Abstract
Realistic fitness landscapes generally display a redundancy-fitness trade-off: highly fit trait configurations are inevitably rare, while less fit trait configurations are expected to be more redundant. The resulting sub-optimal patterns in the fitness distribution are typically described by means of effective formulations, where redundancy provided by the presence of neutral contributions is modelled implicitly, e.g. with a bias of the mutation process. However, the extent to which effective formulations are compatible with explicitly redundant landscapes is yet to be understood, as well as the consequences of a potential miss-match. Here we investigate the effects of such trade-off on the evolution of phenotype-structured populations, characterised by continuous quantitative traits. We consider a typical replication-mutation dynamics, and we model redundancy by means of two dimensional landscapes displaying both selective and neutral traits. We show that asymmetries of the landscapes will generate neutral contributions to the marginalised fitness-level description, that cannot be described by effective formulations, nor disentangled by the full trait distribution. Rather, they appear as effective sources, whose magnitude depends on the geometry of the landscape. Our results highlight new important aspects on the nature of sub-optimality. We discuss practical implications for rapidly mutant populations such as pathogens and cancer cells, where the qualitative knowledge of their trait and fitness distributions can drive disease management and intervention policies.
Highlights
Understanding the interplay between neutrality and selection is considered one of the major challenges in the contemporary theory of biological evolution (Wagner, 1999; Ciliberti et al, 2007; Wagner, 2008; Barghi et al, 2020; Manrubia et al, 2020), aiming to bridge the gap between two historically antipodal theories (Nei et al, 2013)
We will first consider a simple non-redundant, one-dimensional fitness landscape. This case will provide the baseline results for comparison with the dynamics on redundant landscapes, so as to elucidate the dual behaviour triggered by the concomitant presence of neutral and selective traits
We shall discuss the consequent analogies and differences, as well as their practical implications. Contrary to their non-redundant counterpart (Fig. 2), we have shown that redundant landscapes display a dual behaviour, depending on the dynamics’ level of description: full phenotype distributions exhibit survival-of-the-fittest patterns (Fig. 3, panels a-d), where most of the population lies in proximity of the landscape optimum; on the other hand, their correspondent marginal fitness distributions may exhibit sub-optimal patterns (Fig. 3, panels e-f), where most of the population displays less fit but more redundant traits (Fig. 4)
Summary
Understanding the interplay between neutrality and selection is considered one of the major challenges in the contemporary theory of biological evolution (Wagner, 1999; Ciliberti et al, 2007; Wagner, 2008; Barghi et al, 2020; Manrubia et al, 2020), aiming to bridge the gap between two historically antipodal theories (Nei et al, 2013). Less fit phenotypes are able to outperform the fittest ones, if they are endowed with higher ‘mutational robustness’ due to some degree of neutrality. Crucially both on the genetic architecture and on the mutational topology of the evolving system under investigation (Huynen, 1996; Van Nimwegen et al, 1999; Draghi et al, 2010; Aguirre et al, 2011). These features have been well documented in the field of molecular phenotype evolution, where the interplay between neutrality and selection is typically described by the redundancy of Genotype-Phenotype maps.
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