扩散的随机模型被广泛用于研究各类种群(包括动物、植物、种子和细胞)的扩散过程。成像与野外测量技术的进步使得数据常在多尺度上采集:既包括在一系列固定采样区域内获取的计数数据,以表征种群尺度的扩散行为;也包括个体轨迹数据,以考察扩散种群中个体的运动特征。本研究采用基于格点的随机游走模型,分析仅利用计数数据、或结合轨迹数据时,模型参数的可确定程度。我们的分析整合了基于智能体的随机模拟、均场偏微分方程近似、基于似然的参数估计、可识别性分析以及基于模型的预测。这些综合工具表明,仅依赖计数数据有时会导致结构性不可识别问题,而引入轨迹数据可缓解该问题。此外,这些工具还支持我们探究不同实验设计对推断精度的影响,具体通过比较不同轨迹数据采集方案对实际可识别性的影响来实现。本研究中所用全部算法的开源实现可在 GitHub 获取。
Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across a range of scales, including count data collected across a series of fixed sampling regions to characterize population-level dispersal, as well as individual trajectory data to examine at the motion of individuals within a diffusive population. In this work we consider a lattice-based random walk model and examine the extent to which model parameters can be determined by collecting count data and/or trajectory data. Our analysis combines agent-based stochastic simulations, mean-field partial differential equation approximations, likelihood-based estimation, identifiability analysis, and model-based prediction. These combined tools reveal that working with count data alone can sometimes lead to challenges involving structural non-identifiability that can be alleviated by collecting trajectory data. Furthermore, these tools allow us to explore how different experimental designs impact inferential precision by comparing how different trajectory data collection protocols affects practical identifiability. Open source implementations of all algorithms used in this work are available on GitHub.