# Quantifying the Selective, Stochastic, and Complementary Drivers of Institutional Evolution in Online Communities

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Institutional Change

#### 1.1.1. The Arguments for Adaptive Selection

#### 1.1.2. Arguments for Stochasticity

#### 1.1.3. Integrating and Disentangling Selective and Stochastic Forces

#### 1.2. The Price Equation

#### 1.3. Online Communities

**RQ1:**

#### 1.4. Time Variance and Institutional Diversity

**RQ2:**

**RQ3:**

## 2. Materials and Methods

#### 2.1. Data

#### 2.2. Price Equation

_{i}increases without any change in the frequency of administrative rule changes within community ${z}_{i}$. This fitness-correlated process is conceptually equivalent to selection acting at the scale of organizations.

#### 2.3. Bet-Hedging and Information Theory

## 3. Results

#### 3.1. The Price Equation Result

_{i}) and membership size (p

_{i}). We then calculated the average rule proportion weighted by membership size (m) and variations of rule proportions among communities. We partitioned the Price equation into slope-intercept forms (Equation (6). In this equation, the slope reflected the strength of selective forces, and the intercept represented the strength of stochastic forces [58]. As shown in Figure 3, each data point referred to a timestamp associated with variations in rule fractions VAR [z

_{i}] and the average population reach, m. We estimated that communities with administrative rules face positive selective forces (β

_{admin}= 0.117, p < 0.001) and negative stochastic forces (E [δ]

_{admin}= −3.602, p < 0.01). This indicated that, on the one hand, administrative rules have a strong positive correlation with community success in terms of recruiting and maintaining members, resulting in a higher probability that this type of rule structure will be learned by other communities. In other words, this direct, fitness-related benefit contributes to the growth of administrative rules. On the other hand, when driven by stochastic factors, including a lack of information, cultural preference/resistance, path dependency, or individual learning, administrators tend to reduce the proportion of administrative rules, regardless of their positive correlation with community fitness.

_{admin}= 0.147, p < 0.05, see Figure 4a), indicating that information rules are beneficial for community survival.

#### 3.2. Bet-Hedging Result

_{admin}= 1; See Figure 5). In other words, larger numbers of administrative rules can be attributed solely to the earlier implementation of administrative rules. The Price equation suggests that the theoretically optimal strategy is equivalent to the end result of pure natural selection. As such, it is consistent with the Price equation result, i.e., that a positive selective force is the only reason for the increase in the number of administrative rules.

_{information}= 0.703) showed that although informational rules generally have a positive correlation with community survival and success, this correlation varies over time. In a period when the growth rate of informational rules is low, the share of other rules helps the community in difficult times. As for communication and economic rules, although they do not provide individual selective advantages, they can be subsidized to help communities during environmental changes (d

_{communication}= 0.146; d

_{economics}= 0.420).

## 4. Discussion

#### 4.1. Contributions and Implications

#### 4.2. Limitations

#### 4.3. Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Plugins in Minecraft

## References

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**Figure 1.**Model setup (

**a**) Rule share pie chart of a community i at time t: each community has a fraction of administrative rules (${z}_{i}$); (

**b**) Membership size (${p}_{i}$ ) by total rule number (${n}_{i}$) scatter plot at time t; (

**c**) the histogram of the administrative rule fraction (${z}_{i}$) changes from time t to time t + 1, which also changes the average population reach m.

**Figure 2.**Environmental changes over time cause changes in the number of communities but do not seem to change the overall relative proportions of rule types in the population, except for administrative rules. The Price equation assumes a constant correlation between population growth and the implementation of one type of rule. However, the correlation may vary over time in a fast-changing environment. The changing bandwidth of administrative rules in this figure demonstrates that various rules are influenced differently by environmental changes.

**Figure 3.**Communities subject to administrative rules face positive selective forces and negative stochastic forces. Administrative rules have a positive correlation with community fitness, which leads to a higher likelihood of this type of rule structure being learned by other communities. This direct fitness-related benefit is associated with the growth of administrative rules. On the other hand, other “stochastic” forces, including a lack of information, cultural preferences, cultural resistance, and random experiments, reduce the implementation of administrative rules.

**Figure 4.**Communities with informational rules experience positive selective forces, while there are no effects of communication and economic rules on community prevalence. We found positive selection over informational rules but not negative stochastic forces (

**a**). At the same time, neither selection (the slope) nor stochasticity (intercept) in communication (

**b**) and economic rules (

**c**) diverged significantly from 0 over time.

**Figure 5.**Most rules showed a maximum in their selective effect in combination with the other rule types. The bars in the figure illustrate the optimal distribution of rule implementation to maximize the growth rate of one type of rule, demonstrating the influence of implementing other types of rules on this type. For information rules to be expressed at a maximum rate in the population, the calculation suggests that they should be implemented with a 30% mix of other rule types. (This is distinct from the question of whether that maximum is positive, i.e., whether information rules are positively selected for, as shown in Figure 3). Implementing a mix of rules can help communities survive periods when the direct benefits of information rules are low. As a result, institutional diversity contributes to the long-term growth of communication, information, and economic rules. The optimal distribution of administrative rules, i.e., 100%, suggests an absolute strategy for the growth of this dominant rule type. This may be an artifact of the strong positive selection that communities with administrative rules face, particularly relative to other rule types. It is also consistent with the conclusion that the correlation between administrative rules and community fitness does not vary as much over time as it does with other rule types.

State | Growth of Rule i | Growth of Other Rules |
---|---|---|

Good state for centralized rules | G_{1} | g_{1} |

Bad state for centralized rules | g_{2} | G_{2} |

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**MDPI and ACS Style**

Zhong, Q.; Frey, S.; Hilbert, M.
Quantifying the Selective, Stochastic, and Complementary Drivers of Institutional Evolution in Online Communities. *Entropy* **2022**, *24*, 1185.
https://doi.org/10.3390/e24091185

**AMA Style**

Zhong Q, Frey S, Hilbert M.
Quantifying the Selective, Stochastic, and Complementary Drivers of Institutional Evolution in Online Communities. *Entropy*. 2022; 24(9):1185.
https://doi.org/10.3390/e24091185

**Chicago/Turabian Style**

Zhong, Qiankun, Seth Frey, and Martin Hilbert.
2022. "Quantifying the Selective, Stochastic, and Complementary Drivers of Institutional Evolution in Online Communities" *Entropy* 24, no. 9: 1185.
https://doi.org/10.3390/e24091185