Discussion

Open-endedness in fitness landscape is one of the features of technological evolution. However, the nature of this aspect is understudied especially in fields like cultural evolution where many have pointed out the mechanisms that facilitate the growth in technology under a closed fitness landscape. The main goal of this study was to examine the architecture of open-ended fitness landscape through the evolution of logical circuits with varying group sizes, which is one of the mechanisms identified in cultural evolution \cite{Henrich_2004,henrich2017}.
We investigated this through a computer simulation with agents creating logical circuits using circuits that they themselves made in the past trials \cite{Arthur_2006}. In each condition, we added agents that simultaneously created circuits. Agents in group size larger than one were able to use circuits that were created by other agents in the next trial. For simplicity, we excluded interaction between agents to see if increasing in group size alone had any effect on cumulative advancement in technological innovations.
The key results were threefold. As expected we found that in open-ended fitness landscape, group size increased the speed of innovations. When innovation was split between invention and improvement, we found that results differed between the two. In invention, the speed that invention increased was lower than the baseline (which was the n-times the speed of group size-1) and the way that inventions accumulated were similar to a repetitive sigmoidal function. On the other hand, improvement matched that of the baseline and the rate in which improvement increased was square root times the group size, which means that the productivity of group size becomes smaller as group size becomes bigger.
One reason for the decrease in the effect of group size in improvement could be due to a chance that one of the agents in the group create an improvement so efficient that other agents could not improve any further. The chance that any agent create an efficient circuit increase as group size increase. Additional analysis is needed to see whether such efficient circuits were made faster as group size became larger.
The interesting finding is that the function of invention and improvement differed. Especially, invention resembled a sigmoidal function, which is similar to the technology s-curve \cite{christensen2013,foster1986,CHRISTENSEN_2009}. As mentioned by Arthur and Polak (2006), the rapid take-off of invention is subject to goals (e.g. AND circuit, OR circuit, etc.) being met. This means that when a goal is met, inventions using that goal circuit rapidly increase. However, at some point, the limits of using that goal circuit are reached and the growth of inventions stops. Such a result was never reported in cultural evolutionary models and can be considered as a key finding in this study. Nonetheless, since this is a post hoc analysis, whether or not the results that inventions are the same as the technology s-curve is open for debate. Additionally, the reason that this function was not seen in improvement is also an open question and needs further investigation.
Besides the difference between invention and improvement, one of the take-home messages is that even if group size increases, the productivity of one agent being added decreases as group size becomes bigger. This also suggests that an increase in group size is sufficient to maintain technology but not enough to accelerate the speed of innovations. However, we did not include synergetic interactions for simplicity in this study which means there is still room to argue that with interaction, group size does increase the speed of innovations. On the other hand, behavioral sciences have shown that group processes do not always have a positive effect (e.g. groupthink, social loafing). We need further examination to see whether interaction does increase the speed of innovations in an open-ended fitness landscape.
There are still many candidates that may affect the speed of innovations. One example is network structure \cite{Frenken_2006,Powell_1996}\cite{Derex_2016} have reported experimentally that partial connectivity increases the innovations of a group more than a full connected group. Such mechanisms are needed to be explored in future research. So in order to clarify the traits of innovations, not only do we need simulational studies such as this, but empirical studies that bridge between simulations and real-world phenomena.