# Fur Seal Analysis

The first complete draft of Gurarie2008 MovementAnalysis is now up. Eli 21:28, 5 April 2008 (PDT)

# Drafts of Final Sections for the Manuscript Draft for Collaborative Revision

## Data

I applied the movement analysis method to GPS data collected on several foraging trips taken by a nursing female northern fur seal (\emph{Callorhinus ursinus}). Northern fur seals aggregate annually during the summer months at large rookeries. The females give birth usually in late June through July, and, after 8-10 consecutive days of nursing, begin to take foraging trips of up to a week in length to replenish energetic reserves \citep{Gentry1998}. The data analyzed here was collected from a female tagged in summer of 2007 at Dolgaya Rock, one of the Lovushki Islands - a small group in the central Kuril Island chain in Russia which runs between the Pacific Ocean to the southeast and the Sea of Okhotsk to the northwest (see figure \ref{Map}). The Lovushki Islands are the location of one of the largest northern fur seal rookeries in the northwestern Pacific \citep[Burkanov \emph{pers.~comm.}]{Loughlin1984}.

The female discussed in this paper, labeled NFS07-03, was captured on June 21, when her pup was one to three days old, and instrumented with a Fastloc\textregistered GPS data-logging device (MK10-F, Wildlife Computers Inc.) The tag allows for quick fixes and relatively high accuracy, with at least 60\% of the locations within 100 m \citep{Bryant2007}. The MK10-F device was also equipped with dive depth, temperature and light sensors, and the animal was instrumented with a separate stomach temperature sensor. Here, we only consider the movement data; however, the existence of corroborating evidence for foraging behaviors, such as diving and prey capture, makes this an ideal system to explore what can be inferred from pure movement data.

The animal was monitored for 38 days in total, taking seven foraging trips in that time. The first trip occurred 9 days after tagging, on July 1, and lasted just over five days, while the last trip began on July 27 and lasted about two and a half days. On all trips, the fur seal headed in a northwesterly direction towards the Sea of Okhotsk (figure \ref{Map}). A total of 763 position fixes were obtained over all seven trips, with individual trips ranging from 30 and 33 datapoints (trips 5 and 6) to 205 datapoints in length for trip 1. The time intervals between the fixes range widely from a less than a minute to 700 minutes, with the majority (over 80\%) clustered around 15, 30 and 45 minutes. The data required no filtering and were georeferenced using standard methods. Velocities were estimated by dividing displacements by time intervals, and turning angles were calculated directly from the positions.

## Results

I applied the analysis technique to five of the seven trips (those with more than 70 location fixes) with a window of size 30. At an average time interval between measurements of 37 minutes, the window covered on average a period of 18 hours, which seemed to allow for reasonable chance to pick up single behavioral shifts at an acceptable cost to power. The output of analyses with window size 50, corresponding to about a 30 hour period, seemed too insensitive since it is reasonable to expect that behaviors can change significantly more than once in a day.

Model outputs for two of the trips (1 and 7) are presented graphically in figures 7a 7b. The evolution of the estimates for the Vp parameters in time is schematized in 8.

Because the model output is somewhat complex, it is constructive to walk through a single track from beginning to end. The first trip is the longest (5.1 days long) and furthest (max.~distance from rookery 96 km), as is typical for female fur seals taking their first feeding trip after a fasting period associated with birth. The fur seals' initial departure from the rookery is marked by high values of Vp ($\widehat{\mu}$ around 5 km per hour) and a high estimated per-hour auto-correlation ρ = 0.36 (NB~since the time data is in hours, the ρ is an estimate of what the first order auto-correlation coefficient at lag 1 would be if the movement data were collected once an hour exactly without gaps). The first significant changepoint, occuring at 01:53 in the middle of Night 1 was selected as the MLCP by every single one of the 25 windows that passed over it. The models chosen by the BIC were split about evenly between M4 (μ and σ change) and M7 (all three parameters change). The estimates for μ drop from near 4 km/h to around 2 km/h, estimates for σ drop from 1.5 to 0.7, estimates for ρ decrease more gradually from 0.3 to under 0.1. A similarly dramatic changepoint occurs at around 1900 before the fifth and last night of the trip, where fully 30 MLCP's were selected for at either 20:14 or 21:12. The BIC selected models were mixed between M2 (only σ changes), M4 and M7. The track indicates that this final changepoint is associated with a sudden turn south, and a fairly correlated, moderately fast (around 3 km/hour) journey home.

The interim period between these two travelling bouts is marked most significantly by lower autocorrelation, essentially staying below 0.14 during the entire period and reaching near zero values during the fourth night. The mean persistence velocity and deviances, however, vary considerably in this period, and, while significant changepoints are identified at evening/dusk and dawn on all three interim nights, the behavioral pattern at these times varies somewhat. Before Night 2 at 21:15 there is a significant increase in both μ and σ (11 of 15 MLCP's chose M4). At 00:20 there is a notable drop in ρ only (4 of 4 MLCP's chose M3), and at 4:18 there is a significant drop in μ only (11 of 11 MLCP's chose M1). The μ during the evening is fairly high, at 2.5-3.0 km/h. During the day the mean velocity plummets to 0-0.5 km/hour, while the deviance gradually increases until the evening before Night 3. Night 3 again shows an increase in μ and a decrease in σ, but to a lesser extent that Night 2, and again a drop in velocity during the day. Finally, Night 4 is marked by the lowest autocorrelations ( < .01), low velocities ( < 0.5 km/hour) but a moderate deviance (around 0.5 − 1.0 km/hour). The final day shows the greatest tightening of the deviance with no appreciable increase in velocity, until the aforementioned burst home at 21:00.

The analysis of turning velocity Vt for the first track proves less informative than the analysis of Vp. Of the 175 MLCP's that were identified (one for each window), 121 returned M0, the null model of no significant changes in σ or ρ, (in contrast to only 23 of 175 M0's in Vp), 51 selected M2 (change in σ), 3 selected M3 (change in ρ), and none selected M6 (change in both). The value for ρ were all quite low, with a mean value of 0.002 and about half of the estimates equalling zero. It is notable, however, that at the very beginning of the trajectory, the ρ estimates are quite a bit higher (up to 0.04) than in the remainder of the trip, when the animal was moving at its highest velocity. The higher correlation here, and generally negative values for Vt near the beginning indicates that the animal is conducting a persistent, wide left-turning arc. The deviance remained fairly consistent throughout this trajectory, around 1 km/h, tightening most significantly to about 0.4 km/h during the intensive, low correlation, low Vp deviance fourth night of foraging.

Trip 7 displayed some features that were unique compared to the other analyzed trips. Notably, the velocities the fur seal moved at during Trip 7 were much higher with an aggregate Vp mean of 3.8 km/h (s.e.~1.1) compared to 2.0 (s.e.~1.25) for Trip 1. Somewhat atypically, it left in the evening, moving quickly (around 5 km/h) but with low autocorrelation in its persistence velocity. It made a hairpin-like change in direction at dawn after its first night, appearing to turn back to the rookery, turns again in the afternoon to head NW. During Night 2, the fur seal exhibits considerable slowing, low autocorrelations and loops on its own track several times, appears to head out further to sea second time, spends a night moving relatively fastly and with relatively high auto-correlations, and at dawn after Night 3 performs one last hairpin turn and heads back at a very high pace, raching the highest estimated persistence velocity of all trips at 6.4 km/h, likewise attaining the highest autocorrelations of any trips (0.73). It appears to be missing the rookery on its way home by several kilometers, but adjusts near the end. This return trip is likewise marked by some of the highest auto-correlations in the Vt timeseries (up to 0.11), once again indicating a large and consistent turning radius of movement

A comparison of all the aggregated parameter outputs of the model for all of the trips are presented in figure 9. Violinplots are used in order to highlight the multimodal nature of many of the parameters.

## Discussion

The method presented here displays the ability to robustly identify complex behavioral patterns in irregurlarly measured movement data. The maximum likelihood method is sensitive enough to identify changepoints even in very gappy or noisy data, and the BIC model selection method is conservative enough to protect against excessive complexity. The data considered in the application here is highly accurate positionally, but marked with a typical level of gappiness for a marine species. In general, however, the method is applicable to many kinds of data, including ARGOS, archival tags or radio telemetry data. Furthermore, the algorithms are computation quite tractable. While the output is somewhat sensitive to the analysis window size, this variable is easily tuned according to the temporal resolution of the dataset and the consistency of the model output. Because the method is focused on identifying the location and direction of structural shifts, it is also robust to error, though this aspect is not explored in this paper.

An important innovation in the method presented here is the explicit and tractable analysis of the autocorrelation. This relies an analysis of persistence and turning transformations, while, while not as biologically intuitive as raw speed and turning angle data, have attractive statistical properties that allow for an explicit description of the autocorrelation structure. This autocorrelation is readily interpreted in terms of time-scales at which an organism's basic movement patterns (persistence and turning) change. For example, the most significant distinction between the traveling modes and non-traveling behavioral modes in the fur seal tracks was associated with a change in the auto-correlation. Often, this is an even more significant variable than mean velocities. The fur seal's return trips do not necessarily attain appreciably higher velocities than those during the foraging phase (see for example Trip 1, Night 2). Thus, the fur seal can have a high rate of persistence displacement in a given direction but have a much more erratic movement pattern, puctuated by feeding bouts, dives, turns and loops, whereas the steadiness of a directed movement is captured by a higher persistence velocity autocorrelation. A useful index to consider is the time-interval at which the first order correlation drops to some fixed number such as 0.5. Using the relationship $\tau_h=\log(0.5)/\log(\rho)$, we obtain an estimated time to half-autocorrelation ($\hat\tau_h$). For trip 1, this value is around ranges between 30 and 40 minutes for the travelling modes, and between 4 and 15 minutes during the remainder of the trip. Similar patterns, broadly, hold for the remaining trips.

It is worth making a distinction between the information contained in the autocorrelations of persistence and turning and the parameters of standard CRWs. Although this commonly applied mechanistic model of movement is termed the correlated random walk, in fact almost every application of the model assumes independent turning angles and independent velocities and the smoothness of a CRW path is a result of the clustering of the turning angles around zero degrees. In fact, there is a fundamental distinction between independent turning angles and correlated turning angles, which are manifested in larger turning radii. This is well-captured by the auto-correlation coefficient on the turning component of velocity, as, for example, near the beginning or Trip 1 and the end of Trip 7, where the significant rise of the turning velocity auto-correlation is associated with a large scale arcs, as contrasted with the smaller, independent directions shifts that dominate the bulk of the movements. Similarly, any autocorrelation in the velocities is largely accounted for in the persistence velocity correlation.

Returning to Trip 1, the analysis of the movement data over the three nights of foraging, while marked with well-identifiable patterns, indicate a higher behavioral complexity that might have been expected. The primary prey items for are cephalopods and smaller pelagic fish that engage in vertical diel migrations, particularly during the crepuscular hours. It is known that the majority of feeding occurs at night \citep{Goebel1991} and the dive data associated with NFS07-03 corrobarates this expectation, with most dives beginning at around 23:00 and continuing through the early morning (Andrews \emph{pers.~comm.}). During the day, northern fur seals are known to sleep at sea \citep{Gentry1998}. Thus, the movement during daylight hours, which tended to be the least autocorrelated in Trip 1 for the first three daylight periods is more likely to reflect ambient currents. The distinct changes identified before each of the evening bouts correspond to increased activity and changes in absolute orientation, implying an active pursuit of prey. Interestingly, the mean velocity were quite high, particularly during the first evening, implying perhaps that the forage itself is moving, or that the animal is actively seeking forage over a larger territory. Again, the autocorrelations are relatively low throughout, indicating irregular movements and many changes. The behavior during the third night of foraging reflects the closest to the expectation of what active, successful foraging might look like, with the lower variance and the lowest autocorrelations. However, even here there is a distict, oriented, eastward movement.

The other important feature of the method presented here is the ability of the analysis not only to estimate values of parameters, but to identify significant shifts, such that the model output provides both gradual changes in the parameter values and more discrete differences that are presumably assiciated with behavioral choices. The analysis of these behavioral shifts provides a window into the complexity of an animal's movements.

The violinplots of several of the aggregated parameter values do indicate that types of movement can often be broadly clustered into several discrete clusters. Notably, the estimates for the mean persistence velocity for Trips 2, 3 and 4 indicate a clustering of low velocities (around 2 km/h) and a seperate clustering of high velocities (around 5 km/h). Generally, the higher velocities appear less often at night. This pattern is mirrored to a smaller extent in both the persistence and turning autocorrelation coefficients. However, the behavioral trace in figure \ref{Assessment} suggests a striking complexity in behavioral modes, especially as contrasted with the expectation of a few distinct behaviors. In contrast to a landbound terrestrial organism, which is ultimately entriely responsible for its movements, the movement of a marine organism is confounded by ambient movements of the water and currents. The sudden and dramatic shifts between different areas in the parameter space strongly suggest that these signals are reflections of real behavioral choices.

Both a consideration of autocorrelations and the basic structure of a behavioral shift models can be productively implemented on datasets which lack the unavoidable gappiness of marine organism tracking data.

## Conclusions

A top predator like the fur seal is extremely well-adapted to exploiting the and heterogeneous environment of the open ocean to fulfill its survival needs. Its movement is a complicated manifestation of an organism's internal state, access of information, physiological constraints and behavioral responses to environmental cues. The data collected on this movement is an irregular subsampling of this structurally complex, continuously auto-correlated, multi-dimensional process. The analysis method presented here is a purely descriptive attempt to capture and distill the dynamics of the underlying process from noisy and gappy data. The output is a somewhat complex array of estimates, model selections and aggregated averages, but many of the nuanced patterns of movement behaviors emerge in a clear and tractable way.

The ultimate utility of the method, however, will be in its use for answering important questions. The greatest mystery is: How does an organism successfully exploit its environment? In order to approach this challenge, it is necessary to model whatever information about the behavior the analysis method produces against potentially informative covariates. In the study on fur seal movements in the Kuril Islands, for example, detailed data has been collected in parallel on diving events, ambient temperatures and foraging success via stomach temperature sensors. An analysis of these data against the movement model can yield higher level insights into the relationships between the estimated movement parameters and foraging strategies and success. On a larger scale, comparisons can be made between animals in different locations throughout the range, under varying environmental conditions, as well as between different groups (older and younger, male or female). For terrestrial organisms, movement parameters can similarly be modeled as responses against landscape features

# Older Stuff

## Plots of all fur seal analyses

This file: FurSealAllPlots.pdf contains plots of five Northern fur seal tracks and analysis according to the Gurarie-2008 method.

The data are from fur seal number NFS07-03, and include trips 1, 2, 3, 4 and 7, which were long enough for a complete analysis.

The plots on the left show the time-series of velocity and turning angles decomposed into persistence (Vp = Vcos(θ)) and turning (Vt = Vsin(θ)) components. The decompositions were performed using a window size L of 30 and 50 data points.

The black line is the estimate for the mean $\hat\mu$, the red line represents the estimate for the standard deviaion $\hat\sigma$, and the color reflects the auto-correlation $\hat\rho$: bluer colors indicate less auto-correlated movement, while yellow colors indicate more auto-correlated movement. Vertical orange lines indicate points where the estimation routine suggests there was a significant behavioral shift. Thicker lines correspond to a higher number of selected shifts. Grey bands indicate nighttime.

To the right, I present a mapping of the track itself. Colors again indicate the auto-correlation estimate for the persistence component (Vp), while the size of the dots indicates the estimated velocity at each point.

There is (in my view) lots of things to think about here!

Eli 14:44, 2 April 2008 (PDT)

## Data notes

Captured 21st of June. Pup about 1-3 days old. First trip 9 days later. (perinatal period 9 days - Gentry 1998)

1st trip July 1st... Dives at night (Andrews pers. comm.)

38 days of monitoring.

Sleeping at day. Mike Gobel - feeding behavior 1991. (Deep divers and shallow divers - contrasting species).

Nocturnal prey deep-scattering layer, squid, small pelagic fish (scats 22% cephalopod, 50% Atka mackerel, 42% salmon - Waite pers.comm.) (female stomachs almost all contain squid beaks - Andrews pers.comm.)

Wildlife computers: GPS Fastloc, Mk10-F (GPS data-logging device). Featuring:

• Allows for quick listening times (snapshot of constellation)
• Pressure transducer
• light sensor
• water temperature sensor
• accuracy: over 50% around 100 m

Stomach temperature tag allows for potential measurement of foraging success MK10-L.

## Discussion Brainstorm

• 1) Answer the question raised in the introduction
• "how to 'honestly' interpret movement data"?

### Method

• 2) Discuss assumptions in the model, what are the limitations
• 1b) Autocorrelation in data - embrace the autocorrelation, it's a dynamic parameter.

### Data

• 1) Answer the question raised in the introduction "how to 'honestly' interpret movement data"?
• 1a) movement is heterogenous, but there are patterns,
• 1c) data is gappy, no assumptions about the data

### Conclusions

• How is this useful for biologists?