From rules to mechanisms:the emergence of animal territoriality

Institute for Advanced Studies workshopComplexity and the Real World

University of Bristol, 22 June 2010

Luca GiuggioliBristol Centre for Complexity Sciences

Department of Engineering Mathematics and School of Biological Sciences

UNDERSTANDING THE DYNAMICS OFCOMPLEX PROCESSES

2) Choice of a modelling 2) Choice of a modelling approachapproach

3) Distinguishing between mathematical 3) Distinguishing between mathematical rules and measurable mechanisms of rules and measurable mechanisms of interactioninteraction

4) Experimental validation4) Experimental validation

1) Clearly identifiable 1) Clearly identifiable characteristicscharacteristics

1) CLEARLY IDENTIFIABLE CHARACTERISTICS

- Territoriality- Territoriality

- Animal grouping- Animal grouping

2) CHOICE OF THE MODELLING APPROACH

a) What are the temporal and spatial a) What are the temporal and spatial scales?scales?- e.g. the nuclear forces responsible for the existence - e.g. the nuclear forces responsible for the existence

of the atoms in a crystal are irrelevant to the of the atoms in a crystal are irrelevant to the movement of an electron interacting with the crystal movement of an electron interacting with the crystal vibrationsvibrationsb) Are the details of the interaction b) Are the details of the interaction

known?known?- Transition of the linguistic explanations and - Transition of the linguistic explanations and descriptions of the perceived behaviour into descriptions of the perceived behaviour into mathematical languagemathematical language

c) How often and over what range do the interaction c) How often and over what range do the interaction paths occur?paths occur?- Deterministic versus stochastic modelling:- Deterministic versus stochastic modelling:

i) large number of interacting paths i) large number of interacting paths fluctuations are not important (mean field fluctuations are not important (mean field models work)models work)

ii) spatial and/or temporal heterogenous interaction ii) spatial and/or temporal heterogenous interaction stochastic modelling is necessarystochastic modelling is necessary

DISTINGUISHING BETWEEN MATHEMATICAL RULES AND MEASURABLE MECHANISMS OF INTERACTION

a) Is there a metric to quantify animal a) Is there a metric to quantify animal interactions?interactions?- Mathematically one talks about interaction when the - Mathematically one talks about interaction when the effect of two or more variables is not additiveeffect of two or more variables is not additive

- Biologically it often means a series of intertwined - Biologically it often means a series of intertwined actions and reactionsactions and reactions

- The measurement of such actions and reactions - The measurement of such actions and reactions provides the appropriate metricprovides the appropriate metric

ANIMAL GROUPING

ZOA: zone of attraction ZOO: zone of orientation

ZOR: zone of repulsion

Interaction rules considered inanimal collective movement models

ANIMAL TERRITORIALITYInteraction mechanisms considered in

the formation of animal territory

i) Territorial defense:making one’s presence conspicuous to a neighbour through

markingii) 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 wanderitself proportional to the active scent time

ANIMAL TERRITORIALITYDYNAMICAL EMERGENCE

4) EXPERIMENTAL VALIDATION

Question to be askedQuestion to be askedWhat and how sensory modalities are at work in What and how sensory modalities are at work in collective animal movement?collective animal movement?

- In animal grouping it is yet to be - In animal grouping it is yet to be understoodunderstood

- In territory formation we have tested the - In territory formation we have tested the ‘microscopic’ olfactory signal hypothesis ‘microscopic’ olfactory signal hypothesis (scent marking)(scent marking)

When empirical measurements are based on When empirical measurements are based on coarse-grained population-level observations, coarse-grained population-level observations, model predictions cannot be validated against a model predictions cannot be validated against a quantifiable testable hypothesis (animal quantifiable testable hypothesis (animal grouping)grouping)

COLLABORATORS

J.R. PottsBristol Centre for Complexity Sciences

Stephen HarrisSchool of Biological Sciences, University of Bristol