PhD Introduction
A first draft of my thesis intro
Introduction
In 1822, a white stork (Ciconia ciconia) was sighted near the village of Klütz in Germany. This was not uncommon, with white storks appearing over summer across Europe. kellerEuropeanBreedingBird2020 The species had not bred in the UK since 1416, when a pair were nesting in St Giles Cathedral, Edinburgh, until a successful reintroduction program in Sussex in 2020 (mayallDemographicConsequencesManagement2023). What made this sighting uncommon however, was the presence of a 75 cm spear impaled through the bird’s neck. On closer inspection, the spear was not of European origin, but African. The Rostocker Pfeilstorch (literally ‘arrow stork’) had been undertaking its annual migration until it was rudely interrupted by a spear, piercing it’s left side and emerging on the right some 30 cm higher (see Figure 1). Undeterred, it carried on its migration, successfully arriving in Germany where it was promptly shot by a local hunter. Before this unusually persistent stork was found, it was not known what happened to these birds over winter.
Many experts at the time still held Aristotle’s view that birds hibernated over winter as described in his Historia Animalium more than 2000 years previously. aristotleHistoriaAnimalium1910 Other theories were proposed (such as their migration to the Moon, or transfiguration) and persisted into the 1700s. harrisonBirdsMoon1954a Indeed, animal migrations are still not fully understood — direct evidence for the breeding place of the European eel (Anguilla anguilla) only emerged in 2022, despite centuries of investigation. wrightFirstDirectEvidence2022,schmidtIVBreedingPlaces1997
The Rostocker Pfeilstorch was the first concrete evidence in Europe that birds were undertaking large migrations and residing elsewhere (on Earth) over winter. With the development of ringing in 1899 by Hans Christian Cornelius Mortensen, scientists finally had a method to test theories on the migration of birds. The great artist, ornithologist and plagiarist J.J. Audubon also claimed to have developed a similar method in America in 1804, discovering natal philopatry in Eastern Phoebes (Sayornis phoebe), although it later became apparent he was in France at the time (halleyAudubonFamousBanding2018a).
Humans have been tracking animals for millennia, when knowing where animals went and when was key to survival and our evolution as a species. liebenbergPersistenceHuntingModern2006 Only relatively recently however, has the technology been available to monitor animals remotely. The first radio tracking collars weighed almost 11 kg, and were tested on an elk known as Monique in Yellowstone National Park, USA. bensonWiredWildernessTechnologies2010,craigheadSatelliteGroundRadiotracking1972 Since then, GPS tags have got smaller, and more reliable. This technology, along with others such as sonar, radar and mark-and-recapture studies has allowed our knowledge of animal movement to rapidly increase. It is now possible to track wolf packs, great white sharks and elk from anywhere in the world with an internet connection. voyageurswolfprojectAnimations2018,marinecsiTaggingUpdates2010,guarinoRockyMountainAnimals2020 The resulting data has shed light on a wide range of hitherto unknown animal behaviour.
Although the animals mentioned thus far have all been individuals, they all have one thing in common: they are rarely alone. They all migrate en masse, with individuals of the same species. The scale of some collective migrations is awe-inspiring, and has huge impacts on the environment through which they travel and beyond. Swarms of marching locusts forming bands kilometres long with densities reaching 30,000 per square metre can decimate crops across East Africa, Asia and the Middle East. symmonsDesertLocustGuidelines2001a The carbon pump effect of Blue Whales (Balaenoptera musculus), sequestering 130 megatonnes of carbon per year in the Southern Ocean alone, depends upon vast swarms of krill moving across the ocean. pearsonWhalesCarbonCycle2023,savocaBaleenWhalePrey2021 These great movements raise many questions: where do species go? When do they go? What prompts their coordinated movement? How do they synchronise? How predictable are these cycles? What drives them?
While we now understand that eels aren’t made of mud, and birds don’t overwinter on the Moon, when it comes to anthropogenic (human) impacts on these migrations, we’re still in the Dark Ages. lennoxOneHundredPressing2019 To better understand and mitigate our impact, it is imperative we first understand the hows, whys and whens of these collective migrations. This thesis contributes to this understanding, using mathematical and computational models of collective behaviour. The remainder of this chapter provides background on the mathematical modelling of collective behaviour, providing context and introducing key themes of the thesis. Chapter 2 provides a novel numerical study of one such abstract model of collective behaviour (published as buttaNonmeanfieldVicsektypeModels2022a). Chapter 3 narrows the gap between abstraction and reality, extending an existing model of collective navigation to account for a flowing environment. Chapter 4 gives more details on the numerical approach taken in Chapter 2, highlighting the novelties from existing methods. Finally, Chapter 5 discusses the works developed in this thesis and provides an outlook to the future.
Modelling collective migration phenomena, while a personal motivation for the studies in this thesis, is not the only application of the interacting particle system framework as we will come to see. Applications are diverse, and indeed it is this flexibility and applicability that has driven research in the field in recent years. To introduce the field, we divide the modelling of collective behaviour into two (related) strands: agent-based models and partial differential equation (PDE) models.