Technical Reports of the Institute of Cetacean Research (2019)

pp. 14–20

Technical Report (not peer reviewed)

A note on g(0) estimates derived from vessel-based sighting surveys
Megumi Takahashi*
Institute of Cetacean Research, 4–5 Toyomi-cho, Chuo-ku, Tokyo 104–0055, Japan*Contact e-mail: takahashi@cetacean.jp

ABSTRACTThis article introduces the concept of g(0), the probability of detection of animals at zero distance from thetrackline, in the development of abundance estimates of large whales. In the conventional line transect
method, it is assumed that g(0)=1, meaning that all animals on the trackline are detected. However, this assumption is sometimes violated, which causes underestimation of the abundance. Also this article provides
overviews of the methods used to estimate g(0) for large baleen whales, and of the current work of the Institute of Cetacean Research to estimate g(0) based on dedicated sighting surveys in the Antarctic.

INTRODUCTION
Abundance estimates of animals can be based on total
counts (census), sample counts, index counts, among
others. The method producing the most accurate estimate is probably the total census of animals in a given
area. This is possible when the area is small, the visibility
is good, the target species is easily detectable, and when
there is no emigration and immigration. However, these
conditions are diﬃcult to meet for most of the large
whale species. In such cases, the sample counts approach
is more appropriate. Under this approach, the abundance
estimate is extrapolated from data obtained from a partof the total research area.
Distance Sampling (DS) methods (Buckland et al., 2001)

Figure 1.

14

are widely used for estimating whale abundance in large
areas. The line transect method is one of those methods,
in which detailed surveys are conducted along a tracklinethat covers part of the entire survey area (Figure 1A).
The detection probability of whales is not constant but
decreases with the distance from the trackline (Figure
1B). Hence, in conventional line transect methods it isassumed that the detection probability on the trackline,g(0), is equal to 1. This means that all whales on the trackline are detected (Buckland et al., 2001).
However, whale schools are not always detected even
if they are on the trackline because whales dive and because observers could miss the schools on the trackline.
In such cases a g(0) estimate is required for correction ofabundance estimates.

Diagram showing the zigzag tracklines in part of the total research area under the line transect survey (A);and the pattern of detection probability in relation to perpendicular distances (B).

A note on g(0) estimates derived from vessel-based sighting surveys

The objective of this article is to introduce the conceptof g(0) in the development of abundance estimates oflarge whales. Also this article provides overviews of themethods used to estimate g(0) for large baleen whales,
and of the current work of the Institute of Cetacean Research (ICR) to estimate g(0) based on dedicated sighting
surveys in the Antarctic.

AVAILABILITY AND PERCEPTION BIASES
Under the conventional DS methods (Buckland et al.,
1993; 2001), g(0) is assumed as equal to 1. However,when this assumption is violated, conventional DS estimators result in density and abundance being underestimated. In the case of whales, they are not always detected because they spend time underwater. This is known
as ʻavailability biasʼ (Figure 2). This bias is potentially thelargest problem for long-diving species that spend little
time at the surface when the boat or ship surveys are
conducted. For diving species, it may be necessary tomodel diving behavior to estimate the availability bias
(e.g. Barlow, 1999).
Also, the observers could miss some whales available
at the surface for a variety of reasons including visibility
such as glare and mist, fatigue or moments of inattention. This is known as ʻperception biasʼ (Figure 2). Thisbias is potentially largest for species that occur as single
animals or in small groups and do not show much of theirbody when surfacing, such as Hectorʼs dolphin and minke
whales (Dawson et al., 2004).
Both availability and perception biases may reduce thedetection probability. In many cases, there is a combined
eﬀect of these on estimates of abundance and density
for target species. The term ʻvisibility biasʼ is used generi-

Figure 2.

cally to refer to either or both types of biases (Laake andBorchers, 2004).
If the assumption of g(0)=1 is violated then the abundance estimates of the target species will be underestimated. For example, Marsh and Sinclair (1989) estimatedthat 83.3% of dugons (Dugong dugon) were beneath thewater surface and unavailable for detection, while theobserver team only missed 2–17% of the visible dugongs
within a 200 m strip. Laake and Borchers (2004) notedthat the availability bias should not be ignored if it occurs,
because it can be a substantial source of bias that may bemuch larger than perception bias.
Therefore estimates of g(0) for cases of availability andperception biases are important and data required forsuch estimates should be collected.

DATA REQUIRED FROM THE FIELD TO ESTIMATEg(0) IN CASE OF LARGE WHALESThe ICR conducts sighting surveys based on the distancesampling for estimating abundance of large whales. In
general, the surveys follow the Requirements and Guidelines for Conducting Surveys and Analysing Data within
the Revised Management Scheme of the International
Whaling Commission Scientiﬁc Committee (IWC SC)(IWC, 2012). Details of the procedures are found in Hakamada and Matsuoka (2017).
These surveys have been implemented on predetermined zigzag tracklines. The start point is randomly
selected for each survey. The design takes care not tofollow physical features such as isobaths that may be correlated with whale distribution and their migration. For
each whale school sighted, the species is identiﬁed andother data are recorded such as sighting position, school

Diagram showing the detection probability with assumed g(0)=1 (A); and the case of considering availability
and perception biases when g(0) is diﬀerent from 1 (B) (modiﬁed from https://workshops.distancesampling.
org/stand-intermed-2018/slides/mrds1-g0.pdf).
15

Technical Reports of the Institute of Cetacean Research (2019)

size, weather information, etc.
Sighting data are collected from two platforms available in the same vessel, which allows accounting foranimals missed on the trackline. Sighting surveys are
conducted by using a top barrel platform (TOP) and an independent observer platform (IOP). Sighting surveys are
conducted from two platforms independently, following
established procedure protocols (Butterworth and Borchers, 1988; Palka, 1995; Matsuoka et al., 2003; IWC, 2012).
Under the IO mode, sighting surveys are conductedfrom the TOP and the IOP. Personnel at the upper bridgeof the vessels record the sighting information from thetwo platforms and determine if the same sighting is madefrom the two platforms or if some sightings are missedfrom one of the platforms.
Figure 3 shows the research vessel Kaiyo-Maru No.7
(KY7) equipped with TOP, IOP and upper bridge. The vessel has instruments allowing contact between TOP andupper bridge, and between IOP and upper bridge.
During the survey, one or more observers are always in
the TOP, and one observer is in the IOP. Other observers
are in the upper bridge getting sighting information fromthe two platforms. Observers in the top barrel and IOP report the sightings to the upper bridge observers, but that
information is not interchanged between TOP and IOP.
Figure 4 shows a diagram of double-platform sighting
survey and judgment of duplicate status. Here, a single

whale appears three times, which is detected by platform
A (TOP). On the other hand, platform B (IOP) detects thesame whale only during the last surfacing (A3). Observers in the upper bridge receive sighting information (e.g.
distance, angle, species and school size) from platform A
at the ﬁrst sighting (A1) and track this single whale until
platform B observed it. They make a judgment concerning the duplicate status (same whale sighted by the two
platforms).

ANALYTICAL APPROACHES TO ESTIMATE g(0)MRDS method
The method called ʻMark-Recapture Distance Samplingʼ
(MRDS) is one of the methods employed to estimate g(0),which consists of two models: a multiple covariate MarkRecapture (MR) model (for estimating observer detection
rates) and a multiple covariate Distance Sampling (DS)model (for estimating the variation of detection probabilities with distance from the vessel) (Buckland andTurnock, 1992; Alpizar-jara and Pollock, 1996; Quang andBecker, 1997; Borchers et al., 1998; Innes et al., 2002;
Laake and Borchers, 2004; Borchers et al., 2006, Burtet al., 2014). The MRDS method deals only with perception bias.
The probability that either or both observers detect aschool (or animals) is given by:Pˆ .( y, z ) = Pˆ1 ( y , z ) + Pˆ2 ( y , z ) − Pˆ1 ( y, z ) Pˆ2 ( y, z ) ,where y is the perpendicular distance corrected and z
denotes the covariate. Although observers 1 and 2 areconsidered independent from each other under the IO
mode survey, the detection probability of observers canbe correlated because of factors such as school size. This
heterogeneity is denoted in the probabilities of detection
using a logistic form for the detection function:
Pl |3−l( β z) ,( y, z ) =1+ exp ( β + β y +  β z )exp β0 + β1 y +0Figure 3.

Survey vessel equipped with three platforms for
conducting surveys required for g(0) estimate.

Figure 4.
16

1

K
k=1 k+1 k

K
k=1 k+1 k

where, l can take the values 1 or 2 to represent the observers, β 0, β 1…β K represent the parameters to be esti-

Diagram of the double-platform sighting survey conducted by the ICR.

A note on g(0) estimates derived from vessel-based sighting surveys

mated, and K is the number of covariates. When perpendicular distance diﬀered between duplicates, the average
distance of the duplicate pair are used.
On the other hand, the detection probability awayfrom the trackline is described and estimated by the DSmodel as follows:u (u=A or B) is assumed as:12
  x   y  −,
Qu ( x, y ) = μu exp − σ  σ    u   u  

γ

γ


y2 
Half-normal: f ( y, z ) = exp  −,2 
 2σ ( z ) where 0<μ u ≤1, σ u >0, γ 1, γ 2 >0, μ u is the level parameterof the hazard probability function, σ u is the scale parameter, and γ 1 and γ 2 are the shape parameters (Skaug andSchweder, 1999). The corresponding detection function
from this hazard function is explicitly expressed as: − y  − b 
Hazard-rate: f ( y, z ) = 1 − exp ,σ ( z )   λ ∞
gu ( x) = 1 − exp −   Qu ( x, y ) dy 
v
0
  


where σ and b are the parameters of each functional
form.
Both models can include covariates (e.g. school size,
Beaufort, etc.). In addition, the likelihoods can be treatedas MR model and DS model separately or as combinationof those models. The best model usually is selected using
the Akaike Information Criterion (AIC; Akaike, 1973).
The MRDS method do not consider the availability
bias. Hence, the availability bias should be accounted byanalyses of data from additional experiments (e.g. HeideJørgensen et al., 2010).
Hazard probability model: ʻOKʼ method
This method deals with both availability and perception
biases. The method, called the ʻOKʼ method, was developed by Okamura et al. (2003) by extending the modelof Skaug and Schweder (1999), and by combining themerits of the models of Schweder et al. (1997) and Cooke(2001). Okamura et al. (2003) expanded the concept of
the hazard probability model (Skaug and Schweder, 1999)
to avoid the use of external information for considering
diving behavior (the conventional and simple hazard
probability models require an estimate of the surfacing
rate based on external data).
The hazard probability function Q(x,y) for an observer

Figure 5.

γ1  x  = 1 − exp  − λv −1c2u exp − ,σ u  







where λ is surfacing intensity, ν is constant vessel speed
and c 2u =σ u μ u γ 2−1 Γ(γ 2−1), with Γ being the gamma function.
The ʻOKʼ method is a more general and comprehensive
method that integrates the merits of previous hazard
probability models.

ONGOING STUDIES IN THE ANTARCTICThe ʻOKʼ method explained above (Okamura et al., 2003;
Okamura and Kitakado, 2012) was used previously for
estimating Antarctic minke whale (Balaenoptera bonaerensis) abundance from the IDCR/SOWER data collectedfrom the 1985/86 to the 2003/04 austral summer season.
In that study g(0) was estimated less than 1 for Antarctic
minke whales (0.327 to 0.793). Using this result, theabundance estimates of Antarctic minke whale based on
JARPA data were corrected by application of a regression
model (Hakamada et al., 2013).
Preliminary results of the MRDS method on Antarctic
minke whales
Data were obtained during the surveys conducted from

Research area of the study to estimate g(0) of Antarctic minke whale based on MRDS.
17

Technical Reports of the Institute of Cetacean Research (2019)

December to February from the 2014/15 to the 2017/18
austral summer seasons in Antarctic Area IV, V, and VI(Figure 5). As indicated above, the MRDS method for estimating g(0) requires data collected from IO mode survey.
The data comprised a total of 215 schools, including 63
schools which were observed from TOP and IOP (Figure
6, Table 1). Mean school size was 2.23. Also sightings withperpendicular distance of more than 1.5 n.miles, andthose observed when Beaufort status was higher than six,
were excluded from the dataset.
Table 2 shows the AIC values after ﬁtting explanatory
variables to the DS and MR models. For the DS model,
school size and cue were the most important explanatory
variables. For the MR model, platform and school size
were the most important explanatory variables. For thebest model, detection probability on the trackline was
0.676 (CV=0.092) for the TOP, 0.429 (CV=0.145) for the
IOP, and 0.810 (CV=0.066) for the pooled platforms. The
estimated detection function plots are shown in Figure 7.
The detection probability on the trackline for the Antarctic minke whale was similar to the result from the previous
study based on the ʻOKʼ method and IDCR-SOWER datasets (Okamura and Kitakado, 2012). In addition, this result
was similar to that found for North Paciﬁc common minke
whale. For this species the g(0) for TOP and upper bridge
was estimated at 0.798 by the ʻOKʼ method using the IO
passing mode sighting survey data (Okamura et al., 2010).
Future studies
The estimate of g(0) for Antarctic minke whale based on
the MRDS method was similar to that obtained by the ʻOKʼ
method. The estimate considered covariates that aﬀect thedetection functions. However, the analysis only accounts
for perception bias and did not account for availability bias.
Hence, some additional investigations are needed to esti-

Figure 6.

18mate whale diving pattern as in the case of Heide-Jørgensen
et al. (2010). They considered availability correction factors
using data collected from external experiment survey. Also,model development is needed, for example, correction for
non-uniform density of animals within strata using datacollected from external experiment survey, and the use of
the Bayesian hierarchical approach to incorporate habitat
use into a detection model within a mark-recapture distance sampling framework (Oyster et al., 2018), is required.
These studies are ongoing at the ICR.

ACKNOWLEDGEMENTS
I thank the researchers, captains, oﬃcers and crew
members who have participated in all surveys. This work
would not have been possible without the substantial efforts of all of them.
Table 1
Number of sightings of Antarctic minke whales made by eachplatform in each survey. Note that the number of unique sightings is the number of sightings seen by observer 1 plus thenumber seen by observer 2, minus duplicates.
Number of sightings by observers

NumberSurvery ID Platform A Platform B Detected by of uniquebothsightings
(TOP)
(IOP)
(Duplicate)
YS1_1415
YS2_1415
YS3_1516
KY7_1617
YS3_1617
KY7_1718
YS2_1718
Total

14
6
47
6
14
10
79
176

10
1
22
6
10
11
42
102

6
1
14
3
4
5
30
63

18
6
55
9
20
16
91
215

Tracklines and sighting position of Antarctic minke whale observed by each platform (left: TOP; right: IOP).
Gray lines indicate tracklines.

A note on g(0) estimates derived from vessel-based sighting surveys
Table 2
Akaike Information Criterion (AIC) values after ﬁtting explanatory variables to the Distance Sampling (DS) and Mark-Recapture (MR)models. This table shows a part of all result of model ﬁtted for reference. The ﬁnal models chosen are given in bold.
Model ID
35
37
31
32
33
47
103
131
145
54
61
68
40
159

DS modelKey*

Covariate

hn
hn
hn
hn
hn
hn
hn
hn
hn
hn
hn
hn
hr
hr

beaufortcue
size
size+beaufort
size+cuesize+cuesize+cuesize+cuesize+cuesize+cuesize+cuesize+cuesize+cuesize+cue

MR modelCovariate
distance
distance
distance
distance
distance
distance+platform
distance+size
distance+beaufort
distance+cue
distance+platform+size
distance+platform+beaufort
distance+platform+cue
distance
distance+platform+size

AICDS

AICMR

AIC

ΔAIC

141.03134.88126.90128.65115.75115.57115.57115.57115.57115.57115.57115.57118.10118.10472.79472.79472.79472.79472.79437.56469.05473.72474.53434.11438.48439.53472.79434.11613.82607.67599.69601.44588.54553.13584.63589.30590.11
549.69554.06555.10590.89552.21

64.13
57.98
50.01
51.76
38.85
3.44
34.94
39.61
40.42
0.00
4.37
5.42
41.21
2.53

*: hn denotes a Half-normal function; hr denotes a Hazard-rate function.

Figure 7.

Detection function plots for the TOP (A), IOP (B) and both platforms pooled (C) by the MRDS method.

REFERENCES
Akaike, H. 1973. Information theory as an extension of the maximum likelihood principle. pp. 267–281. In: B.N. Petrov and F.
Csaki (eds.) Second International Symposium on Information
Theory. Akademiai Kiado, Budapest. 451 pp.
Alpizar-jara, R. and Pollock, K.H. 1996. A combination linetransect and capture-recapture sampling model for multiple
observers in aerial surveys. Environmental and Ecological
Statistics 3: 311–327.
Barlow, J. 1999. Trackline detection probability for long-diving
whales. pp. 209–221. In: G.W. Garner, S.C. Amstrup, J.
Laake, G.F.J. Manly, L.L. McDonald and D.G. Robertson (eds.)
Marine Mammal Survey and Assessment Methods. Balkema,
Rotterdam, the Netherlands, 287 pp.
Borchers, D.L., Buckland, S.T., Goedhart, P.W., Clarke, E.D. andHedley, S.L. 1998. Horvitz-Thompson estimators for doubleplatform line transect surveys. Biometrics 54: 1221–1237.

Borchers, D.L., Laake, J.L., Southwell, C. and Paxton, C.G.M.
2006. Accommodating unmodeled heterogeneity in doubleobserver distance sampling surveys. Biometrics 62: 372–378.
Buckland, S.T. and Turnock, B.J. 1992. A robust line transect
method. Biometrics 48: 901–909.
Buckland, S.T., Anderson, D.R., Burnham, K.P. and Laake, J.L.
1993. Distance Sampling. London: Chapman and Hall, reprinted 1999 by RUWPA, University of St Andrews. 446 pp.
Buckland, S.T., Anderson, D.R., Burnham, K.P., Laake, J.L.,
Borchers, D.L. and Thomas, L. 2001. Introduction to DistanceSampling: Estimating Abundance of Biological Populations.
Oxford: Oxford University Press. 432 pp.
Burt, M.L., Borchers, D.L., Jenkins, K.J. and Marques, T.A.
2014. Using mark-recapture distance sampling methods online transect surveys. Methods in Ecology and Evolution 5:
1180–1191.
Butterworth, D.S. and Borchers, D.L. 1988. Estimates of g(0) for
minke schools from the results of the independent observer
19Technical Reports of the Institute of Cetacean Research (2019)

experiment on the 1985/86 and 1986/87 IWC/IDCR Antarctic
assessment cruises. Rep. int. Whal. Commn 38: 301–313.
Cooke, J.G. 2001. A modiﬁcation of the radial distance methodfor dual-platform line transect analysis, to improve robustness. Paper SC/53/IA31 presented to the IWC Scientiﬁc
Committee, July 2001 (unpublished). 7 pp. [Available from the
IWC Secretariat].
Dawson, S.M., Slooten, E., DuFresne, S.D., Wade, P.R. andClement, D.M. 2004. Small-boat surveys for coastal dolphins:line-transect surveys of Hectorʼs dolphins (Cephalorhynchus
hectori). Fishery Bulletin 102: 441–451.
Hakamada, T. and Matsuoka, K. 2017. Sighting survey procedures for abundance estimates of large whales in JARPA and
JARPAII, and results for Antarctic minke whales. Technical
Report of the Institute of Cetacean Research (TEREP-ICR) No.
1: 28–36.
Hakamada, T., Matsuoka, K., Nishiwaki, S. and Kitakado, T. 2013.
Abundance estimates and trends for Antarctic minke whales(Balaenoptera bonaerensis) in Antarctic Area IV and V for
the period 1989/90–2004/05. J. Cetacean Res. Manage. 13:
123–151.
Heide-Jørgensen, M.P., Laidre, K.L., Simon, M., Burt, M.L.,
Borchers, D.L. and Rasmussen, M. 2010. Abundance of ﬁnwhales in West Greenland in 2007. J. Cetacean Res. Manage.
11: 83–88.
Innes, S., Heide-Jørgensen, M.P., Laake, J.L., Laidre, K.L.,
Cleator, H., Richard, P. and Stewart, R.E.A. 2002. Surveys ofbelugas and narwhals in the Canadian high Arctic in 1996.
Scientiﬁc Publications of the North Atlantic Marine Mammal
Commission 4: 169–190.
International Whaling Commission. 2012. Requirements andGuidelines for Conducting Surveys and Analysing Data within
the Revised Management Scheme. J. Cetacean Res. Manage.
(Suppl.) 13: 509–517.
Laake, J.L. and Borchers, D.L. 2004. Methods for incomplete
detection at distance zero. pp. 108–189 In: S.T. Buckland,
D.R. Anderson, K.P. Burnham, J.L. Laake, D.L. Borchers and

20

L. Thomas (eds.) Advanced Distance Sampling. Oxford
University Press, Oxford. 416 pp.
Matsuoka, K., Ensor, P., Hakamada, T., Shimada, H., Nishiwaki,S., Kasamatsu, F. and Kato, H. 2003. Overview of minke
whale sightings surveys conducted on IWC/IDCR and SOWER
Antarctic cruise from 1978/79 to 2000/01. J. Cetacean Res.
Manage. 5 (2): 173–201.
Marsh, H. and Sinclair, D.F. 1989. Correcting for visibility bias
in strip transect aerial surveys of aquatic fauna. J. Wildlife
Manage. 53: 1017–1024.
Okamura, H. and Kitakado, T. 2012. Abundance estimates ofAntarctic minke whales using the OK method. Paper SC/64/IA2
presented to the IWC Scientiﬁc Committee, June 2009 (unpublished). 24 pp. [Available from the IWC Secretariat].
Okamura, H., Kitakado, T., Hiramatsu, K. and Mori, M. 2003.
Abundance estimation of diving animals by the double-platform line transect method. Biometrics 59: 512–520.
Okamura, H., Miyashita, T. and Kitakado, T. 2010. g(0) estimates
for western North Paciﬁc common minke whales. Paper
SC/62/NPM9 presented to the IWC Scientiﬁc Committee, June2010 (unpublished). 7 pp. [Available from the IWC Secretariat].
Oyster, J.H., Keren, I.N., Hansen, S.J.K. and Harris, R.B. 2018.
Hierarchical Mark-Recapture Distance Sampling to Estimate
Moose Abundance. J. Wildlife Manage. 82: 1168–1679.
Palka, D. 1995. Abundance estimate of the Gulf of Maine harbor
porpoise. Rep. int. Whal. Commn (special issue) 16: 27–50.
Quang, P.X. and Becker, E.F. 1997. Combining line transect anddouble count sampling techniques for aerial surveys. Journalof Agricultural, Biological, and Environmental Statistics 1:
170–189.
Schweder, T., Skaug, H.J., Dimakos, X.K., Langaas, M. and Oien,
N. 1997. Abundance of northeastern Atlantic minke whales,
estimates for 1989 and 1995. Rep. int. Whal. Commn 47:
453–483.
Skaug, H.J. and Schweder, T. 1999. Hazard models for linetransect surveys with independent observers. Biometrics 55:
29–36.