# The Evolution of Service Ecosystems Based on the Lotka-Volterra Model
## 5 Service Co-Opetition Evolution Experimental Analysis
### Computational Experimental Analysis  
In the computational experimental system, the interaction coefficient \(\alpha\) between atomic services is defined as follows: when different types of service agent nodes cooperate to fulfill a composite demand, they can provide a service volume equivalent to \((1+\alpha)\) times the original amount. In the computational experiment, the coefficient is specifically set to 0.1, 0.5, and 0.9 to observe the evolutionary paths of the service ecosystem under different levels of competition between original atomic services. By parameterizing in this way, we can explore the dynamic behavior of the service ecosystem under various competitive pressures, revealing or verifying potential evolutionary laws. Different time stamps of 0, 400, and 800 ticks are captured during the computational experiments. The evolution process is shown in the Figures 9-11 below:  
As shown in the figures, at the initial stage (0 ticks), 25 service agent nodes of two different atomic types with varying attributes are randomly generated in the environment, represented by yellow and blue dots. As time progresses, the service ecosystem evolves, and different attribute demand agent nodes, marked by red dots, are generated in a stable total amount. These demand agent nodes have various demands for different types and quantities of services. When atomic service agent nodes cooperate to fulfill these demands, the demand agent nodes release profits, which are distributed to the participating service agent nodes, allowing them to accumulate capital. During this process, atomic service agent nodes may undergo evolutionary cooperation, forming composite service agent nodes (represented by black dots) to adapt to the environment and capture market profits more effectively. By analyzing the evolutionary process under different interaction coefficients between original service nodes, the development of new service agent nodes can be studied. Figure 10: An evolution diagram of the computational experiment with \(\alpha=0.5\). Figure 9: An evolution diagram of the computational experiment with \(\alpha=0.1\). Combining the evolution diagrams and the changes in the number of different service types during the evolutionary process, it can be observed that as the interaction coefficient between original services increases, the difficulty for emerging service agent nodes to gain an advantage in the competitive market environment also increases. In the service ecosystem, the degree of cooperation between original services directly affects their ability to meet complex and changing demands in Figure 12a-c. In low competition \(\alpha=0.1\), composite services emerge slowly due to weak competitive pressure. In moderate competition \(\alpha=0.5\), composite services thrive, reaching equilibrium faster. In addition, in high competition \(\alpha=0.9\), composite services struggle to establish due to resource monopolization by atomic services. When these services can efficiently address composite demands through tight cooperation, the unique advantages of emerging composite service agent nodes in the market may diminish. This is because the original services have already established a robust service-provision network through cooperation, making it more challenging for new composite service agent nodes to gain a foothold and demonstrate their competitiveness in the market. Service ecosystem diversity is a key indicator of its development, reflecting the health and innovation potential of the ecosystem. Observing Simpson's Diversity Index from Figure 13a-c, when \(\alpha=0.1\), due to service stagnation, the diversity is low. When \(\alpha=0.5\), the diversity of service competition tends to balance. With the increase of \(\alpha\), competitive exclusion dominates, leading to the collapse of diversity. In conclusion, as the interaction coefficient between original services increases, the Simpson's Index shows a downward trend, indicating a reduction in the ecosystem's diversity.