Evolution & Genetics

Mathematical Biology	|	Mathematics for Human Health	|	Data Knowledge
Ecology	|	Care and Ageing	|	Big Data
Epidemiology	|	Mathematical methods in Medicine	|	Machine Learning
Evolution & Genetics	|

Projects:

• Evolution
• Models of genetic evolution
• Genetics
• Plant breeding
• Integration of HIV in the human genome
• Constitutional chromosomal rearrangements in the human genome

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Project: Models of genetic evolution

Description: In this line, we study in detail and in an unified way, several models used in modelling evolutionary dynamics (i.e., Darwinian evolution). In particular, we rigorously study the Wright-Fisher and the Moran models (finite population stochastic processes), the Kimuraequation (a degenerated partial-differential equation of drift-diffusion type, supplemented by conservation laws) and the replicator equation (an ordinary differential equation, popular in evolutionary game theory). Several different mathematical theories are used, e.g., stochastic process, theory of Markov chains, partial differential equations of elliptic and parabolic type, game theory etc. Currently, all these models are being reformulated in an unified way using variational formalism (gradient flows).

Methods: Probability | Linear Algebra | Differential Equations

CMA Researchers: Fabio A. C. C. Chalub

Publications:

• Fabio A.C.C. Chalub and Max O. Souza. Fitness potentials and qualitative properties of the Wright-Fisher dynamics. J. Theor. Biol., 457:57 – 65, 2018.
• Olga Danilkina, Max O. Souza, and Fabio A. C. C. Chalub. Conservative parabolic problems: Nondegenerated theory and degenerated examples from population dynamics. Math. Meth. Appl. Sciences, 41:4391–4406, 2018.
• Fabio A. C. C. Chalub and Max O. Souza. On the stochastic evolution of finite populations. J. Math. Biol.,75(6-7):1735–1774, 2017.
• Fabio A. C. C. Chalub. An asymptotic expression for the fixation probability of a mutant in star graphs. J. Dyn. Games, 3(3, SI):217–223, 2016.
• Fabio A. C. C. Chalub and Max O. Souza. Fixation in large populations: a continuous view of a discrete problem. J. Math. Biol., 72(1-2):283–330, 2016.
• Fabio A. C. C. Chalub and Max O. Souza. Discrete and continuous SIS epidemic models: A unifying approach. Ecol. Complex., 18(SI):83–95, 2014.
• Fabio A. C. C. Chalub and Max O. Souza. The frequency-dependent Wright-Fisher model: diffusive and non-diffusive approximations. J. Math. Biol., 68(5):1089–1133, 2014.
• A. F. D’Almeida, R. C. Teixeira, and F. A. Chalub. Much or More? Experiments of Rationality and Spite with School Children. North Amer. J. Phsycol., 16(1):163–178, 2014

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Project: Plant breeding

Description:

Methods: Robust Statistics | Genetic statistics

CMA Researchers: Vanda Lourenço

Publications:

• P. C. Rodrigues, A. Monteiro, and V. M. Lourenco. A robust AMMI model for the analysis of genotype-by-environment data. Bioinformatics, 32(1):58–66, JAN 1 2016.
• V M Lourenço P C Rodrigues A M Pires H -P Piepho. A robust DF-REML framework for variance components estimation in genetic studies Bioinformatics, 33(22): 3584–3594, NOV 15 2017

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Project: Integration of HIV in the human genome

Description: Using data from the National Center for Biotechnology Information (NCBI), we determine the preferences of HIV integrations in the human genome.

Methods: Statistical analysis of genetic data | Non-parametric methods | Analysis of variance

CMA Researchers: Elsa Moreira, Inês Sequeira

Publications:

• Juliana Gonçalves, Elsa E. Moreira, Inês Sequeira, António Rodrigues, José Rueff, Aldina Brás: Integration of HIV in the Human Genome: Which Sites Are Preferential? A Genetic and Statistical Assessment. International Journal of Genomics 2016, vol. 2016
• Inês J. Sequeira, Juliana Gonçalves, Elsa E. Moreira, João T. Mexia, José Rueff, Aldina Brás: Genetic and Statistical Study of HIV Integration in the Human Genome. AIP Conference Proceedings. ICNAAM 2013 - 11th International Conference of Numerical Analysis and Applied Mathematics, Rhodes, Greece, 2013

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Project: Constitutional chromosomal rearrangements in the human genome

Description: Using the database of Chromosomal Imbalance and Phenotype in Humans using Ensembl Resources (DECIPHER), we determine which are the chromosomal fragile sites more involved in constitutional chromosomal rearrangements.

Methods: Statistical analysis of genetic data | Data display | Descriptive statistics | Linear regression analysis

CMA Researchers: Inês Sequeira, Dora Gomes

Publications:

• Sequeira I.J., Mexia J.T., Santiago J., Mamede R., Silva E., Santos J., Faria D., Rueff J. and Brás A. (2013), Predominance of constitutional chromosomal rearrangements in human chromosomal fragile sites. Open Journal of Genetics, 3(2A3), 8-13.
• Dora Prata Gomes, Inês J. Sequeira, Carlos Figueiredo, José Rueff and Aldina Brás. (2016). The human chromosomal fragile sites more often involved in constitutional deletions and duplications - A genetic and statistical assessment. AIP Conference Proceedings, 1790(1), 080003.