[tlocoh-info] Calculating temporally overlapping hulls with s=0, can it be done?

[Andy Lyons]

Hi Michelle,

Good question. The short answer is that yes all hulls have a time stamp 
associated with them (specifically the timestamp of the 'parent point'), 
regardless of the value of s (which only affects which other points are 
considered nearest neighbors).

Whether it makes sense or not to pair-up hulls from different 
individuals based on the time stamp of the parent point, when hull 
construction does not take time into consideration, is a good question. 
When s>0, one can say with their head held high that the points that 
compose the hull are in some sense local in both time in space. In that 
case it's reasonable to compare two space-time hulls from different 
individuals at the same time, and take their physical distance apart as 
some kind of association metric at that moment in time.

When time is not included in hull construction, the meaning of a hull is 
more akin to density of usage over the entire sampling interval. In that 
case, the time stamp of the parent point doesn't signify any particular 
characteristic at that moment in time except maybe to say at that 
specific moment the individual was in a high density hull or a low 
density hull. That might have some significance if you see high density 
hulls occurring during a certain time of the day or part of the season. 
Pairing space-only hulls from two individuals at the same time might 
allow you to say whether or not the two individuals tended to be in high 
density or low density hull at the same time, but it wouldn't tell you 
much about their association at that particular time (I think).

That being said, you could incorporate another hull metric 'tspan' (time 
span of the nearest neighbors) to measure the time span of the nearest 
neighbors (regardless of s), and use tspan to compare the window of time 
that two two time-matched hulls represent. If the hulls for individual A 
and individual B have a similar distribution of tspan, you might be able 
to argue that time-paired hulls are a measure of dynamic association at 
the scale of tspan.

Cheers,
Andy


Subject:
Calculating temporally overlapping hulls with s=0, can it be done?
From:
Michelle Pretorius <PRTMIC015 at myuct.ac.za>
Date:
5/7/2021, 3:38 AM

To:
"tlocoh-info at lists.r-forge.r-project.org" 
<tlocoh-info at lists.r-forge.r-project.org>


Hi all,

I would like to calculate hull metrics for pairs of temporally 
overlapping hulls of two individuals (using `lhs.to.add` from the 
`tlocoh.dev` package). However, I have used s=0 for both individuals 
(after following the cross-validation methods set out by Dougherty et 
al. (2017) 
<https://movementecologyjournal.biomedcentral.com/articles/10.1186/s40462-017-0110-4>), 
and thus the hulls were constructed from the closest points in space 
only. Do hulls still have times associated with them even if they are 
formed with s = 0?

Using the `lhs.to.add` and `lhs.to.stats` functions I do /technically/ 
get a result (i.e., there are no errors), but I am wondering if this is 
theoretically sound?

Thank you in advance for any help/advice you can provide.

Best,
Michelle

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