发表机构
School of Basic Sciences, Indian Institute of Technology Bhubaneswar（印度布巴内斯瓦尔理工学院基础科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过捐赠博弈模型，分析加权网络上合作传播的受保护域机制，得出弱选择阈值及最小接触对比度等关键条件，揭示合作成本与网络结构的关系。
AI 中文摘要
一种代价高昂的遗传性状，当其后代创造出有利的局部环境时，可以传播开来。我们探究哪些有限接触结构能够维持这样的集体竞争者，以及它们的优势需要付出何种代价。个体参与一个捐赠博弈，以成本 $c$ 提供收益 $b$。相互加权的接触决定了平均收益和复制对象，而来源则根据收益全局选择。当均匀引入的合作者在互补实验中比背叛者更频繁地接管时，合作受到青睐。精确的涨落响应和快速构型的消除确定了受保护域的形成与竞争是控制过程。尖锐的弱选择阈值下确界为：四环上的 $b/c=3$，五节点路径上的 $7$，以及每个至少六个节点的固定路径上的 $1$。在六节点路径上，全局界限迫使近势垒设计进入该域层级。接触比率之间的多项式关系随后控制无约束优化，并最终蕴含精确的反射对称性。达到阈值 $1+\epsilon$ 需要最小接触对比度 $656\epsilon^{-2}[1+O(\epsilon)]$ 和中性吸收时间阶为 $\epsilon^{-1}$。我们确定了它们的权衡和相关的设计容差。有限选择消耗相同的余量。在受控的小选择窗口内，当对比度超过其精确最小值阶为 $\epsilon^{-1}$ 时，最大固定优势阶为 $\epsilon^{5/2}$。因此，改进的入侵阈值可能需要增加接触异质性、精度和观察时间。
英文摘要
Contacts that protect a cooperative group can also make its founding sites difficult for newborn mutants to reach. We study this tension in a donation game with benefit $b$ and cost $c$ on finite weighted networks. Reciprocal contacts determine averaged payoffs and route copying from sources selected globally with a payoff-dependent bias. We compare takeover probabilities of a cooperator and a defector, each introduced singly into a population of the opposite type. Exact linear response about neutral drift and elimination of fast configurations identify protected domains as collective competitors. Under uniform introduction, the sharp weak-selection threshold infima are $b/c=3$ on the four-cycle, $7$ on the five-site path and $1$ on every fixed path with at least six sites. Introduction through newborn offspring eliminates this advantage on the five-site path. On six sites it preserves the infimum one but raises the minimum contact contrast, the largest weight divided by the smallest, needed for threshold $1+ε$ from $656ε^{-2}$ to $4050ε^{-3}$ at leading order. Global polynomial bounds force every six-site design approaching threshold one into the domain hierarchy. Algebraic relations among contact ratios control optimization over all positive weights and establish exact reflection symmetry of the optimizer at sufficiently large contrast. For uniform introduction, the geometry determines absorption and fixation times and tolerance to contact errors. Nonlinear selection narrows the favorable window, making the fixation-probability difference small near the minimum contrast. A sharp variance-time bound quantifies the observation cost when the site- and type-specific terminal fixation probabilities are independently unknown. The same contacts govern collective persistence, access by mutation and the time to resolve the invasion advantage.
Comments53 pages, 6 figures, 2 tables. v2 expanded results on introduction protocols, resource and time bounds, and observation costs
