From rules to mechanisms: the emergence of animal territoriality Institute for Advanced Studies workshop Complexity and the Real World University of Bristol, 22 June 2010 Luca Giuggioli Bristol Centre for Complexity Sciences Department of Engineering Mathematics and School of Biological Sciences

UNDERSTANDING THE DYNAMICS OF COMPLEX PROCESSES 2) Choice of a modelling approach 3) Distinguishing between mathematical rules and measurable mechanisms of interaction 4) Experimental validation 1) Clearly identifiable characteristics

1) CLEARLY IDENTIFIABLE CHARACTERISTICS - Territoriality - Animal grouping

2) CHOICE OF THE MODELLING APPROACH a) What are the temporal and spatial scales? - e.g. the nuclear forces responsible for the existence of the atoms in a crystal are irrelevant to the movement of an electron interacting with the crystal vibrations b) Are the details of the interaction known? - Transition of the linguistic explanations and descriptions of the perceived behaviour into mathematical language c) How often and over what range do the interaction paths occur? - Deterministic versus stochastic modelling: i) large number of interacting paths fluctuations are not important (mean field models work) ii) spatial and/or temporal heterogenous interaction stochastic modelling is necessary

DISTINGUISHING BETWEEN MATHEMATICAL RULES AND MEASURABLE MECHANISMS OF INTERACTION a) Is there a metric to quantify animal interactions? - Mathematically one talks about interaction when the effect of two or more variables is not additive - Biologically it often means a series of intertwined actions and reactions - The measurement of such actions and reactions provides the appropriate metric

ANIMAL GROUPING ZOA: zone of attraction ZOO: zone of orientation ZOR: zone of repulsion Interaction rules considered in animal collective movement models

ANIMAL TERRITORIALITY Interaction mechanisms considered in the formation of animal territory i) Territorial defense: making ones presence conspicuous to a neighbour through marking ii) Reaction to foreign territory encounter: where and how fast you move away Territorial patterns emerge if the time scales for an animal to patrol the borders is faster than the time scales for which territorial boundaries wander itself proportional to the active scent time

ANIMAL TERRITORIALITY DYNAMICAL EMERGENCE

4) EXPERIMENTAL VALIDATION Question to be asked What and how sensory modalities are at work in collective animal movement? - In animal grouping it is yet to be understood - In territory formation we have tested the microscopic olfactory signal hypothesis (scent marking) When empirical measurements are based on coarse- grained population-level observations, model predictions cannot be validated against a quantifiable testable hypothesis (animal grouping)

COLLABORATORS J.R. Potts Bristol Centre for Complexity Sciences Stephen Harris School of Biological Sciences, University of Bristol