bias estimates for flying seabirds with continuous transect sampling

[Mei-Ling Bai]

Dear all,

we have a dataset of seabird from boat transect surveys. Flying birds were counted continuously and the distance to transect was recorded. I learned that, as observers would preferentially record the birds when they are relatively close to the line, the density is likely to be overestimated.

My question is: is it possible to estimate the bias? I think the factors influencing the bias include: (1) the true distribution of detection probability of the birds; (2) the flying speed of the birds; (3) the speed of the vessel; (4) the flying direction of the birds. Speed of the vessel is known. Flying speed of birds can be taken from literature. And let's assume the flying direction of birds is random. And as we know the resulted, biased distribution, can we back-estimated the original distribution? Or can we at least have an idea of the scale of the bias in ESW or density estimates?

If anyone has practical experiences or knows some literature about the scale of such bias, it would also be very helpful!

Thanks for your help,

Mei-Ling

[Eric Rexstad]

Mei-Ling

Seabirds in flight represent a challenge for boat-based surveys, as you note.  In Buckland et al. (2015), we devote a section (10.2.1) to the subject of boat-based seabird surveys.  In that section, a couple of methods are suggested for dealing with the issue: record birds in flight only when the come abeam of the ship and separate estimation of proportion of time birds spend in flight.  There is also the method of Tasker et al. (1984) for conducting "plot based" sampling of birds in flight.

As for ways to estimate bias, Spear has published several papers that attempt to assess the effect of flight behaviour on seabird densities:

Spear, L., Nur, N., & Ainley, D. G. (1992). Estimating absolute densities of flying seabirds using analyses of relative movement. The Auk, 109, 385–389. https://doi.org/10.2307/4088211

SPEAR, L.B. and AINLEY, D.G. (1997), Flight speed of seabirds in relation to wind speed and direction. Ibis, 139: 234-251. https://doi.org/10.1111/j.1474-919X.1997.tb04621.

There has likely been considerable work on the study of bird flight since the advent of telemetry fitted upon individuals.

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[Ewan Wakefield]

Just to add to Eric's comments, here are some thoughts from the perspective of conducting this type of survey: Estimating the distance to flying birds at sea is very difficult. How did the fieldworkers estimate/measure distances to the birds? Did they validate their distance estimates in any way? 

As you've realised, the fact that seabirds generally move an order of magnitude faster than survey vessels means that the apparent density of birds moving in random directions would be biased upwards. Tasker et al.'s (1984) "snapshot" method was an attempt to deal with this - essentially by carrying out a plot-based survey of seabirds in flight at the same time as a distance survey of birds on the water (which move much more slowly). The methods works by recording birds instantaneously in consecutive plots (normally 300 x 300 m) as you proceed along the a track line. So if the vessel was moving at 10 knots, you'd record a "snapshot" of birds every 300 m.

You don't say whether angles were also recorded. Assuming that they were, and that you're confident that the distances and angles are reasonably unbiased, a draconian but tractable way of treating your data would be to calculate the position of each bird and resample them according to the plot design. If detection really is dependent on distance (many analysis assume perfect detection for large flying seabirds), you could then also apply a standard distance-sampling analysis to account for that.

All the best,

Ewan

--------------------------------------------------

Dr Ewan Wakefield

NERC Fellow,

Institute of Biodiversity Animal Health and Comparative Medicine,

Graham Kerr Building,

University of Glasgow,

Glasgow, G12 8QQ.

Tel: +44 (0)1751 417478

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Email: Ewan.Wa...@glasgow.ac.uk

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[Richard Glennie]

To add further to the comments above: 

I have been working on such methods as you describe, that is, where the we

use the observed biased distribution of distances with some knowledge of animal

movement to "back-estimate" the underlying detection function and so produce

less biased density estimates. 

The work is described in this paper: 

https://www.tandfonline.com/doi/abs/10.1080/01621459.2020.1764362

In that paper, animals are assumed to move according to Brownian motion and

the minimum information needed is an estimate of their speed over a given time

interval and the speed of the vessel. That, together with the distance sampling data, can then be used to

estimate density. This method is implemented in an experimental R package "moveds"

which is located here: https://github.com/r-glennie/moveds 

An alternative approach to just get an initial idea of the bias is to use the 

simple formula given in the following paper: 

https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0121333

This formula can be used to estimate the bias in strip transect sampling (where

detection probability is assumed to be one up to whichever maximum distance you

set the width of the strip to be). For that formula, it is assumed that animals

move in random-orientated straight lines. 

In many situations, this bias computed using the strip transect formula can be

taken as a upper bound on the bias in line transect sampling. However, this is not true in extreme situations

where the detection function falls off steeply with distance and animals move

fast enough to travel from the edge of the transect to the line within their

window of availability for detection, as the bias in the estimated detection function

worsens the overall density estimation bias compared to strip transect sampling. 

This is discussed in the PLOS paper I linked to above.  

[Mei-Ling Bai]

Eric, Ewan and Richard,

Thank you all for your response. Your suggestions are very helpful, so does the references you provided.

Spear et al. (1992) and Glennie et al. (2015) gave me an idea of the bias which I just need. I am also working on the "draconian but tractable way" that Ewan mentioned.

I have further question to Richard: I am interested in trying moveds, but we have no movement data. If we know the speed of the birds, and assign the flying direction is either random (as straight line) or fixed (for migratory birds), could we simulate the movement data? 

All the best,

Mei-Ling

Richard Glennie <gle...@glennies.co.uk> 於 2021年2月16日 週二 下午6:43寫道：

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[Richard Glennie]

You can still use the moveds package without movement data in the way you describe. The vignette for line transects also covers the case where you specify the unknown movement parameter and simulate movement data to see if it looks reasonable. If so, you can then fit the moveds model with that movement parameter fixed to your chosen value rather than estimated from movement data. In this case, I'd probably fit the model under a range of chosen values to see how much the bias is affected. 

It is important to remember that the assumed movement model in moveds is Brownian motion and as animals move in a more directed way than that, moveds may (depending on the relative difference in speeds between the observer and animals) underestimate the bias.