Line-transect surveys

Prepared by: Dr. Jon Aars, PBSG member
Published June 25, 2019

The two most actual methods to estimate polar bear populations are by capture-recapture and by line transect methods. In some areas, a capture-recapture program is already established. The two methods have different strengths and weaknesses, due to the estimates they provide relying upon different set of assumptions. Capture-recapture studies are usually part of a program where samples are collected from individuals and thus provide a lot of additional data besides estimates of population size and survival rates. However, access over many years to mark polar bears has been challenging and logistically difficult in several areas. Wiig and Derocher (1999) advocated a line transect study for the Barents Sea area to estimate the population size, due to the large area and the lack of logistical bases needed for capture-recapture based estimates. This led to the first polar bear line transect survey on a sub-population scale, performed in August 2004 (Aars et al. 2009). A pilot study using line transects from helicopter to estimate polar bear densities in the Chukchi Sea area had earlier been performed by Evans et al. (2003). A new survey in the western part of the Barents Sea area was conducted in 2015. In recent years, several polar bear line transect surveys have also been conducted in Canada, e.g. in the Fox Basin and Hudson Bay areas (Stapleton et al. 2014, 2016; Obbard et al. 2015, 2018). The literature on the method is well documented elsewhere, so I will only give a very brief introduction into the theory, and rather focus on what we learned may help when others will design similar surveys for other polar bear populations.

Short description of the line-transect method

There are several possible ways to estimate the number of individuals within an area. One is to count them all (total count). Total count has no associated uncertainty, but is usually not possible logistically for populations that occupy large areas. An alternative is “strip transects” where observers define a strip of a certain width, and count all individuals within the strip. The estimated densities are then used to extrapolate to the uncovered areas, to gain a population estimate. The assumption is that all individuals within the strip are detected, limiting the strip width. Although one can adjust estimates if one knows the proportion of observations missed, it is important that detection probability does not decrease with distance from the centre of the strip. All observations outside the strip have to be skipped from the analyses. Strip transects has been used and evaluated for polar bears (e.g. Wiig and Bakken 1990).

The line transect method has much in common with the strip transect method, but allow detection probability to decrease with distance from a survey line, and use the detection function to estimate densities. One still needs to observe all individuals “at” the line, or alternatively, to estimate the proportion one misses at the line for a correction.

Assumptions for line transects are (Buckland et al. 2001):

  1. A large number of transects are randomly allocated in the study area independently of the distribution of the survey population
  2. All individuals on the line are detected with certainty (g(0)=1)
  3. Animal movement is slow compared to observer movement
  4. Distances are measured without error

For more details on the line transect methods, see Literature on the subject is: Buckland et al. 2001, 2004, 2015, Borchers et al. 2002., Thomas et al. 2010.

Study design

We assume a helicopter is used for flying transects. In areas with sea ice, it is an easy matter to set up the study design. Lines are spread evenly to cover the whole area. One could use a staggered pattern to exploit all the flying time, but based on the Barents Sea survey, we recommend parallel lines. The small break the observers get when flying between lines may improve the overall vigilance when on the lines. If the survey is along the ice edge, a vessel can move while transects are flown, and also while the helicopter fuel, to reduce the flying time between transects. If survey is over land areas, it is important to place the lines in an orientation to cover different types of habitat evenly. Precision of the estimate is highly dependent on the number of observations, and thus effort. At least 60 different observations is recommended for a polar bear survey, this probably means in the order of 50-100 hrs of flying time minimum for most areas. Money and time will typically be the limiting factor, and the best way to design the study is probably to space lines evenly over the areas of interest based on the allocated number of flying hrs expected. Furthermore, the minimum spacing should be larger than twice the maximum likely distance for detection from the line, to avoid that the same terrain is covered twice. For polar bears, a spacing of at least 2km seems reasonable, based on detection curves from different surveys performed. We used 3km in the Barents Sea survey. The line transect analyses tool DISTANCE (Thomas et al. 2010) allow for covariates with different detection curves to improve the fit of the model. In practice, the number of observations will restrict the number of covariates that can be incorporated in a model for polar bears, habitat type is likely the most actual as detection probability may vary considerably e.g. on land and sea ice. The best time of a survey may be in late summer or autumn when sea ice areas are at a minimum, and when migration of bears is likely not to be directional.

How to measure distances

In the 2004 Barents Sea survey, we tested three ways to measure distances from the line to the detected bears: 1) with a laser. The laser worked in general well on land, but not on sea ice. 2) with a clinometer. Given the altitudes of the helicopter and bear(s) are known, the distance can be calculated from the clinometer angle, the altitude and the distance between the line and bear(s). 3) with GPS positions of the bear(s) and the trackline of the transect. We took a waypoint with a GPS above the position where the bear(s) were first detected, and measured the distances from the line using a GPS software. We designed a study to compare method 2 and 3, and found that method 2 frequently led to biases distance measures, while method 3 provided highly precise and unbiased estimates (Marques et al. 2006). We thus recommend the use of GPS to measure distances, for details see Marques et al. 2006 and Aars et al. 2009. If one considers using a laser on land, access to an open window or door is needed, as the laser does not work through the glass windows.

Helicopter: speed, altitude and observers

Although fixed wing aeroplanes may be used in line distance surveys, we recommend helicopters, mainly because of the larger ability to get out to the point where bears were at observations and measure distance without bias. Based on a small pilot study using a Eurocopter AS350 Ecureuil, we chose to use an altitude of 200 feet and 100 knots speed. In both of our Barents Sea surveys, in 2004 and 2015, we have used that altitude and speed (although conditions, e.g. fog, may temporarily force adjustments both due to security and changes in detection probability). The low altitude was chosen to decrease the likelihood of missing bears on the line. Not only the short distance per see increases the likelihood of spotting bears on the line, most bears move when a helicopter gets that close, and this increases the probability of an observation further. It is important that the helicopter of choice has very good visibility, particularly on and close to the line. The detections of bears and the distances are pooled together independent on the observer and which side of the helicopter the bear was at. There is no reason why the pilot should not be included as an observer: The pilot and a second person in the front of the helicopter should concentrate on the line, as a g(0) close to 1 is vital. One observer at each side in the back seats of the helicopter may observe bears further away, but should also focus on searching close to the line.

Analyzing the data

CREEM at University of St. Andrews, UK, has developed the statistical tool for analyzes of distance data. The program DISTANCE can be downloaded free of charge ( It is now also possible to run Distance through program R, and this is advocated by CREEM due to larger flexibility in data exploration. For most, it will be quite hard to learn how to use the program from scratch. I advocate taking a workshop course that is regularly run at the University of St. Andrews (

Further reading

Aars, J., T.A. Marques, S.T. Buckland M. Andersen, S. Belikov, A. Boltunov, Ø. Wiig. 2009. Estimating the Barents Sea polar bear subpopulation size. Marine Mammal Science, 35-52.

Borchers, D.L., S.T. Buckland and W. Zucchini. 2002. Estimating Animal Abundance. Closed populations. Springer-Verlag, London.

Buckland, S.T., D.R. Anderson, K.P. Burnham, J.L. Laake, D.L. Borchers and L. Thomas. 2001. Introduction to Distance Sampling. Oxford University Press, Oxford.

Buckland, S.T., D.R. Anderson, K.P. Burnham, J.L. Laake, D.L. Borchers and L. Thomas (eds). 2004. Advanced Distance Sampling. Oxford University Press, Oxford.

Buckland ST, Rexstad EA, Marques TA and Oedekoven CS (2015) Distance Sampling: Methods and Applications. Methods in Statistical Ecology. Springer International Publishing.

Evans, T.J., A. Fischbach, S. Schliebe, B. Manly, S. Kalxdorff and G. York. 2003. Polar bear aerial surveys in the eastern Chukchi Sea: A pilot study. Arctic 56: 359-366.

Marques, T.A., M. Andersen, S. Christensen-Dalsgaard, S. Belikov, A. Boltunov, Ø. Wiig, S.T. Buckland and J. Aars. 2006. Comparing distance estimation methods in a helicopter line transect survey. Wildlife Society Bulletin 34:759-763.

Miller D.L. 2015. Distance: Distance Sampling Detection Function and Abundance Estimation. R package version 0.9.3.

Obbard M.E., Stapleton S., Middel K.R., Thibault I., Brodeur V. & Jutras C. 2015. Estimating the abundance of the Southern Hudson Bay polar bear subpopulation with aerial surveys. Polar Biology 38, 1713-1725.

Obbard M.E., Stapleton S., Middel K.R., Szor G, Jutras C. and Dyck, M. 2018. Re-assessing abundance of Southern Hudson Bay polar bears by aerial survey: effects of climate change at the southern edge of the range. Arctic Science 4, 634-55.

Stapleton S., Atkinson S., Hedman D. & Garshelis D. 2014. Revisiting Western Hudson Bay: Using aerial surveys to update polar bear abundance in a sentinel population. Biological Conservation 170, 38-47

Stapleton S., Peacock E. & Garshelis D. 2016. Aerial surveys suggest long-term stability in the seasonally ice-free Foxe Basin (Nunavut) polar bear population. Marine Mammal Science 32, 181-201

Thomas L, Buckland ST, Rexstad EA, Laake JL, Strindberg S, Hedley SL, Bishop JRB, Marques TA & Burnham KP (2010) Distance software: design and analysis of distance sampling surveys for estimating population size. Journal of Applied Ecology 47: 5-14. DOI: 10.1111/j.1365-2664.2009.01737.x

Wiig, Ø. and V. Bakken. 1990. Aerial strip surveys of polar bears in the Barents Sea. Polar Research 8:309-311.

Wiig, Ø. and A. Derocher. 1999. Application of aerial survey methods to polar bears in the Barents Sea. Pages 27-36 in Garner et al., eds. Marine Mammal Survey and Assessment Methods. Balkema, Rotterdam.