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The evolutionary origins of modularity
Jeff Clune, Jean-Baptiste Mouret, Hod Lipson
TL;DR
The paper addresses the unresolved question of why modularity evolves despite the indirect nature of selection for evolvability. Using computational evolutionary experiments, it compares performance-only networks with networks also selected to minimize connection costs, finding that the latter become more modular and more evolvable.
Problem
The paper asks why modularity evolves, given that evolvability provides only an indirect long-term selective advantage.
Method
Computational evolutionary experiments compare networks selected for performance alone with networks selected for performance and minimized connection costs.
Results
Networks selected for performance and connection costs are significantly more modular and adapt faster to new environments than performance-only networks.
Takeaways & Limitations
Selection to reduce connection costs can produce modular networks even in unchanging environments, supporting connection costs as an evolutionary source of modularity.
Takeaways & Limitations
The experiments use computational networks in which nodes are never added or removed.
Abstract
from arXiv · showhide
A central biological question is how natural organisms are so evolvable (capable of quickly adapting to new environments). A key driver of evolvability is the widespread modularity of biological networks--their organization as functional, sparsely connected subunits--but there is no consensus regarding why modularity itself evolved. While most hypotheses assume indirect selection for evolvability, here we demonstrate that the ubiquitous, direct selection pressure to reduce the cost of connections between network nodes causes the emergence of modular networks. Experiments with selection pressures to maximize network performance and minimize connection costs yield networks that are significantly more modular and more evolvable than control experiments that only select for performance. These results will catalyze research in numerous disciplines, including neuroscience, genetics and harnessing evolution for engineering purposes.
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- The article is associated with computational biology, evolution, and systems biology.
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Research
The article is identified as a citation in the Proceedings of the Royal Society B.
- The paper is cited as Clune, Mouret, and Lipson, published in 2013 in Proceedings of the Royal Society B.
1. Introduction
The paper asks why modularity evolves and tests whether direct selection to reduce connection costs can produce modular, evolvable networks. Computational evolutionary experiments compare performance-only selection with joint selection for performance and connection costs across pattern-recognition tasks.
- 1. Introduction: Evolvability is rapid adaptation to novel environments, and biological network modularity is proposed as a major contributor.
- 1. Introduction: Modularity consists of highly connected node clusters that are sparsely connected to other clusters.
- 1. Introduction: The study tests whether modularity evolves as a byproduct of selection to reduce network connection costs rather than because it directly conveys evolvability.
- 1. Introduction: Experiments compare performance-alone selection (PA) with multi-objective selection for performance and connection costs (P&CC).The P&CC cost objective affects selection probabilistically 25 per cent of the time.
- 1. Introduction: Networks solve Boolean pattern-recognition tasks using eight inputs representing an eight-pixel retina and answer whether objects occur on both or either side.
- 1. Introduction: Network modularity is evaluated with an approximation of the modularity metric Q, comparing within-module edges with random-network expectations.
2. Results
Selecting networks to maximize performance while minimizing connection costs produces more modular, higher-performing, and more evolvable networks than performance-only selection. Connection costs push evolution toward low-cost modular regions, and their effects combine with changing environments across task types.
- After 25 000 generations, P&CC networks had higher modularity than PA networks: Q = 0.42 [0.25,0.45] versus Q = 0.18 [0.16,0.19].Left–right decomposition occurred in 56% of P&CC trials and 0% of PA trials.
- P&CC networks outperformed PA networks despite the additional connection-cost constraint: median performance was 1.0 [1.0,1.0] versus 0.98 [0.97,0.98].P&CC networks also had fewer nodes and connections.
- Connection costs pushed populations from high-cost, low-modularity regions toward low-cost, modular regions containing higher-performing solutions.High-performing networks showed an inverse correlation between cost and modularity, while performance-only treatments remained in some high-cost, low-modularity regions.
- P&CC networks adapted faster after environmental transfer, requiring 3.0 [2.0,5.0] versus 65 [62,69] generations from L-AND-R to L-OR-R.The reverse transfer likewise required 12.0 [7.0,21.0] versus 222.5 [175.0,290.0] generations.
- Combining P&CC with MVG produced higher modularity than either force alone, while P&CC remained comparable to the strongest MVG effect.P&CC produced more modularity when environmental change was too slow for MVG to exert a strong effect.
- P&CC produced qualitatively similar modularity and performance advantages in Boolean logic tasks, including separable and hierarchically nested XOR problems.Separate modules appeared in nearly every P&CC trial and almost never in PA trials.
3. Discussion and conclusion
The paper argues that selection to reduce connection costs can generate modularity, which may then support evolvability. It also identifies implications for evolutionary engineering and biological-network modeling.
- 3. Discussion and conclusion: Selection to reduce connection costs produces modular networks even in unchanging environments.The authors describe this modularity as potentially initiating a process later amplified by selection for evolvability.
- 3. Discussion and conclusion: Cost-driven modularity may bootstrap evolvability because selection for evolvability cannot act until sufficient modularity exists.
- 3. Discussion and conclusion: The findings may help evolutionary engineering develop modular designs, a longstanding challenge in the field.
- 3. Discussion and conclusion: Functional modularity can make synthetically evolved networks easier to understand and support efforts to evolve accurate biological-network models.
4. Methods
The methods evolve feed-forward networks on visual and Boolean tasks under alternative multi-objective treatments, then compare performance, modularity, cost, and evolvability-related outcomes. Repeated stochastic trials, statistical testing, alternate cost functions, and landscape sampling assess the robustness of the comparisons.
- Experimental design: Each treatment was repeated 50 times with different random-number-generator seeds, using the highest-performing network per trial for analyses.Main experiments lasted 25,000 generations with populations of 1,000.
- Statistics: Medians with 95% bootstrapped confidence intervals were reported, and statistical significance was assessed with the Mann–Whitney–Wilcoxon rank-sum test.
- Selection treatments: P&CC treatments minimized connection costs based on connection length, while P&CC-NC used the number of connections; PA and P&RO supplied comparison treatments.For length costs, hidden-node positions were optimized for the network topology while input and output locations remained fixed.
- Network models: The study used feed-forward network models with layered nodes, bounded integer weights and thresholds, and discrete layer-by-layer information flow.The model was applied to retina, five-XOR, and hierarchical-XOR problems.
- Evolutionary algorithm: The evolutionary algorithm simultaneously optimized multiple objectives and searched for trade-offs on a Pareto front.Mutations could add, remove, or alter network connections and parameters across generations.
- Robustness checks: P&CC produced significantly higher modularity and performance than PA under biased mutation-rate experiments.Randomly sampling more than two billion solutions found a best retina performance of 62 out of 256 patterns, compared with at least 93% for routinely evolved solutions.
(k) Video of networks from each treatment evolving
The supplementary materials provide a video illustrating network changes across evolutionary time and make the experimental data, source code, and analysis scripts freely available in a permanent online archive.
- Video of networks from each treatment evolving: A video illustrates network changes across evolutionary time for the PA and P&CC treatments.
- Video of networks from each treatment evolving: Experimental data, source code, and analysis scripts are freely available in a permanent online archive.