Canada Spends Logo

Explore our Budget 2026 analysis

Grant: Discovery Grants Program - Individual

St. Francis Xavier University

$14,000.00

Connecting Empirical and Mathematical Approaches to Collective Behaviour

FY 2022-23

Summary
Across scales, biological aggregates form striking patterns, display coordinated, cohesive motion, and function via principles of self-organization, yet complexity at the group level can obscure the underlying mechanisms. Determining how such group behaviour emerges and is sustained involves both direct observation of such groups, and mathematical models to test hypothetical behaviour regimes. My research program lies at this interface. I design and implement observational and experimental studies of collectives, from birds to humans. I develop algorithms to process and analyze these data, to summarize important statistical markers of interaction, and provide tests for comparison across species and condition. I develop, test, and simulate individual based differential-equation models to evaluate hypotheses of what individual interactions explain the observed group-level structure. By informing the construction and validation of these models via empirical data, I tie model predictions directly to the natural phenomena. I have used this empirical-theoretical approach to study large flocks of surf scoters in the field, to infer individual rules of interaction from reconstructed trajectories. Further analysis has revealed insights into the dynamics of order/disorder transitions, patterns of predation avoidance, and collective response to the environment.I will extend my analytical methods to new datasets of collective motion. With a new collaborator in Sydney, Australia, I will analyze a collection of trajectory-based datasets of fish, both in the field and in the lab. These datasets include the collective defensive response to risk in damselfish in the Great Barrier Reef, the effects of inter-fish familiarity on collective behaviour of mosquitofish, and how behavioural parameters are shaped by speciation and environment within the family of Rainbowfish. The degree of control permitted by the laboratory data will allow for the development of an updated, stepwise modelling approach from individuals, to pairs, up to large collectives.In the second main direction, I will study human collective behaviour via aural interactions. This research, based on pilot work already completed, uses an experimental system of humans clapping synchronously (groups of 2 to hundreds) to study what type of interactions allow synchronous clapping to arise, and how order parameters (group frequency, group synchrony) evolve after synchrony is achieved, via a coupled-oscillator modelling framework. This research extends work on human sensorimotor synchronization from the individual to the collective. Furthermore, effects such as group size, rhythmic initialization, and spatial information transfer will be studied.These initiatives contribute to my overall research goal of measuring, and explaining pattern in organized collectives.
Program
Discovery Grants Program - Individual
Location
Nova Scotia, Canada
Recipient Type
Academia
Type
Grant
Source
NSERC's Awards Data

As published

Application id
RGPIN-2017-06094
Name nom
Lukeman, Ryan
Department département
Mathematics, Statistics and Computer Science - Mathematics, Statistics and Computer Science
Organization id
83
Institution établissement
St. Francis Xavier University
Province en
Nova Scotia
Province fr
Nouvelle-Écosse
Country en
CANADA
Country fr
CANADA
Fiscal year exercice financier
2022
Competition year année de concours
2017
Award amount
14000
Program id
RGPIN
Program name en
Discovery Grants Program - Individual
Program name fr
Programme de subventions à la découverte - individuelles
Group en
DISCOVERY RESEARCH
Group fr
RECHERCHE AXÉE SUR LA DÉCOUVERTE
Committee code
1508
Committee name en
Mathematics and Statistics
Committee name fr
Mathématiques et statistique
Area of application code
405
Area of application group en
Environment
Area of application group fr
Environnement
Area of application en
Modelling and mathematical simulation of natural processes
Area of application fr
Modélisation et simulation mathématique des processus naturels
Research subject code
2950
Research subject group en
Applied mathematics
Research subject group fr
Mathématiques appliquées
Research subject en
Applied mathematics
Research subject fr
Mathématiques appliquées
Installment
inst:6
Partie
1
Nb partie
6
Application title
Connecting Empirical and Mathematical Approaches to Collective Behaviour
Application summary
Across scales, biological aggregates form striking patterns, display coordinated, cohesive motion, and function via principles of self-organization, yet complexity at the group level can obscure the underlying mechanisms. Determining how such group behaviour emerges and is sustained involves both direct observation of such groups, and mathematical models to test hypothetical behaviour regimes. My research program lies at this interface. I design and implement observational and experimental studies of collectives, from birds to humans. I develop algorithms to process and analyze these data, to summarize important statistical markers of interaction, and provide tests for comparison across species and condition. I develop, test, and simulate individual based differential-equation models to evaluate hypotheses of what individual interactions explain the observed group-level structure. By informing the construction and validation of these models via empirical data, I tie model predictions directly to the natural phenomena. I have used this empirical-theoretical approach to study large flocks of surf scoters in the field, to infer individual rules of interaction from reconstructed trajectories. Further analysis has revealed insights into the dynamics of order/disorder transitions, patterns of predation avoidance, and collective response to the environment.I will extend my analytical methods to new datasets of collective motion. With a new collaborator in Sydney, Australia, I will analyze a collection of trajectory-based datasets of fish, both in the field and in the lab. These datasets include the collective defensive response to risk in damselfish in the Great Barrier Reef, the effects of inter-fish familiarity on collective behaviour of mosquitofish, and how behavioural parameters are shaped by speciation and environment within the family of Rainbowfish. The degree of control permitted by the laboratory data will allow for the development of an updated, stepwise modelling approach from individuals, to pairs, up to large collectives.In the second main direction, I will study human collective behaviour via aural interactions. This research, based on pilot work already completed, uses an experimental system of humans clapping synchronously (groups of 2 to hundreds) to study what type of interactions allow synchronous clapping to arise, and how order parameters (group frequency, group synchrony) evolve after synchrony is achieved, via a coupled-oscillator modelling framework. This research extends work on human sensorimotor synchronization from the individual to the collective. Furthermore, effects such as group size, rhythmic initialization, and spatial information transfer will be studied.These initiatives contribute to my overall research goal of measuring, and explaining pattern in organized collectives.