Novel applications of machine learning for the study of animal movement

Animal movement data play a crucial role in our endeavour to decode the wildlife dynamics that unfold across the Earth’s varied terrains and waterways. Collecting animal movement data involves employing a variety of modern technologies and techniques. One common method is the use of Global Positioning System (GPS) devices that are attached to animals, providing accurate location data at regular intervals. These devices allow us to track animals’ movements over time and space, giving us access to intricate details about their ranging behaviours and daily routines. These data provide insights into migration patterns, foraging strategies, habitat preferences, and responses to environmental changes and are therefore key to an improved understanding of the behaviours, habitats and ecological interactions of various species. There are many challenges associated with the analysis of such datasets and movement ecologists have been dilligently advancing state-of-the-art statistical methods for analysing animal movement data. This effort is crucial because it enables us to extract meaningful information from the complex, large-scale datasets generated by animal tracking studies. These advanced statistical techniques help uncover hidden patterns, such as the identification of significant stopover sites during migrations or the characterisation of nuanced movement behaviours. Moreover, they facilitate the integration of environmental variables, enhancing our ability to understand how animals respond to changing landscapes and climate conditions. By refining our analytical tools, movement ecologists can provide more accurate and comprehensive insights into wildlife behaviours, aiding conservation efforts and ecological research on a global scale. Throughout this thesis, we will talk about models of animal movement and we will give our contribution to expand the array of statistical methods that can be employed for the analysis of telemetry datasets. We will begin by reviewing some of the most commonly employed methods found in the literature. Then, we will focus on a simple one-dimensional self-propelled particle model used to simulate the dynamics of a group of locusts placed in a ring-shaped arena for an experiment, and we will leverage Gaussian processes to infer microscale properties of the group from macroscale observed variables, without deriving a formal mathematical link between the two scales, which is in many cases intractable. Our focus will then shift to the problem of identifying different behavioural patterns from relocation data. In the fourth chapter we will describe various methods that we have conceptualised all aimed at simulating semi-Markov chains. This will be needed in the subsequent chapter, where we will introduce a flexible model scalable to large datasets that finds its applications in solving the so-called switching problems. This will be achieved by modelling the locations via an integrated OU process and by reconstructing the latent behavioural patterns via a Monte Carlo Expectation-Maximisation algorithm, where the method introduced in the previous chapter will be employed. In Chapter 6 we will employ this method on a flock of sheep, specifically on a group level metric describing the changes in coordination of the group motion. This will enable us to reconstruct the behavioural pattern of the flock. We end the thesis with a conclusion chapter

Modelling multiscale collective behavior with Gaussian processes

Collective behavior is characterized by the emergence of large-scale phenomena from local interactions. It is found in many contexts, including political movements, fads and fashions, and animal grouping. In this paper, we aim to elucidate the mechanisms that underlie observed collective behavior by developing a novel mathematical framework based on equation-free modelling procedures and Gaussian process regression. This allows us to circumvent the possible lack of formal mathematical links between scales and instead use statistical emulation to learn an empirical Fokker-Planck equation. Our approach advances our ability to understand how complex systems function at both the individual and collective level when a formal mathematical description of macroscale dynamics is unavailable

Approximate Bayesian inference for individual-based models with emergent dynamics

Individual-based models are used in a variety of scientific domains to study systems composed of multiple agents that interact with one another and lead to complex emergent dynamics at the macroscale. A standard approach in the analysis of these systems is to specify the microscale interaction rules in a simulation model, run simulations, and then qualitatively compare outputs to empirical observations. Recently, more robust methods for inference for these types of models have been introduced, notably approximate Bayesian computation, however major challenges remain due to the computational cost of simulations and the nonlinear nature of many complex systems. Here, we compare two methods of approximate inference in a classic individual-based model of group dynamics with well-studied nonlinear macroscale behaviour; we employ a Gaussian process accelerated ABC method with an approximated likelihood and with a synthetic likelihood. We compare the accuracy of results when re-inferring parameters using a measure of macro-scale disorder (the order parameter) as a summary statistic. Our findings reveal that for a canonical simple model of animal collective movement, parameter inference is accurate and computationally efficient, even when the model is poised at the critical transition between order and disorder

Inferring the interaction rules of complex systems with graph neural networks and approximate Bayesian computation

Inferring the underlying processes that drive collective behaviour in biological and social systems is a significant statistical and computational challenge. While simulation models have been successful in qualitatively capturing many of the phenomena observed in these systems in a variety of domains, formally fitting these models to data remains intractable. Recently, approximate Bayesian computation (ABC) has been shown to be an effective approach to inference if the likelihood function for a model is unavailable. However, a key difficulty in successfully implementing ABC lies with the design, selection and weighting of appropriate summary statistics, a challenge that is especially acute when modelling high dimensional complex systems. In this work, we combine a Gaussian process accelerated ABC method with the automatic learning of summary statistics via graph neural networks. Our approach bypasses the need to design a model-specific set of summary statistics for inference. Instead, we encode relational inductive biases into a neural network using a graph embedding and then extract summary statistics automatically from simulation data. To evaluate our framework, we use a model of collective animal movement as a test bed and compare our method to a standard summary statistics approach and a linear regression-based algorithm

Inferring microscale properties of interacting systems from macroscale observations

Emergent dynamics of complex systems are observed throughout nature and society. The coordinated motion of bird flocks, the spread of opinions, fashions and fads, or the dynamics of an epidemic, are all examples of complex macroscale phenomena that arise from fine-scale interactions at the individual level. In many scenarios, observations of the system can only be made at the macroscale, while we are interested in creating and fitting models of the microscale dynamics. This creates a challenge for inference as a formal mathematical link between the microscale and macroscale is rarely available. Here, we develop an inferential framework that bypasses the need for a formal link between scales and instead uses sparse Gaussian process regression to learn the drift and diffusion terms of an empirical Fokker-Planck equation, which describes the time evolution of the probability density of a macroscale variable. This gives us access to the likelihood of the microscale properties of the physical system and a second Gaussian process is then used to emulate the log-likelihood surface, allowing us to define a fast, adaptive MCMC sampler, which iteratively refines the emulator when needed. We illustrate the performance of our method by applying it to a simple model of collective motion