Revista de Biología Tropical, ISSN: 2215-2075 Vol. 69(2): 588-600, April-June 2021 (Published Apr. 26, 2021)
Viability of the vaquita, Phocoena sinus (Cetacea: Phocoenidae)
population, threatened by poaching of Totoaba macdonaldi
(Perciformes: Sciaenidae)
Miguel A. Cisneros-Mata
Juan A. Delgado
Demetrio Rodríguez-Félix
1. Instituto Nacional de Pesca y Acuacultura, Calle 20 No. 605-Sur, CP 85400 Guaymas, Sonora, México;
miguel.cisneros@inapesca.gob.mx (*Correspondence), deme771@hotmail.com
2. Tecnológico Nacional de México, km 4 Avenida Tecnológico, Sector Las Playitas, CP 85480 Guaymas, Sonora,
México; delgado.juan@uabc.edu.mx
Received 19-I-2021. Corrected 08-IV-2021. Accepted 16-IV-2021.
Introduction: Despite extensive science-based conservation policy recommendations, with fewer than 20 indi-
viduals remaining, the vaquita (Phocoena sinus) -endemic to the Gulf of California- is the world’s most endan-
gered marine mammal due to incidental catch in fishing nets and whether it can recover is unclear. Objective:
Assess expectations for vaquita over the next two decades. Methods: We identified factors affecting the vaquita,
constructed life tables, derived demographic parameters for different scenarios and conducted a population
viability analysis using stochastic age-structured matrix Leslie models. Results: Analytical results indicate that
the vaquita net growth rate is particularly sensitive to juvenile survival. We find that intensive, ongoing bycatch
in gillnets used to poach totoaba (Totoaba macdonaldi) over the past decade brought the vaquita population to its
current critically low size. Currently this seems to be exacerbated by demographic stochasticity and a potential
Allee effect. Conclusions: If totoaba poaching is eliminated immediately, demographically, vaquita can recover;
its long-term survival will depend on its uncertain genetic status, although a recent study found encouraging
results in this regard.
Key words: vaquita; totoaba; demographic stochasticity; Allee effect; population viability analysis.
Cisneros-Mata, M.A., Delgado, J.A., & Rodríguez-Félix, D.
(2021). Viability of the vaquita, Phocoena sinus (Cetacea:
Phocoenidae) population, threatened by poaching of
Totoaba macdonaldi (Perciformes: Sciaenidae). Revista
de Biología Tropical, 69(2), 588-600. DOI 10.15517/rbt.
DOI 10.15517/rbt.v69i2.45475
Vaquita, Phocoena sinus (Norris & McFar-
land, 1958), endemic to the Northern Gulf of
California (henceforth, UG) is the most endan-
gered marine mammal in the world (Rojas-
Bracho, Reeves, & Jaramillo-Legorreta, 2006;
Jaramillo-Legorreta et al., 2019). It is listed
as Critically Endangered by the International
Union for Conservation of Nature, included
in the US Endangered Species Act and in
Mexico´s list of endangered species (Rojas-
Bracho & Reeves, 2013).
Major efforts have been made to assess
abundance and status of vaquita (Thomas et
al., 2017). The population has decreased from
~1 000 individuals 40 years ago (Taylor & Ger-
rodette, 1993) to only 400-500 in the 1990s
(Gerrodette, Barlow, Taylor, & Silber, 1994).
Conservation policies and the expenditure of
Revista de Biología Tropical, ISSN: 2215-2075, Vol. 69(2): 588-600, April-June 2021 (Published Apr. 26, 2021)
considerable economic resources (US $ 60 mil-
lion up to 2017) (Montalvo & Ortuño, 2017)
have not reversed the vaquita decline. Efforts to
deter bycatch mortality include buy-out of per-
mits and boats, alternative economic activities,
compensations to reduce fishing, and innova-
tions in fishing gear (Avila-Forcada, Martínez-
Cruz, & Muñoz-Piña, 2012; García-Gómez &
Chávez-Nungaray, 2017). Despite efforts, by
2018 the population dropped to < 20 (Jaramil-
lo-Legorreta et al., 2019) raising the question
of whether vaquita can recover. Encouraging
results have been reported recently: mothers
have been sighted with calves (Taylor et al.,
2019). For descriptions of the historical impact
of bycatch from gillnet fishing, particularly
poaching of totoaba, the readers are referred to
D’Agrosa, Lennert-Cody and Vidal (2000) and
the many references in Cisneros-Mata (2020).
To investigate the viability of vaquita we
used stochastic Leslie matrix models (SLMMs),
conducted a population viability analysis
(PVA) (Boyce, 1992; Lamberson, Noon, Voss,
& McKelvey, 1994) and computed probabili-
ties of its persistence through time. SLMMs
simulate effects of random survival and birth
per age class (Caswell, 1989). Important con-
siderations for PVAs are availability of data
and model solutions; analytical solutions and
simulations can be combined in some instances
(Moloney, Cooper, Ryan, & Siegfried, 1994;
Cisneros-Mata, Botsford, & Quinn, 1997).
Often there is scarce life-cycle information
to construct numerical models. Here we use
knowledge on vaquita and related species to
address relative effects of demographic and
anthropogenic factors under several scenarios.
Study area: Vaquita inhabits a small por-
tion of the UG off San Felipe, Baja California,
around Rocas Consag and of El Golfo de Santa
Clara, Sonora at depths of 30 to > 100 meters
(Jaramillo-Legorreta et al., 2019) (Fig. 1; after
Rojas-Bracho et al., 2006). Salinity in the
Colorado River (CR) delta varies from 38 to
35.4 PSU with prevailing anti-estuary condi-
tions (Lavín & Sánchez, 1999).
We compiled information from scientific
literature and reports on vaquita life histo-
ry, threats, and abundance. The only proven
source of vaquita mortality is incidental take
in gillnets and a small proportion in trawl
nets (D’Agrosa et al., 2000; Rojas-Bracho et
al., 2006; Urrutia-Osorio, Jaramillo-Legorreta,
Rojas-Bracho, & Sosa-Nishizaki, 2015; Flessa
et al., 2019). Gillnet mortality from poaching
of the endemic sciaenid fish totoaba (Totoaba
macdonaldi) has been a major threat to vaquita
(Vidal, 1993). The totoaba fishery was banned
in 1975, yet constant poaching persisted (Cis-
neros-Mata, Montemayor-López, & Román-
Rodríguez, 1995), and has recently (for the past
~10 years) severely aggravated (Thomas et al.,
2017; Cisneros-Mata, 2020).
Decimated populations are subject to low
fitness further compromising their existence.
For vaquita, inbreeding depression was dis-
carded when its abundance was in the low to
mid 100s (Rojas-Bracho & Taylor, 1999; Rosel
& Rojas-Bracho, 1999; Taylor & Rojas-Bra-
cho, 1999). Population dynamics at low num-
bers are governed by demographic stochasticity
because survival and fecundity operate at the
individual level increasing the risk of extinc-
tion by chance survival only (Lee, Seather, &
Engen, 2011). Given its current low population
size we consider demographic stochasticity (or
chance events) to be critical for the recovery
of vaquita.
We further hypothesize the existence of an
Allee effect (Dennis, 1989) related to maternal
care, characteristic of several mammal species.
Mothers nurse and protect their newborns (Hill,
Greer, Solangi, & Kuczaj, 2007) as in P. pho-
coena in the North Sea (Camphuysen & Krop,
2011). For this species on the Atlantic coast of
the USA, maternal care lasts between 9 and
10 months (Koopman & Zahorodny, 2008).
In our models we assumed that if there is no
altruistic conspecific care, a newborn will die
if its mother dies, generating a “double death”
effect. We caution that this double death may
not adjust to the traditional definition of Allee
Revista de Biología Tropical, ISSN: 2215-2075 Vol. 69(2): 588-600, April-June 2021 (Published Apr. 26, 2021)
effects, although we considered as such for
reasons discussed below.
We began the analyses by constructing
an age-structured life table (Begon, Mortimer,
& Thompson, 1996). In life tables, l
are age-
specific survival probabilities from birth to age
class x (l
= p
... p
). We used survival
rates of P. sinus and P. phocoena, a related por-
poise from the North American coasts (Gaskin,
Smith, Watson, Yasui, & Yurick, 1984; Fenton
et al., 2017). The probability of surviving from
age class 1 to 2, p
, was 0.71; this is the square
of p
= 0.84, as suggested by Barlow (1986).
and p
were linearly interpolated from those
two values (p
and p
); survival rates for age
classes 4 to 20 were considered constant (0.84).
Annual parturition rates at-age x, m
were 0.9 for age classes 6, while m
considered as 1/2 of m
, and m
was linearly
interpolated. In P. phocoena annual pregnancy
rates vary between 0.91 and 0.24 (Gaskin et
al., 1984). The parturition rate for vaquita is
1-2 years (Hohn, Read, Fernández, Vidal, &
Findley, 1996; Taylor et al., 2019).
Sex ratio was arbitrarily considered 1:1
in all cases. For P. phocoena a slight bias
Fig. 1. Distribution range of Phocoena sinus. The continuous line is the Southern limit of sightings, acoustic recordings, and
recovery of carcasses and the broken lines depict bathymetric contours.
Revista de Biología Tropical, ISSN: 2215-2075, Vol. 69(2): 588-600, April-June 2021 (Published Apr. 26, 2021)
towards males has been observed (Lockyer,
2013; Kesselring, Viquerat, Brehm, & Siebert,
2017). Vaquita longevity is 21 years, and first
reproduction occurs in the fourth year of age
(Barlow, 1986; Hohn, et al., 1996).
With this baseline life table, using the
Euler-Lotka equation (Birch, 1948):
and the Solver tool in Excel, we derived a vec-
tor of “natural” survival rates constrained to
yield 643 vaquitas for 1993. This number, con-
sidered an initial condition for our models, was
back-estimated by eye based on the abundance
trend in Jaramillo-Legorreta et al. (2019) who
give a mean of 550 vaquitas for 1997, 225 for
2008 and 100 for year 2015. The net population
growth rate l for this baseline table was also
estimated from the Euler-Lotka equation.
Reproductive value, v
, the weighted con-
tribution to population growth by individuals
of different ages was computed as (Caswell,
Note that reproductive value for the first
age class will always be 1. To summarize
results, we estimated the average reproductive
value for three age groups which we call here
juveniles (0.5 to 2.5 years), adults (3.5 to 12.5
years) and older adults (13.5 to 21.5 years).
Generation time, the mean age (years) of
mothers of a cohort of newborn daughters, was
obtained as (Pielou, 1977):
where N is the total number of age classes. is
used by the International Union for the Con-
servation of Nature to assess extinction risk of
wild populations (Bird et al., 2020).
We used the baseline life table and per-
formed 2 000 Monte Carlo trials using a SLMM
(Caswell, 1989) to project random annual
vaquita abundance trajectories over 38 years
starting with a total population of 643 in year
1993. Demographic stochasticity was included
considering individual birth and survival rates
as Bernoulli trials (Kokko & Ebenhard, 1996).
Population trajectories were generated drawing
independent, uncorrelated random numbers to
avoid effects in variance (McNamara & Hard-
ing, 2004). This produced a graphical view of
how a vaquita population would have grown
had by-catch mortality not been present; it also
allowed to estimate the net population growth
rate l without consideration of Allee effects
and bycatch mortality.
We then added Allee effects to the same
Leslie matrix to ascertain how this natural
process would affect random population trajec-
tories and l. We considered that if a female that
gave birth died for any reason, her newborn
also died that same year. For each trajectory
we estimated the net annual rate of increase as
= N
(Nur, 1987) where N
is the total
number of vaquitas in a given year t; the mean
annual growth rate was then computed as the
geometric mean over the 38 years, and of the
2 000 random trajectories.
To simulate the effect of bycatch mortal-
ity, we multiplied age-specific survival rates
by a constant factor (< 1) for an initial popu-
lation size of 643 in 1993 constrained to end
with 550 vaquitas in 1997. Parturition rates
remained constant. This allowed us to deter-
mine changes in survival rates and reproductive
values, which we attributed to bycatch mortal-
ity in fishing nets. This procedure was repeated
to fit the mean abundance estimates given also
by Jaramillo-Legorreta et al. (2019) for years
2008, 2015, 2016, 2017 and 2018. We note
that the latest estimate of abundance is for year
2018 (Dr. Lorenzo Rojas, pers. comm., March
17, 2021).
Monte Carlo simulations were used to
determine quasiextinction risk (QR). We
recorded the first passage time, i.e., the year
when a population trajectory first fell below
critical thresholds (Nc); when a trajectory fell
below Nc it was discarded from the origi-
nal 2 000 trajectories. We initiated with a
Revista de Biología Tropical, ISSN: 2215-2075 Vol. 69(2): 588-600, April-June 2021 (Published Apr. 26, 2021)
population having 13 individuals, approxi-
mately corresponding to year 2018 (Jaramillo-
Legorreta et al., 2019). For a given year, QR
was estimated as the ratio of first passage time
and the number of trajectories remaining that
year (Ginzburg, Slobodkin, Johnson, & Bind-
man, 1982).
QRs were computed discarding bycatch
mortality under three Nc scenarios: 5, 10 and
20 vaquitas in years 2023, 2028, 2033, and
2038. In other words, we computed the proba-
bility that the vaquita population will fall below
5, 10 and 20 individuals in those four years
given that bycatch mortality is 100 % eliminat-
ed starting in 2019. Simulations were done in
Matlab® version R2018b, a platform that can
handle matrix algebra appropriately (Miller,
Morgan, Ridout, Carey, & Rothery, 2011).
When Allee effects are considered, sur-
vival rates decrease for the younger age classes,
and the highest impact is attributed to bycatch
mortality (Fig. 2). It is worth noting the resil-
ience of the vaquita population. In the hypo-
thetical case that bycatch is 100 % eliminated
in year 2019 even with a mean number of 13
the model population steadily recovered. This
can be more readily appreciated in the inset
of Fig. 2.
A steady decrease in age-specific sur-
vival was observed in the subsequent periods
of 1993-1997 through 2009-2015, followed by
a sharp decrease in 2016, increase in 2017 and
a final decrease in 2018. Our analysis indicates
that the age groups with the lowest survival
rates are juveniles (0.5 to 3 years), and the old-
est (> 16.5 years) (Fig. 3).
Our analyses indicated that the net popu-
lation growth rate sharply decreased due to
bycatch (Table 1). If no Allee effect is con-
sidered, the population would grow 4.4 %
per year; when the Allee effect is present the
mean net growth rate is 2.6 % per year. When
bycatch mortality is considered, the growth rate
l reduces to < 1 meaning that the population
is declining. The estimated effect of bycatch
plummeted the population for 100 (on aver-
age) or less individuals, as indicated by l < 1.
Generation time decreased concomitantly with
population size, reproductive value of juveniles
and adults, and l.
The reproductive value RV also decreased
with increasing mortality. Table 1 provides the
average reproductive value for three age groups
Fig. 2. 2 000 random trajectories of the vaquita population considering natural mortality, natural mortality and Allee effects,
and natural mortality, Allee effects in addition to bycatch mortality in gillnets. Inset shows a detailed view of the trajectories
considering bycatch mortality as well as the Nc = 5 critical threshold population size.