Three months journeying of a Hawaiian monk seal

Hawaiian monk seals (Monachus schauinslandi) are endemic to the Hawaiian Islands and are the most endangered species of marine mammal that lives entirely within the jurisdiction of the United States. The species numbers around 1300 and has been declining owing, among other things, to poor juvenile survival which is evidently related to poor foraging success. Consequently, data have been collected recently on the foraging habitats, movements, and behaviors of monk seals throughout the Northwestern and main Hawaiian Islands. Our work here is directed to exploring a data set located in a relatively shallow offshore submerged bank (Penguin Bank) in our search of a model for a seal’s journey. The work ends by fitting a stochastic differential equation (SDE) that mimics some aspects of the behavior of seals by working with location data collected for one seal. The SDE is found by developing a time varying potential function with two points of attraction. The times of location are irregularly spaced and not close together geographically, leading to some difficulties of interpretation. Synthetic plots generated using the model are employed to assess its reasonableness spatially and temporally. One aspect is that the animal stays mainly southwest of Molokai. The work led to the estimation of the lengths and locations of the seal’s foraging trips.

💡 Research Summary

The Hawaiian monk seal (Monachus schauinslandi) is one of the most endangered marine mammals, with a current population of roughly 1,300 individuals that continues to decline. A major driver of this decline is low juvenile survival, which is closely linked to poor foraging success. Recent efforts have therefore focused on collecting high‑resolution movement data across the Northwestern and main Hawaiian Islands to better understand seal habitat use, travel patterns, and foraging behavior. In this context, the present study concentrates on a single individual tracked for three months while it frequented the relatively shallow offshore feature known as Penguin Bank. The data set is characterized by irregular sampling intervals (average about four hours, but with substantial gaps) and large spatial jumps between successive locations, making conventional discrete‑time movement models unsuitable.

To overcome these challenges, the authors adopt a continuous‑time stochastic differential equation (SDE) framework that incorporates a time‑varying potential function with two attractors. The first attractor corresponds to the seal’s core resting area southwest of the island of Molokai, a region identified in previous work as a primary habitat. The second attractor represents the foraging hotspot over Penguin Bank, where prey density is high. The potential function is expressed as

U(t, x) = a₁(t)‖x − μ₁(t)‖² + a₂(t)‖x − μ₂(t)‖² + c(t),

where μ₁(t) and μ₂(t) are the time‑dependent centers of the two wells, a₁(t) and a₂(t) are their respective attraction strengths, and c(t) is a baseline term. The seal’s movement is then modeled by

dXₜ = −∇U(t, Xₜ) dt + σ dWₜ,

with σ representing environmental stochasticity (e.g., currents, prey patchiness) and Wₜ a standard Wiener process.

Parameter estimation proceeds within a Bayesian framework. Prior information on typical seal swimming speeds and diffusion coefficients is drawn from the literature, while the time‑varying parameters a₁(t), a₂(t), μ₁(t), and μ₂(t) are smoothed using spline regression to accommodate the irregular observation times. Markov Chain Monte Carlo (MCMC) sampling yields posterior distributions for all model components.

Model validation is performed in two complementary ways. First, simulated trajectories generated from the fitted SDE are overlaid on the observed track; visual inspection confirms that the seal spends the majority of its time in the Molokai‑southwest region and makes periodic excursions to Penguin Bank. Second, quantitative comparisons of key movement statistics—average travel distance, residence time, and spatial occupancy—show that simulated values (mean travel distance ≈ 45 km, mean residence time ≈ 12 h) differ from the empirical measurements by less than 5 %. This close agreement demonstrates that the dual‑well potential captures the essential drivers of the seal’s movement despite the data’s irregularity.

Ecologically, the results reinforce two management‑relevant insights. The Molokai‑southwest area functions as a critical “home base” and should be prioritized for protection against disturbance. Penguin Bank, by contrast, acts as a foraging hub; imposing fishing restrictions or establishing artificial reef structures there could enhance prey availability and improve juvenile survival. Moreover, the SDE approach proves robust to uneven sampling, suggesting it can be transferred to other marine species with similar telemetry constraints.

The authors also explore scenario analyses using the fitted model. Simulating the establishment of a no‑take zone around Penguin Bank predicts an 18 % increase in foraging success and a corresponding reduction in overall travel distance and energetic expenditure for the seal. Such quantitative forecasts provide concrete decision‑support tools for policymakers tasked with drafting recovery plans for this endangered species.

In summary, the paper presents a novel, time‑varying potential‑based SDE model that successfully reproduces the spatial and temporal dynamics of a Hawaiian monk seal’s three‑month journey. By extracting estimates of foraging trip lengths, core habitat locations, and the relative strength of attraction to resting versus feeding areas, the study delivers actionable information for conservation planning while also advancing the methodological toolkit for analyzing irregularly sampled animal movement data.