Inferring Leader-Follower Behavior from Presence Data in the Marine Environment: A Case Study on Reef Manta Rays

TL;DR

The paper addresses inferring directional leader-follower interactions in marine environments from presence data collected at a single site. It introduces a Kolmogorov-Smirnov–based framework that derives a signed KS arrow $A_{KS}$ from lag-time distributions and uses the KS distance $D_{KS}$ with reshuffled nulls to assess significance. Applied to reef manta rays at a Seychelles cleaning station, the method reveals circadian residence patterns, burst-like interevent times with tail exponent $1.38$, and sex- and size-dependent leadership structure. This dyadic, single-location approach provides a principled toolkit for social-network inference in the marine realm and can be extended to acoustic-array datasets to study broader social dynamics across spatial scales.

Abstract

Social interactions are fundamental in animal groups, including humans, and can take various forms, such as competition, cooperation, or kinship. Understanding these interactions in marine environments has been historically challenging due to data collection difficulties. However, advancements in acoustic telemetry now enable remote analysis of such behaviors. This study proposes a method to derive leader-follower networks from presence data collected by a single acoustic receiver at a specific location. Using the Kolmogorov-Smirnov distance, the method analyzes lag times between consecutive presences of individuals to infer directed relationships. Tested on simulated data, it was then applied to detection data from acoustically tagged reef manta rays (\textit{Mobula~alfredi}) frequenting a known site. Results revealed temporal patterns, including circadian rhythms and burst-like behavior with power-law distributed time gaps between presences. The inferred leader-follower network highlighted key behavioral patterns: females followed males more often than expected, males showed stronger but fewer associations with specific females, and smaller individuals followed others less consistently than larger ones. These findings align with ecological insights, revealing structured social interactions and providing a novel framework for studying marine animal behavior through network theory.

Figures (6)

• Figure 1: Two independent homogeneous Poisson processes of rate $\lambda=1$. The sequences were generated up to a maximum time of 100 time units. A Raw event data. Individual A in blue and Individual B in red. B Cumulative distribution of lag times and Kolmogorov-Smirnov arrow, $A_{KS}$, obtained from the sequences shown above. In blue is the cumulative distribution of lag times of Individual A following Individual B, while in red is its conjugate (lag times of B following A). C Distribution of Kolmogorov-Smirnov arrows from 105 realizations of pairs generated as in the sequences above. The distribution shows two peaks around 0, signature of no leader-follower relation.
• Figure 2: Correlated time sequences. Individual A (blue) performs a homogeneous Poisson process of rate $\lambda_1=1$, while Individual B (red) follows the correlated non-homogeneous Poisson process described in the text with parameters $\lambda^*=1, \Delta t=0.2$ and $\delta=4$, i.e., it performs a Poisson process of rate $\lambda_2=1$ except for 0.2 units of time after an event of Individual A, when it performs a Poisson process of rate $\lambda_2=5$. The sequences were generated up to a maximum time of 100 time units. A Raw event data. B Cumulative distribution of lag times and Kolmogorov-Smirnov arrow for the sequences shown above. C Distribution of Kolmogorov-Smirnov arrows from 105 realizations of pairs generated as in the sequences above.
• Figure 3: Assessing significance of the leader-follower relation. A Random uncorrelated sequences with $\lambda_1=\lambda_2=1$ and $t_{\text{max}}=10^3$. In dashed black lines the distribution of KS arrows for the ensemble of those sequences ($10^4$ independent realizations). In green is the distribution of KS arrows for $10^4$ reshufflings of the pair of sequences that gives rise to the arrow marked in red. B Correlated sequences with $\Delta t=0.2, \delta=4$ and a maximum time of $10^3$ time units. The KS arrow distribution for these ensemble of sequences is shown in black ($10^4$ independent realizations), while in green is the distribution of arrows coming from $10^4$ reshufflings of the sequence pair that gives rise originally to the value of the arrow signaled at the red line.
• Figure 4: Temporal heterogeneities in the data. A Raw event data for acoustically-tagged reef manta rays (Mobula alfredi) with more than 100 detection events (females in red and males in blue). B Appearance probability as a function of the hour in the day. The cyan lines correspond to different males, while the pink lines correspond to different females. The red and blue lines are the averages for females and males respectively. The black curve corresponds to the appearance probability of all individuals pooled. C Interevent times distribution, i.e., the distribution of times between consecutive presence events of the same individual.
• Figure 5: Leadership network for acoustically-tagged reef manta rays (Mobula alfredi) detected by a single acoustic receiver placed at a cleaning station at a remote coral reef in Seychelles relative to the sex (Female, pink; Male, blue) and size (node size) of individuals. A Leader-follower network of manta rays at a confidence value $p=0.002$. B and C Types of edges depending on sex and size. An edge of type xy stands for an individual of type x following an individual of type y, where x and y can be f (female) or m (male) for the sexes, or s (small) and B (big) for the sizes. The black symbols are the expected values from $10^4$ reshuffling of the sexes/sizes of the individuals. The x-axis shows the number of such edges, while the y-axis shows the average strength of the edges. Deviation of the real data in the x direction indicates a difference of the number of edges of that kind found in the real network. Deviation in the y direction signals a difference with the expected strength of the leader-follower relation. The arrows show how the results from the original network differ from the results of randomizations.Results for the randomization of sexes.