J-STAGE Advance published date: January 31, 2021

EVALUATION OF A PATERNITY METHODEVALUATION OF A PATERNITY METHOD BASED ON
MICROSATELLITE DNA GENOTYPES FOR
ESTIMATING THE ABUNDANCE OF ANTARCTICMINKE WHALES (BALAENOPTERA BONAERENSIS) IN
THE INDO-PACIFIC REGION OF THE ANTARCTIC
Yumi OHASHI1, Mutsuo GOTO2, Mioko TAGUCHI2,
Luis A. PASTENE2, 3 and Toshihide KITAKADO1*
1

Tokyo University of Marine Science and Technology, 4–5–7 Konan, Minato-ku, Tokyo 108–8477, Japan
2
Institute of Cetacean Research, 4–5 Toyomi-cho, Chuo-ku, Tokyo 104–0055, Japan
3
Project Microbiomes as Bioindicators of the Aquatic Ecosystem Health in Chilean Patagonia,
Centro de Estudios del Cuaternario de Fuego-Patagonia y Antártica (CEQUA),
Punta Arenas, Chile*Corresponding author: kitakado@kaiyodai.ac.jp

Abstract
This study describes a paternity method based on microsatellite DNA genotypes to estimate the abundance of mature male Antarctic minke whales (Balaenoptera bonaerensis) in
the Indo-Paciﬁc region of the Antarctic using a maximum likelihood approach. The analyses
were based on biological and genetic (microsatellite DNA at 12 loci) data from Antarctic
minke whales collected by surveys of the Japanese Whale Research Program under Special
Permit in the Antarctic-Phase II (JARPAII) in the Indo-Paciﬁc region of the Antarctic. A total of 2,126 Antarctic minke whales taken in the austral summer seasons 2006/07, 2008/09,
2009/10, 2010/11 and 2011/12 from locations 35°E to 145°W were used in the analyses. The
abundance of mature males estimated by this method was then extrapolated to estimate totalabundance for comparison with results for abundance obtained using conventional line transect methods in the research area. The total abundance derived from the paternity method(ca. 210,000–220,000) was generally lower than that obtained by the line-transect method(ca. 260,000–410,000), although the ﬁgure from the line-transect method was within the 90%
conﬁdence interval of the estimates by the paternity method, and the area covered by bothmethods was slightly diﬀerent. Additionally, the geographical locations of mother/fetus–father
pairs provided the opportunity to evaluate the current hypothesis on population structure ofthis species in the Indo-Paciﬁc region. Results for the geographical distribution of mother/fetus–father pairs were generally consistent with the hypothesis of separate Eastern Indian
Ocean and Western South Paciﬁc Ocean populations, because 8 of 10 pairs were found in the
expected areas of distribution of either populations. However, two pairs were found in distantareas. As a whole, the results from the present study demonstrated the utility of the paternity
method for estimating the abundance of Antarctic minke whales and for assisting the interpretation of population structure hypotheses.
Key words:

Antarctic minke whale, paternity analysis, population structure, microsatellite DNA.

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Introduction
Population abundance and trajectories provide key information required for eﬀective conservationand management of wildlife. In the case of whaling, the International Whaling Commission (IWC)
developed and adopted the Revised Management Procedure (RMP), a single-species management
procedure1 for calculating commercial catch limits for whaling of baleen whales (Anon, 1994; Punt
and Donovan, 2007). The RMP consists of a series of rules to manage whaling (including multi-stock
scenarios), based largely upon catches determined by a simple generic Catch Limit Algorithm (CLA),
that requires two kinds of information: a time series of abundance estimates and catch-history data.
The key to the approach is that the CLA was rigorously tested by simulation to ensure that it is robust to inevitable scientiﬁc uncertainty, while the implementation of the RMP in speciﬁc multi-stock
situations is also tested by simulation to ensure robustness to evaluate uncertainty in key parameters(known as Implementation Simulation Trials, ISTs). The catch limits set by the CLA take into accountthe uncertainty in the abundance estimates and thus it is important to obtain abundance estimates withgood precision. Abundance information about whales is also required for the development of ecosystem models and multi-species management procedures.
In recent decades, visual surveys using ‘Distance sampling’ approaches (e.g., Buckland et al., 2001)
have been the most common method for estimating the abundance of cetacean species. Amongst otherassumptions, this approach depends upon an assumption that all animals on the trackline are seen (orcan be corrected for the actual detection probability on the trackline—the so-called g(0) value). It isalso assumed that, for estimating trends in a population (rather than trends within a geographical area),
the full population is surveyed each time (diﬃcult for wide-ranging species such as cetaceans). A good
example of the complexity in the use of the line-transect method was the assessment of Antarctic minke whales by the IWC Scientiﬁc Committee (SC), based on three Antarctic circumpolar surveys conducted under the International Decade of Cetacean Research and Southern Ocean Whale and Ecosystem Research (IDCR/SOWER) programs. Obtaining robust abundance estimates from these surveys
and then interpreting the results triggered a decade-long discussion in the IWC SC about the methodof estimating g(0) and possible distributional shifts of whales over time e.g. to unsurveyed areas beyond the ice-edge of the survey region that prevents vessels entering (IWC, 2013).
Mark–recapture methods based on internal marks (Discovery type, e.g., see Buckland andDuﬀ, 1989) or individual identiﬁcation by photographic matching (e.g., Hammond et al., 1990) canbe used to estimate some marine mammal population sizes (Sobtzick, 2010). However, in the case of
Antarctic minke whales the former method is not possible because there are no current catches of thisspecies. Obtaining suﬃcient photographs for photographic identiﬁcation and then matching them isconsiderably more diﬃcult for Antarctic minke whales than say, humpback, right and blue whales.
Given the limitations mentioned above, alternative methods are being investigated for estimating
the abundance of whales. Mark–recapture approaches based on genetic individual identiﬁcation frombiopsy samples have been used to estimate population abundance and to examine the migration patterns of whales (e.g., Palsbøll, 1999). Whilst valuable for smaller populations, the logistics of obtaining a suﬃciently large sample size make it often impractical for large populations.
The most promising recent technique involves paternity testing. For paternity analyses, DNA proﬁles of mother/fetus, usually from a set of microsatellite loci, are used to look for potential fathers of
the fetuses within the sample population. If their fathers are found, the number of matches can be usedin traditional mark–recapture analyses (e.g., see Skaug and Øien, 2004). Paternity analysis and closekin mark–recapture methods based on genetic data have been used to estimate the abundance of North
Atlantic humpback whales (Palsbøll et al., 1997; Nielsen et al., 2001).
This study describes a paternity method based on microsatellite DNA genotypes to estimate the abun1

Sometimes in ﬁsheries the term ‘management strategy’ is used.

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dance of mature male Antarctic minke whales in the Indo-Paciﬁc region of the Antarctic using a maximum
likelihood approach. Mature male abundance is extrapolated to total abundance and the estimates compared with those obtained from conventional line-transect methods in the same research area. The paper
also identiﬁes additional research required to improve the precision of the paternity method for abundance
estimate purposes. Finally, the geographical locations of mother/fetus–father pairs are used to evaluate thecurrent hypothesis on population structure of this species in the Indo-Paciﬁc region of the Antarctic.

Materials and methods
Samples
Samples from a total of 2,126 Antarctic minke whales were available from the surveys of theJapanese Whale Research Program under Special Permit in the Antarctic-Phase II (JARPAII) in the
austral summer seasons 2006/07, 2008/09, 2009/10, 2010/11 and 2011/12. The surveys were conducted in the Indo-Paciﬁc region of the Antarctic, in the IWC Management Areas (see Donovan, 1991)
IIIE (35°–70°E), IV (70°–130°E), V (130°E–170°W) and VIW (170°–145°W) (Fig. 1). For each sampled whale, the following information was available: sample ID, sampling date, sampling location(latitude and longitude), sex and maturity, occurrence of fetus, age and the quality of the age estimation.
The details of the samples used in the analyses are presented in Table 1.
Microsatellite DNA
Each sample (including fetuses) was genotyped using 12 microsatellite DNA loci: EV1, EV104,
GT211, DlrFB14, GT195, GT23, AC045, AC082, AC087, AC137, CA234 and GT129. The details of
the laboratory work for DNA extraction and microsatellite DNA genotyping were reported by Pastene
and Goto (2016). Loci CA234 and GT129 were excluded from the present analyses because of theexistence of null alleles and genotyping errors. Individuals with missing allele data on some loci (576
animals) and some mother/fetus pairs that had mismatching alleles (37 animals) were also excluded
from the statistical analysis.

Fig. 1. IWC management Areas IIIE, IV, V and VIW where the study was conducted. The ﬁgure also shows aschematic representation of the hypothesis of population structure of Antarctic minke whale in the Indo-Pacific region of the Antarctic. At least two populations occur in this region, the Eastern Indian Ocean Population(I) and the Western South Paciﬁc Ocean Population (P), which overlap in a transition area.
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Table 1. Number of sampled individuals used in the analysis. Individuals which had missing data for one ormore loci were excluded from the analysis.

FemaleArea

2006/07

2008/09

2009/102010/112011/12

With fetus(Mother/fetus pair)

IIIE–VW
VE–VIW

0
242

0
43

156
0

0
78

12
79

Immature or mature but
without fetus

IIIE–VW
VE–VIW

0
106

3
63

71
0

0
30

38
38

IIIE–VW
VE–VIW

1331
2651

IIIE–VW
VE–VIW
Mature male
Male

1502
1452

IIIE–VW
VE–VIW

1513
793

IIIE–VW
VE–VIW

Immature male

334
834

IIIE–VW
VE–VIW

0
128

5
71

120
0

0
46

36
37

IIIE–VW
VE–VIW

0
24

5
31

46
0

0
16

13
13

The total number of mature males aged ≥6 years in 2006/07; 2 The total number of mature males aged ≥6 years in 2008/09; 3 The total
number of mature males aged ≥6 years in 2009/10; 4 The total number of mature males aged ≥6 years in 2010/11.
1

Assumptions on population structure
Abundance estimates developed using the paternity method are presented here under two assumptions: (i) no population structure; and (ii) population structure based on the hypothesis proposed by
Pastene and Goto (2016). Regarding (ii), the IWC SC (IWC, 2008) has agreed that there are at least
two genetically distinct populations in this region, one in the east (Paciﬁc or P-population) and theother in the west (Indian or I-population) with a ‘soft’ boundary between these populations in Areas
IVE and VW, which changed by year and sex. For practical purposes, the present study assumes that
the I-population is distributed from Area IIIE to Area VW, and the P-population from Area VE to Area
VIW. Fig. 1 shows a schematic representation of the population structure of Antarctic minke whales in
the Indo-Paciﬁc region, and its relation with IWC Management Areas.
Identiﬁcation of father from mother/fetus genotype proﬁles
The ﬁrst step in the process of using the paternity method to estimate abundance is to examine themicrosatellite DNA proﬁles of the mother/fetus pairs to look for potential fathers within the total sample. The probability of the fetus’s genotype at each locus, given the mother’s and potential father’s
genotype, was calculated following Marshall et al. (1998). Table 2 shows the conditional probabilities
for all compatible mother/fetus–potential father pairs. The possibility of a male being the true father isrejected when the probability of the fetus’s genotype is 0. In this study, 10 loci were used for the estimation, and the 10 probabilities for the fetus’s genotype multiplied. When the results are greater than0, the potential father is considered the true father.
To aid interpretation, the sexual maturity of the males was considered. Males aged six years old orolder were deﬁned as mature males (Tamura and Konishi, 2014; Murase et al., 2020) and the sensitivity of the results to using deﬁnitions of seven and eight years old was also examined.
The geographical positions of mother/fetus and true father pairs were mapped using Generic Map-

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Table 2.

Conditional probabilities for all compatible mother/fetus–potential father pairs.

Fetus’s
genotype (go)Potential father’s
genotype (gp)

Mother’s
genotype (gm)Pr(go|gm,gp)

Pr(go|gm)

BB
BB
BB
BB
BC
BC
BC
BC
BC
BC
BC

BB
BX
BB
BX
BB
BX
BB
BX
BB
BY
BC

BB
BB
BX
BX
CC
CC
CY
CY
BC
BC
BC

1
1/2
1/2
1/4
1
1/2
1/2
1/4
1/2
1/4
1/2

b
b
b/2
b/2
b
b
b/2
b/2
(b+c)/2(b+c)/2(b+c)/2

X represents any allele other than B; Y represents any allele that is neither B nor C. The frequencies of alleles B and C are denoted b and c.
Pr(go|gm,gp) is the probability of the fetus’s genotype given the mother’s and alleged father’s genotypes and Pr(go|gm) is the probability of
the fetus’s genotype given the mother’s genotype (Marshall et al., 1998).

ping Tools (GMT2) (Fig. 2).
Likelihood function for estimating the number of mature males
The likelihood function for the abundance of mature males was obtained as described by Nielsen
et al. (2001). Assuming Ij (i) is the event that the jth potential father is the true father of the ith fetus,
I0 (i) is the event that the potential father is not in the samples, Mi is the ith maternal genotype, Oi is
ith associated genotype of the fetus, Fj is the genotype of the jth potential father, A is the matrix ofallelic frequencies for all loci, N is the abundance of mature males in the area and n is the number ofsampled mature males, then the likelihood function for N is expressed as:
L(N ) ∝

∏ Pr (O | M , F , A, N )
i

i

i

=

∏
i

=

∏
i

 (N − n)

1 n
Pr
(
|
,
)
Pr (Oi | M i , F j ) 
+
O
M
A

i
i
 N

N j=1


n
 (N − n)1
Pr ( Oi |M i , A, I 0 (i ) ) +Pr ( Oi | M i , F j , I j (i ), A, N )  for N > n.

 N

N j=1







(1)

Here, ∑nj=1 Pr (Oi|Mi,Fj) refers to the sum of the probabilities that the father of the ith fetus is the jthpotential father when the ith maternal genotype and the jth potential father are given, and Pr (Oi|Mi,A)
refers to the probability of the ith fetus’s genotype given the ith mother’s genotype. The point estimateof N was computed by maximizing the logarithm of L(N), and the 90% conﬁdence interval of N was
calculated by the likelihood proﬁle as {N; log L(N)≥log L(N̂)−0.5χ 2 (0.10)}, where χ 2 (0.10) is the10th upper percentile of chi-square distribution with the degree of freedom 1.
To estimate the total abundance of Antarctic minke whales, the total was prorated based upon the
proportions of males and females, and immature and mature whales, from the sampled data, under theassumption that the sample was representative of the true population (by assuming an equal selectivity
from the population(s)). The proportion of male whales was 0.436 for the case of a single population,and 0.491 and 0.407 for I- and P-populations, respectively. Also, the proportion of immature whales
2

https://www.generic-mapping-tools.org/

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Fig. 2A. Positions of a mother-fetus pair and its true father. The circle indicates a female caught in 2006/07
and the triangle indicates a male caught in 2006/07. The red and blue boxed numbers are the ages of female
and male, respectively.

Fig. 2B. Positions of a mother-fetus pair and its true father. The circle indicates a female caught in 2006/07
and the triangle a male caught in 2008/09.

Fig. 2C. Positions of a mother-fetus pair and its true father. The circle indicates a female caught in 2006/07
and the triangle a male caught in 2010/11.

under the assumption of knife-edge maturity-at-age six years old was 0.254 for a single population,and 0.299 and 0.225 for I- and P-populations, respectively. For a sensitivity test, eight years old wasused as the maturity age. In this case the immature proportion was 0.317 for a single population, and
0.366 and 0.286 for I- and P-populations, respectively.

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Fig. 2D. Positions of a mother-fetus pair and its true father. The circle indicates a female caught in 2006/07
and the triangle a male caught in 2011/12.

Fig. 2E. Positions of a mother-fetus pair and its true father. The circle indicates a female caught in 2006/07
and the triangle a male caught in 2011/12.

Fig. 2F. Positions of a mother-fetus pair and its true father. The circle indicates a female caught in 2009/10
and the triangle a male caught in 2009/10.

Results
Mother/fetus and mature male pairs
A total of 10 mother/fetus–father pairs were identiﬁed under the assumption of a maturity age of six
years old. There were no cases of multiple fathers for one fetus. True fathers were found for ﬁve mothers/fetuses caught in 2006/07 and ﬁve mothers/fetuses caught in 2009/10.
The location of the matching pairs is shown in Figs. 2A–J. Eight pairs occurred in nearby geographical locations (Figs. 2A–H) while two pairs occurred in distant locations (Figs. 2I, J).
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Fig. 2G. Positions of a mother-fetus pair and its true father. The circle indicates a female caught in 2009/10
and the triangle a male caught in 2009/10.

Fig. 2H. Positions of a mother-fetus pair and its true father. The circle indicates a female caught in 2009/10
and the triangle a male caught in 2009/10.

Fig. 2I. Positions of a mother-fetus pair and its true father. The circle indicates a female caught in 2009/10 andthe triangle a male caught in 2011/12.

The abundance of mature males (population structure information not considered)
Combining data for all years, N̂mature male was estimated to be 68,874 (90%CI=42,625–122,779).
The likelihood proﬁle is shown in Fig. 3. Using the ratios of males to females and immature to mature whales to estimate the total population, the total population size, N̂, was estimated as 211,600(90%CI=130,954–377,210).
The abundance of mature males (population structure information considered)
For the I-population and using data from the two relevant years (2009/10 and 2011/12), the estimat-

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Fig. 2J. Positions of a mother-fetus pair and its true father. The circle indicates a female caught in 2009/10
and the triangle a male caught in 2011/12.

Fig. 3. The likelihood proﬁle for N̂mature male using 10 loci and ﬁve years of mother-fetus pairs and mature males
for analysis without considering population structure (assumption of single population).

ed abundance of mature males N̂mature male was 10,478 (90%CI=4,662–32,212), and the total populationN̂ was 30,432 (90%CI=13,540–93,556). The likelihood proﬁle is shown in Fig. 4A.
For the P-population (2006/07, 2008/09, 2010/11 and 2011/12), the estimated abundance of mature males N̂mature male was 59,961 (90%CI=28,853–161,155), and N̂ was 189,946(90%CI=91,401–510,506). The likelihood proﬁle is shown in Fig. 4B.
There were 9 pairs when the age of sexual maturity in males was changed from six to eight years
old. Therefore, six years old was used for the subsequent analysis of abundance. Comparison of abundance estimates are summarized in Table 3.

Discussion
The main objective of this study was to apply a new paternity method based on maximum likelihood to estimate the abundance of the Antarctic minke whale in the Indo-Paciﬁc region of the Antarctic, and to evaluate this method by comparing the results with those obtained by line-transect methods
in the same region.
Estimates from the paternity methods
There are some technical issues that need to be considered with respect to the paternity method estimates presented here. A key factor relates to the issues that resulted in the exclusion of a considerable
amount of data due to the following reasons:Cetacean Popul. Stud. (CPOPS), Full paper
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Fig. 4A. The likelihood proﬁle for N̂mature male using 10 loci in Areas IIIE, IV and VW using ﬁve years of mother-fetus pairs and mature males for analysis (I-population under the assumption of two populations).

Fig. 4B. The likelihood proﬁle for N̂mature male using 10 loci in Areas VE and VIW using ﬁve years of motherfetus pairs and mature males for analysis (P-population under the assumption of two populations).

(1) genotyping errors indicated by mother/fetus pairs with clearly diﬀerent genotypes (37 pairs);(2) missing allele information for some loci (576 individuals), indicating a genotyping error; and(3) two loci with a high null allele frequency.
Presence of such genotyping errors and null alleles could cause reduction of matching cases, andtherefore the estimated abundance tends to be positively biased. Such errors and allelic dropout can beconsidered in statistical models. However, such technical drawbacks in the DNA experiment should
also be examined and, where possible, corrected so that updated data can be used in future analyses.
Data collected after the 2011/12 austral summer season should be also used.
For practical reasons, the assumption of population structure considered a hard boundary between
the I and P-populations. Reﬁned analyses should consider the probability of assignment of each individual to each population in the overlap area.
Finally, this method considered only the relationship between mother/fetus and father. If other relative categories such as siblings are incorporated into the analyses, then the estimation performance(precision and accuracy) could be improved (Bravington et al., 2016a; b).
Comparison with estimates from line-transect surveys
The preliminary results on abundance can be summarized as follows: i) there were no substantial
diﬀerences in abundance under the two assumptions on population structure; ii) there was a slight
diﬀerence in I-population estimate depending on the assumption for maturity age used, which gave an
impact on the candidate fathers and successful pairs; and iii) the abundance derived from the paternity

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Assumption/Data

JARPA/JARPAII(1989/90–2008/09,
Hakamada andMatsuoka 2014)

93,215(CV=0.35)

III–W III–E

Area III
V–W

56,699*(30,585–95,725)

55,237(CV=0.49)

30,432(90%CI=13,540–93,556)
45,637(90%CI=17,359–192,539)

VI–W

Area IV

207,012*(132,431–299,433)

183,915(CV=0.36)

VI–E

80,835(CV=0.37)

189,946(90%CI=91,401–510,506)
182,458(90%CI=87,924–488,166)

V–E

Area V

211,600(90%CI=130,954–377,210)
228,478(90%CI=137,936–422,368)

Area IV*An average (and the range in brackets) of a series of abundance estimates in Hakamada and Matsuoka (2014).

Line transect
methodIDCR/SOWER(1992/93–2003/04,
IWC 2013)

Paternity analysis Base casewith I- andP-populations
Sensitivity casePaternity analysis Base casewith single
population
Sensitivity case

MethodIWC Management Area

All the estimates were correctedby g(0)estimates. The interval inbrackets is a range of time series
estimates.

All the estimates were correctedby g(0) estimates. The CVs include the additional variance.

Maturity age=8 yrs old

Maturity age=6 yrs old

Maturity age=8 yrs old

Maturity age=6 yrs old

Remarks

Table 3. Results of abundance estimates for the Antarctic minke whales derived from the paternity analysis (in this paper) and a comparison with the estimates obtainedusing the line-transect method from the IWC SOWER programme (IWC, 2013, p.27) and JARPA/JARPAII (Hakamada and Matsuoka, 2014).

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method was similar or somewhat lower than that obtained by the line-transect method (Table 3). It
should be noted that this comparison was not straightforward because the research areas covered by
the two methods are not identical (for example, the western part of Area III and eastern part of Area
VI were not covered by the paternity method). The ﬁgure from the line-transect method, however,tends to be within the 90% conﬁdence interval of the estimates by the paternity method.
Possible advantage of the paternity analysis over the line transect method is a less demanding requirement of the coverage of the habitat area. In the line transect method, the survey is assumed tocover the whole habitat area while the genetic tagging does not require this condition strongly as far
as the sampling is randomly conducted. However, in the paternity analysis, false positive and/or false
negative in matching between mother/fetus and father is crucial, and therefore the method is subject
to over- or under-estimation depending on the quality of matching. Also, if the number of matchingis quite low and the population size is large, “recapture probability” and “actual number of recapture”
might be so low and it could cause a large extent of uncertainty in the abundance estimation. In fact,in our analyses, the matching occurred only in 10 pairs for hundreds of thousands of population size,and hence the 90% CI tends to be wide. To increase the recapture probability, other kinship deﬁnitions
such as half-sibling can be used for improving estimation performance. This warrants further extension of methods to simultaneously account for diﬀerent kinship types and population structure.
Inference of results for population structure hypotheses
The study oﬀered the opportunity to compare the information obtained from this study with the current population structure hypotheses for the Indo-Paciﬁc region. The geographical positions of mother/fetus–true father pairs are broadly consistent with the hypothesis of separate I- and P-populations. A
total of 8/10 pairs was found in the expected areas of distribution of either I- or P-population. For example, ﬁve pairs were found in the expected area of distribution of the P-population while three pairs
were found in the expected area of distribution of the I-population. In two cases, however, mother/fetus–true father pairs were found in quite diﬀerent feeding areas. In the ﬁrst case, the mother/fetus
was caught in the expected area of I population while the true father was found in the expected areaof the P-population. In the second case, the mother/fetus was caught in the expected feeding area of
the I-population while the true father was found in the expected area of the P-population. These two
examples are not inconsistent with the hypothesis of I- and P-populations, because it is expected thatsome whales move longitudinally within the feeding grounds, wherever they breed, and that such
movements are more marked in males (Kitakado et al., 2014; Murase et al., 2020).

Conclusion
The results from this study have demonstrated the utility of the paternity method for obtaining
abundance estimates of the Antarctic minke whale because the estimates are compatible with thoseobtained using the line-transect method. A number of ways to improve the estimates have been identiﬁed.
Acknowledgements

We thank the researchers and crew members who participated in the JARPAII surveys for collecting the data used in theanalyses. We also thank T. Bando (ICR) for facilitating age information for the Antarctic minke whales used in this study
and N. Kanda (Japan NUS, formerly ICR) for his laboratory work for microsatellite DNA genotyping. We acknowledge twoanonymous reviewers for comments and particularly Greg P. Donovan (IWC) for useful suggestions and editorial corrections
that improved this paper substantially.

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Received: March 25, 2020
Accepted: September 23, 2020
Published online: January 31, 2021

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