# Inferring leader-follower behavior from presence data in the marine environment: a case study on reef manta rays

### Submission summary

 As Contributors: Juan Fernandez-Gracia Preprint link: scipost_202204_00019v1 Code repository: https://github.com/juanfernandezgracia/leadership_package Date submitted: 2022-04-12 11:22 Submitted by: Fernandez-Gracia, Juan Submitted to: SciPost Physics Academic field: Physics Specialties: Biophysics Statistical and Soft Matter Physics Approaches: Computational, Observational

### Abstract

Social interactions are ubiquitous in groups of animals, including humans. These interactions might be of different nature, for example, competitive, mutualistic, or kinship; and their global structure is naturally studied with the tools of complex network theory. Traditionally, it has been challenging to examine social interactions in the marine environment given the difficulties associated with data collection, however, developments in acoustic telemetry technologies now present a novel way to remotely examine such behaviour. Here, we propose a method to extract leader-follower networks from presence data collected by a single acoustic receiver at a specific location. The method is based on the Kolmogorov-Smirnov distance between the distribution of lag times between the consecutive presence of an individual followed by the presence of another and its conjugate distribution. After characterising the method through controlled generated data, we apply it to detection data collected for acoustically tagged reef manta rays (Mobula alfredi) by a single acoustic receiver positioned at a frequently visited site. First, we show that the presence of reef manta rays in the vicinity of the cleaning station displays several temporal heterogeneities, such as a circadian rhythm, as well as burst-like behavior, where the time between consecutive presences follows a power-law distribution. Second, we infer the leader-follower network of manta rays and characterize individuals in terms of their position on this network relative to their sex and size. We find, in agreement with biological and ecological insights, that (i) female reef mantas follow more males than expected; (ii) male reef manta rays follow fewer females than expected, but with a stronger association to certain individuals; (iii) reef manta rays follow each other with a weaker association than larger individuals do, while the rest of the reported interactions between individuals appear to be random.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission scipost_202204_00019v1 on 12 April 2022

## Reports on this Submission

### Report

Fernandez-Gracia and coauthors present a general method to create directed networks of follower-leader relationships from the time series of presence data. It is based on the Kolmorogov-Smirnov distance between the interevent time distributions of the agents (nodes). They test their method with synthetic data coming from a Hawkes process and then apply it to a dataset of presence data collected for reef manta rays in the Seychelles. Finally, they draw some conclusions linking the found leader-follower relations in the population of mantas and some metadata, such as the sex or the size.

I would like to start by noting that I have enjoyed reading the article. It is well-written and the length feels appropriate. Moreover, I like interdisciplinary works such as this one, where physics-based methods/concepts (in this case, Hawkes processes, network science) are used to approach problems in other disciplines (in this case, hierarchical relations in an ethological context). I am inclined to recommend the paper for publication, but before doing so I believe that there are some points that still need further clarification and motivation. I present them in the following.

- In the abstract, authors say "more males than expected" and "fewer females than expected". Expected with reference to what? Please specify.

- I wonder whether there is any work or reference the authors can provide where it is motivated the link between physical following (appearance in the cleaning station) and an actual leader-follower roles in some aspect of animal (for the mantas or for other species) culture, such as learning/teaching, mating, etc.

- If I understood correctly, the KS distance is computed between all pairs of mantas, and then those links that present an $|A_{KS}|$ below its value from the reshuffled sequence are ruled out. I would clarify this when the algorithm is introduced, Section 2.1.

- The notation is confusing, since the authors call $t$ both the absolute time (e.g., in the introduction of the models in Sect. 2.2, in Figs. 1A, 2A, 4B, etc.) and relative (interevent) time (e.g., in Figs. 1B, 2B, 4C, etc.). Please solve this by using different symbols.

- For the sake of completeness, please indicate that red and blue in Fig. 4A correspond to female and male (if that is the case).

- I understand how the toy model based on heterogeneous Poisson processes mathematically works, but I find it hard to translate into the physical terms of the manta rays. If Individual A activates and B is to follow her, then the latter will have an increase in her rate during an interval $\Delta t$. This means that during $\Delta t$ the detector should detect B more often once A activates, i.e., A is detected and B has more chances of going in and out of the detector range. Why? If B is following, she should not enter and exit the detector range less frequently? How do the authors justify that this model is a "presence" toy model?

- Regarding the previous point, the authors should specify what they understand by "following", since the detector has a range of 300m of diameter. Is the following close in space and time? Do both manta rays follow similar trajectories in space but with a (more or less) constant time lag, like a kind of marine version of pheromones?

- I miss some more information regarding the longitudinal dimension. The authors differentiate mantas in size (small and big), which I interpret as a proxy for their age. The entire time range they are looking at is close to 3 years. How much, on average, a manta ray live? Can be safely assumed that small/big individuals remain so during the whole observation period?