Table 1.
Predictions made by porting key lessons of learning theory to evolutionary theory.
Confirmed by experiment: † Conditions that facilitate generalised phenotypic distributions, ‡ How generalisation changes over evolutionary time, ◇ Conditions that facilitate generalised phenotypic distributions and ⋆ Sensitivity analysis to parameters affecting phenotypic generalisation.
Fig 1.
Pictorial representation of phenotypes.
(Top) Schematic representation of mapping from phenotypic pattern sequences onto pictorial features. Each phenotypic ‘slot’ represents a set of features (here 4) controlling a certain aspect of the phenotype (e.g., front wings, halteres and antennae). Within the possible configurations in each slot (here 16), there are two particular configurations (state A and B) that are fit in some environment or another (see Developmental Model in S1 Appendix). For example, ‘+ + −−’ in the second slot (from the top, green) of the phenotypic pattern encodes for a pair of front wings (state B), while ‘− − ++’ encodes for their absence (state A). States A and B are the complement of one another, i.e., not neighbours in phenotype space. All of the other intermediate states (here 14) are represented by a random mosaic image of state A and B, based on their respective distance. dA indicates the Hamming distance between a given state and state A. Accordingly, there exist potential intermediate states (i.e., 4 for dA = 1, 6 for dA = 2 and 4 for dA = 3). (Bottom) Pictorial representation of all phenotypes that are perfectly adapted to each of eight different environments. Each target phenotype is analogous to an insect-like organism comprised of 4 functional features. The grey phenotypic targets correspond to bit-wise complementary patterns of the phenotypes on the top half of the space. For example, in the rightmost, top insect, the antennae, forewings, and hindwings are present, and the tail is not. In the rightmost, bottom insect (the bitwise complement of the insect above it), the antennae, forewings, and hindwings are absent, but the tail is present. We define the top row as ‘the class’ and we disregard the bottom complements as degenerate forms of generalisation.
Fig 2.
Conditions that facilitate generalised phenotypic distributions.
Potential phenotypic distributions induced by the evolved developmental process under 1) different time-scales of environmental switching, 2) environmental noise (κ = 35 × 10−4) and 3) direct selection pressure for weak (λ = 38) and sparse connectivity (λ = 0.22). The organisms were exposed to three selective environments (a) from the general class (i). Developmental memorisation of past phenotypic targets clearly depends on the time-scale of environmental change. Noisy environments and parsimony pressures enhance the generalisation ability of development predisposing the production of previously unseen targets from the class. The size of the insect-like creatures describes relative frequencies and indicates the propensity of development to express the respective phenotype (phenotypes with frequency less than 0.01 were ignored). Note that the initial developmental structure represented all possible phenotypic patterns equally (here 212 possible phenotypes).
Fig 3.
How generalisation changes over evolutionary time.
The match between phenotypic distributions generated by evolved GRN and the target phenotypes of selective environments the developmental system has been exposed to (training error) and all selective environments (test error) against evolutionary time for (A) moderate environmental switching, (B) noisy environments, (C) favouring weak connectivity and (D) favouring sparse connectivity. The vertical dashed line denotes when the ad-hoc technique of early stopping would be ideal, i.e. at the moment the problem of over-fitting begins. Favouring weak connectivity and jittering exhibits similar effects on test error as applying early stopping.
Fig 4.
Role of the strength of parsimony pressure and the level of environmental noise.
The match between phenotypic distributions and the selective environments the network has been exposed to (training error) and all possible selective environments of the same class (generalisation error) for (A) noisy environments against parameter κ and under the parsimony pressure weak (B) and sparse (C) connectivity against parameter λ.
Fig 5.
Generalised developmental organisations improve the rate of adaptation to novel selective environments.
Boxplot of the generations taken for the evolved developmental systems to reach the target phenotype for all potential selective environments under different evolutionary conditions. The developmental architecture is kept fixed and only the direct effects on the embryonic phenotype are free to evolve. Organisms that facilitate generalised phenotypic distributions, such as the ones evolved in noisy environments or under the direct pressure on the cost connections, adapt faster to novel selective environments exhibiting enhanced evolvability. The outliers indicate the inability of the corresponding evolved developmental structures to reach that selective target due to strong developmental constraints.