ISSN:
1432-1416
Keywords:
Evolution
;
Molecular evolution
;
Dynamical system
;
Neo-Darwinian evolution
;
Non-Darwinian evolution
;
Neutral theory
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Mathematics
Notes:
Abstract In order to understand generally how the biological evolution rate depends on relevant parameters such as mutation rate, intensity of selection pressure and its persistence time, the following mathematical model is proposed: dN n (t)/dt=(m n (t-μ)N n (t)+μN n-1(t) (n=0,1,2,3...), where N n (t) and m n (t) are respectively the number and Malthusian parameter of replicons with step number n in a population at time t and μ is the mutation rate, assumed to be a positive constant. The step number of each replicon is defined as either equal to or larger by one than that of its parent, the latter case occurring when and only when mutation has taken place. The average evolution rate defined by $$\upsilon _\infty \equiv {\text{ lim}}_{t \to \infty } \sum _{n = 0}^\infty nN_n (t)/t\sum _{n = 0}^\infty N_n (t)$$ is rigorously obtained for the case (i) m n (t)=m n is independent of t (constant fitness model), where m n is essentially periodic with respect to n, and for the case (ii) $$m_n (t) = {\text{ }}s( - 1)^{n + [1/\tau ]} $$ (periodic fitness model), together with the long time average m ∞ of the average Malthusian parameter $$\bar m \equiv \sum _{n = 0}^\infty m_n (t)N_n (t)/\sum _{n = 0}^\infty N_n (t)$$ . The biological meaning of the results is discussed, comparing them with the features of actual molecular evolution and with some results of computer simulation of the model for finite populations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00275397
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