Probability of taking a western North Pacific gray whale 

during the proposed Makah hunt

Jeffery E. Moore and David W. Weller

U.S. Department of Commerce

National Oceanic and Atmospheric Administration

National Marine Fisheries Service

NOAA Technical Memorandum NMFS-SWFSC-506

January 2013
Probability of taking a western North Pacific gray whale 

during the proposed Makah hunt

Jeffery E. Moore and David W. Weller

Protected Resources Division 

Southwest Fisheries Science Center 

National Marine Fisheries Service 

National Oceanic and Atmospheric Administration 

8901 La Jolla Shores Drive 

La Jolla, CA 92037-1022 USA 

U.S. Department of Commerce 

Rebecca M. Blank, Acting Secretary 

National Oceanic and Atmospheric Administration 

Jane Lubchenco, Undersecretary for Oceans and Atmosphere

National Marine Fisheries Service 

Samuel D. Rauch, Acting Assistant Administrator for Fisheries 
i

ABOUT THIS DOCUMENT

The mission of the National Oceanic and Atmospheric Administration (NOAA) is to understand 

and predict changes in the Earth’s environment and to conserve and manage coastal and oceanic 

marine resources and habitats to help meet our Nation’s economic, social, and environmental 

needs. As a branch of NOAA, the National Marine Fisheries Service (NMFS) conducts or 

sponsors research and monitoring programs to improve the scientific basis for conservation and 

management decisions. NMFS strives to make information about the purpose, methods, and 

results of its scientific studies widely available. NMFS Southwest Fisheries Science Center uses 

the NOAA Technical Memorandum NMFS series to achieve timely dissemination of scientific 

and technical information that is of high quality but inappropriate for publication in the formal 

peer-reviewed literature. The contents are of broad scope, including technical workshop 

proceedings, large data compilations, status reports and reviews, lengthy scientific or statistical 

monographs, and more. NOAA Technical Memoranda published by the Southwest Fisheries 

Science Center although informal, are subjected to extensive review and editing and reflect 

sound professional work. Accordingly, they may be referenced in the formal scientific and 

technical literature.

A NOAA Technical Memorandum NMFS issued by the Southwest Fisheries Science Center

may be cited in following manner:

Moore, J.E. and Weller, D.W. 2013. Probability of taking a western North Pacific gray whale 

during the proposed Makah hunt. U.S. Dep. Commer., NOAA Tech. Memo. NMFS-SWFSC506, 13 p.

A copy of this report may be obtained from:

Protected Resources Division

Southwest Fisheries Science Center

National Marine Fisheries Service

National Oceanic and Atmospheric Administration

8901 La Jolla Shores Drive

La Jolla, CA 92037-1022 USA

ACKNOWLEDGEMENTS

We are grateful to the Alaska Fisheries Science Center, Cascadia Research Collective, 

International Whaling Commission, National Marine Mammal Laboratory, NOAA Northwest 

Regional Office, Southwest Fisheries Science Center for their contributions and support of this 

work. We thank Jeff Laake for providing data and significant insight and advice on how to 

approach the analysis. We also extend our appreciation to John Brandon, Bob Brownell, John 

Calambokidis, Greg Donovan, Aimee Lang, Andre Punt and Jon Scordino for their input.
ii

EXECUTIVE SUMMARY

Recent observations of gray whales (Eschrichtius robustus) identified in the western North 

Pacific (WNP) migrating to areas off the coast of North America (Alaska to Mexico) raise

concern about the possibility of the small western population being subjected to the gray whale 

hunt proposed by the Makah Indian Tribe in northern Washington, USA. To address this 

concern, we estimated the probability of striking (i.e. killing or seriously injuring) a WNP whale 

during the Makah hunt using six models from 4 model sets that varied based on the assumptions 

and types of data used for estimation. Model set 1 used WNP and ENP abundance estimates. 

Model set 2 used these abundance estimates, as well as sightings data from the proposed hunt 

area. Model sets 3 and 4 used only the sightings data. Within model sets 1 and 2, two models (A 

and B) differed based upon whether migrating ENP and WNP whales were assumed to be 

equally available to the hunt per capita (A) or whether this assumption is relaxed (B). We 

consider Model 2B the most plausible of all models because model set 2 makes use of all 

available information and 2B contains fewer assumptions than 2A. Based on model 2B, the 

probability of striking ≥1 WNP whale in a single season ranges from 0.007 to 0.036, depending 

on if the median or upper 95th percentile estimate is used and on which maximum is used for the 

total number of whales struck. The probability of striking ≥1 WNP whale out of 5 seasons 

ranges from 0.036 to 0.170 across the same scenarios. The expected number to be struck in a 

single year ranges from 0.01 to 0.04 and from 0.04 to 0.19 across 5 years. For context, these 

strike estimates were compared to different possible values of Potential Biological Removal 

(PBR). We also summarized analogous estimates for the number of WNP whales that would be 

“taken” non-lethally, in terms of the number of attempted but unsuccessful strikes as well as the 

number of animals approached and pursued during the hunt. 
1

INTRODUCTION

Gray whales (Eschrichtius robustus) are recognized as comprising two populations in the North 

Pacific Ocean. Significant mitochondrial and nuclear genetic differences have been found 

between whales in the western North Pacific (WNP) and those in the eastern North Pacific

(ENP) (Lang et al., 2011). The ENP population ranges from wintering areas in Baja California, 

Mexico, to feeding areas in the Bering, Beaufort, and Chukchi Seas (Fig. 1). An exception to this 

generality is the relatively small number (100s) of whales that summer and feed along the Pacific 

coast between Kodiak Island, Alaska, and northern California (Calambokidis et al. 2012). These 

whales are collectively called the Pacific Coast Feeding Group (PCFG). U.S. domestic policy 

defines the PCFG as gray whales observed between 1 June and 30 November from Northern 

California through Northern British Columbia. The International Whaling Commission (IWC) 

has refined this definition to be: PCFG whales are those observed between 1 June and 30 

November from 41°N to 52°N in two or more years (IWC, 2012). The WNP population feeds in 

the Okhotsk Sea off Sakhalin Island, Russia (Weller et al., 1999; Weller et al. 2012), and in 

nearshore waters of the southwestern Bering Sea off the southeastern Kamchatka Peninsula 

(Tyurneva et al., 2010).

Figure 1. Areas in the western and eastern North Pacific mentioned 

in the report.

The historical distribution of gray whales in the Okhotsk Sea greatly exceeded what is found 

today (Reeves et al., 2008). Whales associated with the Sakhalin feeding area can be absent for 

all or part of a given feeding season (Bradford et al., 2008), indicating they use other areas 

during the summer and fall feeding period. Some of the whales identified feeding in the coastal 

waters off Sakhalin, including reproductive females and calves, have also been documented off 

the southern and eastern coast of Kamchatka (Tyurneva et al., 2010). Whales observed off 

Sakhalin have also been sighted off the northern Kuril Islands in the eastern Okhotsk Sea and 

Bering Island in the western Bering Sea (Weller et al., 2003). 

Recently, mixing of whales identified in the WNP and ENP has been observed (Weller et al., 

2012). Lang (2010) reported that two adult individuals from the WNP, sampled off Sakhalin in 

1998 and 2004, matched the microsatellite genotypes, mtDNA haplotypes, and sexes (one male, 
2

one female) of two whales sampled off Santa Barbara, California in March 1995. Mate and 

colleagues (Mate et al., 2011) satellite-tracked three whales from the WNP to the ENP (Mate et 

al., 2011; IWC, 2012). Finally, photographic matches between the WNP and ENP, including 

resightings between Sakhalin and Vancouver Island and Laguna San Ignacio, have further 

confirmed use of areas in the ENP by whales identified in the WNP (Weller et al., 2012, Urbán 

et al., 2012). Despite this level of mixing, significant mtDNA and nuclear genetic differences 

between whales in the WNP and ENP have been found (Lang et al., 2011).

Observations of gray whales identified in the WNP migrating to areas off the coast of North 

America (Alaska to Mexico) raise concern about placing the WNP population at potential risk of 

being harmed or killed incidental to the ENP gray whale hunt proposed by the Makah Indian 

Tribe off northern Washington, USA (IWC, 2012). Given the ongoing concern about 

conservation of the WNP population, in 2011 the Scientific Committee of the International 

Whaling Commission (IWC) emphasized the need to estimate the probability of a western gray 

whale being killed during aboriginal gray whale hunts (IWC, 2012). Additionally, NOAA is 

required to prepare an Environmental Impact Statement (EIS) pertaining to the Makah’s request 

for a waiver under the U.S. Marine Mammal Protection Act (MMPA) in order to hunt gray 

whales (NOAA, 2008). The EIS will include an estimate of the likelihood of Makah hunters 

approaching, pursuing, and attempting to strike a WNP whale in addition to the likelihood of 

actual strikes (assumed to result in death or serious injury).

The objective of this analysis was therefore to estimate the probability that one or more whales 

identified in the WNP might be lethally or non-lethally “taken1

” during the hunt proposed by the 

Makah Indian Tribe. This report updates the analysis of mortality risk provided by Moore and 

Weller (2012), by incorporating feedback from the IWC Scientific Committee on that report and 

by including an analysis of the likelihood of non-lethal as well as lethal take.

METHODS

The probability of striking or taking a WNP whale during the proposed Makah hunt was 

estimated using four different sets of models (6 models total). Models were based on the 

following information: (1) the most recent estimates of WNP and ENP population abundance; 

(2) sightings data from spring 1999-2010 off the coast of northern Washington (NWA) in the 

Makah Usual and Accustomed (MUA) fishing grounds, where the proposed hunt would take 

place; and (3) minimum estimates of the proportion of the WNP population that migrate to ENP 

areas along the North American coast.

Data

Abundance estimates

The most recent WNP abundance estimate (for 2012) is 155, with 95% CI = 142 – 165 (IUCN, 

2012). The most recent ENP estimate (for 2007) is 19,126, with CV = 0.071 (Laake et al., 2009). 

In the models, these estimates were expressed as log-normally distributed random variables with 

parameters μWNP = 5.043, σWNP = 0.0387, and μENP = 9.856, σENP = 0.0709.

 1 Under the U.S. Marine Mammal Protection Act, “take” is defined as “harass, hunt, capture, kill or collect, or 

attempt to harass, hunt, capture, kill or collect.”
3

Sightings in the Makah Usual and Accustomed (MUA) Fishing Grounds

During spring surveys (1 March to 31 May) in 1999-2009, there were 118 “whale-days” in the 

MUA off the NWA coast (Calambokidis et al., 2012), where all sightings of an individual on a 

particular day collectively count as 1 “whale-day” (e.g., multiple sightings of the same individual 

on the same day count as just 1 whale-day, but the same individual seen the next day would

count as a second whale-day). There were 9 gray whale sightings in March. All other sightings 

were in April or May. None of the 118 whale-days observed included WNP whales2

; 35 (29.7%) 

were considered “Pacific Coast Feeding Group” (PCFG) whales; and the rest (83, or 70.3%) 

were assumed to be migrating ENP whales. The photo-identification catalog for whales 

identified in the WNP off Sakhalin Island is characterized by extremely high (> 95%) resighting 

rates since 2002 (Burdin et al., 2012). Therefore, we assumed in this analysis that the absence of 

WNP sightings is not likely due to false negative identification (although it is possible that WNP 

whales were missed during days when MUA surveys were or were not conducted).

Proportion of WNP whales migrating with ENP whales

The proportion of the WNP population that migrates along the North American coast is unknown

but based on recent photo-identification, telemetry, and genetic matches of WNP whales to ENP 

areas, we estimate the value to be at least 0.15, based on there being 23 known matches out of an 

estimated population size of 155 (Mate et al., 2011; IWC, 2012; Urbán et al., 2012; Weller et al. 

2012).

Models

Model set 1

Model set 1 makes use of the ENP and WNP abundance estimates but ignores information 

obtained from sightings in the MUA off the NWA coast. The potential justification for ignoring 

the sightings data is that these may not be representative of the whale compositions that would be 

encountered by hunters, perhaps because of a timing mismatch (if hunt does not occur in 

April/May) or if whales approached by field researchers in motorized boats behave 

fundamentally differently than those approached by hunters in non-motorized boats.

Model 1A - All whales migrating through the MUA area -- WNP and ENP -- are assumed to be 

equally available to the hunt, so that the probability of taking a WNP whale is:

PWNP = mNWNP/NENP

m ~ uniform(0.15, 1)

NWNP ~ log-normal (μWNP, σWNP)

NENP ~ log-normal (μENP, σENP),

where m is the proportion of WNP whales that migrate with ENP whales along the North 

American coast and abundance parameters are as above (see Data section). The lower limit for 

m, 0.15, is based on genetic and photo-identification matching data (see Data section). The 

upper limit of 1 for m is precautionary, as the true value is unknown but could be high. We used

Monte Carlo simulation based on drawing 100,000 random samples from the above distributions 

to estimate the distribution for PWNP.

Model 1B – Rather than assuming PWNP to be directly proportional to the ratio of abundances

(NWNP/NENP), we express our uncertainty in PWNP as a uniform distribution with the upper limit 

 2 Although not in the MUA, Weller et al. 2012 report observing three WNP whales on 2 May 2004 and three more 

on 25 April 2008 near Barkley Sound off the west coast of southern Vancouver Island, British Columbia, Canada.
4

for PWNP based on the maximum (99th percentile) estimate for the number of WNP whales 

available to the hunt divided by a minimum (1st percentile) estimate for the ENP population, i.e.,

PWNP ~ uniform(0, Pmax)

Pmax = m·N99,WNP/N01,ENP.

The interpretation of this model is that, within some plausible upper bound (defined as Pmax), we 

have no information about the per capita probability of taking a WNP whale, given unknown 

differences in migration patterns between WNP and ENP animals. Just as for Model 1A, we use 

a Monte Carlo approach (100,000 samples) to estimate a distribution for PWNP. For each sample, 

PWNP is drawn from the uniform distribution specified by Pmax. Pmax varies with each sample 

based on the draw for m, while the ratio N99,WNP/N01,ENP is fixed. Analysis for Model set 1 was 

conducted in R.

Model set 2

Model sets 2, 3, and 4 differ from Model set 1 in that they use the information from the sightings 

data in the MUA. In these models, it is assumed that the sightings data from the MUA are 

representative of the composition of whales (three groups: ENP, WNP, PCFG) that would be 

available to the hunt. In other words, whales that are most likely to be photographed (i.e., 

approachable in a small boat) are also the most likely to be approached by hunters.

Model set 2 makes use of the MUA sightings data, as well as WNP and ENP abundance 

estimates. WNP whales are assumed to be moving with the ENP migrants, so that the marginal 

probability of a WNP whale being taken is the probability of being a migrant, Pmig (i.e., 

probability of not being a whale from the PCFG), multiplied by the conditional probability of 

being a WNP whale given that it is a migrant (PWNP|mig), i.e., PWNP = PmigPWNP|mig. Pmig is 

estimated using Bayesian MCMC methods assuming that nmig ~ Binomial (N, Pmig), where nmig is 

the number of non-PCFG migrants (83) out of N (118) sightings in the MUA sightings data set. 

Models 2A and 2B differ in how the conditional probability PWNP|mig is estimated.

Model 2A - The distribution for PWNP|mig is given by the estimator for PWNP in Model 1A. Thus, it 

is assumed the per capita probabilities of an ENP or WNP whale being taken are the same. 

Model 2B - The distribution for PWNP|mig is given by the estimator for PWNP in 1B. Thus, this 

model asserts that we have no information (apart from specifying a reasonable upper bound)

about the per capita likelihood of a WNP whale being killed relative to that of an ENP whale.

Model 3

This uses the MUA sightings data but does not make use of information about WNP population 

size or the proportion of WNP whales that migrate with ENP whales. Thus, PWNP estimates are 

solely based on the proportion of animals in the MUA sightings data set that are from the WNP. 

The posterior distribution for PWNP is estimated using MCMC methods assuming that nWNP ~ 

Binomial (N, PWNP), where nWNP = 0, and N = 118. The justification for this model (i.e., for 

ignoring information about WNP abundance) would be that the relative per capita probability of 

taking WNP vs. ENP animals is totally unknown apart from the information contained in the 

sightings data set. For example, WNP whales could be much more (or less) available to the hunt 

than ENP whales due to differences in migration timing or behavior, such that our knowledge 

about the WNP population being very small is irrelevant to the estimates.
5

Model 4

Model 4 is a variant of Model 3, explained below.

Bayesian estimation

Analyses for Models 2, 3, and 4 were conducted in WinBUGS. Posterior distributions for 

parameters were summarized from two MCMC chains, each 50,000 samples in length (100,000 

samples total) following a burn-in of 20,000 samples. These simple models converged quickly 

and clearly (chains well mixed) in all cases (Fig. 2). A uniform [0, 1] prior was used for Pmig in 

model set 2 and for PWNP in model 3 and 4; these are the only parameters for which the prior is 

updated by data (the MUA sightings data) to obtain a new posterior. The posterior distributions 

for PWNP|mig in Models 2A and 2B were not informed by the sightings data and thus are 

essentially determined by informative priors given by the above estimators for these parameters.

pm chains 1:2

iteration

20001 20500 21000 21500 22000

 0.0

 0.002

 0.004

 0.006

 0.008

 0.01

Figure. 2. Example from Model 2A of two MCMC chains (red and blue) mixing for the 

parameter PWNP. 

Estimated parameters

Based on estimates of PWNP for each model, we calculated the probability of striking at least one 

WNP whale (i.e., P(x>0)) out of X total strikes (strikes are treated as lethal takes), the probability 

of non-lethally taking at least one WNP whale out of Y strike attempts (P(y>0)), or the 

probability of non-lethally taking at least one WNP whale out of Z approaches (P(z>0)). We 

also estimated the expected number of WNP takes out of X, Y or Z total takes. These are 

calculated as follows:

P(x > 0) = 1 – (1 – PWNP)

X

P(y > 0) = 1 – (1 – PWNP)

Y

P(z > 0) = 1 – (1 – PWNP)

Z

E(x) = PWNPX

E(y) = PWNPY

E(z) = PWNPZ

For model sets 1, 2, and 3, let X = X* = 5, 7, 20, and 35 gray whale strikes. These were based on 

the description of the Makah Tribe’s proposed gray whale hunt (IWC, 2012 Annex D), which

states the following: 5 is the maximum allowable number of landed whales per year; 7 is the 

maximum number of struck whales allowed per year; 20 is the maximum number allowed to be 

landed over a 5-year period; and 35 is the maximum number that could be struck over a 5-year 

period.
6

For model sets 1, 2, and 4, let X = X** = 3 or 4 strikes in one year and 15 or 20 strikes in 5 years 

of non-PCFG whales. The justification for considering this scenario is that, given other 

management measures within the Makah plan – most importantly the provision to cease the 

annual hunt if a certain number of PCFG whales are struck – it may be unlikely that the 

maximum strike limits in the proposal will be achieved. Implementation trials conducted by the 

Aboriginal Whaling Management Procedure (AWMP) subgroup of the IWC scientific committee 

suggest that, when management measures are considered, the expected number of strikes per 

year to non-PCFG whales would typically be between 3 and 4 (J. Scordino, pers. comm.). 

For Model set 1, estimates for when X = X** are calculated the same as for when X = X*. For 

Model set 2, since it is given that X** are for non-PCFG whales (i.e., migrant whales), then it 

follows that Pmig = 1, so the model 2 estimators for PWNP reduce from PmigPWNP|mig to just 

PWNP|mig, which are the same estimators as for Model set 1. When X = X**, we use Model 4 as a 

variant of Model 3 (which is for X = X*). In Model 3, nWNP ~ Binomial (Ntot, PWNP), where nWNP

= 0, and Ntot = 118 total whale-day sightings, 35 of which were PCFG whales and 83 of which 

were migrating ENP whales. In Model 4, nWNP ~ Binomial (Nmig, PWNP|mig), where Nmig = 83 

whale-day sightings of non-PCFG migrant whales (i.e., we are only evaluating conditional 

probability of being a WNP whale given being migrant whale.

Values of Y for each model were calculated as 4X, and values for Z were calculated as 20X. In 

other words, for every struck whale, there are an estimated 4 strike attempts and 20 whales 

approached in attempt to strike. These numbers are based on the Makah tribe’s experience in the 

1999 and 2000 hunts, for which they stated that for every struck whale, there would be 

approximately 4 attempted strikes and 10 individuals pursued, which are assumed to affect 20 

whales, given an average pod size of two whales (NOAA, 2008). 

Comparison to Potential Biological Removal (PBR)

To contextualize the Table 1 estimates of lethal takes, we provide 5-year estimates of PBR3) for 

comparison. PBR is conventionally calculated as 0.5RmaxNminFR, where Rmax is the maximum 

productivity rate estimate for the population (we used 0.062 based on the 2012 Draft Stock 

Assessment Report; NMFS, 2012), Nmin is the 20th percentile abundance estimate (we used 150

based on WNP abundance parameters), and FR is a recovery factor. We provide PBR estimates 

for FR = 0.1, 0.5, and 1.0. FR = 0.1 is typically used for stocks of endangered species, noting that 

the WNP gray whale stock is listed as Endangered under the U.S. Endangered Species Act and 

Critically Endangered on the IUCN Red List. FR = 0.5 is a recommended default for most stocks

(NMFS 2005), whereas FR = 1.0 may be appropriate for stocks with known and favorable 

population status. The PBR estimate is also supposed to take into the account (be discounted by)

the proportion of the stock using US waters and the proportion of time it is there (NMFS, 2005).

The proportion of the WNP migrating in the ENP range is unknown but characterized in our 

models by a uniform (0.15, 1) distribution. The proportion of time spent in US waters is difficult 

to estimate for migratory animals but is probably on the order of 3 months or 0.25 years. Thus, 

for each value of FR, we calculated a distribution for the 5-year PBR estimate, by multiplying the 

standard equation by 0.25 and by a uniform (0.15, 1) distribution.

 3 Under	the	U.S.	Marine	Mammal	Protection	Act,	PBR	level	is	defined	as	"the maximum	number	of	animals,	

not	including	natural	mortalities,	that	may	be	removed	from	a marine	mammal	stock	while	allowing	that	

stock	to	reach	or	maintain	its	optimum	sustainable population.”
7

RESULTS

Take estimates

Estimated parameters from all model sets are in Tables 1 – 3. Table 1 presents estimates for the 

probability of striking a WNP whale during a single strike event (PWNP), and of striking at least 

one WNP whale (P(x>0)) and the expected number of WNP whales (E(x)) that would be struck 

given X = X* (number of gray whales struck) or X** (number of non-PCFG whales struck). 

Table 2 presents the analogous estimates for the number of attempted strikes (Y = Y* or Y**), 

and Table 3 presents the analogous estimates for the number of whales approached (Z = Z* or 

Z**). We present median estimates and, for precautionary purposes, 95th percentile estimates

from the Monte Carlo or Bayesian posterior distributions.

For X = X*, Y = Y*, and Z = Z* (i.e., out of the total number of events affecting gray whales, 

irrespective of the putative stock affected), parameter estimates were higher for Model set 1 than 

Model set 2. Within these models sets, median parameter estimates were higher for version A 

than B, although upper (95th percentile) estimates were similar. Estimates for Model 3 were 

higher than for the other models, particularly when looking at upper bound (95th percentile) 

estimates, because of the highly skewed and unconstrained posterior for PWNP (Fig. 3).

pm chains 1:2 sample: 100000

 0.0 0.004 0.008

 0.0

 100.0

 200.0

 300.0

pm chains 1:2 sample: 100000

-0.0025 0.0025 0.0075

 0.0

 100.0

 200.0

 300.0

 400.0

p[1] chains 1:2 sample: 100000

 -0.025 0.025 0.075

 0.0

 50.0

 100.0

 150.0

p[1] chains 1:2 sample: 100000

 0.0 0.05 0.1

 0.0

 20.0

 40.0

 60.0

 80.0

Figure 3. Comparison of Bayesian posterior distributions for PWNP for Models 

2A (a), 2B (b), 3 (c), and 4 (d). 

For X = X**, Y = Y**, Z = Z** (i.e., out of the total number of events affecting non-PCFG

whales), model set 1 and model set 2 results are the same (because the estimators are the same), 

but median estimates were higher for version A than B in these model sets (although 95th

percentile estimates were similar). Estimates for Model 4 were higher than for the other models.

In Tables 1 – 3, we highlight (bold) estimates from Model 2B because Model set 2 makes the 

greatest use of available information (i.e., uses all datasets), and model 2B is based on fewer 

assumptions than 2A, and thus we favor Model 2B estimates as the most plausible (see 

Discussion). Estimates from this model for the proposed 5-year hunt period are as follows. The 

median (and 95th percentile) probability of striking a WNP whale within the 5-year permit period 

a b

c d
8

ranged from 0.036 (0.107) to 0.058 (0.170) as X increased from 15 non-PCFG whales to 35 

whales of any putative stock, and the expected number of whales that would be struck ranged 

from 0.04 (0.11) to 0.06 (0.19). The probability of an attempted strike on a WNP whale ranged 

from 0.136 (0.365) to 0.212 (0.524), and the expected number of attempts on WNP whales

ranged from 0.15 (0.45) to 0.24 (0.74). Finally, the probability that a WNP whale would be

pursued or approached by a hunter ranged from 0.519 (0.897) to 0.697 (0.976), and the expected 

number of WNP whales that would be approached ranged from 0.73 (2.26) to 1.19 (3.70). 

In summary, we estimate based on Model 2B a fairly high probability that at least one WNP 

would be taken in the broadest sense of being pursued or approached by Makah hunters (i.e., 

P(z>0) = 0.52 – 0.98, depending on Z and whether the median or upper estimate is used). The 

probability of an attempted strike on least one WNP whale in 5 years was relatively moderate 

(i.e., P(y>0) = 0.14 – 0.52). The probability of actually striking at least one WNP whale during 

the 5-year period was relatively low but non-trivial (i.e., P(z>0) = 0.04 – 0.17).

Table 1. Summary statistics for six models from four model sets. PWNP is probability of taking (striking) a WNP 

whale during a given take event. P(x>0)X are probabilities of striking at least 1 WNP whale out of X events. E(x)X is 

the expected number of struck WNP whales out of X total events. X=X** indicates that events are known to affect 

non-PCFG whales (otherwise X = X*, the number of events to gray whales in general). Cell entries are median and 

upper (95th percentile) probabilities.

Model 1A Model 1B Model 2A Model 2B Model 3 Model 4

PWNP 0.005 (0.008) 0.002 (0.008) for X = X*

0.003 (0.006)

for X = X**

0.005 (0.007)

for X = X*

0.002 (0.005)

for X = X**

0.002 (0.008)

0.006 (0.025) 0.008 (0.035)

1 year

P(x>0)3** 0.014 (0.024) 0.007 (0.023) 0.014 (0.023) 0.007 (0.022) NA 0.024 (0.102)

P(x>0)4** 0.018 (0.031) 0.010 (0.030) 0.018 (0.031) 0.010 (0.030) NA 0.033 (0.134)

P(x>0)5 0.023 (0.039) 0.012 (0.037) 0.016 (0.028) 0.008 (0.026) 0.029 (0.119) NA

P(x>0)7 0.032 (0.054) 0.017 (0.052) 0.022 (0.039) 0.012 (0.036) 0.040 (0.162) NA

E(x)3** 0.01 (0.02) 0.01 (0.02) 0.01 (0.02) 0.01 (0.02) NA 0.03 (0.11)

E(x)4** 0.02 (0.03) 0.01 (0.03) 0.02 (0.03) 0.01 (0.03) NA 0.03 (0.14)

E(x)5 0.02 (0.04) 0.01 (0.04) 0.02 (0.03) 0.01 (0.03) 0.03 (0.13) NA

E(x)7 0.03 (0.06) 0.02 (0.05) 0.02 (0.04) 0.01 (0.04) 0.04 (0.18) NA

5 year

P(x>0)15** 0.067 (0.113) 0.036 (0.108) 0.067 (0.112) 0.036 (0.107) NA 0.117 (0.416)

P(x>0)20** 0.089 (0.147) 0.048 (0.141) 0.089 (0.146) 0.048 (0.141) NA 0.152 (0.512)

P(x>0)20 0.089 (0.147) 0.048 (0.141) 0.063 (0.106) 0.034 (0.101) 0.110 (0.397) NA

P(x>0)35 0.151 (0.244) 0.082 (0.233) 0.107 (0.178) 0.058 (0.170) 0.185 (0.587) NA

E(x)15** 0.07 (0.12) 0.04 (0.11) 0.07 (0.12) 0.04 (0.11) NA 0.12 (0.53)

E(x)20** 0.09 (0.16) 0.05 (0.15) 0.09 (0.16) 0.05 (0.15) NA 0.17 (0.70)

E(x)20 0.09 (0.16) 0.05 (0.15) 0.06 (0.11) 0.03 (0.11) 0.12 (0.50) NA

E(x)35 0.16 (0.28) 0.09 (0.26) 0.11 (0.20) 0.06 (0.19) 0.20 (0.87) NA
9

Table 2. Summary statistics for six models from four model sets. PWNP is probability of taking (attempted strike) a 

WNP whale during a given take event. P(y>0)Y are probabilities of attempting to strike at least 1 WNP whale out of 

Y events. E(y)Y is the expected number of attempted-struck WNP whales out of Y total events. Y=Y** indicates 

that events are known to affect non-PCFG whales (otherwise Y = Y*, the number of events to gray whales in 

general). Cell entries are median and upper (95th percentile) probabilities.

Model 1A Model 1B Model 2A Model 2B Model 3 Model 4

PWNP 0.005 (0.008) 0.002 (0.008) for Y = Y

0.003 (0.006)

for Y = Y*

0.005 (0.007)

for Y = Y

0.002 (0.005)

for Y = Y*

0.002 (0.008)

0.006 (0.025) 0.008 (0.035)

1 year

P(y>0)12** 0.054 (0.091) 0.029 (0.087) 0.054 (0.090) 0.029 (0.087) NA 0.094 (0.349)

P(y>0)16** 0.072 (0.120) 0.039 (0.114) 0.072 (0.119) 0.038 (0.114) NA 0.124 (0.436)

P(y>0)20 0.089 (0.147) 0.048 (0.141) 0.063 (0.106) 0.034 (0.101) 0.110 (0.397) NA

P(y>0)28 0.122 (0.200) 0.066 (0.192) 0.086 (0.145) 0.047 (0.138) 0.151 (0.507) NA

E(y)12** 0.06 (0.10) 0.03 (0.09) 0.06 (0.09) 0.03 (0.09) NA 0.10 (0.42)

E(y)16** 0.07 (0.13) 0.04 (0.12) 0.07 (0.13) 0.04 (0.12) NA 0.13 (0.56)

E(y)20 0.09 (0.16) 0.05 (0.15) 0.06 (0.11) 0.03 (0.11) 0.12 (0.50) NA

E(y)28 0.13 (0.22) 0.07 (0.21) 0.09 (0.16) 0.05 (0.15) 0.16 (0.70) NA

5 year

P(y>0)60** 0.244 (0.380) 0.137 (0.366) 0.243 (0.377) 0.136 (0.365) NA 0.391 (0.883)

P(y>0)80** 0.311 (0.472) 0.178 (0.455) 0.310 (0.468) 0.178 (0.454) NA 0.484 (0.943)

P(y>0)80 0.311 (0.472) 0.178 (0.455) 0.228 (0.360) 0.127 (0.346) 0.373 (0.877) NA

P(y>0)140 0.479 (0.673) 0.291 (0.655) 0.364 (0.543) 0.212 (0.524) 0.558 (0.971) NA

E(y)60** 0.28 (0.48) 0.15 (0.45) 0.28 (0.47) 0.15 (0.45) NA 0.49 (2.11)

E(y)80** 0.37 (0.64) 0.20 (0.61) 0.37 (0.63) 0.20 (0.60) NA 0.66 (2.82)

E(y)80 0.37 (0.64) 0.20 (0.61) 0.26 (0.45) 0.14 (0.42) 0.47 (2.00) NA

E(y)140 0.65 (1.11) 0.34 (1.06) 0.45 (0.78) 0.24 (0.74) 0.82 (3.49) NA
10

Table 3. Summary statistics for six models from four model sets. PWNP is probability of taking (approaching) a 

WNP whale during a given take event. P(z>0)Z are probabilities of approaching at least 1 WNP whale out of Z 

events. E(z)Z is the expected number of approached WNP whales out of Z total events. Z=Z** indicates that events 

are known to affect non-PCFG whales (otherwise Z = Z*, the number of events to gray whales in general). Cell 

entries are median and upper (95th percentile) probabilities.

Model 1A Model 1B Model 2A Model 2B Model 3 Model 4

PWNP 0.005 (0.008) 0.002 (0.008) for Z = Z

0.003 (0.006)

for Z = Z*

0.005 (0.007)

for Z = Z

0.002 (0.005)

for Z = Z*

0.002 (0.008)

0.006 (0.025) 0.008 (0.035)

1 year

P(z>0)60** 0.244 (0.380) 0.137 (0.366) 0.243 (0.377) 0.136 (0.365) NA 0.391 (0.883)

P(z>0)80** 0.311 (0.472) 0.178 (0.455) 0.310 (0.468) 0.178 (0.455) NA 0.484 (0.943)

P(z>0)100 0.373 (0.550) 0.218 (0.532) 0.276 (0.428) 0.157 (0.412) 0.442 (0.920) NA

P(z>0)140 0.479 (0.673) 0.291 (0.655) 0.364 (0.543) 0.212 (0.524) 0.558 (0.971) NA

E(z)60** 0.28 (0.48) 0.15 (0.45) 0.28 (0.47) 0.15 (0.45) NA 0.49 (2.11)

E(z)80** 0.37 (0.64) 0.20 (0.61) 0.37 (0.63) 0.20 (0.60) NA 0.66 (2.82)

E(z)100 0.47 (0.79) 0.25 (0.76) 0.32 (0.56) 0.17 (0.53) 0.58 (2.50) NA

E(z)140 0.65 (1.11) 0.34 (1.06) 0.45 (0.78) 0.24 (0.74) 0.81 (3.49) NA

5 year

P(z>0)300** 0.753 (0.909) 0.521 (0.898) 0.752 (0.906) 0.519 (0.897) NA 0.916 (1.000)

P(z>0)400** 0.845 (0.959) 0.625 (0.952) 0.844 (0.958) 0.624 (0.952) NA 0.963 (1.000)

P(z>0)400 0.845 (0.959) 0.625 (0.952) 0.725 (0.893) 0.494 (0.880) 0.903 (1.000) NA

P(z>0)700 0.962 (0.996) 0.821 (0.995) 0.896 (0.980) 0.697 (0.976) 0.983 (1.000) NA

E(z)300** 1.40 (2.48) 0.74 (2.27) 1.39 (2.36) 0.73 (2.26) NA 2.47 (10.56)

E(z)400** 1.86 (3.18) 0.98 (3.03) 1.85 (3.15) 0.98 (3.02) NA 3.29 (14.07)

E(z)400 1.86 (3.18) 0.98 (3.03) 1.29 (2.23) 0.68 (2.12) 2.33 (9.98) NA

E(z)700 3.26 (5.56) 1.72 (5.30) 2.26 (3.90) 1.19 (3.70) 4.07 (17.46) NA
11

Comparison to PBR

Table 4 provides 5-year estimates of PBR based on FR = 0.1, 0.5, and 1.0. Uncertainty in the 

estimates (e.g., 95% CI) reflects uncertainty in the proportion of the WNP stock that migrates 

with the ENP stock. For FR = 0.1, striking one WNP whale in the 5-year period would exceed 

PBR. For FR = 0.5, one WNP strike could exceed PBR, depending on how many WNP 

individuals migrate with the ENP stock. Fewer WNP whales in U.S. waters would mean higher 

chance that one strike would exceed PBR, but it would also translate into lower probability of 

there being a WNP strike in the first place (i.e., lower than reflected in the Table 1 estimates). 

For FR = 1, striking one WNP whale in the 5-year period would not exceed PBR.

Table 4. Estimates of PBR (5-year total) for the WNP gray whale stock under three different values of FR. 

Uncertainty in the estimates reflects uncertainty in the proportion of the WNP that uses U.S. waters; the lower 

estimate corresponds to a little more than 0.15 of the WNP stock migrating in ENP areas, whereas the upper 

estimate corresponds to nearly all WNP animals migrating in ENP areas.

FR = 0.1 FR = 0.5 FR = 1.0

2.5% 0.10 0.50 0.99

median 0.33 1.67 3.35

97.5% 0.57 2.85 5.69

DISCUSSION

In general, we consider Model set 2 the most plausible of the model sets used, because it makes 

use of information from sightings in the MUA from the NWA coast area as well as relative 

abundance of the WNP vs. ENP. In contrast, Model set 1 ignores the MUA sightings 

information, and Models 3 and 4 ignore our knowledge of the WNP being small relative to the 

ENP. We also feel that, within Model sets 1 and 2, the B-versions of each model are more 

appropriate than A-versions, because the B models make fewer assumptions. The B models 

assume no prior knowledge about PWNP|mig, except to specify a reasonable upper bound, whereas 

the A models assume that WNP and ENP migrants are equally available to the hunt on a per 

capita basis. Therefore, Models 2A and 2B, but especially 2B, may be considered the most useful 

estimates.

Models 3 and 4 are probably the least justifiable, since by ignoring information about the WNP 

population size they allow for upper parameter estimates that are likely implausible. For 

example, if we assume that WNP and ENP animals are equally available to the hunt and there are 

16,000-22,000 ENP animals, then the upper estimate for Model 4 of PWNP = 0.035 corresponds to 

a WNP population estimate of nearly 560-770 animals, which far exceeds existing estimates. 

Alternatively, WNP animals would need to be far more available to hunters on per capita basis 

than ENP animals for behavioral reasons, and there is no reason presently to expect this is the 

case.

Estimates from our analysis are considered precautionary since they assume that the Makah will 

achieve their proposed maximum strike limits. That being said, the results herein offer a

conservative initial step in assessing the potential risk of WNP gray whales incurring mortality 

incidental to the proposed hunt on the ENP population by the Makah Indian Tribe.
12

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