Estimativa do sexo em amostras brasileiras com validação cruzada em populações de diferentes regiões

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UNIVERSIDADE ESTADUAL DE CAMPINAS FACULDADE DE ODONTOLOGIA DE PIRACICABA

MARILIA DE OLIVEIRA COELHO DUTRA LEAL

PIRACICABA 2019

ESTIMATIVA DO SEXO EM AMOSTRAS BRASILEIRAS

COM VALIDAÇÃO CRUZADA EM POPULAÇÕES DE

DIFERENTES REGIÕES.

ESTIMATION OF SEX IN BRAZILIAN SAMPLES WITH

CROSS-VALIDATION IN POPULATIONS OF DIFFERENT

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MARILIA DE OLIVEIRA COELHO DUTRA LEAL

ESTIMATIVA DO SEXO EM AMOSTRAS BRASILEIRAS COM

VALIDAÇÃO CRUZADA EM POPULAÇÕES DE DIFERENTES

REGIÕES

ESTIMATION OF SEX IN BRAZILIAN SAMPLES WITH

CROSS-VALIDATION IN POPULATIONS OF DIFFERENT

REGIONS

Tese apresentada à Faculdade de Odontologia de Piracicaba da Universidade Estadual de Campinas como parte dos requisitos exigidos para obtenção do título de Doutora em Biologia Buco-Dental, na Área de Histologia e Embriologia.

Thesis presented to the Piracicaba Dental School of the University of Campinas in partial fulfillment of the requirements for the degree of Doctor in Oral Biology, in Histology and Embryology area.

Orientador: Prof. Dr. Sérgio Roberto Peres Line

ESTE EXEMPLAR CORRESPONDE À VERSÃO FINAL DA TESE DEFENDIDA PELA ALUNA MARILIA DE OLIVEIRA COELHO DUTRA LEAL E ORIENTADA PELO PROF. DR. SÉRGIO ROBERTO PERES LINE

PIRACICABA 2019

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DEDICATÓRIA

Ao Departamento de Morfologia da Faculdade de Odontologia de Piracicaba, área de concentração Histologia, е às pessoas que convivi nesses espaços ао longo desses anos. А experiência dе υmа produção compartilhada nа comunhão cоm amigos nesses espaços foram а melhor experiência dа minha formação acadêmica.

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AGRADECIMENTOS

À Universidade Estadual de Campinas, na pessoa do Magnífico Reitor Prof. Dr. Marcelo Knobel.

À Faculdade de Odontologia de Piracicaba, na pessoa do Senhor Diretor, Prof. Dr. Francisco Haiter Neto.

A Coordenadoria de Pós Graduação, na figura da Senhora Coordenadora Prof. Dr.ª Karina Gonzalez Silvério Ruiz.

À Equipe Técnica da Coordenadoria de Pós-graduação nas pessoas de Érica A. Pinho Sinhoreti, Raquel Q. Marcondes Cesar, Claudinéia Prata Pradella, Leandro Viganó e Ana Paula Carone, agradeço a paciência, atenção e disponibilidade em sempre me ajudar.

Aos servidores da biblioteca da FOP-UNICAMP pela valiosa disponibilidade e atenção.

Ao programa de pós graduação em Biologia Buco-Dental, na figura da coordenadora Prof. Dr.ª Ana Paula de Souza.

Ao meu orientador, Prof. Dr. Sérgio Roberto Peres Line, grande profissional, pelos seus conhecimentos a mim transmitidos, dedicação, paciência e amizade.

Ao grande mestre e amigo Prof. Dr. Eduardo Daruge Júnior pela amizade e incentivos constantes.

À minha família pelo apoio incondicional em todas as horas. Mãe e pai, saibam que nada aconteceria sem vocês sempre ao meu lado e presentes!

Ao meu marido, Cláudio, confidente e amigo, pelo incentivo constante e compreensão da minha ausência. Sempre alento no desespero e com amor irrestrito. Aos amigos de turma Sarah Costa, Rafael Araújo, Marcos Paulo Salles Machado, Larissa Lopes, Daniel Pignatari, Renato Takeo, Talita Máximo, Yuli Quintero, Denise Rabelo, Tânia Santos, Rodrigo Ivo Matoso, Gilberto Carvalho, Talita Lima e Thais Dezem, Viviane Ulbritch, Cristhiane Schimdt e Juliana Haddad, pois sem vocês tudo seria mais difícil.

Aos meus filhos Claudia e Guilherme pela infinita compressão.

A aqueles que mesmo de forma direta e indireta colaboraram com este estudo.

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O presente trabalho foi realizado com apoio da Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) - Código de Financiamento 001.

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RESUMO

A estimativa do sexo pode ser influenciada pela ancestralidade e a população brasileira foi miscigenada ao longo dos séculos. Crânios são frequentemente usados para estimar o dimorfismo sexual. O objetivo do presente estudo foi estimar o sexo com base em cinco medidas craniométricas de amostras contemporâneas e identificadas de duas diferentes regiões brasileiras com validação cruzada e validação cruzada K-fold. O grupo étnico foi estimado pelo Índice Nasal e pelo Índice Facial Prosopométrico. A amostra do Sul foi usada para estimar um modelo (treino) e então seu desempenho foi testado na amostra do Sudeste (teste). Em um segundo momento, testamos a hipótese inversa: o subconjunto Sudeste foi usado para estimar um modelo e o subconjunto do Sul foi usado para validar os dados do modelo. As duas amostras (Sudeste - Sul) foram unidas em um grupo, a fim de verificar a influência dessa união na predição do sexo. Todos os testes criaram modelos, com uma, duas, três e quatro variáveis independentes. O melhor resultado de validação cruzada para a amostra do Sudeste, 57% de acerto, pode ser atribuído à heterogeneidade da amostra que atua como uma variável interferente na estimativa de sexo. A estimativa do sexo é mais bem realizada sem a interferência da ancestralidade variável. Amostras unidas, Sudeste - Sul, resultaram em uma boa predição (85%), mas com um valor intermediário entre o Sul (89%) e o Sudeste (81%).

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ABSTRACT

Sex estimation might be influenced by ancestry and Brazilian population is miscegenated over centuries. Skulls are often used for estimating sex dimorphism. The purpose of the present study was estimate sex based on five craniometric measurements from contemporary and identified samples from two different Brazilian regions with cross-validation and cross validation K-fold. Ethnic group was estimated by Nasal Index and Prosopometric Facial Index. The southern sample was used to estimate a model (train) and then its performance was tested in the southeast sample (test). In a second moment, we tested the inverse hypothesis. The southeast subset was used to estimate a model and the southern subset was used to validate the model data. The two samples (southeast - south) were united in one group, in order to verify the influence of this union in the prediction of sex. All tests created models, with one, two, three, and four independent variables. The best cross-validation result for the southeast sample, 57% accuracy, can be attributed to the heterogeneity of the sample that acts as an interfering variable in the sex estimate. Sex estimation is best performed without the interference of the variable ancestry. United samples, southeast - southern, resulted in a good prediction (85%), but an intermediate value between southern (89%) and southeast (81%).

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LISTA DE ILUSTAÇÕES

Figure 1. Prosopometric facial index for Southern and Southeast Population. 28

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LISTA DE TABELAS

Table 1. Measures made and their definition. 21

Table 2. Models developed according to number of variables used in southern

train. 24

Table 3. Maximum hit rate Indexes for Southern train and southeast test. 25 Table 4. Models developed according to number of variables used in southeast

train. 25

Table 5. Maximum hit rate Indexes for Southeast train and southern test. 26 Table 6. Models developed according to number of variables used in

southern-southeast sample. 26

Table 7. Southern sample train with one variable 40

Table 8. Southern sample train with two variables 40

Table 9. Southern sample train with three variables. 40 Table 10. Southern sample train with four variables. 40

Table 11. Southeast sample train with one variable. 40

Table 12. Southeast sample train with two variables. 41 Table 13. Southeast sample train with three variables. 41 Table 14. Southeast sample train with four variables. 41 Table 15. Southern and Southeast sample with one variable. 41 Table 16. Southern and Southeast sample with two variables 42 Table 17. Southern and Southeast sample with three variables. 42 Table 18. Southern and Southeast sample with four variables. 42

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LISTA DE ABREVIATURAS E SIGLAS

Ns - espinha nasal anterior

Na - násio

Al - base alar

Pr - próstio

Ba - básio

Zg - zigio

RS - Rio Grande do Sul

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SUMÁRIO

1. INTRODUÇÃO 14

2. ARTIGO: Estimation of sex in brazilian samples with cross-validation in

populations of different regions. 17

3. CONCLUSÃO 36

REFERÊNCIAS* 37

APÊNDICE 1 - Tabelas 40

ANEXOS 43

Anexo 1: Certificação do Comitê de Ética 43

Anexo 2: Comprovante de submissão 44

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1. INTRODUÇÃO

A identidade humana é um conjunto de características que definem o indivíduo como ser único e distinto dos demais. O processo de identificação humana tem como objetivo distinguir características idênticas nas pessoas antes e após a morte.

O perfil biológico do indivíduo é estabelecido baseado na estimativa do sexo, da ancestralidade, da idade cronológica e da altura(1) e com ele busca-se a identificação humana(2). Apesar da pelve ser o osso mais dimórfico do corpo humano(2-4), o crânio é o método mais comumente usados para identificação de restos ósseos na estimativa do sexo(5). A antropometria, no caso de medidas craniométricas, é realizada no crânio, por medidas lineares, angulares e/ou volumétricas(6). A estimativa do sexo desempenha um papel importante na identificação de restos esqueletizados de indivíduos desaparecidos

Há a hipótese geral de que as diversas populações variam em um determinado padrão seu e específico de dimorfismo sexual. Essas variações nas amostras populacionais se dão em função do tempo e da composição ancestral da mesma(4, 7). Os métodos utilizados para identificação humana são comparativos, dependendo da atribuição do material questionado (a qual pertence a população e a qual período) às categorias observadas no material de referência padrão de atribuição conhecida(8, 9). O problema é que as coleções de referência geralmente são originárias da Europa e da América do Norte e não são necessariamente representativas das populações globais contemporâneas(8). Devido à variação populacional, mesmo a estimativa do sexo é tendenciosa quando há falta de dados adequados(9). Por isso, é importante estabelecer parâmetros de estimativa do sexo em amostras populacionais brasileiras a fim de aumentar o índice de acerto do perfil biológico para o sexo na identificação humana da população estudada.

Silva et al (2018) realizaram a análise genética de amostra indivíduos do sul do Brasil (PowerSeq™AUTO/Y) e demonstraram que os sujeitos apresentam um perfil de ancestralidade particular e mais homogêneo quando comparados a outras regiões do país(10). Confirma-se a nossa hipótese de que a amostra do RS possui alta homogeneidade com relação à ancestralidade.

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Fridman et al (2014) analisaram o DNA mitocondrial da população do sudeste do Brasil e inferiram que ela é extremamente heterogênea e que há a coexistência de linhagens matrilineares com três diferentes origens filogeográficas (haplogrupos ameríndios, africanos e europeus)(11). A diversidade genética encontrada na região de controle do mtDNA na população do sudeste brasileiro reforça a importância do aumento de bancos de dados nacionais por ser importante e informativo em casos forenses(11). Esses dados corroboram o nosso achado que atribui a interferência da variável ancestralidade a maior miscigenação de SP.

Ao se colocar as duas amostras juntas, SP e RS, como uma única população, obteve-se índice de acerto máximo de 84% com três variáveis (medidas craniométricas). Esse referencial pode ser utilizado também para aplicação a outros indivíduos e com uma maior abrangência.

Machado et al (2018) analisou pelve humana para estimativa do sexo e os resultados do Diagnose Sexuelle Probabiliste v.2® (DSP2) revelaram que o programa pode ser aplicado até mesmo nas populações mestiças brasileiras (amostra de SP - mesma utilizada por nós) com um bom índice de precisão (90,57% para homens e 85% para mulheres), embora com menor precisão do que para amostras estrangeiras(12).

Apesar a pelve ser o osso mais dimórfico, os crânios são os mais comumente usados em estudos populacionais por serem menos afetados por fatores ambientais e terem maior especificidade genética.Arcos zigomáticos maiores e robustos são típicos nos homens, fato que torna a distância bizigomática (Zg-Zg) é um excelente discriminador para o sexo(13) e consequentemente foi utilizada em diversos estudos com populações da Turquia(14), Estados Unidos da América(15), Japão(16), Austrália(13) e Colômbia(4).

A forma da abertura piriforme é um dos indicadores clássicos da sexualidade morfológica(17). As diferentes etnias devem ser incluídas na avaliação do dimorfismo da abertura piriforme. Diversos autores relataram uma alta variação no tamanho da piriforme abertura em estudos com amostras de etnias diferentes(18). Sugere-se que o dimorfismo sexual na abertura piriforme pode ser influenciado pela ancestralidade, especialmente em populações onde há muita miscigenação. A abertura piriforme é dimórfica e exibe nos homens tamanho e altura maiores(19).

O crânio é a parte do esqueleto mais utilizada em estudos populacionais por ter características genéticas marcantes, ser menos afetados por fatores ambientais,

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por exemplo a nutrição(3) e, serem mais facilmente encontrados nos locais de crime. A antropologia estuda a morfologia física da cabeça e face para categorizar indivíduos e populações. Em 1779 a classificação racial dos seres humanos foi estabelecida em cinco grupos raciais principais: europeu, mongol, malaio, etíope e americano. Desde então padrões de medição são utilizados no estabelecimento do perfil biológico em medicina legal e forense(3). A estimativa de ancestralidade é o componente mais difícil de um perfil biológico(20). Grandes bancos de dados são necessários, e uma compreensão da história cultural da população em questão é crucial para a interpretação dessas diferenças(20).

O grupo étnico é bem complicado de ser estimado na população brasileira devido à grande miscigenação. As populações puras não são comuns em nosso país devido aos vários fluxos migratórios de outros países nas décadas passadas, fluxo migratório rumo à região Sudeste, principalmente no estado de SP estimulado pela busca de empregos e pelo fato cultural de não haver segregação racial. Porém, ao se fazer uma análise histórica percebe-se que existiu a concentração de determinadas raças em regiões específicas, por exemplo a população negra na Bahia é dominante até os dias atuais e a população do Sul do Brasil é predominantemente branca devido às origens europeias, assim como existem os núcleos asiáticos na cidade de São Paulo.

O objetivo desse estudo foi estimar o sexo baseado em medidas craniométricas de amostras brasileiras com validação cruzada em populações de diferentes regiões. As amostras são contemporâneas, distintas e identificadas.

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2. ARTIGO: Estimation of sex in brazilian samples with cross-validation in populations of different regions.

Artigo submetido ao periódico: Journal of Forensic Sciences: Reports (Anexo 2).

Autoria: Marilia de Oliveira Coelho Dutra Leal, Sarah Teixeira Costa, Eduardo Daruge Júnior, Luiz Francesquini Júnior, Fábio Delwing, Manuel Alexander Jara Espejo, Sérgio Roberto Peres Line.

Abstract

Sex estimation might be influenced by ancestry and Brazilian population is miscegenated over centuries. Skulls are often used for estimating sex dimorphism. The purpose of the present study was estimate sex based on five craniometric measurements from contemporary and identified samples from two different Brazilian regions with cross-validation and cross validation K-fold. Ethnic group was estimated by Nasal Index and Prosopometric Facial Index. The southern sample was used to estimate a model (train) and then its performance was tested in the southeast sample (test). In a second moment, we tested the inverse hypothesis. The southeast subset was used to estimate a model and the southern subset was used to validate the model data. The two samples (southeast - south) were united in one group, in order to verify the influence of this union in the prediction of sex. All tests created models, with one, two, three, and four independent variables. The best cross-validation result for the southeast sample, 57% accuracy, can be attributed to the heterogeneity of the sample that acts as an interfering variable in the sex estimate. Sex estimation is best performed without the interference of the variable ancestry. United samples, southeast - southern, resulted in a good prediction (85%), but an intermediate value between southern (89%) and southeast (81%).

Keywords: Forensic Anthropology Population Data; Sexing Estimation; Miscegenation; Craniometric Measurements

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Introduction

The biological profile of the individual is established based on the estimation of sex, ancestry, age at death and height [1]. These parameters sought the human identification [2]. Usually, the first parameter established in a biological profile is sex, since it plays a significant role in the identification of skeletal remains of missing individuals. Os coxae is preferable, for these matters. The results of the Diagnosis Sexuelle Probabiliste v.2® (DSP2) study revealed that the program can be applied even in the Brazilian crossbred population with a good index (90.57% for men and 85% for women), even though with less precision than in foreign samples [3]. Although the os coxae is the most dimorphic bone in the human body [2-4], the skull is the most commonly used method for identification of bone remains in the estimation of sex [5]. Anthropometry, on craniometric measurements, is performed in the skull by linear, angular and/or volumetric measurements [6].

The skull is the part of the skeleton most commonly used in population studies because it has marked genetic characteristics and is less affected by environmental factors, such as nutrition [4,7]. Anthropology studies the physical morphology of the head and face to categorize individuals and populations.

Greater and robust zygomatic arches are typical in men, a fact that makes zygomatic distance (ZgZg) an excellent discriminator for sex [8] and consequently has been used in several studies with populations of Turkey [9], United States of America [10], Japan [11], Australia [08] and Colombia [4]. Piriform aperture shape is one of the classic indicators of the dimorphism of morphological sexuality [12], exhibiting larger size and height in men [13]. Different ethnicities should be included in the evaluation of the dimorphism of the piriform aperture. Several authors reported a high variation in pyriform aperture size in studies with samples from different ethnic groups [14]. It is suggested that sexual dimorphism in the piriform aperture can be influenced by ancestry, especially in populations where there is a lot of miscegenation.

There is a general hypothesis that populations range from an own particular pattern of sexual dimorphism. These variations in population samples are due to the time and ancestry [4,7]. The methods used for human identification are comparative, depending on questioned material allocation (population source and period) to the categories observed in the standard reference material of known assignment [15,16]. The problem is that reference collections generally originate in Europe and North America and are not necessarily representative of contemporary global populations

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[15]. Due to population variation, even sex estimation is biased when there is a lack of adequate data [16].

Genetic studies proved Brazilian mixed population. A study that carried out the genetic analysis of individuals from southern Brazil (PowerSeq™AUTO/Y) demonstrated that the individuals present a profile of a particular and more homogeneous ancestry when compared to other regions of the country [17]. However, another study that analyzed only mitochondrial DNA from the population of Southeastern Brazil inferred that it is extremely heterogeneous and the coexistence of matrilineal lines with three different phylogeographic origins (Amerindian, African and European haplogroups). The genetic diversity found in the control region of mtDNA in the Brazilian Southeast population reinforces the importance of increasing the national database to be important and informative in forensic cases [18].

The ethnic group is very complicated to be estimated in the Brazilian population due to the great miscegenation. Pure populations are not common in our country due to the various migratory flows of other countries in the past decades, migratory flow towards the Southeast region, especially the state of São Paulo, stimulated by the search for jobs and the cultural fact of not having racial segregation. However, when making a historical analysis it is noticed that the concentration of certain ancestry in specific regions existed, for example the black population in Bahia is dominant until the present day and the population of the South of Brazil is predominantly white due to the European origins.

It is important to establish sex estimation parameters in contemporary Brazilian population samples in order to increase the correctness index of the biological profile for sex in the human identification of the mixed studied population. Therefore, the objective of this study was to estimate the sex based on craniometric measurements of Brazilian samples with cross-validation in populations from different regions. The samples are contemporary, distinct and identified.

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Materials and Methods

This study used two Brazilian populations of different regions (southern and southeast), separately and united, specified below.

Southeast Population

Osteological and Tomographic Biobank is located at the School of Dentistry of Piracicaba, University of Campinas (UNICAMP). It is made up of recent and modern bones cataloged from 250 skeletons of individuals who died between 2008 and 2010, who were exhumed between 2013 and 2014 in the Nossa Senhora da Conceição – Amarais Public Cemetery. The skeletons belong to a contemporary population of the city of Campinas/São Paulo and surroundings. Skeletons are in good state of conservation and were identified by means of a death certificate. A total of 162 adult skulls were included at random and were evaluated in this study, being 84 males and 78 females.

The mean age at death of the individuals used in this study was 55 years. Female mean was 63 years (± 20, 43), and male mean was 48 years (± 15, 24). Information access on the skeletal sample was minimal, sex and age were only accessed after skull measurements, to ensure sample anonymity.

Study was approved and submitted to the Research Ethics Committee of the School of Dentistry of Piracicaba - University of Campinas, under protocol no. 541719160/2016.

Southern Population

The sample from the State of Rio Grande do Sul consists of 209 human skulls (106 males and 103 females), with age at death greater than 22 years, who were in identified graves in the Cemetery of the Santa Casa de Porto Alegre, in the city of Porto Alegre / Rio Grande do Sul. The study was developed during the year 2010 and the skeletons were randomly included. Access to information on the sex of the skeletons was made by means of the funerary register of the cemetery itself, only after the measurements in the skulls. Essentially, the study was performed as a blind test for data identification. After the proper measurements and notes, the bones went to the common grave in its entirety.

Study was submitted and approved by the Research Ethics Committee of the School of Dentistry of Piracicaba - University of Campinas, under protocol no. 138/2010.

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Samples from Southern and Southeast bone collections analyzed together.

Inclusion and Exclusion Criteria

The inclusion criteria were: skull selection of individuals of both sexes, older than 22 years (southern sample) and 18 years old (southeast sample) at the time of death, intact, with no signs of trauma and / or notorious anomalies. As an exclusion criterion, skulls outside the desired age group or submitted to necropsy (craniotomy), as well as those with morphological anomalies, signs of trauma, stable fixation material or any alterations that impaired the measurements were not used in this study.

Measures

Five traditional face measures were collected from specimens for sex estimating and are specified in table 1.

Table 1. Measures made and their definition. Measurements Definition

Ns-Na Distance between nasal bone and anterior nasal spine Al-Al Distance between right alar base and left alar base Na-Pr Distance between nasal bone and prostium

Ba-Na Distance between basium and nasal bone Zg-Zg Distance between right and left zygomatic arch

Ethnic group was also estimated by Nasal Index and Prosopometric Facial Index. The nasal index relates percentage in the frontal plane the maximum nasal width with the height of the nose [19] and Prosopometric Facial Index is obtained by a percentage relation and in the frontal plane of the measurements: maximum height of the facial mass with the maximum width of the face [14]:

All craniometric measurements were performed with a precision digital caliper - Mitutoyo® (São Paulo / Brazil), and a digital compass tip (iGaging / China), in regions where the use of the caliper was not compatible. Both instruments had their ends attached and were zeroed with each measurement, in order to prevent minor variations of the equipment, and guarantee the fidelity of the results. The data of all the measurements were notated by the researcher in files developed for this purpose, and later inserted in a worksheet of the program Microsoft Excel® for the accomplishment of the statistical analyzes.

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Cross-validation is a statistical analysis technique developed to evaluate the application capacity of a model created from a sample in another distinct sample [12]. Its objective is to predict the accuracy of this new model developed in practice, that means, how it works for another sample.

The central concept of cross-validation techniques is the partitioning of the sample into mutually exclusive subsets, and then some of these subsets are used to estimate the best model (training data) and the rest of the subsets (validation or test data) are used to validate this best model [12].

In the present study, first, the southern sample was used to estimate a model (train) and then its performance was tested in the southeast sample (test). In a second moment, we tested the inverse hypothesis. The southeast subset was used to estimate a model and the southern subset was used to validate the model data.

Cross-validation k-fold

In K-Fold cross-validation, the sample is typically divided into five to ten subsets, then one of the subgroups is randomly selected to be the validation or test group for the entire sample. The rest of the subgroups join together to train their model created from it and apply it to the validation group in order to compare the result and see what the error rate was. This method repeats until all groups have passed the validation group and all have an error percentage, at the end the average error of their model is calculated.

In the present study, when applying cross-validation k-fold, the model was tested one hundred times. That is, the southern and southeast sample together was divided into ten subsets, nine subsets were pooled and were to build a model while one subset was used as test. Until a total of one hundred repetitions were reached and a minimum error rate. The validation analysis was repeated one hundred times with random resampling of the southern and southeast sample.

Number of Independent Variables

In the models developed for the three samples: southeast, southern and southeast - southern, we tried to verify with how many independent variables, that is, with the insertion of how many craniometric measurements a more predictive model was reached for that specific population. The limit was reached with three independent variables for all samples.

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Overfitting occurs when model fits data. In other words, the model is only for the data of the base (sample) that was used for its construction. The obvious way to detect overfitting is to maintain precision control on the test data as per the drills. One notices when the accuracy of test data is no longer improving, so it is time to stop training. Overfitting occurs when the model has low bias and cannot generalize very well because it has more complexity (number of variables) than necessary and therefore considers attributes that it should not. Therefore, this model will not serve to predict data in another sample.

For the models developed in the three samples: southeast, southern and southeast - southern, it is noticed that increasing the complexity of the model, that is, inserting more variables (craniometric measurements), the better complexity of the model is achieved with three variables. By inserting the fourth variable, although the error rate of the training sample continues to decrease, the error rate of the test sample begins to increase. Thus, limit was reached when it came to an overfitting with three independent variables for all samples.

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Results

Southern train

First, it was used the southern sample as the train population in order to create models with one, two, three to four independent variables. The results summarized below show the prediction accuracy using the sample Southern as train.

Table 2. Models developed according to number of variables used in southern train.

Number of Variables

Models Developed

One Model nº 05 = 32.35 - 0.31 x ZgZg

Two Model nº 04 = 44.25 - 0.37 x NsNa - 0.25 x ZgZg

Three Model nº 05 = 46.15 - 0.28 x NsNa - 0.1 x NaPr - 0.24 x ZgZg

Four Model nº 04 = 51.2 - 0.2 x NsNa - 0.1 x NaPr - 0.13 x BaNa - 0.21 x ZgZg

The results with one variable showed a maximum hit rate of 84% with measure ZgZg. Five models were developed, with mean of prediction accuracy ranging from 50-84%. It is interesting to note that the mean accuracy of variable (ZgZg) was 84% for both sexes. When model number 5, with one variable is applied in southeast sample as a test, 75% is the highest score.

The results with two variables showed a maximum setpoint of 88% with the use of two independent variables (NaNa and ZgZg). Seven models were developed, with mean prediction accuracy ranging from 77-88%. When calculating the mean score for all models by separating the sexes, hit rate for females was 87% and for males was 89%. When model number 4, with two variables is used as a test in the southeast sample, the maximum hit rate is 51%.

The results with three variables presented a maximum success rate of 89% with the use of three independent variables (NsNa, NaPr and ZgZg). Nine models were developed, with mean of prediction accuracy ranging from 79-89%. The mean prediction accuracy adjustment of all models for males was 88% and for female was 90%. When model number 5, with three variables is used in the southeast sample as a test, the maximum hit rate is 57%.

The results with four variables presented a maximum success rate of 89% with the use of four independent variables (NsNa, NaPr, BaNa and ZgZg). Five models were developed, with mean prediction accuracy ranging from 84-89%. The mean prediction accuracy adjustment of all models for males was 89% and for female was

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90%. When model number 04, with four variables, is applied to the southeast sample as test, the maximum hit rate is 60%.

Table 3. Maximum hit rate Indexes for Southern train and southeast test.

Number of Variables

Model Southern train Southeast test

One 05 84% 75%

Two 04 88% 51%

Three 05 89% 57%

Four 04 89% 60%

Southeast train

The Southeast sample was used as the train with one, two, three, and four independent variables (table 4).

Table 4. Models developed according to number of variables used in southeast train.

Number of Variables

Models Developed

One Model nº 01 = 18.04 - 0.37 x NsNa

Two

Model nº 03 = 25.67 - 0.29 x NsNa - 0.12 x BaNa Model nº 10 = 28.79 - 0.11 x BaNa -0.14 x ZgZg

Three Model nº 10 = 28.93 - 0.072 x NaPr - 0.084 x BaNa - 0.13 x ZgZg

Four Model nº 04 = 32.83 -0.27 x NsNa - 0.018 NaPr -0.05 x BaNa - 0.12 x ZgZg

The results with one variable showed a maximum hit rate of 76% with variable (NsNa). Four models were developed, with mean of prediction accuracy ranging from 68-76%. When calculating the mean score for all models by separating the sexes, hit rate for females was 74% and for males was 77%. When model number 1, with only one variable is used in Southern sample as a test, the maximum hit rate is 74%.

The results with two variables showed a maximum setpoint of 78% with the use of two independent variables (NsNa and ZgZg). Ten models were developed, with mean of prediction accuracy ranging from 68-78%. When calculating the mean score for all models by separating the sexes, hit rate for females was 76% and for males was 81% in model nº 04. When model number 4, with two variables, is applied to the southern sample as test, the maximum settling index is 59%.

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The results with three variables showed a maximum hit rate of 81% with variables (NsNa, BaNa and ZgZg). Ten models were developed, with mean of prediction accuracy ranging from 74-81%. When calculating the mean score for all models by separating the sexes, hit rate for females was 79% and for males was 83%. When model number 06 with three variables is applied to the southern sample as a test the maximum settling index is 64%.

The results with four variables showed a maximum hit rate of 80% with variables (NsNa, AlAl, NaPr and BaNa) in model nº 01. Five models were developed, with mean of prediction accuracy ranging from 77-80%. When calculating the mean score for all models by separating the sexes, hit rate for females was 77% and for males was 82%. When model number 1, with four variables, is applied to the southern sample as test the maximum hit rate is 73%.

Table 5. Maximum hit rate Indexes for Southeast train and southern test.

Number of Variables

Model Southeast train Southern test

One 01 76% 74%

Two 04 78% 59%

Three 06 81% 64%

Four 01 80% 73%

Southeast – Southern

The two samples (Southeast - South) were united in one group, in order to verify the influence of this union in the prediction of sex. Models with one, two, three and even four variables were developed. Cross-validation k-fold was also applied in this sample to ensure predictive accuracy.

Table 6. Models developed according to number of variables used in southern-southeast sample.

Number of Variables

Models Developed Maximum Hit rate

One Model nº 01 = 21.35 - 0.43 x NsNa 78% Two Model nº 04 = 28.41 - 0.43 x NsNa - 0.06 x ZgZg 80% Model nº 10 = 31.89 - 0.25 x BaNa - 0.06 x ZgZg 80%

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Three Model nº 06 = 37.62 - 0.31 x NsNa - 0.15 x BaNa -0.063 x ZgZg

85%

Four Model nº 04 = 38.26 -0.24 x NsNa -0.07 x NaPr -0.13 x BaNa -0.07 x ZgZg

85%

The results with one variable showed a maximum hit rate of 78% with variable (NsNa). Five models were developed, with mean of prediction accuracy ranging from 58-78%. When calculating the mean score for all models by separating the sexes, hit rate for females was 76% and for males was 79%.

The results with two variables showed a maximum hit rate of 80% with variables (NsNa and ZgZg) in model 04 and variables (BaNa and ZgZg) in model 10. Ten models were developed, with mean of prediction accuracy ranging from 62-80%. When calculating the mean score for all models by separating the sexes, assertiveness for females was 79% and for males was 81% (model 04) and females was 82% and for males was 78% (model 10).

Results with three variables showed a maximum hit rate of 85% with variables (NsNa, BaNa and ZgZg). Ten models were developed, with mean of prediction accuracy ranging from 74-85%. When calculating the mean score for all models by separating the sexes, hit rate for females was 82% and for males was 86%.

Results with four variables showed a maximum hit rate of 85% with variables (NsNa, NaPr, BaNa, ZgZg) in model 04. Five models were developed, with mean of prediction accuracy ranging from 78-85%. When calculating the mean score for all models by separating the sexes, hit rate for females was 85% and for males was 85% too.

Ethnic Group Estimate

i. Prosopometric Facial Index

When analyzing the ethnic group based on the Upper Facial Index (Prosopometric) for both samples, it can be seen that, for the Southern sample, the morphological traits have survived and resisted the racial mix that probably has not yet been so strong in this region. On the other hand, when the southeast sample data are analyzed, the heterogeneity of the ethnic group is high. The results show that 42% are Amerindian, 39% are African and 19% are European, confirming the great heterogeneity of the sample of the Southeast population (Figure 1).

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Figure 1. Prosopometric facial index for Southern and Southeast Population. ii. Nasal Index

The nasal index did not reach the same result in relation to ancestry, since both Southern and Southeast samples were very heterogeneous for this variable. In the Southern population, the sample was predominantly European (38%), Amerindian (35%) and African (27%). However, when Southern sample was separated by sex and the nasal index was applied again, we noticed the influence of the sex as variable on this index. For males, the sample remains predominantly European (55%), Amerindian (30%) and African (15%). When analyzing only the female nasal index, the sample shows a different distribution, Europeans are 20%, Amerindian 41% and Africans 39% (Figure 2). It is possible to notice the predominance of the Amerindians, after the Africans and in smaller value are the Europeans.

Figure 2. Southern nasal index.

207 32 2 63 0 67 0 100 200 300 Southern Southeast Abs olu te p op u lation s am p le

Ethinic Group Estimation

Prosopometric Facial Index for Southern and

Southeast Population

European African Amerindian

0 20 40 60 80 100

Southern Nasal Index Male Southern Nasal Index Female Southern Nasal Index Abs olu te p op u lato in sam p le

Ethinic Group Estimation

Southern Nasal Index

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Discussion

The use of discriminant functions based on morphometric data is one of the most approved methods for estimation of sex and ancestry in skeletons [16]. The estimation of sex based on craniometric measurements of two samples (Southeast - South), when united in one sample of Brazilian population, besides establishing new parameters to estimate sex, already presented a very good hit rate, 85%, with only three variables (Table 06). However, it is noticed that when the southern sample is used as reference population this index was even higher, 89%, with only three variables (Table 03). Therefore, when southeast models are used as reference population this index were low, 81% with three variables (Table 05). These results can be explained by the fact that the southern population is genetically more homogeneous than southeast [17]. This fact corroborates our findings, which resulted in almost all individuals classified as European (99%) in the southern sample. Therefore, genetic homogeneity is reflected in the craniometric models, being a variable that favorably interferes on sex estimation.

Observing the results of ethnic group estimation of the two samples studied, southern and southeast, our findings corroborate in a precise way the previous work referring to the high percentage of Europeans in the South of the country [19-22]. Homogeneity of the southern population sample is confirmed when we use the Upper Facial Index, where the majority of the sample population is European (99%) and only (1%) is African. This confirms the hypothesis of non-interference of the ancestry variable in this population, because it is very homogeneous, on sex estimation.

Results allowed to infer that, on the contrary to what some studies suggest, sex has less influence on the nasal bone and the form of pyriform aperture than the ancestry in European and non-European groups of South Africa [23,24]. In our study, sex showed a good influence on the piriform aperture so much that the piriform aperture height measurement (NsNa) was an excellent indicator of sexual dimorphism in the southern sample. When we dissociate the southern sample in the male and female sex, we noticed that in the male sample the nasal index, despite demonstrating the heterogeneity of the group, is shown to be predominantly European. The female part of the southern sample is heterogeneous, and the European ancestry has a lower value, showing a divergence with the result obtained for the facial prosopometric index in the same sample. Study using the same southeast sample also showed that the nasal index is of little importance in estimating ancestry for this population [25].

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There are some possible explanations for this result. We can first attribute these metrical differences in piriform aperture to the physiological difference that exists between the two sexes. Study found that differences in the facial region may be the result of larger airways in males as a response to a higher energy requirement which may explain why the region is so sexually dimorphic [26]. Second, anthropological studies suggest that the climate influences width and height of the pyriform opening [27] by heating and humidity. For example, in cold and dry climates, heating and humidification of inspired air is facilitated by passage into a narrower piriform aperture (narrow alar base) which causes an increase in the contact surface and a longer period during which the air is inspired [28]. Therefore, it is speculated that shape of piriform aperture is adapted to the environment reflecting geographic variations.

A research carried out with a sample of Brazilian Europeans analyzed genetically the ancestral origin of the Y chromosome (paternal origin) and the mitochondrial DNA (maternal origin) in Brazilian population. Results showed that 33% of Brazilian Europeans descended from an indigenous ancestor by the maternal ancestor and none descended from ancestral indigenous by the paternal lineage [20]. Although few craniometry studies make cross validation between population of different regions, this study applied cross-validation in the two populations, southeast and southern. It is possible to infer that the best hit rate indexes were reached with Southern sample as train (84-89%). However, when these more predictive models from Southern sample are used in the southeast sample as a test by means of cross-validation, hit rate is not satisfactory and range between 51-75% (Table 03).

Based on results of cross validation between different populations, when evaluating southeast sample as train, hit rate rates are low and range from (76-81%). On the other hand, when the predictive models created from southeast sample are used in the southern sample, results are better, but far from good. In an attempt to seek an explanation for such poor results in the southeast sample, the samples were separated to verify heterogeneity of populations. The greater accuracy in sex prediction for the southern sample can be attributed to non-interference of another variable, ancestry, since it is a sample of European.

The best results in both samples were achieved with only two or three independent variables. Four variables are not necessary, since maximum predictive values were already achieved with two or three variables. Southern sample as train, with two independent variables, maximum hit rate was 88% (Table 03) and with three

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independent variables were 89%. This last one, the same as the rate achieved with four variables. Only one percentage point difference when inserting one more variable in the model. In southeast sample as train, with two independent variables, hit rate was 77% (Table 05) and with three independent variables was 81%. With four variables was 80%, one percentage point lower than with three independent variables.

The three variables (NsNa, NaPr and ZgZg) were used to the train southern sample and had the best model with 89% accuracy (Table 02 and 03). However, the same model when applied in the southeast test sample reached only 60% of accuracy (Table 03). The three variables (NsNa, BaNa and ZgZg) were used to the train southeast sample and had the best model with 81% accuracy (Tables 04 and 05). However, the same model when applied in the southern test sample reached a 75% accuracy (Table 05). Therefore, the best prediction model is based on the southern sample with three variables (89%), although the test sample prediction in southeast sample (57%) was much lost.

When southern and southeast samples are separated in training and test, there is a difference in models’ prediction. Always the training sample, the original sample, has higher scores than the test sample. Nevertheless, variations between samples are smaller when the two populations are united in the same sample (southeast - southern sample).

The best k-fold cross-validation result for the southeast - southern sample was 85% accuracy with three variables (NsNa, BaNa and ZgZg). Therefore, these results can be extended to a larger population, which encompasses a large parcel of the Brazilian population. Even with the widening of the sample, more mixed, the results are positive and prove that the model can be used for the Southern and Southeast regions of the country.

When checking the number of variables needed to establish an ideal model, in the southern sample, was achieved with three measures, in 89% accuracy. This limit was established, because from four variables the average accuracy remains at 89 %. The same phenomenon occurs with the southeast sample with three independent variables. Southeast model accuracy is 81%, and with four variables the accuracy is 80%. In the complete sample, southeast - southern, limit of variables is three too, 85% accuracy.

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Conclusion

The results revealed that sex estimation is best performed without the interference of the variable ancestry. The low cross-validation result for the southeast sample, 57% accuracy, can be attributed to the heterogeneity of the sample that acts as an interfering variable in the sex estimate.

Three craniometric measurements allowed a more predictive model for populations with high degree of miscegenation, as the Brazilian one.

The samples united (southern and southeast) resulted in a good prediction (85%), but it had an intermediate value between southern (89%) and southeast (81%).

Funding Sources

This work was supported by the Coordination for the Improvement of Higher Education Personnel (CAPES) [grant numbers 1592353, 03/2016 - 02/2018]

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References

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[16] L. Manthey, R.L. Jantz, A. Vitale, C. Cattaneo, Population specific data improves Fordisc, Forensic Sci Int 292 (2018) 263.e1-263.e7.

[17] D.S.B.S. Silva, F.R. Sawitzki, M.K.R. Scheible, S.F. Bailey, C.S. Alho, S.A. Faith, Genetic analysis of Southern Brazil subjects using the PowerSeq™ AUTO/Y system for short tandem repeat sequencing, Forensic Sci Int Genet 33 (2018) 129-135. [18] C. Fridman, R.S. Gonzalez, A.C. Pereira, M.M. Cardena, Haplotype diversity in mitochondrial DNA hypervariable region in a population of southeastern Brazil, Int J Legal Med 128(4) (2014) 589-93.

[19] F. Saloum de Neves Manta, R. Pereira, R. Vianna, A. Rodolfo Beuttenmüller de Araújo, D. Leite Góes Gitaí, D. Aparecida da Silva, E. de Vargas Wolfgramm, I. da Mota Pontes, J. Ivan Aguiar, M. Ozório Moraes, E. Fagundes de Carvalho, L. Gusmão, Revisiting the genetic ancestry of Brazilians using autosomal AIM-Indels, PLoS One 8(9) (2013) e75145.

[20] J. Alves-Silva, M. da Silva Santos, P.E. Guimarães, A.C. Ferreira, H.J. Bandelt, S.D. Pena, V.F. Prado, The ancestry of Brazilian mtDNA lineages, Am J Hum Genet 67(2) (2000) 444-61.

[21] R.R. Moura, A.V. Coelho, V.e.Q. Balbino, S. Crovella, L.A. Brandão, Meta-analysis of Brazilian genetic admixture and comparison with other Latin America countries, Am J Hum Biol 27(5) (2015) 674-80.

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3. CONCLUSÃO

O resultado de validação cruzada baixo para a amostra de SP, 66% de acerto, pode ser atribuído a heterogeneidade da amostra que atua como variável interferente na estimativa do sexo.

As amostras misturadas - RS e SP - resultaram em uma boa predição (84%), porém de valor intermediário entre RS (89%) e SP (81%).

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* De acordo com as normas da UNICAMP/FOP, baseadas na padronização do International Committee of Medical Journal Editors - Vancouver Group. Abreviatura dos periódicos em conformidade com o PubMed.

REFERÊNCIAS*

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2. Best KC, Garvin HM, Cabo LL. An Investigation into the Relationship between Human Cranial and Pelvic Sexual Dimorphism. J Forensic Sci. 2018;63(4):990-1000. 3. Kanchan T, Krishan K, Gupta A, Acharya J. A study of cranial variations based on craniometric indices in a South Indian population. J Craniofac Surg.

2014;25(5):1645-9.

4. González-Colmenares G, Sanabria Medina C, Rojas-Sánchez MP, León K, Malpud A. Sex estimation from skull base radiographs in a contemporary Colombian population. J Forensic Leg Med. 2019;62:77-81.

5. Small C, Schepartz L, Hemingway J, Brits D. Three-dimensionally derived interlandmark distances for sex estimation in intact and fragmentary crania. Forensic Sci Int. 2018;287:127-35.

6. Casado AM. Quantifying Sexual Dimorphism in the Human Cranium: A Preliminary Analysis of a Novel Method. J Forensic Sci. 2017;62(5):1259-65. 7. Godde K, Thompson MM, Hens SM. Sex estimation from cranial

morphological traits: Use of the methods across American Indians, modern North Americans, and ancient Egyptians. Homo. 2018;69(5):237-47.

8. Francisco RA, Evison MP, Costa Junior MLD, Silveira TCP, Secchieri JM, Guimarães MA. Validation of a standard forensic anthropology examination protocol by measurement of applicability and reliability on exhumed and archive samples of known biological attribution. Forensic Sci Int. 2017;279:241-50.

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9. Manthey L, Jantz RL, Vitale A, Cattaneo C. Population specific data improves Fordisc. Forensic Sci Int. 2018;292:263.e1-.e7.

10. Silva DSBS, Sawitzki FR, Scheible MKR, Bailey SF, Alho CS, Faith SA. Genetic analysis of Southern Brazil subjects using the PowerSeq™ AUTO/Y system for short tandem repeat sequencing. Forensic Sci Int Genet. 2018;33:129-35.

11. Fridman C, Gonzalez RS, Pereira AC, Cardena MM. Haplotype diversity in mitochondrial DNA hypervariable region in a population of southeastern Brazil. Int J Legal Med. 2014;128(4):589-93.

12. Machado MPS, Costa ST, Freire AR, Navega D, Cunha E, Daruge Júnior E, et al. Application and validation of Diagnose Sexuelle Probabiliste V2 tool in a

miscegenated population. Forensic Sci Int. 2018;290:351.e1-.e5.

13. Franklin D, Cardini A, Flavel A, Kuliukas A. Estimation of sex from cranial measurements in a Western Australian population. Forensic Sci Int. 2013;229(1-3):158.e1-8.

14. Ekizoglu O, Hocaoglu E, Inci E, Can IO, Solmaz D, Aksoy S, et al.

Assessment of sex in a modern Turkish population using cranial anthropometric parameters. Leg Med (Tokyo). 2016;21:45-52.

15. Abdel Fatah EE, Shirley NR, Jantz RL, Mahfouz MR. Improving sex estimation from crania using a novel three-dimensional quantitative method. J Forensic Sci. 2014;59(3):590-600.

16. Ogawa Y, Imaizumi K, Miyasaka S, Yoshino M. Discriminant functions for sex estimation of modern Japanese skulls. J Forensic Leg Med. 2013;20(4):234-8. 17. Rogers TL. Determining the sex of human remains through cranial morphology. J Forensic Sci. 2005;50(3):493-500.

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18. Hoffman BE, McConathy DA, Coward M, Saddler L. Relationship between the piriform aperture and interalar nasal widths in adult males. J Forensic Sci.

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APÊNDICE 1 - Tabelas

Table 7. Southern sample train with one variable

Variable 1 Mean accuracy

1. NsNa 0.7754

2. AlAl 0.4947

3. NaPr 0.775

4. BaNa 0.7753

5. ZgZg 0.8373

Table 8. Southern sample train with two variables

Variable 1 Variable 2 Mean accuracy

1. NsNa AlAl 0.7754 2. NsNa NaPr 0.7947 3. NsNa BaNa 0.8324 4. NsNa ZgZg 0.8803 5. AlAl NaPr 0.775 6. AlAl BaNa 0.7657 7. AlAl ZgZg 0.823 8. NaPr BaNa 0.8233 9. NaPr ZgZg 0.8562 10. BaNa ZgZg 0.8516

Table 9. Southern sample train with three variables.

Variable 1 Variable 2 Variable 3 Mean accuracy

1. NsNa AlAl NaPr 0.7947

2. NsNa AlAl BaNa 0.8279

3. NsNa AlAl ZgZg 0.8947

4. NsNa NaPr BaNa 0.847

5. NsNa NaPr ZgZg 0.8901

6. NsNa BaNa ZgZg 0.885

7. AlAl NaPr BaNa 0.8186

8. AlAl NaPr ZgZg 0.8513

9. AlAl BaNa ZgZg 0.8563

Table 10. Southern sample train with four variables. Variable

1

1. NsNa AlAl NaPr BaNa 0.8373

2. NsNa AlAl NaPr ZgZg 0.8851

3. NsNa AlAl BaNa ZgZg 0.8803

4. NsNa NaPr BaNa ZgZg 0.8949

5. AlAl NaPr BaNa ZgZg 0.8562

Table 11. Southeast sample train with one variable.

1. NsNa 0.7587

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3. BaNa 0.728

4. ZgZg 0.7225

Table 12. Southeast sample train with two variables.

Table 13. Southeast sample train with three variables.

10. NaPr BaNa ZgZg 0.7651

Table 14. Southeast sample train with four variables.

Variable 1 Variable 2 Variable 3 Variable 4 Mean accuracy

5. AlAl NaPr BaNa ZgZg 0.7651

Table 15. Southern and Southeast sample with one variable.

1. NsNa 0.7752

2. NaPr 0.6651

3. BaNa 0.7409

4. ZgZg 0.6149

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Table 16. Southern and Southeast sample with two variables

Table 17. Southern and Southeast sample with three variables.

10. NaPr BaNa ZgZg 0.8091

Table 18. Southern and Southeast sample with four variables.

Variable 1 Variable 2 Variable 3 Variable 4 Mean accuracy

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ANEXOS

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