标题： 生命找到一条路：自适应阈值网络中合作结构的出现 显示英文标题

标题： Life Finds A Way: Emergence of Cooperative Structures in Adaptive Threshold Networks

摘要： 长期以来，关于新的组织层次是如何演化的存在长期的争论。 这似乎不太可能，因为合作必须胜过竞争。 一个被广泛研究的例子是自催化集合的出现，这似乎是有生命进化的先决条件。 通过一个简单的模型，我们研究了合作与对抗之间的偏倚如何影响网络动态，结果表明即使在普遍的对抗性互动中，高阶组织也会出现。 一般来说，我们观察到系统中元素数量的定量增加会导致质的转变。 我们提出了一种随机阈值定向网络模型，该模型结合了节点特定的特性与动态边形成和节点移除，模拟任意程度的合作与竞争。 在我们的框架中，内在节点值通过各种阈值规则确定定向链接。 我们的模型生成了一个带有符号边的多图（反映支持/对抗，标记为“帮助”/“伤害”），最终产生两个平行但相互依赖的阈值图。 在我们的方法中引入时间增长和节点周转，可以探索社区的演化、适应和潜在崩溃，并揭示连接性和韧性中的相变。 我们的发现扩展了经典的随机阈值和Erdős-Rényi模型，在生物和经济背景下的适应性系统中提供了新的见解，特别强调对集体可供性集的应用。 这个框架也应该对预测微生物群落在土壤中的持续实验有帮助。 显示英文摘要

摘要： There has been a long debate on how new levels of organization have evolved. It might seem unlikely, as cooperation must prevail over competition. One well-studied example is the emergence of autocatalytic sets, which seem to be a prerequisite for the evolution of life. Using a simple model, we investigate how varying bias toward cooperation versus antagonism shapes network dynamics, revealing that higher-order organization emerges even amid pervasive antagonistic interactions. In general, we observe that a quantitative increase in the number of elements in a system leads to a qualitative transition. We present a random threshold-directed network model that integrates node-specific traits with dynamic edge formation and node removal, simulating arbitrary levels of cooperation and competition. In our framework, intrinsic node values determine directed links through various threshold rules. Our model generates a multi-digraph with signed edges (reflecting support/antagonism, labeled ``help''/``harm''), which ultimately yields two parallel yet interdependent threshold graphs. Incorporating temporal growth and node turnover in our approach allows exploration of the evolution, adaptation, and potential collapse of communities and reveals phase transitions in both connectivity and resilience. Our findings extend classical random threshold and Erd\H{o}s-R\'enyi models, offering new insights into adaptive systems in biological and economic contexts, with emphasis on the application to Collective Affordance Sets. This framework should also be useful for making predictions that will be tested by ongoing experiments of microbial communities in soil.