Pros and Cons of local adaptation scans

Guillaume Achaz

doi:10.24072/pci.evolbiol.100061

Pros and Cons of local adaptation scans

Guillaume Achaz based on reviews by Lucas Gonçalves da Silva and 1 anonymous reviewer

A recommendation of:

Separate the wheat from the chaff: genomic analysis of local adaptation in the red coral Corallium rubrum

Pratlong M, Haguenauer A, Brener K, Mitta G, Toulza E, Garrabou J, Bensoussan N, Pontarotti P, Aurelle D (2018), bioRxiv, 306456, ver. 3 peer-reviewed and recommended by Peer Community in Evolutionary Biology https://doi.org/10.1101/306456

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Abstract

ZH-CN

Separate the wheat from the chaff: genomic analysis of local adaptation in the red coral Corallium rubrum

Genomic data allow an in-depth and renewed study of local adaptation. The red coral (Corallium rubrum, Cnidaria) is a highly genetically structured species and a promising model for the study of adaptive processes along an environmental gradient. Here, we used RAD-Sequencing in order to study the vertical genetic structure of this species and to search for signals of local adaptation to depth and thermal regime in the red coral. Previous studies have shown different thermotolerance levels according to depth in this species which could correspond to genetic or environmental differences. We designed a sampling scheme with six pairs of 'shallow vs deep' populations distributed in three geographical regions as replicates. Our results showed significant differentiation among locations and among sites separated by around 20 m depth. The tests of association between genetics and environment allowed the identification of candidate loci under selection but with a potentially high rate of false positive. We discuss the methodological obstacles and biases encountered for the detection of selected loci in such a strongly genetically structured species. On this basis, we also discuss the significance of the candidate loci for local adaptation detected in each geographical region and the evolution of red coral populations along environmental gradients.

Local adaptation, RAD Seq, Corallium, outlier loci

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فصل القمح عن القشر: التحليل الجينومي للتكيف المحلي في المرجان الأحمر Corallium Rubrum

تسمح البيانات الجينومية بإجراء دراسة متعمقة ومتجددة للتكيف المحلي. المرجان الأحمر (Corallium Rubrum، Cnidaria) هو نوع عالي التركيب وراثيًا ونموذج واعد لدراسة عمليات التكيف على طول التدرج البيئي. هنا، استخدمنا تسلسل RAD لدراسة التركيب الوراثي الرأسي لهذا النوع والبحث عن إشارات التكيف المحلي مع العمق والنظام الحراري في المرجان الأحمر. أظهرت الدراسات السابقة مستويات مختلفة من التحمل الحراري وفقًا للعمق في هذا النوع والتي يمكن أن تتوافق مع الاختلافات الجينية أو البيئية. لقد صممنا نظامًا لأخذ العينات يتضمن ستة أزواج من المجموعات السكانية "الضحلة مقابل العميقة" الموزعة في ثلاث مناطق جغرافية كنسخ متماثلة. أظهرت نتائجنا تمايزًا كبيرًا بين المواقع وبين المواقع التي يفصل بينها عمق حوالي 20 مترًا. سمحت اختبارات الارتباط بين علم الوراثة والبيئة بتحديد المواقع المرشحة قيد الاختيار ولكن مع احتمال ارتفاع معدل الإيجابية الكاذبة. نناقش العوائق والتحيزات المنهجية التي تمت مواجهتها للكشف عن مواضع مختارة في مثل هذه الأنواع ذات البنية الوراثية القوية. وعلى هذا الأساس، نناقش أيضًا أهمية المواقع المرشحة للتكيف المحلي المكتشفة في كل منطقة جغرافية وتطور مجموعات المرجان الأحمر على طول التدرجات البيئية.

التكيف المحلي، RAD Seq، المرجان، المواقع الخارجية

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Separar el trigo de la paja: análisis genómico de adaptación local en el coral rojo Corallium rubrum

Los datos genómicos permiten un estudio profundo y renovado de la adaptación local. El coral rojo (Corallium rubrum, Cnidaria) es una especie altamente estructurada genéticamente y un modelo prometedor para el estudio de procesos adaptativos a lo largo de un gradiente ambiental. Aquí utilizamos RAD-Sequencing para estudiar la estructura genética vertical de esta especie y buscar señales de adaptación local a la profundidad y al régimen térmico en el coral rojo. Estudios anteriores han demostrado diferentes niveles de termotolerancia según la profundidad en esta especie, lo que podría corresponder a diferencias genéticas o ambientales. Diseñamos un esquema de muestreo con seis pares de poblaciones 'superficiales versus profundas' distribuidas en tres regiones geográficas como réplicas. Nuestros resultados mostraron una diferenciación significativa entre ubicaciones y entre sitios separados por alrededor de 20 m de profundidad. Las pruebas de asociación entre genética y ambiente permitieron la identificación de loci candidatos bajo selección pero con una tasa potencialmente alta de falsos positivos. Discutimos los obstáculos metodológicos y los sesgos encontrados para la detección de loci seleccionados en una especie tan fuertemente estructurada genéticamente. Sobre esta base, también discutimos la importancia de los loci candidatos para la adaptación local detectados en cada región geográfica y la evolución de las poblaciones de coral rojo a lo largo de gradientes ambientales.

Adaptación local, RAD Seq, Corallium, loci atípicos

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Séparez le bon grain de l'ivraie : analyse génomique de l'adaptation locale chez le corail rouge Corallium rubrum

Les données génomiques permettent une étude approfondie et renouvelée de l'adaptation locale. Le corail rouge (Corallium rubrum, Cnidaria) est une espèce hautement structurée génétiquement et un modèle prometteur pour l'étude des processus adaptatifs le long d'un gradient environnemental. Ici, nous avons utilisé le séquençage RAD afin d'étudier la structure génétique verticale de cette espèce et de rechercher des signaux d'adaptation locale à la profondeur et au régime thermique du corail rouge. Des études antérieures ont montré des niveaux de thermotolérance différents selon la profondeur chez cette espèce qui pourraient correspondre à des différences génétiques ou environnementales. Nous avons conçu un plan d'échantillonnage avec six paires de populations « peu profondes ou profondes » réparties dans trois régions géographiques sous forme de répétitions. Nos résultats ont montré une différenciation significative entre les emplacements et entre les sites séparés par une profondeur d'environ 20 m. Les tests d'association entre génétique et environnement ont permis l'identification de locus candidats en sélection mais avec un taux de faux positifs potentiellement élevé. Nous discutons des obstacles et biais méthodologiques rencontrés pour la détection de loci sélectionnés chez une espèce aussi fortement structurée génétiquement. Sur cette base, nous discutons également de l'importance des loci candidats pour l'adaptation locale détectés dans chaque région géographique et de l'évolution des populations de coraux rouges le long des gradients environnementaux.

Adaptation locale, RAD Seq, Corallium, locus aberrants

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गेहूं को भूसी से अलग करें: लाल मूंगा कोरलियम रूब्रम में स्थानीय अनुकूलन का जीनोमिक विश्लेषण

जीनोमिक डेटा स्थानीय अनुकूलन के गहन और नए सिरे से अध्ययन की अनुमति देता है। लाल मूंगा (कोरलियम रूब्रम, निडारिया) एक अत्यधिक आनुवंशिक रूप से संरचित प्रजाति है और पर्यावरणीय ढाल के साथ अनुकूली प्रक्रियाओं के अध्ययन के लिए एक आशाजनक मॉडल है। यहां, हमने इस प्रजाति की ऊर्ध्वाधर आनुवंशिक संरचना का अध्ययन करने और लाल मूंगा में गहराई और थर्मल शासन के लिए स्थानीय अनुकूलन के संकेतों की खोज करने के लिए आरएडी-अनुक्रमण का उपयोग किया। पिछले अध्ययनों ने इस प्रजाति में गहराई के अनुसार अलग-अलग थर्मोटॉलेरेंस स्तर दिखाया है जो आनुवंशिक या पर्यावरणीय मतभेदों के अनुरूप हो सकता है। हमने प्रतिकृति के रूप में तीन भौगोलिक क्षेत्रों में वितरित 'उथली बनाम गहरी' आबादी के छह जोड़े के साथ एक नमूना योजना तैयार की। हमारे परिणामों ने स्थानों और लगभग 20 मीटर की गहराई से अलग साइटों के बीच महत्वपूर्ण अंतर दिखाया। आनुवंशिकी और पर्यावरण के बीच संबंध के परीक्षणों ने चयन के तहत उम्मीदवार लोकी की पहचान की अनुमति दी, लेकिन झूठी सकारात्मकता की संभावित उच्च दर के साथ। हम ऐसी दृढ़ता से आनुवंशिक रूप से संरचित प्रजातियों में चयनित लोकी का पता लगाने के लिए आने वाली पद्धतिगत बाधाओं और पूर्वाग्रहों पर चर्चा करते हैं। इस आधार पर, हम प्रत्येक भौगोलिक क्षेत्र में पाए गए स्थानीय अनुकूलन के लिए उम्मीदवार लोकी के महत्व और पर्यावरणीय ढाल के साथ लाल मूंगा आबादी के विकास पर भी चर्चा करते हैं।

स्थानीय अनुकूलन, आरएडी सेक, कोरलियम, बाहरी लोकी

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小麦をもみがらから分離：赤サンゴ Corallium rubrum の局所適応のゲノム解析

ゲノムデータにより、局所適応に関する徹底的な新たな研究が可能になります。アカサンゴ (Corallium rubrum、刺胞動物門) は、高度に遺伝的に構造化された種であり、環境勾配に沿った適応プロセスの研究にとって有望なモデルです。ここでは、この種の垂直遺伝構造を研究し、赤サンゴの深さと温度状況に対する局所適応のシグナルを探索するために、RAD シーケンスを使用しました。これまでの研究では、この種の深さに応じて異なる耐熱性レベルが示されており、これは遺伝的または環境の違いに対応している可能性があります。私たちは、3 つの地理的地域に分布する「浅い母集団と深い母集団」の 6 つのペアを反復として使用するサンプリングスキームを設計しました。私たちの結果は、場所間、および深さ約 20 m 離れたサイト間で大きな差異があることを示しました。遺伝学と環境の間の関連性のテストにより、選択中の候補遺伝子座の同定が可能になりましたが、偽陽性率が高くなる可能性がありました。我々は、このような強く遺伝的に構造化された種において選択された遺伝子座を検出するために遭遇する方法論的な障害とバイアスについて議論します。これに基づいて、各地理的領域で検出された局所適応候補座の重要性と、環境勾配に沿った赤サンゴ個体群の進化についても議論します。

局所適応、RAD Seq、Corallium、外れ値遺伝子座

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Separe o joio do trigo: análise genômica da adaptação local no coral vermelho Corallium rubrum

Os dados genômicos permitem um estudo aprofundado e renovado da adaptação local. O coral vermelho (Corallium rubrum, Cnidaria) é uma espécie altamente estruturada geneticamente e um modelo promissor para o estudo de processos adaptativos ao longo de um gradiente ambiental. Aqui, utilizamos o Sequenciamento RAD para estudar a estrutura genética vertical desta espécie e buscar sinais de adaptação local à profundidade e ao regime térmico no coral vermelho. Estudos anteriores mostraram diferentes níveis de termotolerância de acordo com a profundidade nesta espécie, o que pode corresponder a diferenças genéticas ou ambientais. Projetamos um esquema de amostragem com seis pares de populações 'superficiais vs profundas' distribuídas em três regiões geográficas como réplicas. Nossos resultados mostraram diferenciação significativa entre locais e entre locais separados por cerca de 20 m de profundidade. Os testes de associação entre genética e ambiente permitiram a identificação de loci candidatos sob seleção, mas com uma taxa potencialmente elevada de falsos positivos. Discutimos os obstáculos metodológicos e vieses encontrados para a detecção de loci selecionados em uma espécie tão fortemente estruturada geneticamente. Nesta base, também discutimos a importância dos loci candidatos para adaptação local detectados em cada região geográfica e a evolução das populações de coral vermelho ao longo dos gradientes ambientais.

Adaptação local, RAD Seq, Corallium, loci discrepantes

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Отделите зерна от плевел: геномный анализ локальной адаптации красного коралла Corallium Rubrum

Геномные данные позволяют провести углубленное и обновленное изучение местной адаптации. Красный коралл (Corallium rubrum, Cnidaria) — высокогенетически структурированный вид и многообещающая модель для изучения адаптационных процессов в условиях градиента окружающей среды. Здесь мы использовали RAD-секвенирование для изучения вертикальной генетической структуры этого вида и поиска сигналов локальной адаптации к глубине и температурному режиму у красного коралла. Предыдущие исследования показали разные уровни термотолерантности в зависимости от глубины у этого вида, что может соответствовать генетическим различиям или различиям в окружающей среде. Мы разработали схему выборки с шестью парами «неглубоких и глубоких» популяций, распределенных в трех географических регионах в качестве повторов. Наши результаты показали значительную дифференциацию между локациями и участками, разделенными глубиной примерно 20 м. Тесты на связь между генетикой и окружающей средой позволили идентифицировать выбранные локусы-кандидаты, но с потенциально высоким уровнем ложноположительных результатов. Мы обсуждаем методологические препятствия и предубеждения, возникающие при обнаружении избранных локусов у столь сильно генетически структурированных видов. На этой основе мы также обсуждаем значение локусов-кандидатов для местной адаптации, обнаруженных в каждом географическом регионе, и эволюцию популяций красных кораллов в соответствии с экологическими градиентами.

Локальная адаптация, RAD Seq, Corallium, выбросы локусов

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区分小麦和谷壳：红珊瑚 Corallium rubrum 局部适应的基因组分析

基因组数据可以对局部适应进行深入和更新的研究。红珊瑚（Corallium rubrum，Cnidaria）是一种高度遗传结构的物种，也是研究沿环境梯度的适应过程的有前途的模型。在这里，我们使用 RAD 测序来研究该物种的垂直遗传结构，并寻找红珊瑚局部适应深度和热状况的信号。先前的研究表明，该物种根据深度的不同耐热性水平也不同，这可能与遗传或环境差异相对应。我们设计了一个抽样方案，其中分布在三个地理区域的六对“浅层与深层”群体作为重复。我们的结果显示，位置之间以及相距约 20 m 深度的地点之间存在显着差异。遗传学和环境之间的关联测试允许识别选择中的候选基因座，但假阳性率可能很高。我们讨论了在如此强烈的遗传结构物种中检测选定基因座时遇到的方法学障碍和偏差。在此基础上，我们还讨论了各个地理区域检测到的局部适应候选位点的意义以及红珊瑚种群沿环境梯度的演化。

局部适应、RAD Seq、Corallium、离群基因座

Submission: posted 24 April 2018
Recommendation: posted 11 December 2018, validated 13 December 2018

Cite this recommendation as:
Achaz, G. (2018) Pros and Cons of local adaptation scans. Peer Community in Evolutionary Biology, 100061. 10.24072/pci.evolbiol.100061

Recommendation

The preprint by Pratlong et al. [1] is a well thought quest for genomic regions involved in local adaptation to depth in a species a red coral living the Mediterranean Sea. It first describes a pattern of structuration and then attempts to find candidate genes involved in local adaptation by contrasting deep with shallow populations. Although the pattern of structuration is clear and meaningful, the candidate genomic regions involved in local adaptation remain to be confirmed. Two external reviewers and myself found this preprint particularly interesting regarding the right-mindedness of the authors in front of the difficulties they encounter during their experiments. The discussions on the pros and cons of the approach are very sound and can be easily exported to a large number of studies that hunt for local adaptation. In this sense, the lessons one can learn by reading this well documented manuscript are certainly valuable for a wide range of evolutionary biologists.
More precisely, the authors RAD-sequenced 6 pairs of 'shallow vs deep' samples located in 3 geographical sea areas (Banyuls, Corsica and Marseilles). They were hoping to detect genes involved in the adaptation to depth, if there were any. They start by assessing the patterns of structuration of the 6 samples using PCA and AMOVA [2] and also applied the STRUCTURE [3] assignment software. They show clearly that the samples were mostly differentiated between geographical areas and that only 1 out the 3 areas shows a pattern of isolation by depth (i.e. Marseille). They nevertheless went on and scanned for variants that are highly differentiated in the deep samples when compared to the shallow paired samples in Marseilles, using an Fst outliers approach [4] implemented in the BayeScEnv software [5]. No clear functional signal was in the end detected among the highly differentiated SNPs, leaving a list of candidates begging for complementary data.
The scan for local adaptation using signatures of highly divergent regions is a classical problem of population genetics. It has been applied on many species with various degrees of success. This study is a beautiful example of a well-designed study that did not give full satisfactory answers. Readers will especially appreciate the honesty and the in-depth discussions of the authors while exposing their results and their conclusions step by step.

References

[1] Pratlong, M., Haguenauer, A., Brener, K., Mitta, G., Toulza, E., Garrabou, J., Bensoussan, N., Pontarotti P., & Aurelle, D. (2018). Separate the wheat from the chaff: genomic scan for local adaptation in the red coral Corallium rubrum. bioRxiv, 306456, ver. 3 peer-reviewed and recommended by PCI Evol Biol. doi: 10.1101/306456
[2] Excoffier, L., Smouse, P. E. & Quattro, J. M. (1992). Analysis of molecular variance inferred from metric distances among DNA haplotypes: application to human mitochondrial DNA restriction data. Genetics, 131(2), 479-491.
[3] Pritchard, J. K., Stephens, M., & Donnelly, P. (2000). Inference of population structure using multilocus genotype data. Genetics, 155(2), 945-959.
[4] Lewontin, R. C., & Krakauer, J. (1973). Distribution of gene frequency as a test of the theory of the selective neutrality of polymorphisms. Genetics, 74(1), 175-195.
[5] de Villemereuil, P., & Gaggiotti, O. E. (2015). A new FST‐based method to uncover local adaptation using environmental variables. Methods in Ecology and Evolution, 6(11), 1248-1258. doi: 10.1111/2041-210X.12418

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Conflict of interest:
The recommender in charge of the evaluation of the article and the reviewers declared that they have no conflict of interest (as defined in the code of conduct of PCI) with the authors or with the content of the article. The authors declared that they comply with the PCI rule of having no financial conflicts of interest in relation to the content of the article.

Reviews

Evaluation round #2

DOI or URL of the preprint: 10.1101/306456

Version of the preprint: 2

Author's Reply, 05 Dec 2018

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Our reply is in attached file. Please note that the BioRXiv file includes all corrections, except formatting for PCI (we are waiting for the formal recommendation), the formatted version can be uploaded here: https://amubox.univ-amu.fr/s/rRjj7YXiC4JZRAL

Decision by Guillaume Achaz, posted 23 Nov 2018

Dear authors,

Please first apologize for the delay in responding to your submission. My agenda has been sadly very compact. I think your revised version is even better than the first one. I will be happy to recommend your preprint for PCI Evol Biol, provided that you can fix few minor details listed below. I believe this would not you very take long. I shall then quickly post my recommendation.

Gene diversity, although now defined, is used in your ms. Please replace all its occurrences by expected heterozygosisty that is a much more explicit wording.
Table 3: MAF<1% actually means MA Counts<4 for most sites, unless there are too many missing data. In this last case, could you provide some extra information on missing genotypes ? (maybe mean and 95% of the distribution)
Table 2, 4 : could you add one letter for the region in parenthesis after the name. This will considerably ease the reading.
Table 4: remove Tajima's D from the legend. Fourth column head is "number of private alleles" and non integers are reported. Is this a mean. If yes, please use "average number of private alleles". Otherwise please explain.
Table 5 : disturbing to read that Fst of 0.01 is "highly significant". I guess this is only due to the size of the dataset in terms of loci, that are assumed to be independent.

May I suggest (but feel free to refuse) to change the title from "Separate the wheat from the chaff: genomic analysis of local adaptation in the red coral Corallium rubrum" to "Separate the wheat from the chaff: genomic scan for local adaptation in the red coral Corallium rubrum"

as the ms is not really an "analysis" of local adaptation but rather a quest for it.

Evaluation round #1

DOI or URL of the preprint: https://doi.org/10.1101/306456

Version of the preprint: 1

Author's Reply, 17 Oct 2018

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Decision by Guillaume Achaz, posted 17 Oct 2018

Dear authors,

Two external reviewers and myself have carrefully read your ms entitled "Separate the wheat from the chaff: genomic analysis of local adaptation in the red coral Corallium rubrum" and we all agree that this ms is sound, interesting and certainly deserves to be recommded by PCI Evol Biol. As pointed out by the reviewers, the main strength of this ms is the indepth discussion of the pros and cons of the methods and results you provide. I agree with their opinion.

We nonetheless have few suggestions that could potentially improve the overall quality of this ms. I believe the suggested corrections will be easily addressed and that I will be able to recommend the revised version without any further opinion from the two external reviewers. Please revise and respond to all comments (see below) before I can recommend this article.

Best regards,

Guillaume Achaz

:: Suggestions from G Achaz ::

Major: (A) can the authors provide basic analysis of within samples diversity (sample size, #sites, paiwise difference, Tajima's D, etc). (B) did the authors try to infer model parameter (using a mix of demography and structure) using appropriate methods like the ones implemented in dadi (or any other equivalent approach). (C) please shorten and/or lower the importance of the detection of selection as there isn't obvious positive conclusions from it.

Minor: l43 "between" is repeated in tandem l70 replace "high" by "strong"? l189, l270, table4 what is gene diversity? pairwise differences (i.e. heterozygosity)? l194 I don't understand what is the meaning here of 'centered' l282-283, l294, l345 this seems surprising. Why would the sex contribute to genetic differentiation? Am I missing something obvious? l309 you mean 20 instead of 10? l357 which axis are you refering to? pc1? l384 I would be more cautious as this pattern is not visible in the Fst analysis.

Reviewed by anonymous reviewer 1, 16 May 2018

This manuscript describes the population genetic analysis of the red coral Corallium rubrum, using RAD-Seq data from three populations in the mediterranean see, and samples at two depth. In order to describe the genetic structure of the species, the authors used a combination of principal components analysis (PCA), bayesian inference (STRUCTURE), analysis of molecular variance (AMOVA), and measures of fixation idenx (Fst). The authors find that geographical location is the main factor explaining the genetic variance, depth showing an effect only in one population. The authors conduct a careful discussion about potential confounding factors, in particular regarding outlier genes with high Fst values.

This is a well-conducted study with an interesting discussion, both with methodological and biological implications, notably with respect to adaptation in the context of climate change.

I only have minor comments:

l276: "principal components reflected the geographical and depth origin"... As discussed later in this paragraph, the depth only appear to have an effect in one population. It would be more accurate to write something like "principal components reflected the geographical and, to some extant, depth origin"
l58: as written, the authors seem to oppose natural selection and gene flow, while the two phenomena are not at the same level... Just like mutations, gene flow can be neutral or selected. Maybe rephrase?
l235-236: a threshold of 1% was used for the chi2 test and then corrected with a FDR or 5%? This is unusual... Either a threshold on the FDR was used, or p-values were adjusted for multiple testing, but one does not "correct" p-values using a threshold.
l271, Wilcoxon test: not clear what was compared to what: Marseille vc. pooled Corsica + Banyuls? A Kruskal-Wallis test + posthoc would be more appropriate here (see "agricolae" package in R for non-parametric posthoc tests)
l283: Reference is a bit unclear. Do the author mean something like "The 5th axis of the PCA separated all individuals according to their sex, independently of their geographical origin, as observed in a previous study (Pratlong et al. 2017)" ?
l298-299: two times "the results"
l309, "even for populations separated by 10m": unclear which populations are refered to
l324: it is unclear which test was performed there, as there are two Fst values per population and it seems like the authors made one comparison per population?
l376, at a genomic SCALE ?
Figure 1: while the depth of the sampling site is coded in the sample name, it would be ore clear to have it explicitly indicated (for instance using two distinct plotting symbols)

Reviewed by Lucas Gonçalves da Silva, 23 May 2018

Dear editors and authors,

I would like to congratulate the authors, because the study is extremely interesting, relevant, with well designed, with consistent methods and great results.

I think a very positive point of the work is the discussion around the limitations of the study. The authors assume and describe these limitations, and this is always very important in genomic scale studies.

The only point left to be desired from my point of view was the discussion and characterization of the study in the context of implications for species-focus conservation. This species is considered endangered by IUCN and included within the Mediterranean Red List of Endangered Species. I believe that the isertion of informations about conservation status (introduction and discussion) will help the applicability of work in decision making, and can enrich the work in general.

Figures and tables are satisfactory.

L36 - "... we also discuss ..." L42 - "adaptation by species ..." L43 - remove "between" L87 - missing space

I would love to see a niche modeling with this data, applying maxent, maxlike or some other likelihood algorithm for SDM (or more than only one). It is not something to be included in this paper, but I recommend authors to do so, since they have enough data for this. If you are interested, I leave the communication channel open with me via the editor of PCI Ecol Evo. Editors are authorized to send my email contact, if the authors want it. I strongly recommend the acceptance of this paper.

Best Regards.

Dr. Lucas Gonçalves lucas_gonc@yahoo.com.br