Migratory geomagnetic navigation as a spatial optimisation problem

Migratory birds find their way across long-distances using cues from their local environment – this is called true navigation. Migratory navigation is a multi-modal process, meaning that animals switch between cues depending on the environmental conditions. One of the cues that they may use is Earth’s magnetic field. Birds may use various geomagnetic values (intensity, inclination) for navigation, yet in spite of substantial literature on the topic, there is still no consensus on how they use different values and how they combine them with each other (1).

One way of studying geomagnetic navigation is by simulating migratory movement using different models that incorporate information on both properties of the animal’s movement and on the geomagnetic field. Simulations are then compared with the actual migratory flights to identify models that are the most similar to what occurred in reality. It is now possible to create very accurate measurements of the field at each location and time in the animal tracking data (2), which opens a number of possibilities for modelling geomagnetic navigation. Previous work used agent-based models (3) and step-selection analysis (4), but none of these methods is able to model the problem of navigation as a multi-modal process that evolves through time. That is, navigation may need more than one cue and the choice of which cue to use at which time depends on environmental conditions. For example, birds migrating at night might rely on the geomagnetic field to find their way across long distances, but may use visual landmarks to decide when it is time to stop, thus creating an optimal navigational strategy from several cues.

This methodological research project will explore if spatial optimisation algorithms are a suitable new way of modelling the multi-modal navigation process. Spatial optimisation uses mathematical modelling to find solutions to spatial decision problems under strictly defined conditions. It is well-known in geography for location-allocation modelling (5), however, it has also been used for route selection in human mobility (6) and may therefore be a suitable way for modelling migratory navigation.

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Image Captions

Linking satellite geomagnetic data to bird tracking data, image by Urska Demsar


We will define multi-modal geomagnetic navigation as a spatial optimisation problem. A spatial optimisation algorithm maximises or minimises an objective related to a geographic problem. This involves defining a suitable objective function with specific constraints. In terms of geomagnetic navigation, the objective function could be a route to the target destination under specific geomagnetic conditions while minimising navigational errors. The student will define and test objective functions for different navigational strategies (compass navigation, map navigation) using different geomagnetic values (intensity, inclination) or combinations of values. Additionally, constraints will be added in terms of environmental conditions, including visibility (using information on cloud-cover), day/nighttime, and proximity to geographic features (coastlines, major rivers) to account for a possibility of switching to landmark-based navigation.

We will then test various spatial optimisation algorithms to find the optimal navigational solutions. Spatial optimisation algorithms are divided into two general groups: 1) traditional mathematical programming methods and 2) heuristics. Algorithms from group 1) develop an exact solution to an optimisation problem, this includes well-established methods such as linear programming or mixed integer programming. Sometimes however the exact solution does not exist or may not be computationally achievable in a short time. Algorithms from group 2) address this problem by iteratively modifying a suboptimal solution with the goal to location the best solution possible, usually a near-optimal solution. These algorithms operate faster than traditional mathematical programming algorithms and may therefore be more suitable for large movement data sets. There are a number of heuristics algorithms, including specific methods such as simulated annealing, moth-flame algorithm, great deluge algorithm but also more general groups, such as evolutionary/genetic algorithms. Evolutionary algorithms may prove particularly suitable for geomagnetic navigation, since they define agents that operate according to specific rules and model evolution of these rules through cross-over into new generations of agents. This process could mimic the natural evolution of navigational rules for bird species where offspring learn migratory patterns from patterns, such as for example greater white-fronted geese (Anser Albifrons), whose navigation we have studied previously (2,3).

The student will start by preparing a review on spatial optimisation algorithms and on models of geomagnetic navigation. The project continues with a series of simulation experiments, where for each algorithm we will model migratory flights of the greater white-fronted geese, which migrate between western Europe and Russian Arctic. We will define objective functions based on various geomagnetic values and navigation strategies. We will then use the chosen algorithm to simulate their flights based on real geomagnetic and environmental conditions. Simulated trajectories will then be compared to the actual migratory trajectories and their similarity assessed using trajectory similarity measures (dynamic time-warping, dynamic interaction indices, etc.). The goal is to identify which algorithm and which objective function creates trajectories that are the best fit to how geese migrate.

Scientific reproducibility: this project is based on open science principles. We will use open data (tracking and geomagnetic) and produce new methods as open tools (as Free and Open Source Software). Besides exploring geese migration, this project has a potential for wide impact in ecology through applicability of our methods to any other migratory species which uses geomagnetic information to find their way, including other bird species, turtles, whales and other sea mammals.

Student background: this is a methodological project which would suit a technical candidate (with background in spatial data science, geographic information science, computer science or statistics) with an interest of using their technical skills to solve problems in ecology and animal movement. Knowledge of coding (in Python and/or R) and algorithms theory is desirable.

Project Timeline

Year 1

1) Advanced training in software/data science skills (e.g. advanced Python skills), 2) literature review on geomagnetic migratory navigation and spatial optimisation algorithms, 3) First experiment: modelling navigation with evolutionary algorithms.

Year 2

1) Finish first experiment, including writing a journal paper on the topic, 2) Second experiment: modelling navigation with heuristic algorithms for spatial optimisation. Write a journal paper from this. 3) Attend an international conference (GIScience).

Year 3

1) More experiments with other spatial optimisation algorithms: moth-flame algorithm, great deluge algorithm, etc. 2) Publish papers, 3) Attend an international conference (AGILE). 4) Start preparing portfolio thesis.

Year 3.5

1) Finish papers and 2) finalise thesis.

& Skills

Student will identify where he/she needs skills in the Training Needs Analysis. These will be acquired in GradSkills courses by The Centre for Educational Enhancement and Development (CEED) in St Andrews, IAPETUS2 training events and in external courses, such as AniMove (http://animove.org/).

Training will be through active supervision, consisting of regular meetings (live/virtual) of the supervisory team with the student. Student will attend research meetings and seminars of the Bell-Edwards Geographic Data Institute (https://begin.wp.st-andrews.ac.uk/), on research and career progression topics (publishing, time management, proposal writing). Student’s progress will be formally evaluated through annual review at the University of St Andrews

References & further reading

1. https://doi.org/10.1038/s41586-018-0176-1
2. https://doi.org/10.1186/s40462-021-00268-4
3. https://doi.org/10.1016/j.ecoinf.2022.101689
4. Zein B et al. 2023, Geomagnetic night vision: A data-driven approach to study geomagnetic navigation in a migratory bird, under review.
5. https://doi.org/10.1002/9781118786352.wbieg0156
6. https://doi.org/10.5194/isprs-archives-XLII-4-W4-381-2017

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