Abstract
Models of competitive template replication, although basic for replicator dynamics and primordial evolution, have not yet taken different sequences explicitly into account, neither have they analyzed the effect of resource partitioning (feeding on different resources) on coexistence. Here we show by analytical and numerical calculations that Gause's principle of competitive exclusion holds for template replicators if resources (nucleotides) affect growth linearly and coexistence is at fixed point attractors. Cases of complementary or homologous pairing between building blocks with parallel or antiparallel strands show no deviation from the rule that the nucleotide compositions of stably coexisting species must be different and there cannot be more coexisting replicator species than nucleotide types. Besides this overlooked mechanism of template coexistence we show also that interesting sequence effects prevail as parts of sequences that are copied earlier affect coexistence more strongly due to the higher concentration of the corresponding replication intermediates. Template and copy always count as one species due their constraint of strict stoichiometric coupling. Stability of fixed-point coexistence tends to decrease with the length of sequences, although this effect is unlikely to be detrimental for sequences below 100 nucleotides. In sum, resource partitioning (niche differentiation) is the default form of competitive coexistence for replicating templates feeding on a cocktail of different nucleotides, as it may have been the case in the RNA world. Our analysis of different pairing and strand orientation schemes is relevant for artificial and potentially astrobiological genetics.
Highlights
Gause (1934) in the Golden Age of theoretical ecology formulated the principle of competitive exclusion, proposing in effect what usually is being referred to as ‘‘complete competitors cannot coexist’’ [1]
Despite interesting sequence effects, competing template replicators yield to Gause’s principle of competitive exclusion so that the number of stably coexisting template species cannot exceed the number of nucleotide species on which they grow, one of the findings is that plus and minus strands together count as one species
To understand the mechanism of coexistence of template replicators we formulated the dynamics of polynucleotide replication
Summary
Gause (1934) in the Golden Age of theoretical ecology formulated the principle of competitive exclusion, proposing in effect what usually is being referred to as ‘‘complete competitors cannot coexist’’ [1]. In the ‘‘default’’ model of Eigen with constant total population concentration the fastest replicator (and its associated mutant cloud) wins, consonant with ‘‘survival of the fittest’’; the tacit assumption being that the competing sequences are complete competitors in the sense of Gause. More detailed investigations of RNA replication kinetics have greatly improved these models, taking into account saturation of the replicase enzyme, asymmetry of plus and minus RNA strands, and replicationally inert double-strand formation [7,8,9]; the latter phenomenon yielding coexistence due to the selflimitation of growth. Szathmary and Gladkih [12] showed that the consequential parabolic growth leads to stable dynamical coexistence. None of these models included a detailed analysis of base composition and sequence effects on coexistence.
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