{"product_id":"the-quasispecies-equation-and-classical-raphal-cerf-9783031086656","title":"The Quasispecies Equation and Classical Population Models","description":"\u003cp\u003eThis monograph studies a series of mathematical models of the evolution of a population under mutation and selection. Its starting point is the quasispecies equation, a general non-linear equation which describes the mutation-selection equilibrium in Manfred Eigen's famous quasispecies model. A detailed analysis of this equation is given under the assumptions of finite genotype space, sharp peak landscape, and class-dependent fitness landscapes. Different probabilistic representation formulae are derived for its solution, involving classical combinatorial quantities like Stirling and Euler numbers.\u003c\/p\u003e\u003cp\u003eIt is shown how quasispecies and error threshold phenomena emerge in finite population models, and full mathematical proofs are provided in the case of the Wright-Fisher model. Along the way, exact formulas are obtained for the quasispecies distribution in the long chain regime, on the sharp peak landscape and on class-dependent fitness landscapes.\u003c\/p\u003e\u003cp\u003eFinally, several other classical population models are analyzed, with a focus on their dynamical behavior and their links to the quasispecies equation. \u003c\/p\u003e\u003cp\u003eThis book will be of interest to mathematicians and theoretical ecologists\/biologists working with finite population models.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Rapha? Cerf, Joseba Dalmau\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3031086651\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783031086656\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 08\/01\/2023\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 242\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.79lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.53d","brand":"Rapha? Cerf","offers":[{"title":"Paperback","offer_id":44212935426303,"sku":"9783031086656","price":159.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_49a9edde-b32a-4162-8d32-72c381208b63.jpg?v=1692111124","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-quasispecies-equation-and-classical-raphal-cerf-9783031086656","provider":"WR Book House","version":"1.0","type":"link"}