modularity

Le Nagard H, Chao L & Tenaillon O 2011 The emergence of complexity and restricted pleiotropy in adapting networks. BMC Evol Biol 11:326.

  • the cost results from the difficulty of having to optimize many phenotypes simultaneously
  • it is manifested by the decreasing fraction of beneficial mutations as dimensionality increases
  • the rate of adaptation decreases
  • the drift load increases
  • drift load represents the loss of fitness due the effects of genetic drift on the fixation rate of beneficial and deleterious mutations
  • although previous studies have used Fisher's geometrical model to examine the effect of complexity on evolution, none have allowed dimensionality to change as a result of evolution and adaptation
  • experimental studies of complexity with real biological organisms are possible
  • a systematic investigation is still difficult
  • we chose therefore to use computational models employing artificial neural networks evolving asexually under a mutation-selection-drift process as an alternative
  • the final evolutionary process we used can be called "adaptive dynamics" [29] since it is similar to the one used in this field
  • populations were always monomorphic except when a single mutant appeared
  • based on the mutant fitness fi relative to the resident fitness f0, the mutant either immediately invaded the population and became the new resident or disappeared
  • the probability of invasion P(f0 → fi), depended on the evolving population size N and, using Sella and Hirsh formalism [30], was computed as:
  • P(f0 → fi) = (1 − (f0 / fi)2) / (1 − (f0 / f1)2N) ... (5)
  • the negative correlation between pleiotropy and our three metrics of complexity indicated that complexity evolved by incorporating mutations with restricted effects on the response of the networks
  • to determine whether the restriction also created structuring in which particular group of weights interacted preferentially with different subsets of phenotypes, we searched for modularity by applying the bipartite leading eigen vector approach to the matrix of connections from weight to phenotypes
  • some large scale estimates of pleiotropy within an organism have only been provided recently
  • consistently with the results of our toy model, analysis of mouse QTL [38], or yeast, nematode and mouse knock outs [39] have suggested that pleiotropy was very restricted [37]
  • mutations affected a fraction of the phenotypes measured and not all as considered classically for a long time in Fisher's geometric model
  • previous analyses of phenotypic complexity have mostly focused on the consequences of complexity on evolution, rather than on the selective forces acting on it
  • it appeared costly to have a high complexity due to a limited number of beneficial mutations
  • a limited rate of adaptation
  • or a higher drift load
  • these models assumed that all organisms independently of their complexities could potentially reach the same maximal fitness
  • if strong correlations between mutations effects exist within an organism, this organism has low complexity because it can only explore a fraction of the phenotypic space
  • it could not reach a high fitness when placed in a challenging environment
  • the way to reach a higher fitness is then to decouple mutation effects such that mutations affect a subset of phenotypes and not all
  • the accessible phenotypic space becomes larger and its number of dimensions, i.e. the phenotypic complexity of the organism is increased
  • restrictive pleiotropy's link to complexity is consistent with Ohno's hypothesis
  • much as how restrictive pleiotropy can decouple two phenotypes in our model, gene duplication allows the two gene copies to evolve freely
  • sub-functionalization following a gene duplication (in which the two derived copies of a gene are required to replace the function of the ancestral gene) provides a perfect example of a mechanism by which pleiotropy can be reduced
  • as the selection acting on complexity appears to be indirect in our system (Figure 7), our results are compatible with the idea that chance or genetic drift may play a role in the emergence of complexity [42]
  • this is equivalent to the idea that sub-functionalization may initially result from non-selective forces, but may in the longer term be recruited by natural selection to fine tune the adaptation and therefore support long term incremental evolution of complexity