Discriminant function analysis

1. Deceptive species are a characteristic trait of insect–plant mutualisms. Deception of pollinators is essential for reproduction in diverse plant species; however, mimicry in seed dispersal is almost unknown. Myrmecochory, the dispersal of diaspores by ants, is a mutualism in which the elaiosome, a lipid-rich seed appendage, works as an ant reward. This coevolved interaction may be exploited by cheating, non-rewarding diaspores that mimic elaiosomes.2. Our study assesses the impact of the morphology and fatty acid composition of diaspores on ant dispersal in rewarding and cheating myrmecochores and non-myrmecochorous species. Four elaiosome types (defined by Sernander 1906) were included in our research: the ‘Viola odorata type’, with a clearly defined elaiosome, the similar but diplochorous ‘Euphorbia type’ with an additional ballistic dispersal of diaspores, and the ‘Puschkinia’ and ‘Hepatica’ types, which we classify as ‘cheaters’ as they mimic ant rewards by chemical cues.3. We tested the influence of morphology, chemical composition of diaspores and presence of rewards on removal rates of diaspores, dummies impregnated with seed extracts and pure fatty acids and scent-standardized diaspores in a population of Formica polyctena ants with 10 European spring ephemerals, mostly Ranunculaceae. The main free fatty acids of diaspores were identified by gas chromatography and mass spectrometric analysis.4. Removal rates of diaspores and dummies treated with seed extracts were significantly influenced by their fatty acid composition. Discriminant function analysis confirmed oleic acid as the main trigger substance eliciting seed-removal behaviour by ants in most species. Oleic acid content and removal rates differed among elaiosome types and were highest in rewarding myrmecochores, lower in cheaters and smallest in non-myrmecochorous seeds. Removal rates of scent-standardized diaspores did not differ among mutualists and cheaters suggesting a selective pressure for morphological adaptation and were lowest in non-myrmecochorous species, thus corroborating an influence of diaspore morphology on ant-removal patterns.5. For the first time, we demonstrate chemical mimicry in myrmecochory as a means of seed dispersal. Evolutionary stability of the ant–seed mutualism is maintained by the ability of ants to discriminate between certain types of rewards and to respond with differential diaspore distribution rates.

En este trabajo se presentan los resultados obtenidos de una muestra 112 esqueletos referenciados de adultos contemporáneos (49 femeninos y 63 masculinos) sin evidencia de patología o lesiones que alteraran su morfología y que forman parte de la colección osteológica del Laboratorio de Antropología Física del Departamento de Anatomía de la Facultad de Medicina de la UNAM. Con la utilización de un vernier digital se evaluaron 6 medidas (dos longitudes y cuatro anchuras)  por cada uno de los huesos cinco huesos del metacarpo y 6 medidas para los 5 huesos del metatarso. Se aplicaron pruebas estadísticas para verificar normalidad de la muestra, dos tipos de pruebas t y un estadístico de Lambda de Wilks para obtener funciones discriminantes. Logrando poco más de 30 funciones por encima del 80% de asignación correcta. Teniendo al segundo metacarpo y al primer metatarso como los huesos mas dimórficos de la muestra.

The identification of human skeletal remains is one of the most important objectives of anthropologists working in medico-legal contexts. The establishment of identity from human bones is based on four main characteristics: age, sex, ethnicity and stature. The majority of these characteristics can be established relatively quickly if the skeleton is complete. However, this is not always the case and often the skeletal specialists have to work with incomplete and severely fragmented remains.
The correct determination of sex using skeletal remains generally depends on the completeness of the pelvis and the skull as best indicators of sex. The craniofacial element of the skull is rather fragile and easily damaged by external factors. The cranial base is one of the regions of the skull which survive more intact.
The primary objective of this thesis is to establish the sexual dimorphism of a specific anatomical area of the skull base: the foramen magnum region. This analysis has not been undertaken before in any English population. Therefore, sexual dimorphism is examined using a British 18th and 19th century London crypt sample.
Discriminant analysis is carried out and population-specific sex determination functions are developed using the foramen magnum, the occipital condyles and a combination of both. Furthermore, a newly developed semi-automated method for the extraction of foramen magnum data from digital images is assessed and the effect of advanced age on the metric dimensions of the foramen magnum region is analysed.
Results demonstrate the existence of significant sexual dimorphism in this sample of English crania. The newly developed functions based on a combination of foramen magnum and occipital condyle variables permit the correct determination of sex of this collection with 71.9%. Functions using only foramen magnum variables achieved 68.4% correct identifications whilst occipital condyle functions provided the highest correct classification percentage of 76.7%. The semi-automated method proved to be useful and promising for future research application. No significant age effect in the foramen magnum region was found. Overall, sexual dimorphism is evident in the foramen magnum region of the St. Bride’s crania. New discriminant functions developed during this study are useful for sex determination but these methods should not be used in forensic cases without prior testing on modern samples.

Increasing medical expenditures is a major economic challenge for the United States.  From 1990 to 2009, total per capita health care expenditures increased 284% and are expected to exceed $12,000 per capita by 2020. Although previous research has tested the impact of a single health behavior on medical expenditures, no empirical studies have examined the link between patterns of health-related behavior and medical expenditures.  The current research was grounded in typological methods, complex systems, dynamic systems, and complex adaptive systems theories.  The research question assessed the predictive validity of an individual case’s probabilistic distance from patterns of health-related behavior at the center of cluster groups identified typologically on medical expenditures while controlling for the predictive effects of a case’s probabilistic distance from remaining central patterns of health-related behavior, age, and sex. A random sample of 3,955 adults was taken from a 2003 Florida commercial health plan database. Participant probabilistic distance from patterns of health-related behavior was assessed using posterior probabilities derived from discriminant function analysis. Multiple regression analysis was used to analyze the research question and results supported the positive predictive effects of patterns of health-related behavior on medical expenditures as participants emulated the patterns with increasing acuteness.  This research supports positive social change by demonstrating the need for policy development to address health behavior pattern contributions to increasing expenditures at national, regional, community, and individual levels.  This research expands the predictive effects of single health-related behaviors on medical expenditures to multiple health-related behaviors.

After viewing this presentation, attendees will gain a greater understanding of the morphological differences seen between male and female modern pubic bones and how those shape differences can be captured using a 3D geometric morphometric approach.

This presentation will impact the forensic science community by quantifying nonmetric shape analyses that are widely used in sexing human pubic bones through a 3D geometric morphometric approach for analysis. Using a 3D geometric morphometric approach allows for the utilization of landmarks and semi-landmarks to accurately capture the slight shape differences that nonmetric observations are not able to obtain.

Sex estimation methods for human skeletal remains have been a highly researched and debated topic in biological anthropology. A plethora of studies have been performed using various statistical methods, in part because os coxae variation spans a large spectrum and does not always fit into distinct nonmetric categories. Growing in popularity is the utilization of 3D geometric morphometric techniques; studies have been performed using landmarks and semi-landmarks to sex os coxae with a high degree of accuracy.

Generally, it is believed that male pubic bones tend to be shorter and triangular in shape, while females have a longer and squarer shape. Previous studies acknowledge the need to quantify nonmetric methods while sexing os coxae, but do not specifically test the widely used nonmetric visual method of sexing males on the basis of short or triangular pubic bones and females on the basis of long or square pubic bones.

In this research, 35 known male and 35 known female specimens from the William M. Bass Donated Skeletal Collection at the University of Tennessee (UT) and 24 unknown specimens from the Forensic Anthropology Unit at the New York City Office of Chief Medical Examiner (NYC OCME), were scanned using a NextEngine 3D laser scanner. The os coxae were edited in Geomagic and 8 landmarks were placed on the left pubic bone. The landmarks were chosen to highlight the portion of the pubic bone associated with the triangular and rectangular shape differences between males and females. These points were placed on the dorsal aspect of the bone since there are fewer irregularities and span from the superior and inferior portions of the pubic symphysis, along the obturator foramen opposite the symphysis points, and up to the most superior point of the obturator foramen. The points were aligned using a Generalized Procrustes Analysis, and then a Principal Components (PC) analysis was employed to distinguish meaningful shape differences. A Discriminant Function Analysis (DFA) was then run on the PC scores to determine how accurate the captured portion of the pubic bone is in determining sex. The known specimens were placed in their proper sex categories for the DFA analysis, while the unknown specimens were left ungrouped to compare the nonmetric analyses of those os coxae found in their case reports versus their assigned group in the DFA analysis.

Using the 12 PC scores that contained significant shape information, the DFA analysis was able to classify 95.7% (94% males, 97% females) of the known UT pubic bones correctly into their skeletal sex groups with a 92.9% (91% males, 94% females) leave-one-out cross-validation accuracy. For the unknown NYC OCME specimens, 83.3% of the specimens matched their case reports. Intra-observer error was tested by placing the landmarks on the specimens a second time and running the same analyses. The results were an original classification accuracy of 97.1% (94% males, 100% females), a cross-validation accuracy of 91.4% (86% males, 97% females), with 87.5% of the unknown specimens matching their case reports. The differences in percentages between these two analyses are slight, and the changes were due to specimens that fell within the overlapping regions found on the PC plots.

The results capture the major morphological differences between male and female pubic bones. These differences match the nonmetric categories of a triangular shape in males and a square shape in females, which were found on the first PC, but it also captures 11 other significant PC variations that cannot be observed from visual assessments. This experiment has high accuracy results and can be a good categorization method for unknown specimens in future studies.

Determination of sex from the skeleton is vital to medicolegal investigations. There is no longer any question that populations differ in size and proportions and these differences affect the metric assessment of sex. The extent of variation in sexual dimorphism among Asian Mongoloids within and between regions has not been quantified by discriminant function analysis, nor have standards for most groups been introduced for the humerus. Therefore, the purpose of this research is to establish metric standards for sex determination from the humerus of Chinese, Japanese and Thais, as well as to compare size and sexual dimorphism in these Asian Mongoloid populations. The database for this study consisted of documented skeletal samples from China (N = 87), Japan (N = 90), and Thailand (N = 104). Six standard dimensions, including maximum length, vertical head diameter, minimum midshaft diameter, maximum midshaft diameter, midshaft circumference, and epicondylar breadth were taken and subjected to stepwise and direct discriminant function analysis. Of dimensions selected by the stepwise function, vertical head diameter and epicondylar breadth were the only elements common to all three groups. Overall, mean accuracies were highest using formulae produced by the stepwise procedure and ranged from 86.8% in the Chinese to 92.4% in the Japanese to 97.1% in the Thais. Group comparisons also revealed that while the Chinese had the largest measurements, they were the least dimorphic. The reverse was true for the Thais and the Japanese were intermediate on both counts. In cross validation tests, classification accuracy decreased in all cases where a formula from one group was applied to another. It was therefore concluded even though all individuals were Asian Mongoloids, these regionally diverse populations exhibited significant metric differences that affect sex determination from the skeleton. These findings confirm those of previous studies that there is a need for group specific metric standards of assessment.