caa a22 4500 477067247 CHVBK 20180405111415.0 cr unu---uuuuu 170330e19960101xx s 000 0 eng 10.1007/BF02458287 doi (NATIONALLICENCE)springer-10.1007/BF02458287 Behera Narayan Development Biology and Genetics Laboratory, Indian Institute of Science, 560 012, Bangalore, India aut Variational principles in evolution [Elektronische Daten] [Narayan Behera] For a one-locus selection model, Svirezhev introduced an integral variational principle by defining a Lagrangian which remained stationary on the trajectory followed by the population undergoing selection. It is shown here (i) that this principle can be extended to multiple loci in some simple cases and (ii) that the Lagrangian is defined by a straightforward generalization of the one-locus case, but (iii) that in two-locus or more general models there is no straightforward extension of this principle if linkage and epistasis are present. The population trajectories can be constructed as trajectories of steepest ascent in a Riemannian metric space. A general method is formulated to find the metric tensor and the surface in the metric space on which the trajectories, which characterize the variations in the gene structure of the population, lie. The local optimality principle holds good in such a space. In the special case when all possible linkage disequilibria are zero, the phase point of then-locus genetic system moves on the surface of the product space ofn higher dimensional unit spheres in a certain Riemannian metric space of gene frequencies so that the rate of change of mean fitness is maximum along the trajectory. In the two-locus case the corresponding surface is a hyper-torus. Society for Mathematical Biology, 1996 Bulletin of Mathematical Biology Kluwer Academic Publishers 58/1(1996-01-01), 175-202 0092-8240 58:1<175 1996 58 11538 https://doi.org/10.1007/BF02458287 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02458287 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Behera Narayan Development Biology and Genetics Laboratory, Indian Institute of Science, 560 012, Bangalore, India aut NATIONALLICENCE 773 0- Bulletin of Mathematical Biology Kluwer Academic Publishers 58/1(1996-01-01), 175-202 0092-8240 58:1<175 1996 58 11538 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer