On the networked architecture of genotype spaces and its critical effects on molecular evolution

Abstract

Evolutionary dynamics is often viewed as a subtle process of change accumulation that causes a divergence among organisms and their genomes. However, this interpretation is an inheritance of a gradualistic view that has been challenged at the macroevolutionary, ecological and molecular level. Actually, when the complex architecture of genotype spaces is taken into account, the evolutionary dynamics of molecular populations becomes intrinsically non-uniform, sharing deep qualitative and quantitative similarities with slowly driven physical systems: nonlinear responses analogous to critical transitions, sudden state changes or hysteresis, among others. Furthermore, the phenotypic plasticity inherent to genotypes transforms classical fitness landscapes into multiscapes where adaptation in response to an environmental change may be very fast. The quantitative nature of adaptive molecular processes is deeply dependent on a network-of-networks multilayered structure of the map from genotype to function that we begin to unveil.

Keywords: adaptive multiscapes; genotype–phenotype map; molecular promiscuity; network-of-networks; phenotypic plasticity; punctuated dynamics.

Figure 1.

Punctuated behaviour in macroevolution, ecology and molecular dynamics. (a) Non-uniform pattern of extinctions (red symbols) and originations (green symbols) in the last 610 Myr (0 is present). Each point corresponds to a geological epoch, vertical lines separate geological periods, as indicated. The vertical axis gives the percentage of extinction/origination per estimated diversity at each epoch and per million years. Data from [12], geological epochs and periods as in [13]. (b) Minor changes in environmental variables might cause large, nonlinear responses in the state of a variety of systems. In some cases, two stable solutions (black curves) coexist with an unstable solution (red curve) for a range of values of a control parameter. The trajectories of systems might follow the path indicated by the grey arrows as that parameter increases, suffering a sudden jump from the upper to the lower branch. Hysteretic behaviour appears and prevents the recovery of the initial state when the environmental variable is reverted. When the system is initiated close to the unstable branch, it may attain any of the two possible stable solutions (black thin arrows). (c) In the genotype space, nodes represent genotypes and links correspond to single mutational moves. Heterogeneous molecular populations contain a set of genotypes with variable abundances, the latter represented through circle size. Fitter regions in genotype space might be difficult to find if there are few mutational incoming pathways (grey arrows). The population might be trapped in the red phenotype for a relatively long time (stasis) when compared with the transition to the new state once suitable mutations have appeared (punctuation).

Figure 2.

Some examples of simple GP maps. For each model, and from left to right, we depict an example phenotype, some of the sequences in its neutral network (mutations that do not change the phenotype are highlighted in red), and the schematic functional form of the probability distribution p(S) of phenotypes sizes S found in computational or analytical studies. (a) RNA sequence-to-minimum-free-energy secondary structure. Mutations that do not disrupt the secondary structure appear with different probability in loops or stacks. In two-letter alphabets, the distribution of phenotype sizes is compatible with a power-law function [49], while in four-letter alphabets p(S) is well fit by a lognormal distribution [50]. For long sequences, only the right-most part of p(S) can be seen under random sampling of the genotype space [50] (shaded). (b) The HP model, in its compact (as in the figure) or non-compact versions, has been studied as a model for protein folding. In non-compact versions, the distribution p(S) has a maximum at S = 1 and decays with a fat tail [51], while in compact versions p(S) resembles a lognormal distribution [52]. (c) toyLIFE is a minimal model with several levels. HP-like sequences are read and translated to proteins that interact through analogous rules to break metabolites. The p(S) of toyLIFE is compatible with a lognormal distribution [53]. (d,e) Effective models where phenotype is defined in relation to the composition of sequences allow to analytically calculate the functional form of p(S). Two examples are (d) Fibonacci's model [54], where p(S) follows a power-law distribution and (e) an RNA-inspired model [55] which yields a lognormal distribution of p(S).

Figure 3.

Genomic shifts result from the network-of-networks structure of the space of genotypes. Without loss of generality, we assume that λ_1,A < λ_1,B and the whole population is initially in network A. In (a–c), colours indicate the fitness of each node, as shown by the colour scale, and circle size is indicative of the number of individuals at each node. Though nodes in network B are represented with small circles, we assume they have no population initially. (a) Two weakly coupled regions of a unique NN. Differences in their eigenvalues only depend on differences in their topology. (b) Two different NNs with different fitness. The effect of fitness and topology can be separated, both affect their eigenvalues. (c) Two weakly connected regions in a fitness landscape. The effects of fitness and topology cannot be decoupled. (d) In all cases, the time of transitions is a stochastic variable, but the transition is fast once the mutational pathway is found (red curves, corresponding to different realizations of the process). In changing or noisy environments, the fitness value of each sequence might vary in time, so transitions are decorated by fluctuations (grey curve) whose strength grows as the tipping point is approached.

Figure 4.

Waddington's genetic assimilation under the light of genotype networks. Each layer of the network represents a different environment. Here, there are two environments: normal conditions and heat shock. As in previous figures, circle size is proportional to the number of individuals populating that node—small circles represent unpopulated nodes. The colour of each node represents now its phenotype, instead of its fitness. Note that every genotype appears in both layers, and that connections between them are the same in both environments: the only property that changes is the phenotype. (a) A population of flies develops wings with a cross-vein (the wild-type phenotype, wt, blue) when bred in normal conditions. (b) When exposed to heat shock during development, some of the flies in the original population develop new wings without cross-veins (the cross-veinless phenotype, cv, yellow). (c) Breeding the flies under heat shock and then selecting for those flies expressing the cross-veinless phenotype, the population drifts towards a new part of genotype space, exploring a new neutral network (or possibly increasing fitness in the new environment). (d) After some time, the population is bred again in normal conditions, and some flies in the population keep expressing the cross-veinless phenotype. Their phenotype has been genetically assimilated.