Regulatory mechanism predates the evolution of self-organizing capacity in simulated ant-like robots

The evolution of complexity is one of the prime features of life on Earth. Although well accepted as the product of adaptation, the dynamics underlying the evolutionary build-up of complex adaptive systems remains poorly resolved. Using simulated robot swarms that exhibit ant-like group foraging with trail pheromones, we show that their self-organizing capacity paradoxically involves regulatory behavior that arises in advance. We focus on a traffic rule on their foraging trail as a regulatory trait. We allow the simulated robot swarms to evolve pheromone responsiveness and traffic rules simultaneously. In most cases, the traffic rule, initially arising as selectively neutral component behaviors, assists the group foraging system to bypass a fitness valley caused by overcrowding on the trail. Our study reveals a hitherto underappreciated role of regulatory mechanisms in the origin of complex adaptive systems, as well as highlights the importance of embodiment in the study of their evolution.


Supplementary
. Measures of group foraging performance, highlighting the effect of pheromone communication. The source data are the same as Fig. 2. Total number of foraging bouts per swarm is a measure of swarm fitness. Bars indicate that the food was found by robots in state S1 (white, searching independently) or S3 (orange, being recruited). Error bars show SD (n = 100 000 trials each).    In this note, we describe a detail of the population genetic analysis of stochastic tunneling. We follow Proulx's formula (1) to calculate (the probability of extinction of the final genotype lineage arising from a single swarm of the intermediate genotype with relative swarm fitness rx; x ∈ {0, -}) for Wright-Fisher populations. In the Wright-Fisher formulation, unlike the Moran model, the population at generation t + 1 is produced from the population at generation t all at once. The probability distribution of an intermediate genotype at generation t + 1 is given by the following binomial distribution: which represents the probability that the population (size = N) including i mutants (fitness relative to resident = r) at generation t changes to the population including j mutants at generation t + 1.
We define as the probability that no successful secondary (final) genotype with relative swarm fitness a (probability of fixation = U(a)) is produced starting from the state where i swarms with intermediate genotype are present. For each possible state i, is given by: Waiting time comparisons. Each of the 50 triplets of relative fitness values (r0, r-, and a), together with the population genetic model of stochastic tunneling described above, yielded a pair of analytical estimates of waiting time that assumed the evolutionary paths with, respectively, neutral and inferior intermediates. We compared the pairs of estimates and regarded the path with the shorter waiting time as the realized one in an evolving population. We repeated the procedure (i.e., resampling 50 quadruplets) 1000 times to obtain the distribution of the frequency of evolutionary runs (out of 50) that had a path with the neutral intermediate genotype {1,0,1;0}.
We made a simplified assumption about the genotype-phenotype mapping of robotic traits, in contrast to a standard approach taken by evolutionary robotics studies (e.g., 2, 3) such as a neural network with synaptic links evolving by genetic algorithm. In evolutionary swarm robotics, complex outcomes are derived from two hierarchical sources: the complexity of genotype-phenotype mapping attributed to each agent and the complexity of interactions between agents. Our approach separates these two sources, making the former simple and the latter intact. The simplified assumption of genetic architectures will complement the standard approach by fostering a deeper understanding of underlying evolutionary forces that lead to complex adaptive systems.
Although simple, our genotype-phenotype mapping enables biological realism of the phenotypes. First, a biologically realistic interpretation of the selectively neutral allele b3 = 1 in the multilocus genotype {b1,b2,b3;p} = {1,0,1,0} (i.e., the behavior presuming pheromone communication in its absence) could be that the trait b3 involves the behavior that is specifically released when colliding with the food-laden agent (with state S2). The difference between b1 = 1 and b3 = 1 is that the latter requires a cognitive ability to assess collision partners (i.e., with or without food).
We can also consider different genetic coding of the three behavioral traits (b1-b3) to treat correlated phenotypes. Because the priority-giving behavior is phenotypically the same for b1 to b3, it is reasonable to consider their pleiotropic origin. First, we assume that the prioritygiving behavior is regulated irrespective of the three internal states (S1-S3) of the robots. This means that b2 = b3 = 1 is a pleiotropic byproduct of b1 = 1. Each evolutionary simulation run continued until the population reached the genotype with the highest swarm fitness among possible genotypes. All evolutionary simulations (50 replicates) resulted in the genealogy undergoing {0,0,0;0}→{1,1,1;0}→{1,1,1;1}, indicating that the regulatory mechanism (b1 = b2 = b3 = 1) predated the pheromone detection ability (p = 1). This result is easily explained by a comparison of swarm fitness; that is, the swarm fitness of the genotype {1,1,1;0} is much greater than that of the genotype {0,0,0;0} than is that of the genotype {0,0,0;1} (Fig. 2).
These alternatives for genetic coding assume that the behaviors on the foraging trail (b2 = 1 and b2 = b3 = 1) are a byproduct caused by the same genetic control as b1 = 1. Since b1 = 1 has an adaptive function in the absence of pheromone communication by improving the swarm fitness (Fig. 2), pleiotropically induced b2 = b3 = 1 (in the first case) and b3 = 1 (in the second case) can be regarded as a case of spandrel (4), that is, a neutral byproduct of previous adaptation in other contexts (see Discussion). The above analyses confirmed the evolutionary precedence of regulatory behavior irrespective of genetic coding of phenotypes or of the number of behavioral genes compared to the pheromone-responsiveness gene.