Selfish intracellular replicators: a two-level selection minimalist mathematical model
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Selfish intracellular replicators: a two-level selection minimalist mathematical model Raul Abreu de Assis1 · Polyanna Possani da Costa Petry1 · Chiara Maria Seidel Luciano1 · Mazílio Coronel Malavazi2
Received: 16 July 2015 / Revised: 26 December 2015 / Accepted: 28 December 2015 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2016
Abstract A mathematical model of the interaction between two levels of selection (intracellular and cellular) is presented. The paradigm is that of a selfish intracellular replicator, such as a strand of selfish DNA, that reproduces itself at the expense of the efficiency of the structure of the cell. A mathematical analysis is conducted and conditions for the survival of the selfish replicators are obtained explicitly. Our results indicate that, if reproduction is asexual, mechanisms of horizontal transfer of genes are essential for the fixation of such replicators in the population and also that less harmful replicators have a better chance of infecting a whole population, while aggressive ones will usually successfully infect only a part of it. Keywords replicators
Differential equations · Natural selection · Levels of selection · Model · Selfish
Mathematics Subject Classification
92B05
1 Introduction Life on Earth is organised in hierarchical levels. Self-replicating molecules group together to form the genetic material, which in turn is organised inside cells that may compose mul-
Communicated by Geraldo Diniz.
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Raul Abreu de Assis [email protected]; [email protected] Polyanna Possani da Costa Petry [email protected] Chiara Maria Seidel Luciano [email protected] Mazílio Coronel Malavazi [email protected]
1
Dep. Matemática, UNEMAT, Sinop, MT 78550-000, Brazil
2
ICNHS, UFMT, Sinop, MT 78557-257, Brazil
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ticellular organisms and so forth, up to the scale of species and clades (Barton et al. 2007; Futuyma 2009; Gould 2002). The role of those distinct levels in the formation of the adaptations observed in the living beings is controversial (Wilson 2006). Some authors have defended a vision of “group selection” to explain certain types of behavior in animals, such as ritualistic fighting (“gloved fists” contests), or the reduction in reproduction rate under adverse conditions (Wynne-Edwards 1962, 1986). This type of approach depicted the group as a relevant unit of selection, as a complementary form to the selection at the individual level and also responsible for generating adaptations at the group level. Such an approach was criticised (Williams 1966; Dawkins 1976) and alternative explanations that sought to explain those observations using only selection at the individual level were proposed (Smith and Price 1973; Smith 1976, 1982). There is still, however, controversy about the relative importance of the hierarchical levels in the process of natural selection (Okasha 2001). In particular, Nowak et al. suggest that group selection may have a fundamental role in the origin of the social insects. While discussing
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