Evolutionary dynamics of parabolic replicators

G. Meszena, 
Department of Biological Physics, Eötvös University, 
Pázmány Péter sétány 1A, H-1117 Budapest, Hungary
Collegium Budapest (Institute for Advanced Study), 
Szentháromság utca 2, H-1014 Budapest, Hungary

E. Szathmary
Department of Plant Taxonomy and Ecology, Eötvös University, 
Pázmány Péter sétány 1C, H-1117 Budapest, Hungary 
Collegium Budapest (Institute for Advanced Study), 
Szentháromság utca 2, H-1014 Budapest, Hungary

Selection 2(1-2): 147-159 (2001)

Abstract

The growth of many artificial replicators is approximately parabolic 
(sub-exponential) in solution, due to the self-inhibition through duplex 
formation by the association of single-stranded molecules. This type of 
growth implies "survival of everybody" under a selection constraint. 
Parabolic growth requires high enough concentration so that the single 
strands can find one another. The selective outcome is more complicated 
when spontaneous decay of molecules is also taken into account. When double 
strands decompose at a slower rate than single strands, coexistence or 
survival of the fittest becomes a quantitative issue. Here we investigate 
the evolution of parabolic replicators by the methods of adaptive dynamics. 
Directional selection for higher replication rate in general results in a 
"parabolic quasispecies", due to the fact that the fittest template is 
followed by a moving shadow of inferior templates that owe their presence 
to parabolic growth. Under the assumption of cross-hybridisation between 
non-identical templates molecular coexistence disappears when such pairing 
is sufficiently non-selective, because replicators do not inhibit themselves 
more than they limit the others. At intermediate specificity of pairing 
adaptive branching of the population becomes feasible, due to the fact that 
distant enough sequences are able to escape from cross-limitation by other 
sub-populations.