Fig 1.
Evolvability in the abstract model.
The average evolvability of individuals in the population, averaged over 50 independent runs is shown for the Control condition (with no extinction events), the Extinction 1000, 2000, and 4000 conditions (with extinctions regularly spaced respectively 1000, 2000,and 4000 generations, and the Extinction Random condition (where extinctions are spaced randomly with interval lengths chosen uniformly between 1000 and 4000 generations). In the Control condition there is no significant increase in evolvability following the initial 2000 generations, during which all niches become saturated (Mann-Whitney U-test;p > 0.05). However in each of the Extinction conditions, evolvability is significantly higher by the end of evolution (Mann-Whitney U-test;p < 0.05). The final average evolvability for each condition is statistically significantly different from each other condition (Mann-Whitney U-test;p < 0.05 for each pair-wise comparison of conditions’ final average evolvability). The conclusion is that the more frequent the extinction events, the more evolvable the final population.
Fig 2.
Representative evolvability snapshots in the abstract model.
A heatmap of evolvability over the space of niches is shown for representative runs of the Control and Extinction Random conditions at 2,000 and 15,0000 generations. Lighter shades indicate higher evolvability, with the same scale across all four snapshots. By 2,000 generations, the Control condition has nearly saturated all the niches (a). From the saturation point to the 15,000 generation snapshot (b), the Control condition evolves only through drift. In contrast, in this particular run of the Extinction Random condition, at 2,000 generations (c), evolution can be seen recovering from an extinction event. In particular, five clusters of organisms are spreading at different speeds (relative to their evolvability) through the space of niches. In this way more evolvable lineages will spread through more niches and will be more likely to persist across extinctions. At 15,000 generations (d), the Extinction Random condition exhibits higher evolvability than the Control. The conclusion is that extinction events lead to higher evolvability.
Fig 3.
Evolvability in the evolutionary robotics model.
The average evolvability of the population over generations of evolution is shown for the (a) wheeled robot and (b) biped robot tasks, averaged first over the population, and then over 60 independent runs. Relative to the Control condition, in all pair-wise comparisons populations in each of the Extinction conditions demonstrate significantly higher average evolvability (Mann-Whitney U test; p < 0.05), and variance in evolvability (Fligner’s test; p < 0.05) by 5000 generations. Figs (c) and (d) illustrate how evolvability is distributed in final populations; the evolvability of individuals in final populations is aggregated over all independent runs for each condition (bands in the boxes divide quartiles, and whiskers denote 1.5 times IQR). The conclusion is that extinction events tend to increase both evolvability.
Fig 4.
Behavioral diversity in the evolutionary robotics model.
The dynamics of how specializations (i.e. niches) are occupied over generations is shown for the (a) wheeled robot and (b) biped robot tasks, averaged over 60 independent evolutionary runs. The Control condition populates monotonically more specializations over evolution because it is not subject to extinction events. In contrast, in the Extinction conditions extinctions decimate the population at regular intervals. The individuals left untouched in a few specializations then repopulate the vacated ones. Lineages with greater phenotypic variability (i.e. greater evolvability) spread through more niches and thus are more likely to persist through extinctions. Accordingly, the Extinction conditions rebound increasingly quickly after each extinction event, indicating that later generations are more evolvable. In some conditions (e.g. the Extinction 600 in the wheeled robot task), despite regular decimation, the number of specializations eventually becomes greater than in the Control condition. (Note that when extinctions occur at random intervals, averaging obfuscates this dynamic. However, S2 Fig shows that individual Extinction Random runs indeed proceed through similar accelerating rebounds as the other Extinction conditions.
Fig 5.
Evolutionary success in the evolutionary robotics model.
The ability of evolution to generate well-adapted solutions is shown for the (a) wheeled robot and (b) biped robot tasks. In the (a) wheeled robot task, a successful robot can navigate the full extent of the maze. In the (b) biped robot task, a successful robot can walk a long distance. Pair-wise comparisons of average performance show that the Control condition never significantly outperforms any of the Extinction conditions, while the Extinction 600 condition significantly outperforms the Control condition in both domains (Mann-Whitney U-test for biped comparisons, Fisher’s exact test for maze comparisons; p < 0.05). Extinction events thus improve the final performance in both tasks.
Fig 6.
Simulated mobile robot used in the maze navigation experiment.
Rangefinder sensors allow the robot to perceive obstacles, and the motors controlling its wheels enable the robot to traverse its environment.
Fig 7.
Top-down view of the maze navigated by robots in the maze navigation experiment.
The circle indicates where a robot begins its trial. The trial is considered successful if the robot travels to the top left corner within 400 simulated timesteps. This particular maze is used because it is well studied [13, 27, 30, 31] and has been found to provide potential for interesting and diverse behaviors to evolve.
Fig 8.
The evolved ANN controlling the maze robot.
The initial topology is a fully connected network with no hidden nodes. Topologies change during evolution through structural mutations that add new nodes and connections. Connection weights are perturbed through continuous-valued weight mutations; the weights are capped between −3.0 and 3.0.
Fig 9.
The simulated robot used in the biped experiment.
The robot has motors that apply forces to achieve the joint angles that are output by the ANN. The controller has the challenging task of keeping the robot from falling while traveling as far from the starting point as possible.
Fig 10.
The evolved ANN controlling the biped robot.
As in the maze experiment, the initial topology is a fully connected network with no hidden nodes and evolves through structural mutations throughout evolution. The ANN outputs control the motors for each of the robot’s six degrees of freedom: one in both its left and right knees (LK and RK), and two in each hip (LH1, LH2, RH1, and RH2). The ANN receives as input whether each of its feet touch the ground. As in the maze experiment, evolution discovers ANNs that achieve high fitness in the task.