Social and ecological factors influencing movement and organizational patterns in sheep Habiba, Caitlin Barale, Ipek Kulahci, Rajmonda Sulo and Khairi Reda complementary approaches from ecology and computer science

How do we identify the key individuals in a group? Personality 'types’ Group social dynamics Group movement patterns

Approaches Ecology Direct observation Information on: Proximity Individual movement patterns Behavior Interactions Individual state Computer Science Remote sensing Information on: Proximity Group-level movement patterns Clustering Velocity Turning angle

How can we use concepts from computer science to study animal behavior? Association visualizations Static networks GPS clustering algorithms Dynamic networks Social network analysis Agent-based modeling

GPS Data  Data Collection  General Statistics  Map with GPS readings overlaid (Khairi)

Personality Analysis PCA to generate personality ‘types’ Static social networks Association visualizations

Push/pull Push/pushed Followed pulls Pull/follower Push/follower Lactation state Join time in the mornings Group joining Alone grazing Location- front Location- back Location- edge Location- front during movement Personality components

Push/pull Push/pushed Followed pulls Pull/follower Push/follower Lactation state Join time in the mornings Group joining Alone grazing Location- front Location- back Location- edge Location- front during movement Personality components PCA component 1 - spatial PCA component 2 - behavioral

PCA 2 Push/pull Push/pushed Followed pulls PCA1 Location- back Location- edge Location- front during movement Personality scores

Group movement can be initiated either by pulling or pushing

Pull-follow and displacement networks What does the network look like from the perspective of individuals?

Social Network metrics Degree Betweenness Closeness Cluster coefficient Eigenvector

Key individuals – pull network Size: # of times an individual pulls Color: PCA category Lactating Not-lactating

Key individuals – push network Size: # of times an individual is pushed Color: PCA category Lactating Not-lactating

Key individuals – nearest neighbor network Size: # of times two individuals are neighbors while aligned-grazing Color: PCA category Lactating Not-lactating

Moving from static networks to dynamic ones

Static Vs Dynamic Networks T = i … T = i+1T = i+2T = i+3T = i+4 …

GPS clustering  What is an edge ?  Use k-means algorithm to spatially cluster gps readings. Any two sheep in the same cluster have an edge between them.  Use the Simple Structure Index (SSI) to determine the number of optimal clusters in each time interval

 Using different graph theoretic measures, the goal is to identify sampling rates at which the measures contain minimal noise while still being informative of the underlying dynamics in the network. What is the right temporal resolution?  Apply information theoretic concepts to quantify noise and information and compute the best trade- off across different sampling rates.

Algorithm TWIN  For w < w max * Compute the interaction network. * Compute the different structure measures such as density, and centrality, etc.  Quantify the amount of noise and information inherent in the network measure.  Compute a measure of goodness of fit based on a trade-off between the two.

TWIN Results Optimal interval = 3min Optimal interval = 5min

GPS data - issues  Data Quality  Discrepancy of sensor readings on the same sheep  Missing Values

Static Vs Dynamic Networks T = i … T = i+1T = i+2T = i+3T = i+4 …

Diffusion Process Independent Cascade Diffusion Model pr

Diffusion Process Linear Threshold Diffusion Model өiөi өjөj өkөk өlөl b i,j b j,l b i,l b k,l b i,k

Independent cascade

Text Linear threshold model

Community Identification A dynamic community is a subset of individuals that stick together over time. NOTE: Communities ≠ Groups t=1 t=2 t=3 t=4 t=5

Approach: Assumptions Individuals and groups represent exactly one community at a time. Concurrent groups represent distinct communities. Desired Required Conservatism: community affiliation changes are rare. Group Loyalty: individuals observed in a group belong to the same community. Parsimony: few affiliations overall for each individual.

Approach: Color = Community V alid coloring: distinct color of groups in each time step

Dynamic structure measures

Interesting behavioral aspects to model –Social foraging Alignment Sub-group formation from local interactions “Exploratory” random walks –Foraging strategy How do sheep find good food in patchy landscape? How does information about food resources spread in the herd? Competition –Pull and push Agent-based model

Interesting behavioral aspects to model –Social foraging Alignment Sub-group formation from local interactions “Exploratory” random walks –Foraging strategy How do sheep find good food in patchy landscape? How does information about food resources spread in the herd? Competition –Pull and push Agent-based model

–Sheep watch closest N neighbors and react to their behavior –No personality variance among agents –Agents assumed to be “hungry”. They graze continuously without rest –Agents have 3 states: GRAZE, WALK, PANIC –Low vegetation quality and patchy landscape; agents need to move frequently to maximize gain Assumptions

Agents switch back and forth between grazing and social walking State transition governed by a Gaussian timer –Grazing bouts: mean=6 sec, SD=2 sec –Social walking: mean=2-8 sec (depending on isolation), SD=2.5 sec Certain events cause agents to switch state –Agents minimize grazing and take longer walks if they are isolated from subgroup Timing

Local rules Collision avoidanceCohesionAlignment Random biased-walks P = 0.05 (when walking) Pulling

Agents that find themselves drifting away turn back and rejoin the subgroup Subgroup awareness

Demo

Conclusions

Sheep 15 – an influential individual?? Central in the observational networks –High betweeness and degree –Highest number of successful pulls Role in correlational plots –Often an outlier –Makes trends more significant GPS – doesn’t stand out Why?? Missing data…

Sheep 19 – a loner?? Static networks Not well connected –>>> Animation Little interaction with others in herd GPS – consistently low spread values

Are social network measures of individuals consistent across the three networks? Push & pull networks: + correlation (betweenness & closeness) Push & nearest neighbor networks: - correlation (eigenvector & closeness)

Network comparison  Is there consistency between observational subgroups and GPS clustering data?  Is there consistency between personality analysis obtained from observations and that obtained from GPS data aggregated at the “optimal” time interval?

Bite rate correlates with relative position p < 0.005, R 2 = 0.47

CS future directions Community structure evolution. Compare the observational data with “unsupervised” data collection and interpretation methods. Network comparison of different population to discover their social dynamics independent of their environment and other factors.