Telemetry and probability of detection

[dhpstroud]

I'm curious if anyone has heard of folks using CJS or multi-state models to determine the probability of detection for each acoustic receiver in a reservoir or lake setting, where individuals do not move in a linear fashion. I've seen it accomplished successfully in study areas where fish move continuously in one direction (e.g. http://mikemelnychuk.files.wordpress.co ... hw-res.pdf).
In my study area, fish move freely back and forth between any number of receivers. If you have any ideas about novel ways to set this up, please feel free to contact me.
Cheers!

[murray.efford]

This caught my eye because it seems to have something in common with SECR - the bit about detector-specific probability of detection. Usually in SECR we expect individuals to be localised in the habitat (i.e. occupy distinct home ranges). However, you can force a non-localised (and hence virtually non-spatial) model by fixing the spatial scale parameter (sigma) to a very large number. The detector-specific detection probability (g0) remains estimable, I think.

As you present the problem, it seems you don't care about other open population parameters (survival etc.). If this is the case then a simple model fit in 'secr' should do the trick: secr.fit (CH, fixed = list(sigma=1e6), ...). CH would be a 'proximity' or 'count' capthist object. Known spatial elements (size and geometry of lake as a habitat mask, locations of detectors as a trap layout) are included. You can also compare with a model in which sigma is estimated (they may have home ranges).

Murray

[dhpstroud]

Thank you for your feedback. I am unfamiliar with SECR, but after a quick search it looks promising. It does appear that one has to know how to use R or SAS ... Unfortunately I have not had the opportunity to learn either yet.
At any rate, I do not want to know what the probability of a fish moving to a certain receiver, I am interested in the probability of detection to a certain receiver given that the fish is present. Does SECR have this capability?

[murray.efford]

I do not want to know what the probability of a fish moving to a certain receiver, I am interested in the probability of detection to a certain receiver given that the fish is present. Does SECR have this capability?

Not quite sure what you mean by 'present' - I assume 'present in the lake', in which case the answer is Yes.

Also: the Windows software Density allows you to fit SECR models without learning R (of course you do have to learn something about Density and SECR). To fix the sigma parameter go to Options | ML SECR and click the button for 'manual' initial values; then double click the 'Link function' box for sigma until it says 'fixed' and type the desired large number into the Initial box for sigma. You will want to use a habitat mask to define the extent of the lake.

Learning R is worth it - then you can fit these models in 'secr' with detector-specific covariates and other bells and whistles.

Murray

[Halfyard]

The major difference between using CJS in a 'linear' system (see also Lacroix 2008 and Halfyard et al. 2013, links below) is that individual receivers (or arrays of receivers) act as the 'sampling occasion' as the model is based off of a spatial framework (i.e. the movement in space), not a temporal framework (i.e. through time). When p is calculated in a linear system, it represents the probability of detecting the individual as it crosses the receiver (or array of receivers) in space. In this case, p equates to the functional detection efficiency of the receiver, which is the likelihood of detecting at least one tag transmission if the fish is present.

In the non-linear system you are discussing, I believe you would need to revert to the temporal framework. Thus, estimates of p would represent the probability of detecting an individual fish at each sampling occasion (e.g. across a 1-week period) for the total 'listening' effort of all deployed receivers. This should not be confused with detection efficiency (performance) of individual receivers, which would need to be assessed using sentinel tags (see Mike Melnychuk's PhD thesis for a good review - Univ. British Columbia).

Hope this helps,

Eddie Halfyard

http://www.ingentaconnect.com/content/n ... 9/art00022
http://www.nrcresearchpress.com/doi/abs ... iCbtj_pySq

[mcmelnychuk]

It seems like a multi-state model might be a good way to go, with receiver stations representing spatial states, so long as you don't have too many receivers and you're not after too fine a temporal resolution for your given sample size. How many receivers in the lake are we talking about (and are they grouped into clusters)?; how many tagged fish do you have?; what kind of a study duration & tag life do you have?; and do you tend to detect fish consistently after tagging (say most weeks, months, or seasons), or only sporadically? The requirements for estimated parameters (p, survival, transitions) may be too great for your dataset, but there could be the possibility of estimating p at each receiver over the given time step (weekly, monthly, seasonally...), especially if you can reasonably assume p's at a given receiver are either constant over a full year, or p's for all receivers vary individually but follow the same seasonal trend.
To follow up on Murray's comment, are you interested in p per se, or only as a means to estimate survival etc.?

p.s. thanks for the nod Eddie Halfyard!

Mike

[dhpstroud]

How many receivers in the lake are we talking about (and are they grouped into clusters)?; how many tagged fish do you have?; what kind of a study duration & tag life do you have?; and do you tend to detect fish consistently after tagging (say most weeks, months, or seasons), or only sporadically? The requirements for estimated parameters (p, survival, transitions) may be too great for your dataset, but there could be the possibility of estimating p at each receiver over the given time step (weekly, monthly, seasonally...), especially if you can reasonably assume p's at a given receiver are either constant over a full year, or p's for all receivers vary individually but follow the same seasonal trend.
To follow up on Murray's comment, are you interested in p per se, or only as a means to estimate survival etc.?

I am interested in determining the probability of detection at each receiver only. Not survival nor the transition probability. I would like to use this data to better understand the number of fish entraining over Grand Coulee Dam that were missed by the receivers downstream.

There are anywhere from 4 up to 26 non-clustered receivers that were in my array, ranging from 1.5 to 6.5km apart. My receivers are mostly in a straight line (you can see a map of the study area here: https://docs.google.com/file/d/0B-fbyPv ... sp=sharing ), except for a few along the two primary rivers that flow into the reservoir. We share data with folks upstream who have two more receiver arrays. Most individuals (n~25 per year) are detected continuously for several months. The transmitters pinged every ~2 minutes (1-3 min randomized delay).

Most years of tracking data have about 500,000 independent detections (and therefore occasions because each one has a unique time stamp). It's a tremendous amount of data, which presents an issue with the numerical optimization step in MARK, and even working within the PIMs becomes a headache.

I'm concerned that any type of condensed time step (days, weeks, seasons) results in a loss of the very data I'm trying to enumerate. I toyed around with condensing the input to a daily step, but had lots of issues with fish being detected at multiple receivers in that one occasion. For instance, some individuals were detected moving back and forth between receivers upwards of 50+ times in a single day (e.g. multi state encounter history: ABCE...). This is the micro-movement data that I am most interested in - all those little misses between consecutive receivers where the fish SHOULD have been detected A--> B-->C-->D-->E ...etc. assuming it moved from A -->E.

... there has got to a better way to tackle this issue!

[dhpstroud]

I should mention, I just performed a quick pivot table with the date/time grouped by day & hour. I still have fish detected at 4 or 5 receivers in a one hour occasions. When I break it down into 10 minute occasions I still have some fish detected at 3 receivers.

... What would folks think of adding a 'total missed detection count' as a co-variate for each receiver 'state'? I have already combed through the data and directly counted each missed detection by looking at each fishes chronological encounter history and determining when it must have passed a receiver but was undetected.

[ganghis]

Probably best to think outside of the box (i.e. CMR) on this one. I would do something with sufficient statistics (encounter history modeling sounds hopeless due to sample size). For instance, conditioning on the first known location of each fish and ending with the last known location, you might add up the total number of observed transitions for each animal. Then one could consider a Poisson likelihood where the counts are distributed with a Poisson distribution and parameters dependent on movement and detection probabilities (afraid you'll have to model movement here, even if you don't care about them). For instance, the Poisson intensity for A-->B (observed in B) could be psi_AB p_B. The Poisson intensity for A-->C (observed in A and C but not B) would be psi_AB (1-p_B) psi_BC p_C. Maybe include a random effect for individual (probably on movement but I guess certain fish might also be more prone to sneaking past your detection array).

It's probably not quite that straightforward (I'm usually missing something), but that's at least the first way I'd try to proceed.

-Paul Conn