDI”) (10). When there is large size overlap between the sexes, this procedure is expected to correct for bias stemming from allocating sex via the sample mean. However, it shares with the MM the assumption that all males are larger than all females, and it has been shown (as with the MM) to overestimate weak skeletal size dimorphism, such as in chimpanzees (6, 10).Another approach for estimating dimorphism is to use the empirical correlation observed between the m/f ratio and the coefficient of variation (CV; the SD divided by the mean). In traits that show a range of size dimorphism levels among taxa or populations, there is a strong tendency of a larger total CV to be associated with a larger m/f ratio. Using such a relationship, the m/f ratio of fossils can be estimated (11) via regression using known-sex extant samples (12–14) or simulated data (15, 16). However, as demonstrated in validation studies (15, 17), the CV method (hereafter, the “CVM”) is susceptible to within-sex CV (hereafter, “wsxCV”) levels and can overestimate, especially when sexual dimorphism is weak to moderate, as do the MM and BDI. This is because, when the two sex distributions substantially overlap, it is difficult to distinguish whether a large total CV stems from large sexual size dimorphism or large within-sex variance, the latter generally unknown in fossil assemblages.Here, we introduce the “posterior density peak” (hereafter “pdPeak”) method , a method of estimating the m/f ratio in fossil assemblages of unknown sex via a Bayesian mixture model. We model the background population from which the fossil sample is derived by three parameters, the male and female means and the common within-sex variance (all in log scale). Applying the Bayes theorem, we assign probabilities to the combinations of these three parameters that realize the sample distribution in hand. By this method, the distance between the two subgroups (dimorphism level) and within-subgroup variation can be evaluated simultaneously in terms of the fit of the model to a given sample distribution. In other words, “shape ” of the sample distribution is considered when estimating size dimorphism. Fig. 1 illustrates how a population with the same total variation (combined-sex CV) can contain divergent latent distributions with a range of m/f ratios and within-sex variances, resulting in entirely different overall distributional shapes. It is clear that distribution shape is important in inferring distance (dimorphism) between subgroup means. We show that our method resolves the m/f ratio better than the other methods when male–female distributions overlap substantially.Open in a separate windowFig. 1.Variation in shape of population distributions with a constant CV of 10%. (A–D) Hypothetical population (combined-sex) distributions with the same overall variation (CV of 10%) are plotted for several subgroup conditions. Log-normal distributions of males and females with a common wsxCV are mixed in equal proportions. Overall CV is fixed at 10% and the female mean at 10 mm. The wsxCV is set in four ways: 8%, 7%, 6%, and 5% (from left to right). Solid black curves indicate overall distributions, dashed curves are the latent within-sex distributions, red is for female, and blue is for male. Vertical dashed lines indicate within-sex means. The same distributions are shown in E–H segregated to subpopulations by the mean. Vertical solid lines indicate the presumed sex means of the mean method (MM). The true male mean/female mean (m/f ratio), as well as the MM ratio (mean of presumed males divided by that of the presumed females), is shown below each wsxCV condition. Note that the MM increasingly overestimates as the male and female distributions increasingly overlap (from right to left). The Rd values (see Application to Actual Cases), i.e., the distance between means in within-sex SD units, are 1.6, 2.2, 2.9, and 3.8, respectively in A, B, C, and D. Note also that, under the same overall CV, the true m/f ratio can vary substantially depending on wsxCV.We present the pdPeak method and evaluate its performance by 1) using computer-generated samples from simulated populations and 2) applying the method to a large dataset of extant anthropoid canine crown metrics of known sex. We compare the pdPeak method with the other most commonly used methods, the MM, BDI, and CVM. Lastly, we apply the pdPeak method to an actual sample of fossil canines to explore its potential in human evolutionary studies.In evaluating the pdPeak method, we focus on canine crown size for simplicity. The canine crown diameter m/f ratios seen in the extant great apes and modern humans are summarized in SI Appendix, Table S1. In extant great apes, the m/f ratio ranges from ∼1.2 to ∼1.5. The most dimorphic is the gorilla, with maximum canine crown diameter m/f ratios of ∼1.4 to 1.5. The same ratios of chimpanzees and orangutans range from ∼1.2 to 1.4, with the least dimorphism seen in the bonobo lower canine (13, 18–22). To the contrary, in humans, the m/f ratio of canine crown diameters varies among populations, predominantly between 1.03 and ∼1.10 (23). Based on this, we focus on discerning m/f ratios of the 1.1 to 1.2 interval, the range bridging the extant great ape and human conditions.     

From the Cover: Canine sexual dimorphism in Ardipithecus ramidus was nearly human-like

Body and canine size dimorphism in fossils inform sociobehavioral hypotheses on human evolution and have been of interest since Darwin’s famous reflections on the subject. Here, we assemble a large dataset of fossil canines of the human clade, including all available Ardipithecus ramidus fossils recovered from the Middle Awash and Gona research areas in Ethiopia, and systematically examine canine dimorphism through evolutionary time. In particular, we apply a Bayesian probabilistic method that reduces bias when estimating weak and moderate levels of dimorphism. Our results show that Ar. ramidus canine dimorphism was significantly weaker than in the bonobo, the least dimorphic and behaviorally least aggressive among extant great apes. Average male-to-female size ratios of the canine in Ar. ramidus are estimated as 1.06 and 1.13 in the upper and lower canines, respectively, within modern human population ranges of variation. The slightly greater magnitude of canine size dimorphism in the lower than in the upper canines of Ar. ramidus appears to be shared with early Australopithecus, suggesting that male canine reduction was initially more advanced in the behaviorally important upper canine. The available fossil evidence suggests a drastic size reduction of the male canine prior to Ar. ramidus and the earliest known members of the human clade, with little change in canine dimorphism levels thereafter. This evolutionary pattern indicates a profound behavioral shift associated with comparatively weak levels of male aggression early in human evolution, a pattern that was subsequently shared by Australopithecus and Homo.

A small canine tooth with little sexual dimorphism is a well-known hallmark of the human condition. The small and relatively nonprojecting deciduous canine of the first known fossil of Australopithecus, the Taung child skull, was a key feature used by Raymond Dart for his inference that the fossil represented an early stage of human evolution (1). However, recovery of additional Australopithecus fossils led to the canine of Australopithecus africanus to be characterized as large (compared to that of humans or “robust australopithecines”) and its morphology primitive, based on a projecting main cusp and crown structures lacking or hardly expressed in Homo (2). Later, the perception of a large and primitive canine was enhanced by the discovery and recognition of Australopithecus afarensis and Australopithecus anamensis (3–8), the latter species extending back in time to 4.2 million years ago (Ma). Although assessments of canine size variation and sexual dimorphism in Au. afarensis were hampered by limited sample sizes (9, 10), some suggested that the species had a more dimorphic canine than do humans, equivalent in degree to the bonobo (11) or to chimpanzees and orangutans (12). Initially, Au. anamensis was suggested to express greater canine dimorphism than did Au. afarensis (13, 14). However, based on a somewhat larger sample size, this is now considered to be the case with the tooth root but not necessarily its crown (15–17).Throughout the 1990s and 2000s, a pre-Australopithecus record of fossils spanning >6.0 to 4.4 Ma revealed that the canines of these earlier forms did not necessarily exceed those of Au. afarensis or Au. anamensis in general size (18–28). However, all these taxa apparently possessed canine crowns on average about 30% larger than in modern humans, which makes moderately high levels of sexual dimorphism potentially possible. Canine sexual dimorphism, combined with features such as body size dimorphism, inform sociobehavioral and ecological adaptations of past and present primates, and therefore have been of considerable interest since Darwin’s 1871 considerations (29–57). In particular, the relationship of canine size dimorphism (and/or male and female relative canine sizes) with reproductive strategies and aggression/competition levels in primate species have been a continued focus of interest (14, 33, 35–45, 49–56). Conspecific-directed agonistic behavior in primates related to mate and/or resource competition can be particularly intense among males both within and between groups (14, 44, 57). It is widely recognized that a large canine functions as a weapon in intra- and intergroup incidences of occasional lethal aggression (45, 58–61), and a large, tall canine has been shown or inferred to significantly enhance male fitness (50, 56). Hence, canine size and dimorphism levels in fossil species provide otherwise unavailable insights into their adaptive strategies.Here, we apply a recently developed method of estimating sexual size dimorphism from fossil assemblages of unknown sex compositions, the posterior density peak (pdPeak) method (62), and reexamine canine sexual dimorphism in Ardipithecus ramidus at ∼4.5 Ma. We include newly available fossils recovered from the Middle Awash and Gona paleoanthropological research areas in the Afar Rift, Ethiopia (26, 63, 64) in order to obtain the most reliable dimorphism estimates currently possible. We apply the same method to Australopithecus, Homo, and selected fossil apes, and evaluate canine sexual dimorphism through evolutionary time.We operationally define canine sexual dimorphism as the ratio between male and female means of basal canine crown diameters (the m/f ratio). Because the canines of Ar. ramidus, Au. anamensis, and extant and fossil apes are variably asymmetric in crown shape, we examine the maximum basal dimension of the crown. This can be either the mesiodistal crown diameter or a maximum diameter taken from the distolingual to mesiobuccal crown base (7, 27, 65). In the chronologically later Au. afarensis and all other species of Australopithecus sensu lato and Homo, we examine the more widely available conventional metric of buccolingual breadth, which corresponds to or approximates the maximum basal crown diameter. In anthropoid primates, canine height is more informative than basal canine diameter as a functional indicator of aggression and/or related display (14, 41–44). We therefore also examine available unworn and minimally worn fossil canines with reliable crown heights.     

The short form-12 and the measurement of health status in patients with cerebral aneurysms: performance, validity, and reliability

OBJECT: Cerebral aneurysms can affect a patient's health status by rupture and stroke, impingement on neural structures, treatment side effects, or psychological stress. The authors assessed the performance, validity, and reliability of the Short Form-12 (SF-12), a self-administered written survey instrument, to assess health status in patients with cerebral aneurysms. METHODS: A cohort of 170 patients with cerebral aneurysms who were seen at a neurosurgery clinic underwent structured interviews including measurement of their health statuses (SF-12 physical component summary [PCS] and mental component summary [MCS]), functional status (Glasgow Outcome Scale score, modified Rankin Scale score, and Barthel Index), and mental health (Hospital Anxiety and Depression Scale score). The SF-12 scores were compared with US population norms by performing t-tests with unequal variances. The validity of the SF-12 was assessed by comparing the PCS and MCS scores with each patient's functional status and mental health scores by using rank-order methods. Inter-item reliability was assessed using the Cronbach alpha statistic. Patients with cerebral aneurysms had decreased health status PCS and MCS scores when compared with population norms (p < 0.001 for all). A history of subarachnoid hemorrhage (SAH) (p = 0.006) and previous surgical or endovascular treatment (p = 0.047) was associated with worse PCS scores. The validity of the SF-12 was supported by the relationship between the PCS and MCS scores and the patient's functional status and mental health (p < 0.001 for all). The reliability of the SF-12 was documented by the Cronbach alpha statistic (alpha = 0.76). CONCLUSIONS: Patients with cerebral aneurysms have a diminished physical and mental health status as measured using the SF-12. The presence of SAH and aneurysm treatment are associated with a worse physical health status. The SF-12 is a valid and reliable instrument for measuring health status in patients with cerebral aneurysms.     

Comparison of the short test of mental status and the mini-mental state examination in mild cognitive impairment

BACKGROUND: The Mini-Mental State Examination (MMSE) is the most widely used brief screening measure of cognition, but it is not sensitive in detecting mild memory or other cognitive impairments. The Short Test of Mental Status (STMS) was specifically developed for use in dementia assessment and was intended to be more sensitive to problems of learning and mental agility that may be seen in mild cognitive impairment (MCI). OBJECTIVE: To compare the STMS and MMSE for detecting or predicting MCI. DESIGN: Comparison of STMS and MMSE scores at baseline among 4 groups of patients: 788 patients with stable normal cognition, 75 patients with normal cognition at baseline but who developed incident MCI or Alzheimer disease during follow-up, 129 patients with prevalent MCI at baseline, and 235 patients with prevalent mild Alzheimer disease. All patients and control subjects for this study were evaluated through the Mayo Alzheimer's Disease Patient Registry or the Mayo Clinic Alzheimer's Disease Research Center, Rochester, Minn, using a standardized diagnostic approach. RESULTS: The STMS was slightly more sensitive than the MMSE in discriminating between patients with stable normal cognition and patients with prevalent MCI. The STMS was superior to the MMSE in detecting deficits in cognition in individuals who had normal cognition at baseline but later developed incident MCI or Alzheimer disease. CONCLUSIONS: Compared with the MMSE, the STMS was better able to document MCI and was more sensitive in detecting deficits in cognition in individuals who had normal cognition at baseline but later developed incident MCI or Alzheimer disease.     

Influence of delaying treatment after symptoms develop from subarachnoid hemorrhage: a preliminary analysis

Patients experiencing subarachnoid hemorrhage (SAH) symptoms may delay seeking medical attention, not realizing the severity of these symptoms. The purposes of this study were to determine (a) the length of time between the development of SAH symptoms in patients and when treatment was initially sought and (b) whether the delay in hospital admission had an effect on patient outcomes. Inclusion criteria were age (18-75 years) and diagnosis of severe SAH. Consent was obtained on 90 eligible patients admitted to the neurovascular intensive care unit. Outcomes were assessed at 3 months using the Glasgow Outcome Scale (GOS) and Modified Rankin Scale (MRS). Initial time delay, calculated by subtracting the time of initial symptom development from the time of admission to the emergency department (ED), ranged from 0.08 to 103 hours. There was no relationship between the initial time delay and GOS or MRS scores. There was a significant difference between the time to initial ED admission to a trauma ED and to a community ED; patients were admitted within 2.7 hours to a trauma ED admission, compared to 7 hours for a community ED admission. There was a significant relationship between the Hunt and Hess Scale and GOS and between the Hunt and Hess and MRS. There was a significant relationship between the Fisher Grade and GOS and between the Fisher Grade and MRS. This study shows that patients may delay treatment for nearly 7 hours after initial symptoms develop. This suggests that laypersons are not aware of SAH symptoms, thereby delaying ED admission and care. The study also suggests that more severe symptoms upon admission to the ED were related to poorer outcomes. Initial clinical presentation is a useful predictor for SAH outcomes. This study supports the idea that the general public needs to be educated on the symptoms of SAH.     

Symptomatic cavernous sinus aneurysms: management and outcome after carotid occlusion and selective cerebral revascularization

BACKGROUND AND PURPOSE: Therapeutic internal carotid artery (ICA) occlusion for symptomatic intracavernous artery aneurysms can result in ischemic infarction despite normal clinical balloon test occlusion (BTO). We evaluated outcomes in patients with symptomatic cavernous sinus aneurysms in whom clinical BTO was normal, who underwent carotid occlusion with selective bypass surgery guided by physiologic BTO using quantitative cerebral blood flow (CBF) analysis by means of stable xenon-enhanced CT. METHODS: After a normal clinical BTO, 26 consecutive patients with symptomatic cavernous sinus aneurysms underwent a baseline xenon-enhanced CT CBF analysis followed by a second CBF analysis, during which repeat BTO was performed. Patients with a decrease in cortical CBF to below 30 mL/100 g/min were considered moderate risk and those with greater than 30 mL/100 g/min were low risk for developing postocclusion ischemic infarction. Moderate-risk patients underwent cerebral revascularization followed by proximal carotid occlusion. Low-risk patients underwent carotid occlusion alone. Patients were clinically followed up for at least 3 months after carotid occlusion. All patients underwent head CT at least 1 month after carotid occlusion. RESULTS: Eight patients were moderate risk and 18 low risk. Mean follow-up was 15.3 months. Mean CT follow-up was 10.2 months. No low-risk patient developed a postocclusion ischemic deficit by examination or infarct by CT. One patient in the moderate-risk group developed right hemiparesis and a left posterior middle cerebral artery infarction by CT 2 months after carotid occlusion. CONCLUSION: In this series, BTO combined with quantitative CBF analysis was a safe and reliable technique for identification of patients at risk for ischemic infarction after carotid occlusion, despite a normal clinical BTO.     

Aneurysms of the intracavernous carotid artery: a multidisciplinary approach to treatment

Of 43 cavernous sinus aneurysms diagnosed over 6 1/2 years, 23 fulfilled indications for treatment; of these 19 were treated, eight surgically and 11 with interventional radiological techniques. Six small and two giant aneurysms were treated surgically: four were clipped, two were repaired primarily, and two were trapped with placement of a saphenous-vein bypass graft. Seven large and four giant aneurysms were treated with interventional radiological techniques: in five cases the proximal internal carotid artery (ICA) was sacrificed; one aneurysm was trapped with detachable balloons; and five were embolized with preservation of the ICA lumen. The mean follow-up period was 25 months. At follow-up examination, three patients in the surgical group were asymptomatic, two had improved, and three had worsened. Three of these patients had asymptomatic infarctions apparent on computerized tomography (CT) scans. At follow-up examination, four radiologically treated patients were asymptomatic, five had improved, two were unchanged, and none had worsened. One patient had asymptomatic and one minimally symptomatic infarction apparent on CT scans; both lesions were embolic foci after aneurysm embolization with preservation of the ICA. It is concluded that treatment risk depends more on the adequacy of collateral circulation than on the size of the aneurysm. A multidisciplinary treatment protocol for these aneurysms is described, dividing patients into high-, moderate-, and low-risk groups based on pretreatment evaluation of the risk of temporary or permanent ICA occlusion using a clinical balloon test occlusion coupled with an ICA-occluded stable xenon/CT cerebral blood flow study. Radiological techniques are suggested for most low-risk patients, while direct surgical techniques are proposed for most moderate- and high-risk patients.     

Brainstem death with persistent EEG activity: evaluation by xenon-enhanced computed tomography

A patient with brainstem infarction met the clinical criteria for brain death but had persistent EEG activity, complicating our decision to withdraw life support. We evaluated cerebral blood flow with xenon-enhanced computed tomography (Xe/CT), which documented the absence of posterior circulation flow and persistent, low, anterior circulation flow. This information led us to withdraw life support, despite the presence of EEG activity. The Xe/CT method noninvasively measures local cerebral blood flow and may enhance diagnostic certainty in complicated brain-death evaluations.