Narwhals: Arctic Odontocetes Research

• Narwhals are high‐Arctic odontocetes distinguished by elongated tusks and extreme diving capabilities, serving as model organisms for behavioral and ecological studies.
• Recent research integrates irregular telemetry, biologging, and state‑space models to quantify movement, habitat selection, and responses to bathymetry and anthropogenic noise.
• Advanced methodologies such as U‑Net for buzz detection and time‑warping regression for tusk analysis enable precise inference on foraging strategies and age estimation.

Searching arXiv for recent narwhal-related papers to ground the encyclopedia entry. arxiv_search(query="narwhal telemetry behavior movement age tusk accelerometer", max_results=10, sort_by="submittedDate") Narwhals (Monodon monoceros) are high‑Arctic odontocetes distinguished by an elongated tusk, extreme diving capacity, and marked dependence on acoustically mediated behavior. Recent quantitative work on narwhals spans movement ecology, habitat selection, foraging inference, age estimation, and disturbance responses, with a particular emphasis on methods that accommodate irregular telemetry, complex fjord coastlines, and biologging signals of varying periodicity (Dupont et al., 10 Jun 2026, Ngô et al., 2021, Nielsen et al., 2024, Delporte et al., 2024). Across these domains, narwhals appear as a model system for inference under severe observational constraints: Argos and Fastloc telemetry with large anisotropic error, accelerometer records with extreme class imbalance, elemental tusk chronologies with nonstationary periodicity, and movement trajectories constrained by shoreline geometry and anthropogenic noise (Dupont et al., 10 Jun 2026, Ngô et al., 2021, Nielsen et al., 2024, Delporte et al., 2024).

1. Taxonomic and ecological characterization

Narwhals are high‑Arctic odontocetes and are described as one of the most mysterious marine mammals because of their isolated habitat in the Arctic region (Ngô et al., 2021). They are distinguished by their elongated tusk and by extreme diving capacity, reaching depths of $>1800$ m (Ngô et al., 2021). Their tusk is the elongated, spiraled upper left canine, and it records a lifetime of growth in dentin and cementum (Nielsen et al., 2024).

Foraging occurs in disphotic and aphotic zones and relies on echolocation (Ngô et al., 2021). Reported prey include Greenland halibut, polar cod, capelin, and squid (Ngô et al., 2021). Seasonal ecology is recurrent across the literature: migration between fjords and offshore habitats, diet shifts, and environmental gradients are invoked to explain cyclic signatures in tusk dentin, while fjord residency structures both exposure to anthropogenic noise and fine‑scale movement constraints (Nielsen et al., 2024, Delporte et al., 2024).

A central implication of these observations is that narwhal ecology is simultaneously pelagic, benthopelagic, and topographically constrained. This suggests that analytical frameworks must connect local movement decisions, broad‑scale utilization distributions, and seasonal life‑history archives rather than treating these as separate problems.

2. Movement, habitat selection, and utilization distributions

Recent telemetry analysis in Qikiqtaaluk, Nunavut, Canada used 18 tagged narwhals from August–October 2017, focusing on the 12 individuals equipped with satellite tags that recorded both Fastloc GPS and Argos locations over approximately two months, from 1 August to 2 October (Dupont et al., 10 Jun 2026). Tracks were split at gaps longer than two hours to mitigate discretization bias, yielding highly irregular sampling, with time gaps ranging from 3.6 seconds up to 2 hours and an average interval of about 15 minutes (Dupont et al., 10 Jun 2026).

The movement process was modeled as an underdamped Langevin diffusion in continuous time, with location $\mu_t$, velocity $v_t$, friction $\gamma>0$, speed scale $\sigma>0$, and stationary location density $\pi(\mu)$ derived from a resource selection function (RSF) (Dupont et al., 10 Jun 2026). The RSF is written as

$$w(\boldsymbol{x}) = \exp\!\left(\boldsymbol{\beta}^{\top}\mathbf{z}(\boldsymbol{x})\right),\qquad \pi(\boldsymbol{\mu}) = \frac{w(\boldsymbol{\mu})}{\int_{\Omega} w(\boldsymbol{\mu'})\, d\boldsymbol{\mu'}},$$

with movement driven by gradients of the log stationary density,

$$\nabla \log \pi(\boldsymbol{\mu}) = \sum_{k} \beta_k \nabla c_k(\boldsymbol{\mu}).$$

The corresponding stochastic differential equation is

$$d\boldsymbol{\mu}_t = \boldsymbol{v}_t\, dt,\qquad d\boldsymbol{v}_t = -\gamma\,\boldsymbol{v}_t\, dt + \sigma^2 \nabla \log \pi(\boldsymbol{\mu}_t)\, dt + \sqrt{2\gamma}\,\sigma\, d\boldsymbol{B}_t.$$

This formulation yields a unique joint stationary distribution whose location marginal is the utilization distribution (UD) (Dupont et al., 10 Jun 2026).

In the narwhal application, the primary environmental covariate was bathymetry $c_1(\mu)$ from the GEBCO 2024 grid, and the squared distance to water, $\mu_t$0, was included both as a covariate in the stationary distribution and as a penalty to discourage latent positions on land (Dupont et al., 10 Jun 2026). The coefficient for $\mu_t$1 was constrained to be negative, reflecting avoidance of land (Dupont et al., 10 Jun 2026). No time‑varying covariates such as sea ice were included, consistent with the stationarity assumptions of the Langevin formulation (Dupont et al., 10 Jun 2026).

The fitted unified Langevin state‑space model recovered a strong bathymetry effect,

$\mu_t$2

indicating preference for deeper waters in the study area (Dupont et al., 10 Jun 2026). The corresponding two‑step method substantially shrank the effect toward zero,

$\mu_t$3

The resulting UDs placed the highest 10% of log‑UD values in waters deeper than about 780 m, with core areas aligned with deep fjord channels (Dupont et al., 10 Jun 2026). The unified model estimated $\mu_t$4, corresponding to an average movement speed of about 6.9 km·h$\mu_t$5, and $\mu_t$6, implying a persistence timescale of approximately $\mu_t$7 minutes for velocity autocorrelation to drop by about 95% (Dupont et al., 10 Jun 2026).

These findings formalize a broad ecological picture: narwhal space use in late summer–early fall is concentrated in deep fjord channels, and local movement appears to follow bathymetric gradients into deeper waters (Dupont et al., 10 Jun 2026). A plausible implication is that depth acts not merely as a static descriptor of habitat but as a gradient field shaping both transient trajectories and long‑run space use.

3. Telemetry error, complex coastlines, and single‑stage inference

Marine narwhal telemetry routinely violates the assumptions of regular sampling and negligible measurement error (Dupont et al., 10 Jun 2026). In the Qikiqtaaluk dataset, Fastloc GPS observations were modeled with a circular error of 50 m radius, whereas Argos locations had large anisotropic errors characterized by Kalman‑filtered error ellipses, with a semi‑major axis median of 5 km and a third quartile of 15 km (Dupont et al., 10 Jun 2026). The observation model was

$\mu_t$8

where $\mu_t$9 was formed from Argos ellipse parameters $v_t$0 and a scaling parameter $v_t$1, and $v_t$2 for Fastloc GPS (Dupont et al., 10 Jun 2026).

The principal methodological problem is that habitat covariates depend on latent true locations, making standard state‑space formulations difficult when measurement error is large and covariates vary sharply near coastlines (Dupont et al., 10 Jun 2026). The reported solution uses the Laplace approximation to integrate jointly over true locations and habitat covariates along latent paths, implemented in Template Model Builder (TMB) (Dupont et al., 10 Jun 2026). The marginal likelihood is

$v_t$3

and the approximate marginal log‑likelihood is

$v_t$4

with $v_t$5 the conditional mode of the random effects and $v_t$6 the Hessian of the joint negative log density with respect to latent states (Dupont et al., 10 Jun 2026).

To respect the land–water constraint, the model incorporated a spatial penalty,

$v_t$7

together with penalties on $v_t$8 and $v_t$9 to prevent unrealistic parameter inflation (Dupont et al., 10 Jun 2026). This matters empirically because raw narwhal tracking data in complex fjords often contain apparent land positions. In the Qikiqtaaluk study, raw data contained 1,825 locations on land; the unified model moved 1,381 of these to water and moved 193 water points onto land, leaving 637 on land, whereas the two‑step approach did not correct any land points and left all 1,825 on land (Dupont et al., 10 Jun 2026).

Simulation results under Argos‑like error and irregular missing observations show why the single‑stage approach is consequential. The Langevin state‑space model maintained high overlap between true and estimated UDs, with Bhattacharyya’s affinity $\gamma>0$0 even under large measurement errors, and remained robust to increasing missingness (Dupont et al., 10 Jun 2026). With 50% measurement error relative to $\gamma>0$1, the two‑step bias for a strong positive coefficient was $\gamma>0$2, approximately 60% attenuation, versus $\gamma>0$3, approximately 2.5% attenuation, for the unified model; coverage of 95% confidence intervals remained approximately 0.85–0.97 for the unified model but was essentially zero for the two‑step method beyond 20% error (Dupont et al., 10 Jun 2026).

The broader significance is methodological as much as biological. Narwhals inhabit precisely the settings—irregular sampling, intricate coastlines, mixed telemetry streams, and strong positional uncertainty—in which prefilter‑then‑analyze workflows are most vulnerable to attenuation and spurious precision (Dupont et al., 10 Jun 2026).

4. Foraging behavior, buzzes, and accelerometer inference

Narwhal foraging has been studied using high‑frequency behavioral tags deployed on five adult males in Scoresby Sound, East Greenland, during summer 2018 (Ngô et al., 2021). These Acousonde tags recorded tri‑axial accelerometry at 100 Hz, pressure‑derived depth at 10 Hz, and acoustics at 25,811 Hz, with the first 24 h post‑tagging removed to mitigate capture and tagging effects (Ngô et al., 2021). The total dataset comprised 121.8 h, 43,841,100 accelerometer samples, and 2,615 buzz events with cumulative duration 1 h 31 min 56.8 s (Ngô et al., 2021).

In toothed whales, terminal buzzes are rapid click trains with short inter‑click intervals $\gamma>0$4 ms, and they mark the final phase of prey capture attempts (Ngô et al., 2021). Acoustic buzz detections served as ground truth in this study: analysts reviewed 30‑min Acousonde files in MTViewer and validated outputs from a custom buzz detector at 10 Hz, with buzz lengths ranging from 0.4 to 6.7 s (Ngô et al., 2021). The practical goal was to infer prey capture attempts directly from accelerometer and depth data, thereby avoiding the logistical and archival burden of continuous high‑rate acoustic monitoring (Ngô et al., 2021).

Dive context was explicitly modeled. A dive was defined as a continuous period reaching at least 20 m, with 10 m marking onset and end; the bottom phase was the time at or deeper than 75% of maximum dive depth, and dive phase was encoded as surface, descending, bottom, or ascending (Ngô et al., 2021). Classical models used 1‑s windows with 50% overlap and 27 engineered features, including per‑axis mean, standard deviation, root mean square, MinMax, mean depth, magnitude features, peak features, cross‑axis correlations, and dive‑phase one‑hot indicators (Ngô et al., 2021). Positive windows numbered 6,348 out of 526,086 total, reflecting severe class imbalance (Ngô et al., 2021).

Three automated buzz detection methods were evaluated: logistic regression, random forest, and a deep learning U‑Time/U‑Net architecture for time‑wise segmentation (Ngô et al., 2021). The U‑Net was a 1D fully convolutional encoder–decoder with repeated blocks of convolution plus batch normalization, max‑pooling in the encoder, symmetric upsampling in the decoder, concatenative skip connections, and a final sigmoid activation for per‑sample buzz probabilities (Ngô et al., 2021). Best reported hyperparameters were 4 initial filters, kernel size 4, batch size 8, Adam with learning rate 0.01, Dice loss, and early stopping up to 301 epochs with a patience of 150 epochs after the best validation epoch (Ngô et al., 2021).

The U‑Net consistently outperformed logistic regression and random forest across overlap and distance criteria and generalized well to held‑out individuals, except for some degradation on narwhal 20158 (Ngô et al., 2021). At the dive level, in an explicit subset example, the U‑Net produced $\gamma>0$5, $\gamma>0$6, $\gamma>0$7, $\gamma>0$8, yielding precision $\gamma>0$9 and recall $\sigma>0$0 for classifying foraging dives (Ngô et al., 2021). Random forest frequently predicted zero buzzes for foraging dives, and logistic regression tended to underestimate buzz counts (Ngô et al., 2021).

A central biological finding is negative: narwhals did not exhibit reliable large RMS jerk signatures concurrent with buzzes (Ngô et al., 2021). Jerk was defined as

$\sigma>0$1

with discrete approximation

$\sigma>0$2

and RMS jerk computed over 200 ms windows (Ngô et al., 2021). Precision of buzz prediction from big RMS jerk was $\sigma>0$3 for thresholds $\sigma>0$4 mG/s; at higher thresholds precision could approach 1 for some individuals, but recall dropped near zero (Ngô et al., 2021). The reported interpretation is that this absence of pronounced jerks is consistent with suction feeding and with prey types such as squid in the water column, rather than raptorial strikes documented in some other marine mammals (Ngô et al., 2021).

This work reframes narwhal foraging inference as a signal segmentation problem under extreme rarity. A plausible implication is that buzz counts per dive and time spent buzzing can serve as scalable behavioral summaries for future prey‑intake and bioenergetic models, even when acoustic data are unavailable (Ngô et al., 2021).

5. Tusk growth layers, time warping, and age estimation

Narwhal tusks preserve a longitudinal record of lifetime growth, making them sclerochronological archives as well as anatomical structures (Nielsen et al., 2024). As new dentin is laid down radially, the tusk forms annual growth layer groups (GLGs), described as paired opaque and translucent increments analogous to tree rings and fish otolith annuli (Nielsen et al., 2024). Elemental profiles, particularly barium normalized by calcium, often show two peaks per year corresponding to summer–winter contrasts (Nielsen et al., 2024).

The age‑estimation problem arises because growth rate is not uniform over life, so periodicity in distance is nonstationary and distance cannot be mapped to calendar time by a constant scale factor (Nielsen et al., 2024). To address this, a time‑warping regression model was introduced in which the observed signal $\sigma>0$5 at equidistant spatial points $\sigma>0$6 satisfies

$\sigma>0$7

with

$\sigma>0$8

Here $\sigma>0$9 is the amplitude of the slow annual component, $\pi(\mu)$0 the amplitude of the fast semiannual component, $\pi(\mu)$1 the phase, and $\pi(\mu)$2 a strictly increasing warping map from distance to phase time (Nielsen et al., 2024).

The warping function is

$\pi(\mu)$3

where the instantaneous frequency $\pi(\mu)$4 follows a Cox–Ingersoll–Ross square‑root diffusion,

$\pi(\mu)$5

Under $\pi(\mu)$6, $\pi(\mu)$7 remains positive except at $\pi(\mu)$8, so time never goes backward (Nielsen et al., 2024). The total number of annual cycles through location $\pi(\mu)$9 is

$$w(\boldsymbol{x}) = \exp\!\left(\boldsymbol{\beta}^{\top}\mathbf{z}(\boldsymbol{x})\right),\qquad \pi(\boldsymbol{\mu}) = \frac{w(\boldsymbol{\mu})}{\int_{\Omega} w(\boldsymbol{\mu'})\, d\boldsymbol{\mu'}},$$0

and because the barium record shows two peaks per year, age equals the total cycles (Nielsen et al., 2024).

The case study concerned a tusk collected from the Inuit hunt at Niaqornat, West Greenland, identified as ID 956 and harvested in 2010 (Nielsen et al., 2024). The tusk was cut longitudinally, one half was subdivided into 12 pieces, and each piece was analyzed along a dentin transect by laser ablation inductively coupled plasma mass spectrometry at GEUS (Nielsen et al., 2024). Fourteen elements and isotopes were acquired, but the analysis centered on barium‑137 normalized by calcium‑43 (Nielsen et al., 2024). Each piece was fit separately, and fitted growth‑time processes were concatenated chronologically to reconstruct a full life‑course warp (Nielsen et al., 2024).

The age estimate for tusk 956 was 51 years, with a 95% confidence interval of 44–60 years (Nielsen et al., 2024). This was compared with an expert manual GLG count of 57 and bomb‑pulse radiocarbon dating indicating 54, both consistent with the model‑based interval (Nielsen et al., 2024). On heterogeneous simulated signals spanning 2–12 cycles, 92% of estimates fell within 1 cycle of truth and fewer than 1% deviated by more than 3 cycles (Nielsen et al., 2024).

The importance of this result extends beyond chronology. Accurate ages anchor life‑history schedules, age‑specific survival and fecundity, age‑structured population models, and conservation assessments for populations subject to rapid environmental change (Nielsen et al., 2024). This suggests that tusk chemistry can function as a temporally indexed ecological archive, not only a counting device for age.

6. Anthropogenic noise, constrained movement, and fjord geometry

Anthropogenic underwater noise is increasing in the Arctic, and narwhals are regarded as vulnerable because they depend on sound for vital functions (Delporte et al., 2024). Controlled exposure work in Scoresby Sound, Southeast Greenland, examined six male narwhals equipped with FastLoc GPS receivers in August 2018 (Delporte et al., 2024). GPS positions were recorded at surfacing times with a median interval of approximately 5 minutes; only 0.3% of intervals exceeded 2 hours, and 4,815 positions were retained after excluding the first 12 hours after tagging and two measurements implying velocity $$w(\boldsymbol{x}) = \exp\!\left(\boldsymbol{\beta}^{\top}\mathbf{z}(\boldsymbol{x})\right),\qquad \pi(\boldsymbol{\mu}) = \frac{w(\boldsymbol{\mu})}{\int_{\Omega} w(\boldsymbol{\mu'})\, d\boldsymbol{\mu'}},$$1 km/h (Delporte et al., 2024).

The exposure platform was an offshore patrol vessel equipped with two 6 m‑deep airguns, sailing at 4.5 knots from August 25 to September 1, 2018, with synchronous shots every 80 s (Delporte et al., 2024). Exposure began when a narwhal first entered line of sight with the ship, and sound exposure was operationalized as inverse distance to ship,

$$w(\boldsymbol{x}) = \exp\!\left(\boldsymbol{\beta}^{\top}\mathbf{z}(\boldsymbol{x})\right),\qquad \pi(\boldsymbol{\mu}) = \frac{w(\boldsymbol{\mu})}{\int_{\Omega} w(\boldsymbol{\mu'})\, d\boldsymbol{\mu'}},$$2

when in line of sight and zero otherwise, with ship distances spanning 2.68–63.8 km (Delporte et al., 2024).

Because Scoresby Sound is a complex fjord system with narrow channels and extensive shoreline, the movement model incorporated boundaries directly in the drift rather than via reflection (Delporte et al., 2024). The baseline correlated velocity model used

$$w(\boldsymbol{x}) = \exp\!\left(\boldsymbol{\beta}^{\top}\mathbf{z}(\boldsymbol{x})\right),\qquad \pi(\boldsymbol{\mu}) = \frac{w(\boldsymbol{\mu})}{\int_{\Omega} w(\boldsymbol{\mu'})\, d\boldsymbol{\mu'}},$$3

where $$w(\boldsymbol{x}) = \exp\!\left(\boldsymbol{\beta}^{\top}\mathbf{z}(\boldsymbol{x})\right),\qquad \pi(\boldsymbol{\mu}) = \frac{w(\boldsymbol{\mu})}{\int_{\Omega} w(\boldsymbol{\mu'})\, d\boldsymbol{\mu'}},$$4 is the movement persistence timescale, $$w(\boldsymbol{x}) = \exp\!\left(\boldsymbol{\beta}^{\top}\mathbf{z}(\boldsymbol{x})\right),\qquad \pi(\boldsymbol{\mu}) = \frac{w(\boldsymbol{\mu})}{\int_{\Omega} w(\boldsymbol{\mu'})\, d\boldsymbol{\mu'}},$$5 controls speed magnitude, and $$w(\boldsymbol{x}) = \exp\!\left(\boldsymbol{\beta}^{\top}\mathbf{z}(\boldsymbol{x})\right),\qquad \pi(\boldsymbol{\mu}) = \frac{w(\boldsymbol{\mu})}{\int_{\Omega} w(\boldsymbol{\mu'})\, d\boldsymbol{\mu'}},$$6 controls rotational turning (Delporte et al., 2024). In the constrained rotational correlated velocity model, angular velocity becomes a smooth function of distance to shore and heading relative to the shore normal: $$w(\boldsymbol{x}) = \exp\!\left(\boldsymbol{\beta}^{\top}\mathbf{z}(\boldsymbol{x})\right),\qquad \pi(\boldsymbol{\mu}) = \frac{w(\boldsymbol{\mu})}{\int_{\Omega} w(\boldsymbol{\mu'})\, d\boldsymbol{\mu'}},$$7 A spline representation was used in the empirical model,

$$w(\boldsymbol{x}) = \exp\!\left(\boldsymbol{\beta}^{\top}\mathbf{z}(\boldsymbol{x})\right),\qquad \pi(\boldsymbol{\mu}) = \frac{w(\boldsymbol{\mu})}{\int_{\Omega} w(\boldsymbol{\mu'})\, d\boldsymbol{\mu'}},$$8

with tensor‑product splines in heading angle and inverse distance to shore (Delporte et al., 2024).

Population‑level baseline estimates were $$w(\boldsymbol{x}) = \exp\!\left(\boldsymbol{\beta}^{\top}\mathbf{z}(\boldsymbol{x})\right),\qquad \pi(\boldsymbol{\mu}) = \frac{w(\boldsymbol{\mu})}{\int_{\Omega} w(\boldsymbol{\mu'})\, d\boldsymbol{\mu'}},$$9 hours (95% CI: [1.06, 1.71]), $$\nabla \log \pi(\boldsymbol{\mu}) = \sum_{k} \beta_k \nabla c_k(\boldsymbol{\mu}).$$0 km/h (95% CI: [4.12, 5.12]), and $$\nabla \log \pi(\boldsymbol{\mu}) = \sum_{k} \beta_k \nabla c_k(\boldsymbol{\mu}).$$1 (95% CI: [−0.14, 0.13]) (Delporte et al., 2024). Shoreline‑induced tortuosity appeared in the smooth $$\nabla \log \pi(\boldsymbol{\mu}) = \sum_{k} \beta_k \nabla c_k(\boldsymbol{\mu}).$$2: at 250 m from shore, rotation magnitude reached $$\nabla \log \pi(\boldsymbol{\mu}) = \sum_{k} \beta_k \nabla c_k(\boldsymbol{\mu}).$$3 rad/hour as $$\nabla \log \pi(\boldsymbol{\mu}) = \sum_{k} \beta_k \nabla c_k(\boldsymbol{\mu}).$$4, while the shore effect was approximately absent at distances $$\nabla \log \pi(\boldsymbol{\mu}) = \sum_{k} \beta_k \nabla c_k(\boldsymbol{\mu}).$$5 km (Delporte et al., 2024). This indicates that spatial constraints increase turning near shore, aligning or steering movement away from the boundary (Delporte et al., 2024).

Sound exposure altered both persistence and speed. The response coefficients were $$\nabla \log \pi(\boldsymbol{\mu}) = \sum_{k} \beta_k \nabla c_k(\boldsymbol{\mu}).$$6 (95% CI: [−4.77, −2.04]) and $$\nabla \log \pi(\boldsymbol{\mu}) = \sum_{k} \beta_k \nabla c_k(\boldsymbol{\mu}).$$7 (95% CI: [0.23, 1.25]), so that

$$\nabla \log \pi(\boldsymbol{\mu}) = \sum_{k} \beta_k \nabla c_k(\boldsymbol{\mu}).$$8

At $$\nabla \log \pi(\boldsymbol{\mu}) = \sum_{k} \beta_k \nabla c_k(\boldsymbol{\mu}).$$9 km, this implies approximately a 50% decrease in $$d\boldsymbol{\mu}_t = \boldsymbol{v}_t\, dt,\qquad d\boldsymbol{v}_t = -\gamma\,\boldsymbol{v}_t\, dt + \sigma^2 \nabla \log \pi(\boldsymbol{\mu}_t)\, dt + \sqrt{2\gamma}\,\sigma\, d\boldsymbol{B}_t.$$0 and a 16% increase in $$d\boldsymbol{\mu}_t = \boldsymbol{v}_t\, dt,\qquad d\boldsymbol{v}_t = -\gamma\,\boldsymbol{v}_t\, dt + \sigma^2 \nabla \log \pi(\boldsymbol{\mu}_t)\, dt + \sqrt{2\gamma}\,\sigma\, d\boldsymbol{B}_t.$$1 (Delporte et al., 2024). Recovery distances for a 10% deviation from baseline were 32.5 ± 6.7 km for persistence and 7.8 ± 2.9 km for speed; for a 50% deviation they were 4.9 ± 1.0 km and 1.8 ± 0.4 km, respectively (Delporte et al., 2024).

The study therefore supports a specific interpretation of noise response in narwhals: increased speed and decreased movement persistence under ship and seismic exposure suggest heightened arousal and evasive maneuvering, while fjord boundaries can magnify these effects by forcing more tortuous trajectories in constrained corridors (Delporte et al., 2024). The associated management recommendation in the source is precautionary stand‑off distances of $$d\boldsymbol{\mu}_t = \boldsymbol{v}_t\, dt,\qquad d\boldsymbol{v}_t = -\gamma\,\boldsymbol{v}_t\, dt + \sigma^2 \nabla \log \pi(\boldsymbol{\mu}_t)\, dt + \sqrt{2\gamma}\,\sigma\, d\boldsymbol{B}_t.$$2 km to limit persistence reductions in critical narwhal habitats (Delporte et al., 2024).

7. Methodological synthesis, limitations, and research directions

Recent narwhal research is notable for the convergence of biologging, stochastic process models, and constrained inference. The unified Langevin state‑space model links local movement decisions to a global utilization distribution while integrating over latent positions and covariates in TMB (Dupont et al., 10 Jun 2026). The accelerometer‑based U‑Net frames prey capture detection as dense segmentation under high imbalance, using raw tri‑axial acceleration plus depth rather than extensive handcrafted preprocessing (Ngô et al., 2021). The tusk time‑warping model translates nonuniform dentin growth into a monotone stochastic phase process, with SAEM, SMC, and parametric bootstrapping used to recover age with uncertainty (Nielsen et al., 2024). The constrained rotational velocity model embeds shoreline effects directly into continuous‑time drift and uses Kalman filtering with Laplace approximation for mixed‑effects estimation (Delporte et al., 2024).

Several limitations recur across these studies. In movement ecology, discrete‑time Gaussian approximations assume locally constant habitat gradients, with bias increasing as $$d\boldsymbol{\mu}_t = \boldsymbol{v}_t\, dt,\qquad d\boldsymbol{v}_t = -\gamma\,\boldsymbol{v}_t\, dt + \sigma^2 \nabla \log \pi(\boldsymbol{\mu}_t)\, dt + \sqrt{2\gamma}\,\sigma\, d\boldsymbol{B}_t.$$3 grows; the Qikiqtaaluk analysis mitigated this by splitting gaps $$d\boldsymbol{\mu}_t = \boldsymbol{v}_t\, dt,\qquad d\boldsymbol{v}_t = -\gamma\,\boldsymbol{v}_t\, dt + \sigma^2 \nabla \log \pi(\boldsymbol{\mu}_t)\, dt + \sqrt{2\gamma}\,\sigma\, d\boldsymbol{B}_t.$$4 hours (Dupont et al., 10 Jun 2026). Stationary UDs require time‑invariant covariates and coefficients, so seasonal covariates such as sea ice or temperature would change the interpretation of $$d\boldsymbol{\mu}_t = \boldsymbol{v}_t\, dt,\qquad d\boldsymbol{v}_t = -\gamma\,\boldsymbol{v}_t\, dt + \sigma^2 \nabla \log \pi(\boldsymbol{\mu}_t)\, dt + \sqrt{2\gamma}\,\sigma\, d\boldsymbol{B}_t.$$5 from a long‑run distribution to an instantaneous selection surface (Dupont et al., 10 Jun 2026). In disturbance modeling, covariates such as shoreline angle, inverse distance to shore, and inverse distance to ship are computed from noisy positions without full error propagation, and the drift‑based constraint does not provide a formal reflecting boundary guarantee (Delporte et al., 2024). In behavioral classification, back‑mounted tags may under‑represent head and jaw kinematics, and labels depend on acoustic detections at 10 Hz with manual verification of positives rather than exhaustive acoustic review (Ngô et al., 2021). In tusk analysis, phase $$d\boldsymbol{\mu}_t = \boldsymbol{v}_t\, dt,\qquad d\boldsymbol{v}_t = -\gamma\,\boldsymbol{v}_t\, dt + \sigma^2 \nabla \log \pi(\boldsymbol{\mu}_t)\, dt + \sqrt{2\gamma}\,\sigma\, d\boldsymbol{B}_t.$$6 and autocorrelation $$d\boldsymbol{\mu}_t = \boldsymbol{v}_t\, dt,\qquad d\boldsymbol{v}_t = -\gamma\,\boldsymbol{v}_t\, dt + \sigma^2 \nabla \log \pi(\boldsymbol{\mu}_t)\, dt + \sqrt{2\gamma}\,\sigma\, d\boldsymbol{B}_t.$$7 can be weakly identified, early pieces with few cycles destabilize $$d\boldsymbol{\mu}_t = \boldsymbol{v}_t\, dt,\qquad d\boldsymbol{v}_t = -\gamma\,\boldsymbol{v}_t\, dt + \sigma^2 \nabla \log \pi(\boldsymbol{\mu}_t)\, dt + \sqrt{2\gamma}\,\sigma\, d\boldsymbol{B}_t.$$8, and secondary fast cycles can induce residual skewness beyond the two‑harmonic model (Nielsen et al., 2024).

The research directions stated in these sources are correspondingly concrete. Habitat and movement models could incorporate additional covariates such as distance to coast, slope, sea‑ice concentration, or seasonally varying coefficients, and could explore anisotropic movement such as channel‑following behavior (Dupont et al., 10 Jun 2026). Accelerometer studies could integrate dive‑profile features more explicitly, use domain adaptation and transfer learning, and add magnetometers, gyroscopes, or jaw accelerometers to refine kinematic proxies (Ngô et al., 2021). Tusk analyses could extend the harmonic basis, model multiple elements jointly, maintain laser paths strictly within dentin, and archive calibration standards for cross‑piece comparability (Nielsen et al., 2024). Noise‑response models could incorporate underwater sound propagation metrics such as SPL or SEL rather than inverse distance alone, propagate measurement error into covariates, and examine post‑exposure recovery dynamics (Delporte et al., 2024).

Taken together, these studies depict narwhals as a species whose biology is inseparable from the statistical structure of the data used to study them. Deep fjord channels emerge as core habitats, buzzes as a tractable proxy for foraging effort, tusk elemental cycles as a probabilistic record of age and seasonality, and shoreline‑constrained motion as a critical mediator of disturbance response (Dupont et al., 10 Jun 2026, Ngô et al., 2021, Nielsen et al., 2024, Delporte et al., 2024).