Linking the evolution of evolvability with generalisation in learning systems

Explaining how organisms adapt in novel selective environments is central to evolutionary biology [1–5]. Living organisms are both robust and capable of change. The former property allows for stability and reliable functionality against genetic and environmental perturbations, while the latter provides flexibility allowing for the evolutionary acquisition of new potentially adaptive traits [5–9]. This capacity of an organism to produce suitable phenotypic variation to adapt to new environments is often identified as a prerequisite for evolvability, i.e., the capacity for adaptive evolution [7, 10, 11]. It is thus important to understand the underlying variational mechanisms that enable the production of adaptive phenotypic variation [6, 7, 12–18].

Phenotypic variations are heavily determined by intrinsic tendencies imposed by the genetic and the developmental architecture [18–21]. For instance, developmental biases may permit high variability for a particular phenotypic trait and limited variability for another, or cause certain phenotypic traits to co-vary [6, 15, 22–26]. Developmental processes are themselves also shaped by previous selection. As a result, we may expect that past evolution could adapt the distribution of phenotypes explored by future natural selection to amplify promising variations and avoid less useful ones by evolving developmental architectures that are predisposed to exhibit effective adaptation [10, 13]. Selection though cannot favour traits for benefits that have not yet been realised. Moreover, in situations when selection can control phenotypic variation, it nearly always reduces such variation because it favours canalisation over flexibility [23, 27–29].

Developmental canalisation may seem to be intrinsically opposed to an increase in phenotypic variability. Some, however, view these notions as two sides of the same coin, i.e., a predisposition to evolve some phenotypes more readily goes hand in hand with a decrease in the propensity to produce other phenotypes [8, 30, 31]. Kirschner and Gerhart integrated findings that support these ideas under the unified framework of facilitated variation [8, 32]. Similar ideas and concepts include the variational properties of the organisms [13], the self-facilitation of evolution [20] and evolution as tinkering [33] and related notions [6, 7, 10, 12]. In facilitated variation, the key observation is that the intrinsic developmental structure of the organisms biases both the amount and the direction of the phenotypic variation. Recent work in the area of facilitated variation has shown that multiple selective environments were necessary to evolve evolvable structures [25, 27, 34–36]. When selective environments contain underlying structural regularities, it is possible that evolution learns to limit the phenotypic space to regions that are evolutionarily more advantageous, promoting the discovery of useful phenotypes in a single or a few mutations [35, 36]. But, as we will show, these conditions do not necessarily enhance evolvability in novel environments. Thus the general conditions which favour the emergence of adaptive developmental constraints that enhance evolvability are not well-understood.

To address this we study the conditions where evolution by natural selection can find developmental organisations that produce what we refer to here as generalised phenotypic distributions—i.e., not only are these distributions capable of producing multiple distinct phenotypes that have been selected in the past, but they can also produce novel phenotypes from the same family. Parter et al. have already shown that this is possible in specific cases studying models of RNA structures and logic gates [34]. Here we wish to understand more general conditions under which, and to what extent, natural selection can enhance the capacity of developmental structures to produce suitable variation for selection in the future. We follow previous work on the evolution of development [25] through computer simulations based in gene-regulatory network (GRN) models. Many authors have noted that GRNs share common functionality to artificial neural networks [25, 37–40]. Watson et al. demonstrated a further result, more important to our purposes here; that the way regulatory interactions evolve under natural selection is mathematically equivalent to the way neural networks learn [25]. During evolution a GRN is capable of learning a memory of multiple phenotypes that were fit in multiple past selective environments by internalising their statistical correlation structure into its ontogenetic interactions, in the same way that learning neural networks store and recall training patterns. Phenotypes that were fit in the past can then be recreated by the network spontaneously (under genetic drift without selection) in the future or as a response to new selective environments that are partially similar to past environments [25]. An important aspect of the evolved systems mentioned above is modularity. Modularity has been a key feature of work on evolvability [6, 29, 41, 42] aiming to facilitate variability that respects the natural decomposable structure of the selective environment, i.e., keep the things together that need to be kept together and separate the things that are independent [6, 12, 20, 41]. Accordingly, the system can perform a simple form of generalisation by separating knowledge from the context in which it was originally observed and re-deploying it in new situations.

Here we show that this functional equivalence between learning and evolution predicts the evolutionary conditions that enable the evolution of generalised phenotypic distributions. We test this analogy between learning and evolution by testing its predictions. Specifically, we resolve the tension between canalisation of phenotypes that have been successful in past environments and anticipation of phenotypes that are fit in future environments by recognising that this is equivalent to prediction in learning systems. Such predictive ability follows simply from the ability to represent structural regularities in previously seen observations (i.e., the training set) that are also true in the yet-unseen ones (i.e., the test set). In learning systems, such generalization is commonplace and not considered mysterious. But it is also understood that successful generalisation in learning systems is not for granted and requires certain well-understood conditions. We argue here that understanding the evolution of development is formally analogous to model learning and can provide useful insights and testable hypotheses about the conditions that enhance the evolution of evolvability under natural selection [42, 43]. Thus, in recognising that learning systems do not really ‘see into the future’ but can nonetheless make useful predictions by generalising past experience, we demystify the notion that short-sighted natural selection can produce novel phenotypes that are fit for previously-unseen selective environments and, more importantly, we can predict the general conditions where this is possible. This functional equivalence between learning and evolution produces many interesting, testable predictions (Table 1).

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larger image TIFF original image Download: 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. https://doi.org/10.1371/journal.pcbi.1005358.t001

In particular, the following experiments show that techniques that enhance generalisation in machine learning correspond to evolutionary conditions that facilitate generalised phenotypic distributions and hence increased evolvability. Specifically, we describe how well-known machine learning techniques, such as learning with noise and penalising model complexity, that improve the generalisation ability of learning models have biological analogues and can help us understand how noisy selective environments and the direct selection pressure on the reproduction cost of the gene regulatory interactions can enhance evolvability in gene regulation networks. This is a much more sophisticated and powerful form of generalisation than previous notions that simply extrapolate previous experience. The system does not merely extend its learned behaviour outside its past ‘known’ domain. Instead, we are interested in situations where the system can create new knowledge by discovering and systematising emerging patterns from past experience, and more notably, how the system separates that knowledge from the context in which it was originally observed, so that it can be re-deployed in new situations.

Some evolutionary mechanisms and conditions have been proposed as important factors for improved evolvability. Some concern the modification of genetic variability (e.g., [36, 44, 45] and [46]), while others concern the nature of selective environments and the organisation of development including multiple selective environments [36], sparsity [47], the direct selective pressure on the cost of connections (which can induce modularity [27, 44] and hierarchy [48]), low developmental biases and constraints [49] and stochasticity in GRNs [50]. In this paper, we focus on mechanisms and conditions that can be unified and better understood in machine learning terms, and more notably, how we can utilise well-established theory in learning to characterise general conditions under which evolvability is enhanced. We thus provide the first theory to characterise the general conditions that enhance the evolution of developmental organisations that generalise information gained from past selection, as required to enhance evolvability in novel environments.