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Some thoughts on the segmentation null model presented at Hawk Mountain


Frederic and Luca proposed a null model to compensate incongruities introduced by disparate temporal sampling intervals.  The debut null model that Frederic and Luca presented intrinsically assumed constant velocity.  It was pointed out that a more complicated (realistic?) movement model could be used to introduce non-constant velocities into the null model.  After thinking about this more, I tend to prefer the parsimony of constant velocity, especially as it pertains to avian flight.  Wind effects aside, birds more or less fly at a constant velocity.  For example, every day I see resident bald eagles flying in my neighborhood - moving up and down the beach, from tree to tree, etc., and they are always flying roughly, say, 50 km/hr.  In other words, I've never seen an eagle fly (air speed), say, 5 km/hr.  Sure, we know large birds can slow their flight velocity somewhat (but they have to stay aloft), or even greatly increase it for short durations, but for the goal of segmenting migration tracks, I like the parsimony of simply applying a reasonable velocity that is representative of sustained movement.

The segmentation method examined lengths of the tracking segments. It was noted that other metrics could be examined under the same model framework.  I've been thinking about the utility of the internal turning angle (0-180 degrees) that is formed by two consecutive tracking segments.  This turning angle could be used to scale the tracking segment lengths for the purpose of emphasizing (or not) consecutive tracking segments that possess persistent directionality.  Chronologically moving through the tracking segments, and considering 2 segments at a time (s1 followed by s2, with lengths "d1" and "d2" and internal turning angle "a"), a scaled distance metric could be calculated as:

d_scaled = (d1 + d2) * a

This metric, however, may be hypersensitive to Argos spatial errors, and to sampling frequency as well.  I was thinking about the utility of an angle-scaled distance in the context of an idealized seabird scenario (obviously not a raptor).  Consider a seabird that flies, say, 75 km out to sea to forage and then returns to its colony/nest, over and over again during breeding -- relatively long tracking distances, but non-directional. Then, after the breeding season, it migrates along the coast, say, in 75 km increments.  The small internal turning angles associated with 'out-and-back' foraging-trip would scale the associated distances smaller, while the distances associated with the more directional migration segments would be scaled larger.  But, a pitfall occurs when multiple at-sea locations during a single foraging trip get recorded, and hence, the small turning angle associated with the long foray segments becomes decoupled (similarly for stopovers during migration). Perhaps an a priori smoothing method could be applied to the raw tracking data to overcome this conundrum, but it would require a predefined threshold.  For example, short-distance tracking segments could be ignored until their consecutive cumulative distance exceeded some threshold (say 75 km for the seabird example), after which the initial and ending locations would be passed forward to the smoothed output data set.

In all, however, I can't say that I have anything new to propose that could definitively improve upon the original ideas presented at Hawk Mountain.  I realize that the variably-scaled radius would/should eventually capture the idealized seabird migration, while simultaneously providing information about relative scales of landscape occupancy.  Nice work Frederic and Luca -- keep forging ahead!

The way forward

Hi all,

In my view the constant velocity assumption does not reflect anything real but is needed simply because we still cannot measure the variance. Let me note that airspeed is largely unknown because we rarely know anything about the wind speed the bird experiences, and even our perception of the wind direction is vague, as models and measurements show that wind direction on the ground can be opposite to what the birds experience say 500 or 1000 m above the ground. We invested huge efforts to model wind speed for estimating airspeeds (Nir's project), but overall our bird movement data today is merely groundspeed, and all our fine-scale data reveal substantial variation in this property. Beyond the obvious effects of the unknown wind speeds, and the inherent differences among soaring vs. gliding vs. flapping flight modes, we have evidence from foraging vultures for rather abrupt changes in flight speed by perhaps 50% and even more, presumably, e.g., once a carcass is detected, which can make for bouts of different groundspeeds. We have no comparable data for migrating raptors. As for scale issues, whether this non-negligible variance in flight velocity inflates or deflates once we move from 1Hz to one position per hour or so is probably case-specific – I don't know, anyone has any clue for general guidelines beyond the Mandel PNAS paper (which compares hourly and daily sampling rates)? We might test this with the few long-term high-res data we have for foraging vultures, but again, we do not have any comparable data from migrating birds. My bottom line suggestion is to consider constant velocity a questionable assumption we are forced to take given the quality of our data.

On another matter, a colleague in Tel Aviv University has just drawn my attention to the work of Ilan Golani's group on segmentation. Please see Check their "Path segmentor" module which is based on the EM (Expectation-Maximization) algorithm fitting a Gaussian mixture model to the frequency distribution of maximal speeds of the animal’s motion segments (between stops). They apply it to 10Hz movement data obtained from videos measuring movement in small "open-field" (what a strange name!) arenas. I am not sure if anything here could help the raptor segmentation project, but perhaps some insights can be drawn from the 15-20 years this group has invested to address the segmentation problem. Note that they collaborate with an excellent group of statisticians (Yoav Benjamini known from his FDR papers). Also note that their website provides links to relevant publications.

Hope this helps. Best wishes,


The way forward

The various methods and variables that are being suggested (fractal dimensionality by Roland, internal turning angles by Douglas, angle and speed by Raymond, and RGB colour by Kamran) might very well improve the multiscale segmentation analysis. It is difficult to know a priori which one could be more advantageous. They all have their own merits but depending on the specific questions one might be clearly preferable than others.

The way we will find out is by actually complicating the null model. Practically speaking, we will slightly modify the ballistic null model, by using a variety of movement behaviours that are at our disposal starting from Levy type to correlated random walks, etc., or a combination of them. These modifications will serve the purpose of taking into account most of the features present in migrating raptors and/or their data sets. At the same, the theoretical grounding of these null models has the additional advantage of allowing us to clearly show and quantify what are the features that the method we propose could become useful for. And, finally, the observations gathered by analyzing these various null models will also help us to choose a graphical 'threshold' for segmenting the data sets in relation to migration, stopovers, etc..

3 metrics in a colorspace, RGB vs HSL


Intriguing idea by Kami to combine 'segmentation' results for 3 metrics into an RGB colorspace for visualization. I'd love to see a draft. Kami suggested distance, angle, and for example altitude. If angle were to mean azimuth (say from an instantaneous GPS measurement), then the circular nature of the azimuth variable could be represented as "HUE" (which is also circular) in a Hue-Saturation-Lightness colorspace. For better or worse, that would mean the colors in the graph would be driven by the directionality (compass) of movement. In such a colorspace, the distance metric might be well suited to the Saturation value; such that longer distances have richer color saturation. I guess that would leave Lightness to a metric such as altitude; if the metric was inverted before graphing, then lower altitudes would wash-out to very pale (white) colors. hmmm.... obviously some experimentation would be in order if an analysis were to strive in this direction. Using GPS altitude data would also require (for most species) some post-processing with DEMs to estimate above-ground altitude.

Alternatively, and maybe more informative or relevant, an angle metric could strive to represent persistent directionality by examining the turning angles (0-180 degrees) associated with short bursts of tracking segments, and perhaps derived from all pairwise combinations of locations during the short burst.

Kami, at the workshop you mentioned some ideas about using a clustering (EOF) approach to address the need for segmentation. Would not multivariate results (distance, angle, altitude, etc.) lend themselves even more to your ideas? I hope you will revisit your intitial thoughts if/when the time seems appropriate. Producing color graphics that depict the outputs of Fred and Luca's analytical approach are great for visualization, but ulitmately, we would like to create segments (or clusters). I think the clustering idea could prove very useful for investigating degrees of similarity in space-time migratory behavior within species (say age classes, such as juveniles vs breeding adults) or among species. But, ultimately, defining migratory segments in terms of, say, dates when migration started or ended, will likely require threshold definitions, as Luca pointed out at Hawk Mountain.

Finally, I was wondering if Raymond has witnessed anomalies in his GPS instantaneous flight speed and altitude data? I've found that sometimes we get data that places the PTT (Microwave Telemetry units) several hundreds of meters above the ground surface, but with 0 (zero) velocity. Microwave told me that unless a PTT is moving >40 km/hr, that instantaneous velocity can be difficult to estimate and sometimes return a value of 0 (zero).

And one last note, all of the early generation Microwave Telemetry GPS PTTs (and many of the new ones too) report GPS altitude in units of 1-meter in an 11-bit sensor field. This effectively means that the altitude data "roll-over" every 2048 meters. That is, a PTT that is 2050 meters altitude will be reported in the final Microwave Telemetry data as having 2 meters altitude. A PTT at 4098 meters altitude will also be reported in the data as having 2 meters altitude... etc. We recognized this problem a couple of years ago, and have since had Microwave Telemetry divide our altitude estimates by 10 before packing them into an 11-bit value; hence, our PTTs report altitude with 10-meter precision but the values don't 'roll over' until the PTT exceeds 20,480 meters. Yet, to this day, I see data from other AVIAN studies using relatively new MWT PTTs that still report 1-meter precision and roll over every 2048 meters (grrrr....).

best regards,
Dave Douglas

combining multivariate analysis in one graph


I was just thinking of the last comment and thought that it might be possible to use the RGB colour concept to come up with one figure for three layers of data. This way Fred and Luca could use their method and do the multiscaling on distance, angle and a third variable for example altitude. Given the constant speed assumption, which also to me seems reasonable they could produce a multicolour plot where each of these variables occupy either Red (1:255), Green or Blue. I am not sure whether this makes sense, but intuitively it should be possible to produce a single graph, how it could be interpreted is yet another question.

Cheers, Kami

some more thoughts

Just a small addition. I fully agree with David that a null model with constant speeds is probably the best as variation in (hourly) distance is mostly due to differences in the fraction of time aloft, and not due to small differences in instantaneous speeds.

In addition to the idea to also look at turning angle as the 'dependent variable' I thought about a few other possibilities. The GPS logger for example also provides details about instantaneous speed (as measured by the gps unit) and altitude (which can be transferred to altitude above the ground). Frederic and Luca showed us the graphs for the number of locations per radius, but this could as well be any of the abovementioned variables (angle, speed, altitude). It would be very cool to see all these four graphs under each other. Possibly there are even ways to combine them, but I am unsure how to scale angles to for example number of observations.

Cheers, Raymond