Recent theoretical work has highlighted several mechanisms giving rise to so-called long transient dynamics. These long transients tantalizingly appear to replicate dynamics seen in real systems—with one critical difference: ecological data is noisy, a reality theoretical work often ignores. In general, stochasticity is known to have important consequences: it can qualitatively alter model dynamics as well as impact our ability to infer underlying processes through statistical analysis. To explore the effect of stochasticity on qualitative model behavior and the implications for our ability to infer underlying mechanisms, we generated time series from a simple model of long transient behavior with multiplicative noise. We then examined whether noise qualitatively changes the expected dynamics of the system and the insights that four different statistical methods could provide about the underlying dynamics. We found that the expected duration of the long transient was significantly reduced in the stochastic model compared to the deterministic model. These transient dynamics arise for parameterizations very near to a bifurcation point in the deterministic model, and we also found that as we varied parameterizations to include two alternative stable states, stochasticity caused the population to jump from one basin of attraction to another, resulting in time series that suggest long transient dynamics. Despite challenges estimating the underlying model parameters, we illustrate that statistical inference on a single realization may still provide insight into the presence of a ghost attractor. Further, we highlight that inference improves, across parameterizations, for an increasing number of realizations of the process.

最近的理论工作强调了产生所谓的长瞬态动力学的几种机制。这些长瞬变似乎复制了真实系统中看到的动态——有一个关键区别：生态数据是嘈杂的，现实理论工作经常忽略。一般来说，众所周知，随机性会产生重要的后果：它可以定性地改变模型动态，并影响我们通过统计分析推断潜在过程的能力。为了探索随机性对定性模型行为的影响以及对我们推断潜在机制的能力的影响，我们从具有乘法噪声的长瞬态行为的简单模型生成了时间序列。然后，我们检查了噪声是否会定性地改变系统的预期动态，以及四种不同的统计方法可以提供关于潜在动态的见解。我们发现，与确定性模型相比，随机模型中长瞬态的预期持续时间显着减少。这些瞬态动态出现在非常接近确定性模型分岔点的参数化时，我们还发现，当我们改变参数化以包括两个替代的稳定状态时，随机性导致种群从一个吸引池跳到另一个吸引池，导致时间系列表明长期瞬态动态。尽管在估计基础模型参数方面存在挑战，我们说明了对单个实现的统计推断仍然可以洞察鬼吸引子的存在。此外，我们强调，对于越来越多的过程实现，推理在参数化方面有所改进。