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FlightR: Distance Traveled Between Specific Time Periods (w/ Uncertainty)

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I would like to estimate (with uncertainty) the cumulative distance traveled by an organism between two specific time periods. Let's say that I used the find.times.distribution function to identify that a tagged bird most likely commenced spring migration on 1 April 2016 and most likely reached its breeding grounds on 23 April 2016. 


I would like to sum the distance traveled by that bird between every consecutive twilight from 1 April to 23 April. The ideal final result would be something like, "The cumulative spring distance traveled between 1 April and 23 April was median=1034.2 km (95% credible interval: 650.2 to 1840.2 km). 


Getting the median cumulative distance is easy:

sum(spDists(cbind(migration.longitude.values, migration.latitude.values),segments=TRUE,longlat=TRUE))


But I cannot figure out a 'good' way to estimate the uncertainty component. 


One (non-parsimonious) solution would be:

1) generate 95% isopleths (with the plot_util_distr function) for every twilight [or perhaps just every day] between 1 April and 23 April,

2) generate 1000 random points (assuming a uniform distribution) within the confines of each 95% isopleth,

3) create 1000 paths/polylines that run between all 23 isopleths (using a single point in each isopleth),

4) and finally measure the length of those 1000 paths and create summary statistics (median, mean, 0.25 and 0.975 percentile values).


I had been trying to modify the get_ZI_distances function in FlightR to avoid my non-parsimonious solution, but I have so far failed miserably. Hopefully a better programmer than myself can provide some help.


Thank you and cheers,

Jason Hill

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  Hi Jason,

 The question you ask is not an easy one, at least I do not know the only best solution.

 Have a look at the 


 Function estimates distances and uncertainties for movement between stationary points in different ways:

 All the movements(1e6) for every transition between twilights are stored in the result object.. So functions estimates distances using them. Unfortunately it probably is not the best way to go as these distances really depend on uncertainties of estimates. Some distance always accumulates even if there is not movement and mean stays stationary but particels just exchange positions..

Another way function looks at the distances is just a distance connecting stationary points (Distance2) . This metric look better to me, but it does not have uncertainties. 

  I am happy to discuss other way of dealing with this problem.



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Thanks Eldar,

Hmm, I appreciate that this is a challenging concept, especially given your point about the distance accumulating even when the animal is stationary (due to the particles mixing around). This is tough. I'm just not familiar enough with particle models. If I was running a standard MCMC Bayesian analysis in JAGS then I'd simply monitor the latitude & longitude median value for each twilight (so that the median for each twilight would have its own distribution of uncertainty). But we certainly don't want 1 million estimates of each median lat/long for each twilight!


But if it was possible to save a random subset (e.g., 100?, 1000?) of those medians then I think it would be straight-forward to do something like this overly-simple example below,



But this idea fails to take advantage of the full power of your particle model approach. Thanks for your help Eldar,



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  The main problem is that I do not store complete tracks (it is hard as PF resamples them every time so one could not know form the beginning which should be stored).


  Regarding your MCMC - Where would you get e.g. 1e3 medians? For each transition you will have one median and uncertainty, right? Or am I missing something?


  But FLightR stores all points and all transitions, so one can write a function that generates a sample of probable tracks. I will think a bit more about it and will try to come up with some function for it. Let me know if you want to code it yourself, I will appreciate it.

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Sorry, I wasn't clear there--yes you are right--one median. If you had an MCMC model that estimated lat/long at discrete time steps, and you saved 3000 iterations, then from the posteriors (out$sims.list) you could draw a sample of those 3000 estimates of each lat/long (or just use all 3000 of them, of course). 


I'll see what I can do. 



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So I was playing around with this yesterday, and perhaps I'm walking myself back a bit from my suggestion. I'm analyzing data on a grassland bird species that spends most of its time on the ground (maybe my thoughts would be different if I were analyzing 'cleaner' data from a bird that perches in the open (e.g., a kestrel). Bottom line: my data aren't neat and pretty. If I measure the great-circle distance between the median lat/lon estimate for every twilight that falls between when the bird left the winter grounds and arrived on the breeding grounds, then I get a distance estimate that seems (to me) overly large. As Eldar pointed out, even when the bird is stationary my path/route length would be accumulating distance because the particles (and the associated median location for each twilight) are still moving around. Also, if you have any "unlikely locations" [e.g., the bird reverses direction for a short time] that survive the FlightR outlier routine, then the migration distance quickly becomes inflated. If your FlightR estimates make a nice simple path, then the below discussion probably won't be of interest to you.


I think the uncertainty estimate, associated with the path distance, would be enormous with my data. I'm thinking about this approach by Arizaga (


Arizaga estimated the median lat/lon for stationary periods on spring migration, and then calculated the route distance between the wintering grounds, each stationary period during migration, and the breeding grounds. FlightR already has the tools to make this analysis easy. I see some limitations to this approach as well--especially if a bird flew around (not across) some large geographic feature [e.g., the Mediterranean Sea or the Gulf of Mexico]. 


Here's one approach based off of Arizaga:



# first, run the find.times.distribution function to ID the median date estimates of when the 
# bird left the wintering grounds and arrived on the breeding grounds
# Note: instead of longitude (from Eldar's example), I used latitude and adapted the approach used by 
# Jahn et al. 2013 (http://www.bioone.org/doi/abs/10.1525/auk.2013.12077) to decide when the bird left
# the breeding or wintering grounds
# something like this for the wintering ground arrival time:
Index.BIRD(winter.lat.BIRD+1)) #create imaginary line +1 degree north of the median latitude estimate
# of the first stationary period on the wintering grounds
# run the stationary.migration.summary
save(BIRD.migration.summary, file="BIRD.migration.summary.RData") # save results for later analysis
# let's say that the migration summary identifies 6 stopover events that occurred between the time period
# between departure from the wintering grounds and arrival on breeding grounds
# in this fake example, those stationary periods correspond with the 5th-10th stationary periods
# in the stationary.periods results
# row-bind them together
library(sp) # measure segments between locations and sum them to estimate route length
sum(spDists(BIRD.spring.migration.path,segments=1,longlat=TRUE)) # this is one possible estimate of spring migration distance
# now compare that estimate to the great-circle distance directly between wintering grounds and breeding grounds
spDists(matrix(c(winter.lon.BIRD, winter.lat.BIRD,breeding.lon.BIRD,breeding.lat.BIRD),nrow=2,ncol = 2,byrow = T),segments=T,longlat=T)
#Note: see the "TDR" statistic used by Arizaga et al. to compare the above two estimates
library(raster) # save spring migration route as shapefile if so desired


I've tried these approaches with only one(!!) bird so far: preliminary results (for n=1, so interpret with caution please)

Great-circle distance between wintering and breeding grounds = 3635.9 km [this is the shortest possible distance flown]

Spring migration route distance based on my above code = 3921.192

"Connecting-all-of-the-twilights" distance method that I previously suggested = 5319.8

Distance estimate from FlightR's find.time.distribution = ~5252.1 km


Just my preliminary thoughts, and of course, there's no way to determine (for my data) which one is most accurate

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