A Conditionally Markovian Reformulation of Memory-Mediated Animal Movement Using Cognitive Maps

Memory plays a crucial role in shaping animal movement behaviors. There are powerful new models emerging for understanding memory effects via continuous-time stochastic differential equations (SDEs). However, these models are non-Markovian and computationally difficult to implement as a result of intractable likelihood functions. To address such issues, we establish a connection between discrete-time and continuous-time animal movement models and introduce a conditional Markov process, facilitated by a so-called filtration or dynamically updated cognitive map. Such cognitive maps are allocentric mental representations of an individual’s surroundings, which change over time, and have been shown to influence animal movement and habitat use. We reformulate the non-Markovian memory-mediated animal movement SDE (M3) model originally developed by Fagan et al. (2023) by incorporating cognitive maps to create a Markov process conditioned on the associated cognitive map. This new formulation facilitates parameter inference and enhances computational efficiency. Introducing cognitive maps into the M3 model transforms the non-Markovian SDE model to a conditionally Markovian model that is coupled to an auxiliary filtration that is described as a cognitive map. This cognitive map, in turn, is described by a spatially distributed system of ordinary differential equations, which describe how the animal's spatial memory changes over time. The reformulation offers practical advantages by making the likelihood function computationally tractable and avoiding large-scale integrals. Simulations show that our cognitive map-based model (CM-M3) preserves the key movement patterns of the original M3 model—bounded wandering, convergence, and cyclic paths. We also demonstrate improved simulation speeds using optimized cell sizes and interpolation, and explore parameter inference methods that address the issue of intractable likelihoods.

A Conditionally Markovian Reformulation of Memory-Mediated Animal Movement Using Cognitive Maps

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SHIBAI ZHANG

"A Conditionally Markovian Reformulation of Memory-Mediated Animal Movement Using Cognitive Maps"

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