块结构生态系统的近似消息传递
Approximate message passing for block-structured ecological systems
AI总结：
针对具有方差和相关性剖面的随机非对称相互作用矩阵的广义Lotka-Volterra系统，利用近似消息传递方法推导出平衡丰度分布的固定点方程，并揭示块结构对物种持久性和群落稳定性的非局部影响。
摘要：
生态相互作用网络很少是同质的：物种自然形成具有不同相互作用结构的群落，导致相互作用矩阵中出现块结构的方差和相关性剖面。我们研究了广义Lotka-Volterra系统的平衡性质，其相互作用矩阵是随机的、非对称的，并具有方差和相关性剖面。基于异质和相关随机矩阵的近似消息传递（AMP）的最新进展，我们推导出一组自洽的固定点方程，在大$n$极限下，这些方程刻画了平衡丰度分布。特别地，我们证明了该极限分布是由方差和相关性剖面驱动的截断高斯的显式混合。然后，我们通过三个涉及两个相互作用群落的应用来说明这一结果的生态学意义。首先，我们展示了单个群落内相关性剖面的局部变化会引发物种持久性的系统范围响应，揭示了持久性动力学的非局部性质。其次，我们发现以互利或竞争相互作用为主的群落对日益增加的群落间耦合更为稳健，而以捕食-被捕食相互作用为主的群落则更容易崩溃。第三，我们证明了在完全没有相关性的情况下，仅非对称相互作用方差就能在群落之间产生反馈回路。
英文摘要：
Ecological interaction networks are rarely homogeneous: species naturally form communities with distinct interaction structures, resulting in block-structured variance and correlation profiles in the interaction matrix. We study the equilibrium properties of generalized Lotka-Volterra systems whose interaction matrices are random and non-symmetric with variance and correlation profiles. Based on recent advances in approximate message passing (AMP) for heterogeneous and correlated random matrices, we derive a set of self-consistent fixed-point equations that, in the large-$n$ limit, characterize the equilibrium abundance distribution. In particular, we show that this limiting distribution is an explicit mixture of truncated Gaussians, driven by the variance and correlation profiles. We then illustrate the ecological implications of this result through three applications involving two interacting communities. First, we show that local changes in the correlation profile within a single community induce system-wide responses in species persistence, revealing the non-local nature of persistence dynamics. Second, we find that communities dominated by mutualistic or competitive interactions are more robust to increasing inter-community coupling, whereas communities structured by predator-prey interactions are more prone to collapse. Third, we demonstrate that asymmetric interaction variance alone, in the complete absence of correlation, can generate feedback loop between communities.
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