Bringing order to seal pup movements

Baby seals rarely stray far from their homes. But they do explore, gradually, the area around which they were born, roaming further and further until they are ready to be on their own. For Annika Betken and Alexander Schnurr, seal pup movement represents an ideal test case for their method of applying ordinal analysis to multivariate data sets.

Ordinal analysis can be powerful; the ability to sort data can reveal trends and hidden patterns. But of course, such analysis requires that the data in question be orderable.

“The problem is that we want to work ordinal, but we’re intrinsically multivariate, so we cannot directly have any order,” said Schnurr. “There’s no canonical order in two dimensions.”

To solve this problem for their seal pup data, the authors incorporated the concept of depth. Each pup moved about a central point, so they ordered each point based on how far it was from that center. That let them perform some basic analysis on the movement of these baby seals.

“Based on our analysis, we could say that [seal pup movement] corresponds to an anti-persistent biased random walk rather than to a persistent biased random walk,” said Betken. “It would rather change directions than stay with the direction it started.”

In addition to modeling seal pup movement, the authors say this type of depth analysis can be applied to a wide range of multivariate time series. Similar solutions could be found for bacteria movement and storm cell paths. More abstractly, this technique could also be used to analyze stock market data or brain scan readouts.

“We could also do some forecasting with it,” said Betken. “At the moment, we’re just analyzing the data retrospectively.”

Source: “Depth patterns and their applications in animal tracking,” by Annika Betken and Alexander Schnurr, Chaos (2026). The article can be accessed at https://doi.org/10.1063/5.0335659 .

This paper is part of the Classical Ordinal Patterns and Beyond Collection, learn more here.