Technical Reports of the Ins�tute of Cetacean Research (2020)

pp. 41–47

Technical Report (not peer reviewed)

Use of gene�c data for abundance es�mate purposes: a brief review
of methods and case studies by the Ins�tute of Cetacean Research
Megumi Takahashi*
Institute of Cetacean Research, 4–5 Toyomi-cho, Chuo-ku, Tokyo 104–0055, Japan*Contact e-mail: takahashi@cetacean.jp

ABSTRACT

Sigh�ng surveys by the line transect method is the most used approach to es�mate abundance in whales.
Sigh�ng surveys have some limita�ons associated with bad weather and sea condi�ons, and with the diﬃculty
to cover all areas of distribu�on of the stocks. Given these limita�ons, alterna�ve methods are being inves�gated for es�ma�ng the abundance of whales. This paper presents an overview of the current gene�c methods for abundance es�ma�on in whales. These methods are based on the mark-recapture (MR) approach andcan be divided into two groups: i) those based on the history of individual iden�ﬁca�on (genotyping basedon biopsy samples), and ii) those based on kinship informa�on including paternity analysis and close-kin MR(based on biopsy samples and/or catches). This paper also presents informa�on on case studies conducted by
the Ins�tute of Cetacean Research.

INTRODUCTION
Abundance es�ma�on is one of the most importantsources of informa�on required for the conserva�onand management of whales. The analysis of sigh�ng
data collected by the line transect (LT) method (Buckland
et al., 2001) is the most common approach for es�mating the abundance of whales. However, the use of thismethod has some limita�ons. For example, bad weather
and sea condi�ons can prevent the surveys, while someareas are inaccessible to the surveys (e.g., polynyas in the
Antarc�c or territorial waters of other countries).
The mark-recapture (MR) method (Hammond, 1986;
Pollock et al., 1990) based on Discovery-type tags isanother method used for abundance es�ma�on. However, this method depends on whaling opera�ons for therecovery of the tags, and this has been limited in recent
years. MR methods can be used for individual whales
iden�ﬁed by natural marks (photo-iden�ﬁca�on), however not all species have dis�nc�ve marks for individual
iden�ﬁca�on, and the method would not be prac�cal forabundant popula�ons.
Given these limita�ons, alterna�ve methods for abundance es�ma�on of whales are being explored. In recent
years, several methods for abundance es�ma�on basedon gene�c individual iden�ﬁca�on and kinship inference
have been reported. This paper presents an overview of
those methods and outlines some case studies conduct-

ed by the Ins�tute of Cetacean Research (ICR).

BASIC CONCEPT OF MARK-RECAPTURE
The MR method is widely used in ecology, par�cularly
to es�mate popula�on size and some biological parameters such as survival rates. The MR method relies on
sampling and re-sampling individual animals. A capture
history simply describes whether or not an animal was
captured in a series of sampling occasions during a periodof data collec�on. It is usually represented by a series of
1 (captured) and 0 (not captured). The key idea of the MR
method is to determine the ra�o of marked individuals
to unmarked individuals in the target popula�on, i.e.,es�mate p (capture probability) from the propor�on ofmarked animals that are recaptured. Figure 1 shows thesitua�on of marks and mark-recaptures in two samplingoccasions (two-sample es�mator).
In Figure 1, M is the number of individuals marked in a
popula�on in the ﬁrst year; c is the total number captured
in the second year (with and without a mark); R is thenumber of captured in the second year that are marked(recaptured); and N is the size of the popula�on at the�me of marking and release.
The simplest MR method is the ʻPetersen methodʼ also
known as ʻLincoln methodʼ (Seber, 1982):
R
M
=
.
c
N
41

Technical Reports of the Ins�tute of Cetacean Research (2020)

The propor�on of marked animals in the second �me
R/c is an es�mate of the probability of capturing individual (p̂), so that:
M
.
Nˆ =
pˆ

Chapmanʼs modiﬁca�on of Petersenʼs two-sample es�mator (Chapman, 1951) is more appropriate in situa�onsof small sample sizes, and is expressed as follows:N=(M +1)(c +1)
− 1.
R +1

Here,
M=number of individuals captured in the ﬁrst year;
c=number of individuals captured in the second year;
R=number of individuals captured in both years.
Mul�ple sampling occasions
In the case of the two-sample es�mator in Figure 1, theassump�on of ʻclosed popula�onʼ is adopted (births,
immigra�on, emigra�on and death are not considered).
For mul�ple sampling occasions involving a long periodof �me, the assump�on of ʻopen popula�onʼ is more appropriate, and immigra�on, emigra�on, birth and deathshould be considered (Figure 2).
In the case of mul�ple sampling occasions, the JollySeber (JS) model (Jolly, 1965; Seber, 1965), an open
popula�on model, is the most appropriate. This model
is very ﬂexible and, in addi�on, can provide es�mates ofsurvival, recruitment and popula�on growth rates.
There are a number of formula�ons based on the JS fores�ma�ng abundance and related parameters, such as
the ʻPOPAN,ʼ Link-Barker and Pradel recruitment, and the
Burnham JS and Pradel-λ formula�ons. In par�cular, thePOPAN formula�on (Schwarz and Arnason, 1996) can provide abundance and net births by using the full likelihood
approach. Net birth refers to all animals that enter a�ersampling occasion i and survive un�l sampling occasion i+1.

ABUNDANCE ESTIMATES BASED ON GENETIC
DATA
The main advantages of using gene�c tags for individual
iden�ﬁca�on and abundance es�mates based on MR are
that: i) they are permanent and ii) they exist in all individuals. It is important that the gene�c approach for individual iden�ﬁca�on and kinship inferences are reliable.
The gene�c basis for individual iden�ﬁca�on and kinshipinferences is shown in Taguchi (this issue).

42

Figure 1.

Diagram showing the basic idea of the MR method
based on individual iden�ﬁca�on of humpback
whales by photographic matching.

Methods based on the history of individual iden�ﬁca�on
The most common approach for gene�c individual iden�ﬁca�on is based on biopsy sampling and genotyping,based on a number of nuclear marker loci. One of themost used markers is microsatellite DNA. If two biopsy
samples, taken in diﬀerent occasions/loca�ons present
the same genotype, then it is assumed that those biopsies were taken from the same individual (see Taguchi,
this issue).
Some studies are presented here as examples ofabundance es�mates in whale popula�ons based on
biopsies, gene�c individual iden�ﬁca�on and the MR
methods. Palsbøll et al. (1997) conducted an analysis ofsix microsatellite loci for 3,060 skin samples collectedfrom humpback whales throughout the North Atlan�c.
They detected 2,368 unique genotypes and, because
the samples with iden�cal genotypes were of the same
sex, they considered that the 3,060 samples represented
2,368 individual whales. There was a total of 692 ʻrecaptures.ʼ The abundance and its conﬁdence intervals (CI)were es�mated based on the data collected in 1992 and1993 and the two-sample es�mators. The abundance
was es�mated at 4,894 (95% CI: 3,374–7,123) for males
and 2,804 (95% CI: 1,776–4,463) for females.
Based on 354 biopsy samples collected from the
New Zealand subantarc�c southern right whales during the austral winter from 1995 to 1998, Carroll et al.
(2011) were able to amplify 302 samples with 9–13 microsatellite loci. They iden�ﬁed 235 unique individuals
during these four winter surveys. They es�mated thesuperpopula�on abundance using the POPAN JS model,

Use of genetic data for abundance estimate purposes

Figure 2.

Diagram showing the situa�on of mul�ple sampling under the assump�on of open popula�on. A popula�on changes in
number and density due to births, deaths, immigra�on and emigra�on. Note that, φi represent the probability of (apparent)
survival un�l the next sampling occasion; pi is the probability of being captured and re-captured; Bi is the net number of
new individuals joining the study area (modiﬁed from h�p://www.phidot.org/so�ware/mark/docs/book/pdf/chap12.pdf ).

which provided an es�mate of 910 non-calf whales (95%
CI: 641–1,354) in 1998.
Methods based on kinship informa�on
An addi�onal advantage of DNA tags is that they contain
informa�on about kinship among individuals. Hence, kinship rela�onship can be used for abundance es�mates
based on the classic MR using ʻrecapture of selfʼ to ʻrecapture of closely-related kinʼ. Several studies used DNA
proﬁles to detect instances of paternity or other kinshiprela�onships in whale popula�ons (see Taguchi, thisissue). For this approach, samples obtained from biopsy
sampling as well as from catches can be used.
Paternity analysis
For the aim of paternity inference, Marshall et al. (1998)
derived likelihood ra�os with codominant markers taking account of typing error, and deﬁned a sta�s�c Δ for
resolving paternity. The likelihood ra�o can be wri�en as:
P ( D | H1 )L ( H1 , H 2 | D ) =,P( D | H 2 )In this formula�on, P(D|Hi) is the probability of obtaining data D, i.e., genotypes of oﬀspring, mother andpoten�al father at a par�cular locus, under hypothesis Hi(i=1, 2) . The hypothesis of H1is that the poten�al father
is the true father, and this is tested against hypothesis H2
wherein the poten�al father is an unrelated individual
selected at random from the popula�on.
Nielsen et al. (2001) presented a new method for paternity analysis in natural popula�ons based on genotypic
data that can take the sampling frac�on of puta�ve parents into account. They developed an approach for es�ma�ng parentage probabili�es for paternity assignment,
which is a Bayesian alterna�ve to the method developedby Marshall et al. (1998). They used the term ʻparentage
probabilityʼ to describe the posterior probability that apar�cular individual/puta�ve father might be the actual
father of a known oﬀspring. They applied the method togenotypic data (six microsatellite DNA loci) collected from
North Atlan�c humpback whales.
The method of Nielsen et al. (2001) is brieﬂy describedhere following the nota�ons of the authors. They notedthat the objec�ve was to es�mate the posterior probability that a par�cular individual might be the father ofa known oﬀspring. Let Ij (i) indicate the event that the jthpoten�al father is the father of the ith oﬀspring. The ithmaternal genotype is Mi, the associated genotype of theoﬀspring is Oi, the genotype of jth poten�al father is Fj,
and A is the matrix of allelic frequencies for all loci. If nof N males on the breeding ground were sampled, theposterior probability of paternity could be calculated as:Pr( I j (i ) | M i , F, A, N )=Pr(Oi | M i , Fj ).
n
 j=1 Pr(Oi | M i , Fj ) + ( N − n)Pr(Oi | M i , A)

In this formula�on Pr(Oi|Mi, Fj) is the shorthand nota�on for Pr(Oi|Mi, Fj, Ij(i)). ∑nj=1 Pr(Oi|Mi, Fj) refers to thesum of the probability that ith fetus has jth poten�alfather as itʼs father when ith maternal genotype and jth
poten�al father are given. Assuming Mendelian segrega�on and independence among loci, the probability of anobserved oﬀspring genotype, given the maternal genotype and the genotype of a par�cular poten�al father
Pr(Oi|Mi, Fj), could be calculated using standard methods(e.g., Thompson, 1975; 1976). Likewise, Pr(Oi|Mi, A)
can be calculated assuming Hardy-Weinberg equilibrium and independence among loci (linkage equilibrium).
(N−n)Pr(Oi|Mi, A) refers to the probability of the ith
43Technical Reports of the Ins�tute of Cetacean Research (2020)

fetusʼs genotype given the ith motherʼs genotype. In es�ma�ng the posterior probability that a poten�al father isthe father of an oﬀspring, assump�ons need to be maderegarding the prior probability of a poten�al father being
the father. In the absence of other informa�on, it is assumed that the prior probability that a par�cular maleis the father is 1/N, where N is the number of poten�ally
breeding males in the breeding area (Nielsen et al., 2001).
Here, assuming independence among oﬀspring, thelikelihood func�on for N can be calculated as:
L( N ) ∝∏ Pr(O | M , F, A, N )
i

i

i

=

1
 ( N − n)Pr(Oi | M i , A) +
N
N

∏ 
i



n
j=1


Pr(Oi | M i , F j )  ,


N≥ n.

The maximum-likelihood es�mate of N and the conﬁdence interval is provided, for example, using parametricbootstrapping. Note that the es�mate based on this approach such as parent-oﬀspring genotypes is an es�mateof the current (i.e., at the �me of sampling) male popula�on size. To es�mate the total abundance of the target
popula�on/species, addi�onal informa�on is required.
For example, the propor�ons of males and females, andthe sexual maturity of whales from the sample, under theassump�on that the sample was representa�ve of thetrue popula�on.
Based on the method above, the maximum-likelihoodes�mate of N was 6,540 breeding male humpback whales(95% CI: 3,700–17,000) using parametric bootstrapping(Nielsen et al., 2001).
CKMR method
CKMR is a recent extension of the ordinary MR methods
used to es�mate animal abundance and other popula�onparameters. The CKMR approach was ﬁrst described bySkaug (2001) working on microsatellite data (10 loci) of
North Atlan�c common minke whales. He derived an es�mator for the total popula�on size based on the numberof parent-oﬀspring pairs (POPs).
Subsequently Bravington et al. (2016a) extended theclassic MR framework (Lincoln-Petersen type es�mator
mainly) by incorpora�ng close-kin informa�on. Whereas
ordinary MR methods only consider the subsequentiden�ﬁca�on of the same animal as a recapture, CKMR
expands this by also viewing the gene�c iden�ﬁca�on ofa rela�ve (e.g., parent-oﬀspring, full-sibling, half-sibling)
as a recapture.
Below is the simplest version of the CKMR by Bravington et al. (2016a). This is a two-sample es�mator for the44

adult popula�on size, which is the close-kin version of the
Lincoln-Petersen popula�on size es�mator:
 = 2 nJ n A .
(1)
N
A
H
Consider a sample of nJ juveniles and nA adults fromthe same popula�on. Each sampled juvenile can be considered a ʻmarkʼ of its two adult parents. The genotypeof each of the nJ juvenile samples is compared to each of
the nA adult samples, to check if a ʻmarkʼ is recaptured.
The probability that the adult happens to be one of thejuvenileʼs two parents is 2/NA, where NA is adult popula�on size. The expected number of parent-oﬀspring pairs
across all nA·nJ comparisons is then 2nA nJ/NA. Equa�ng
this to the observed number of parent-oﬀspring pairs
gives the CKMR version of the Lincoln-Petersen es�mator. Hence, if the en�re set of nJ ×nA comparisons yields H
which is the number of parent-oﬀspring pairs, then adultabundance can be es�mated as eq. (1).
In a more realis�c se�ng, some types of kinship probabili�es are likely to be present, and therefore, an explicitsta�s�cal MR model is required. That is, the prior probability that a pair is a POP is set by a popula�on dynamics
model, which accounts for pair-speciﬁc data, and which
includes demographic parameters such as adult abundance, individual survival probability, age of maturity, percapita birth rate and probably age-speciﬁc fecundi�es.
For example, probability that individual i with covariates zi (date of capture for example) is the mother ofindividual j with covariates zi is represented as:

P (i is j ′s mother| zi , z j ) i′s reproductive output in j ′s year of birth = E 
Total female reproductive output
in j ′s year of birth| zi , z jwhere E() is the expected value and the absolute abundance (of females) now enters implicitly through thedenominator.
Not only parent-oﬀspring (PO) but also other kinshiprela�onships such as half-sibling can be considered in the
CKMR. A pairwise comparison between individuals i andj gives rise to a kinship category Kij taking values from a
discrete set k={PO, HS, . . .} (see also Taguchi (this issue)).
These probabili�es are the building blocks of the pseudolikelihood shown below.
Demographic parameters can be es�mated from thelog-likelihood summed over all pairwise comparisons.
The joint distribu�on of {Kij; 1 ≤ i < j ≤ n} is too complicated to permit the construc�on of a full likelihood. Instead,a pseudo-likelihood approach (Skaug, 2001; Bravington
et al., 2016a) which involves only the marginal probabili-

Use of genetic data for abundance estimate purposes�es of the Kij in eq. (2) was used.
lP (θ ) = ∑1 ≤ i < j ≤ n log P ( K ij = kij | zi , z j ; θ ) .

(2)

Let θ denote the vector of all parameters that govern
the basic quan��es, for example, total popula�on size
(males and females): N, individual survival probability: φ,per capita average birth rate: β and capture probability at
a given sampling occasion: p).
The CK greatly expands the scope of MR because avariety of samples can be used, including biopsy samples
and samples from catches. However, age informa�on isessen�al for precise CKMR es�mates because it iden�ﬁes the �me of ʻmarkingʼ, which is the year the sampled
animal was born.
Bravington et al. (2016b) used the approach above forthe case of the southern blueﬁn tuna, using microsatellite
data at 20–25 loci.

CASE STUDIES BY THE ICR
Based on the histories of individual iden�ﬁca�on
Pastene et al. (2018) examined a total of 157 biopsy samples of southern right whales collected by IDCR/SOWER
and JARPA/JARPAII surveys in austral summer between
1987/88 to 2013/14 in the longitudinal sector between
80°E and 135°E (Figure 3). These southern right whales
are associated with the South West Australia popula�on.
Biopsy samples were examined with 14 microsatellite
DNA loci. A�er removing four duplicates, the sample
sizes for the individual iden�ﬁca�on became 153. Eight
incidences of individual matching (ʻmark-recaptureʼ)
were detected (four males and four females). Individual
matching by mul�locus genotypes was supported by mitochondrial DNA analyses (same haplotype), sex determina�on (same sex), and in two cases where pictures wereavailable, by photo-iden�ﬁca�on. Es�mate of abundance

Figure 3.

Geographical distribu�on of southern right whales
in Area IV examined by Pastene et al. (2018). Red:
females; Blue: males.

was based on the POPAN model implemented in RMark(Laake, 2013). This preliminary analysis considered theassump�on of constant apparent survival, constantprobability of capture and constant probability of entry
through the years.
The results of the preliminary analyses showed similar annual abundance es�mates to those obtained bysigh�ng data in the same area and a similar period. For
example, the es�mate of abundance by the gene�cʻmark-recaptureʼ method was 1,619 (95% CI: 868–3,151)
individuals for 2015/16, similar to the most recent(2007/08) sigh�ng survey abundance es�mate of 1,557(95% CI: 871–2,783) individuals using the LT method in
the same area.
Future analyses
The analysis conducted on southern right whales assumed constant apparent survival rate, constant capture
probability, and constant probability of entry throughthe years. Some addi�onal inves�ga�ons are required toevaluate the eﬀect of changing these assump�ons on theabundance es�mates. State-space models and hierarchical Bayesian approach have already been proposed as aconvenient and ﬂexible framework for specifying stochas�c models for the dynamics of wild animal popula�ons(Gimenez et al., 2009; Kéry and Schaub, 2011; Hendrix
et al., 2012), and these models could be used for southern right whales in the future. Such models consider individual diﬀerences of the survival rate. Furthermore, thedetec�on/capture probability, as a random eﬀect can beevaluated by the state-space model.
Gene�c databases for Antarc�c blue and humpback
whales are available at the ICR, and the abundance es�ma�on approach for southern right whales can also be
used for these other species.
One issue with mark-recapture analyses, regardlessof which method of individual iden�ﬁca�on is used, isthat the study area must provide adequate opportuni�es for ʻcapturingʼ all individuals within a popula�on.
However, this is hardly feasible because many popula�ons are widely and unevenly distributed. Therefore, forobtaining more accurate abundance es�mates, applying
analy�cal techniques that take account of unsampledloca�ons are also suggested for future analyses (e.g., Frasier et al., 2020). Also, more informa�on on the biologicalfeatures of the species, such as migra�on and habitat use
pa�erns, are required.
Paternity analyses
Kanda et al. (2014) conducted a study on paternity in45

Technical Reports of the Ins�tute of Cetacean Research (2020)

Antarc�c minke whales based on samples collected by
JARPA and JARPAII surveys. Speciﬁcally, genotypic data ofa maximum of 12 microsatellite DNA loci were preparedfrom 137 fetuses collected from females captured during
the 2003/04 JARPA survey, and their poten�al fathers
were sought among 1,779 males collected from 2001/02
JARPA to 2010/11 JARPAII surveys.
One mother-fetus-father trio was detected using
CERVUS (Marshall et al., 1998), a computer program forassignment of parents to their oﬀspring using gene�cmarkers. This single match was used to tenta�vely es�mate the mature male number in the Eastern Indian
Ocean Stock (I stock) of Antarc�c minke whales using thePetersen mark-recapture method modiﬁed by Chapman.
Only mature males (n=677) (sexual maturity criteria ofKato, 1987) were used in the es�mates.
The abundance es�mate of the mature male component of the stock was 46,782 (CV=0.572) animals.
Assuming the mature/immature ra�o and the sex ra�owere 1 : 1, respec�vely, the total stock size was es�matedas 187,128 animals. This es�mate was higher than the
JARPA/JARPAII (51,474) and the IDCR (151,174) sigh�ng
surveys es�mates in similar areas. Kanda et al. (2014)
noted that their analysis es�mated total stock size, while
the JARPA/JARPAII and IDCR analyses es�mated the number of individuals distributed in the research area basedon sigh�ng surveys, which would explain the diﬀerences.
Ohashi et al. (in-press) further examined the popula�on size of mature males of Antarc�c minke whales
based on paternity analysis. Their analyses were basedon biological and gene�c (microsatellite DNA at 12 loci)data collected by JARPAII in the Indo-Paciﬁc region of the
Antarc�c. A total of 2,126 Antarc�c minke whales taken in
the austral seasons 2006/07, 2008/09, 2009/10, 2010/11
and 2011/12 were used in the analyses. Two assump�ons
on stock structure were considered, a single stock in the
research area and two stocks in the research area (the I
stock and the Western South Paciﬁc Stock (P stock)).
For abundance es�ma�on, the approach of Nielsen
et al. (2001) outlined above was used. For the hypothesisof a single stock, the abundance of mature males wases�mated as 68,874 (90% CI: 42,625–122,779). Using the
propor�on of male and immature whales of 0.436 and
0.254, respec�vely, the es�mate of total popula�on was
211,600 (90% CI: 130,953–377,210). This es�mate waslower than that from the IDCR/SOWER sigh�ng surveys(413,202) and of the same order of JARPA/JARPAII es�mates in Areas IV and V (263,711).

46

Future analyses
Ohashi et al. (in-press) reported that there are some technical issues in their analyses on Antarc�c minke whales
that should be improved in the future. Firstly, there is aneed to op�mize the use of the available gene�c data andsolve issues, for example, on genotyping errors and missing allele informa�on for some loci. The second issue isrelated to the assump�ons of the stock structure hypothesis. The current hypothesis on stock structure of Antarc�c minke whales suggests a transi�on sector shared by
the two stocks rather than a hard longitudinal boundary
between them as assumed in the paternity analysis. Thistransi�on sector should be considered in future paternity
analyses.
In addi�on, Ohashi et al. (in-press) noted that future
analyses should consider not only the rela�onship between mother/fetus and father, but also some other kinship rela�onships (e.g., half-sibling) following the work of
Bravington et al. (2016a) outlined above. Therefore, thenext challenge for the ICR research on this topic is the applica�on of the CKMR method for abundance es�ma�on,which op�mizes the use of the available gene�c data.
Comparison of abundance between MR and LT methods
As noted by Kanda et al. (2014) and Pastene et al. (2018),es�mates of abundance, using the ordinary MR approachbased on gene�c data, refer to the total popula�on/stock
size. The es�mates based on sigh�ng data under the LT
approach, refer to the abundance of animals in a speciﬁcarea and a speciﬁc period of a survey. Then, the diﬀerence in es�mates will depend on the sigh�ng survey coverage and on the movement of individuals into and out of
the sigh�ng survey area (Hammond, 2010).

ACKNOWLEDGEMENTS
I thank T. Hakamada (ICR) for technical assistance on themethodology outlined in this paper, and L.A. Pastene(ICR) for his assistance in preparing this report.

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