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H 1 Applying the infinitesimal model

Auteurs : Etheridge, Alison (Auteur de la Conférence) ; Barton, Nicholas H. (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The infinitesimal model is based on the assumption that, conditional on the pedigree, the joint distribution of trait values is multivariate normal, then, selecting parents does not alter the variance amongst offspring. We explain how the infinitesimal model extends to include dominance as well as epistasis. Then, the evolution of a population depends on just a few quantities, which define the components of genetic variance and the inbreeding depression. In practice, the main difficulty in applying the infinitesimal model in the presence of dominance is that one must calculate the probabilities of identity by descent amongst up to four genes, which means that very many identity coefficients must be traced. We show how these coefficients can be calculated and approximated, allowing the infinitesimal model to be applied to help understand the evolutionary consequences of inbreeding depression.

    Keywords : Infinitesimal model; generalised central limit theorem

    Codes MSC :
    60F05 - Central limit and other weak theorems
    60K30 - Applications (congestion, allocation, storage, traffic, etc.), See also {90Bxx}
    92D10 - Genetics

    Ressources complémentaires :

    Informations sur la rencontre

    Nom de la rencontre : Thematic Month Week 2: Mathematical Models in Evolutionary Biology / Mois thématique Semaine 2 : Modèles mathématiques en biologie de l'évolution
    Organisateurs de la rencontre : Champagnat, Nicolas ; Coville, Jérôme ; Gomulkiewicz, Richard ; Hamel, Francois ; Roques, Lionel
    Dates : 10/02/2020 - 14/02/2020
    Année de la rencontre : 2020
    URL Congrès : https://conferences.cirm-math.fr/2302.html

    Citation Data

    DOI : 10.24350/CIRM.V.19605003
    Cite this video as: Etheridge, Alison ;Barton, Nicholas H. (2020). Applying the infinitesimal model. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19605003
    URI : http://dx.doi.org/10.24350/CIRM.V.19605003

    Voir aussi


    1. BARTON, Nicholas H., ETHERIDGE, Alison M., et VÉBER, Amandine. The infinitesimal model: Definition, derivation, and implications. Theoretical population biology, 2017, vol. 118, p. 50-73. - https://doi.org/10.1016/j.tpb.2017.06.001