Source-linked AI summary
Incorporating uncertainty into the study of animal social networks
David Lusseau, Hal Whitehead, Shane Gero
TL;DR
Animal social-network analyses often discard association strength and treat observations as fixed rather than sampled estimates. The paper introduces weighted-network statistics, bootstrapping, and randomization tests, with case studies showing insight into social-unit interactions and community structure.
Problem
Existing animal social-network analyses commonly disregard association strength and treat observed interactions as invariant values rather than statistical samples.
Method
The paper applies weighted network statistics to association matrices and uses bootstrapping and randomization tests to assess sampling uncertainty and departures from random association.
Results
The case studies show that the methods provide insight into interactions within social units and community structure, including calves’ central roles and social-unit differences in clustering.
Takeaways & Limitations
Weighted statistics, bootstrapping, and randomization provide a more realistic view of animal social networks while assessing uncertainty at individual and whole-network levels.
Abstract
from arXiv · showhide
Over the past decade network theory has been applied successfully to the study of a variety of complex adaptive systems. However, the application of these techniques to non-human social networks has several shortfalls. Firstly, in most cases the strength of associations between individuals is disregarded. Secondly, present techniques assume that observed interactions are invariant values and not statistical samples taken from a population. These two simplifications have weakened the value of these techniques when applied to the study of animal social systems. Here we introduce a set of behaviorally meaningful weighted network statistics that can be readily applied to matrices of association indices between pairs of individual animals. We also introduce bootstrapping techniques that estimate the effects of sampling uncertainty on the network statistics and structure. Finally, we discuss the use of randomisation tests to detect the departure of observed network statistics from expected values under null hypotheses of random association given the sampling structure of the data. We use two case studies to show that these techniques provide invaluable insight in the dynamics of interactions within social units and in the community structure of societies.
Defining weighted networks
Animal association data can be represented as weighted networks in which edge weights preserve the strength of relationships between individuals. Association indices derived from observations define these weighted networks.
- Defining weighted networks: Weighted networks preserve variation in relationship strength that binary networks discard.
- Defining weighted networks: Association indices range from 0, meaning never associated, to 1, meaning always associated.
- Defining weighted networks: Nodes represent individual animals, while edge widths are proportional to pairwise association indices.
Incorporating uncertainty in centrality measures
The study uses bootstrapped association data to quantify uncertainty in individual centrality measures within a sperm-whale social unit. These measures reveal that calves can occupy significantly central positions in the association network.
- Incorporating uncertainty in centrality measures: The GOS social unit comprised five adult females, one juvenile male, and one male calf observed in 515 cluster samples over 72 days.
- Incorporating uncertainty in centrality measures: Centrality measures quantify different aspects of individuals’ positions, including sociability, relationship heterogeneity, connectedness, and clustering.
- Incorporating uncertainty in centrality measures: Bootstrapping resamples observations with replacement, repeatedly reconstructs association matrices, and estimates confidence intervals for network measures.The procedure typically uses 1000 replicates.
- Incorporating uncertainty in centrality measures: The analysis found that calves can play a significantly central role by contributing most significantly to the social network.
Defining community structure
The paper defines animal communities from weighted association networks and uses modularity with bootstrapping to represent uncertainty in social-unit membership.
- Community structure describes how individuals segregate into groups, including in fission-fusion societies without spatially separated ranges.
- Modularity identifies a parsimonious division that maximizes weighted associations within communities and minimizes them between communities.Its coefficient Q compares within-community associations with the expected value under random association, accounting for individual strengths.
- The bottlenose dolphin association matrix reproduced the previously identified division into two social units.The analysis used school-membership data from 437 schools observed over 126 days between 1999 and 2002.
- Bootstrapping showed two social cores but left some dolphins with varying or equal probabilities of belonging to either unit.For the network, Qmax=0.1 with a 95% confidence interval of 0.088-0.12.
Understanding social behavior: randomization techniques
The paper uses constrained randomization to separate social preferences and gregariousness from sampling effects in observed clustering.
- Observed association patterns can reflect attraction or avoidance of particular individuals, general gregariousness, and sampling.
- Randomized networks must preserve the data’s sampling structure because simple Erdös-Rényi networks may be inappropriate.
- The study compared the real weighted dolphin network with 1000 Bejder-Manly randomized networks generated using 100 flips per permutation.
- The observed clustering coefficient was 0.440 versus 0.443 for randomized networks, with p=0.001.Aggregation explained most observed clustering, while differences between social units suggested variation in association preferences.
Conclusions
Weighted-network statistics, bootstrapping, and randomization provide more realistic and uncertainty-aware analyses of animal social networks.
- Weighted statistics represent relationship diversity more realistically than binary network analyses and complement traditional techniques.
- Bootstrap and randomization techniques assess uncertainty from data structure and sampling at both individual and whole-network levels.
- These methods cannot replace insufficient data; they estimate confidence in observed variation.
- Interpreting network statistics requires considering social preferences, gregariousness, and sampling contributions to observed association rates.