588

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.

ABSTRACT

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.

v69i2.45475

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

589

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.

MATERIALS AND METHODS

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

590

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

x-1

). 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

was

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.

591

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):

(1)

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,

1989):

(2)

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):

(3)

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

t+1

(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

592

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).

RESULTS

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.

593

Revista de Biología Tropical, ISSN: 2215-2075, Vol. 69(2): 588-600, April-June 2021 (Published Apr. 26, 2021)

(juveniles, adults, and older adults). When

bycatch mortality is considered, as the number

of vaquitas decreased through time the mean

RV also decreased almost 75 % for juveniles

(1.66 to 0.51); for adults, RV decreased almost

by half (3.31 to 1.61), and for the older adults,

RV reduced only slightly (1.60 to 1.48).

A graphic depiction of reproductive value

is given in Fig. 4, which shows how Allee

effect and bycatch affects these demographic

parameters.

For the three thresholds of vaquitas con-

sidered (5, 10, 20) the probability of quasiex-

tinction (QR) decreases through time because

of an upward mean population trend starting in

2022 (Table 2, cf. inset Fig. 2).

DISCUSSION

In this work we assumed that the rela-

tive number of bycaught vaquitas reflect the

age structure, decreasing in numbers with

age. In a sample of 56 collected carcasses

-the majority bycaught in gillnets- most (33)

were juveniles followed by older adults (16)

and adults (7) (Hohn et al., 1996); no vaquitas

were found of ages 3 to 6 or 17 to 20 years.

This could be the result of a relatively small

Fig. 3. Annual age-specific survival rates of vaquita under various scenarios. Nat + Allee represents schedules including

natural mortality and an Allee effect related to maternal care. The remaining lines represent the survival schedules assuming

added bycatch mortality to fit estimated annual abundances in Jaramillo-Legorreta et al. (2019).

TABLE 1

The effect of Allee effect and bycatch on population size (N), net population growth rate (l) and mean reproductive value

(RV), and generation time ( ) for three age groups of vaquitas: juveniles (j), adults (a) and older adults (oa)

Scenario/Parameter N (vaquitas) Year

RVj RVa RVoa

Natural 643 1993 1.044 1.74 3.09 1.51 9.2

Natural + Allee 643 1993 1.026 1.66 3.31 1.60 9.4

Natural + Allee + Bycatch 550 1197 0.965 1.28 3.05 1.63 8.7

Natural + Allee + Bycatch 225 2015 0.938 1.14 2.79 1.59 8.2

Natural + Allee + Bycatch 100 2015 0.910 1.02 2.57 1.56 7.7

Natural + Allee + Bycatch 40 2016 0.429 0.46 1.70 1.65 4.2

Natural + Allee + Bycatch 25 2017 0.648 0.57 1.66 1.43 5.1

Natural + Allee + Bycatch 13 2018 0.557 0.51 1.61 1.48 4.7

594

Revista de Biología Tropical, ISSN: 2215-2075 Vol. 69(2): 588-600, April-June 2021 (Published Apr. 26, 2021)

sample size or other, unknown factors. Our

assumption is based on the facts that 1) fish-

ing effort in the vaquita habitat including

poaching of totoaba increased as compared to

the 1990s (Rodríguez-Quiroz, Aragón-Noriega,

Valenzuela-Quiñonez, & Esparza-Leal, 2010),

and 2) bycatch of vaquita increased accord-

ingly (Urrutia-Osorio et al., 2015).

Demographic stochasticity acts on individ-

ual rates at small population sizes (Lande, 1993;

Fig. 4. Age-specific reproductive values for three models of P. sinus. Years and abundance (in parentheses) are shown as

well as net growth rate l. The 643 vaquitas for year 1993 were estimated from data in Jaramillo-Legorreta et al., (2019) and

represent the initial condition for our models.

TABLE 2

Quasiextinction risk of a model vaquita population starting with a size of 13 in 2018 and assuming that bycatch mortality

is eliminated starting in 2019. Allee effect and demographic stochasticity are considered in 2 000 simulations

Threshold (# vaquitas)

Year

2023 2028 2033 2038

5 0.0094 0.0103 0.0056 0.0034

10 0.0340 0.0132 0.0061 0.0045

20 0.0500 0.0254 0.0094 0.0099

595

Revista de Biología Tropical, ISSN: 2215-2075, Vol. 69(2): 588-600, April-June 2021 (Published Apr. 26, 2021)

Legendre, Clobert, Moller, & Sorci, 1999).

With few conspecifics, Allee effects and demo-

graphic stochasticity might further depress

growth rate (Courchamp, Clutton-Brock, &

Grenfell, 1999; Berec, Angulo, & Courchamp,

2007), not evident at high population numbers

(Akçakaya, 2000). Allee effects emerge due to

decreased cooperation by conspecifics in deci-

mated populations (Lande, 1998); for vaquita

we use the term facilitation instead of coopera-

tion (Courchamp et al., 1999) because survival

of a female vaquita that just gave birth will

increase the likelihood of her calf to survive.

We did not find evidence for Phocoeanidae

of alloparental altruistic care of newborns by

conspecifics (Mann & Smuts, 1998; Gero,

Engelhaupt, Rendell, & Whitehead, 2009).

Therefore, survival of a mother and her new-

born represents an important proportional gain

in the decimated vaquita population.

An Allee effect is defined as “a posi-

tive relationship between any component of

individual fitness and either numbers or den-

sity of conspecifics” (Stephens, Sutherland,

& Freckleton, 1999). Here we find that this

double death effect results in a decline in per

capita growth rate as compared to the absence

of double death. Per capita growth is defined

as r = ln (l) (Caswell, 1989) and, as shown

in Table 1, with a double death effect l (and

thus r) decreases. Consequently, this double

death effect correlates with fitness, hence our

definition as an Allee effect. This is the first

work considering the double death effect in

vaquita, which has the potential to reduce

population growth. Rojas-Bracho et al. (2006)

estimated that the maximum vaquita population

net growth rate l was lower than 1.04 (or 4 %

per year). Our baseline analytical estimate of l

for a population without Allee effect is 4.4 %

per year, and when an Allee effect is included

l decreases to 2.6 % per year. Hohn et al.,

(1996) found pregnant and lactating juveniles

in their sample of gillnetted vaquitas, providing

evidence in favor of this demographic process.

When bycatch mortality was included, l

decreased to -3.5 % per year in year 1997 and

to -44.3 % per year in 2018. Previous works

show that fishing decreases the reproductive

value (RV) and λ in shark populations (Galluc-

ci, Taylor, & Erzini, 2006). For vaquita bycatch

mortality is the “harvested” portion of the

population which according to our calculations

reduces RV. Further, our results (cf. Table 1)

corroborate that in age-structured populations

there is a direct relationship between l, and

RV (Schaffer, 1981; Caswell, 1982; O’Grady,

Reed, Brook, & Frankham, 2008).

Despite demographic stochasticity and an

Allee effect acting as assumed in the present

work, vaquita has the potential to recover from

exceedingly small numbers. If bycatch mortal-

ity is eliminated in 2019, the model population

recover from only 13 individuals in 2018. This

seems to be related to the high sensitivity of l

to survival of the youngest age-classes and of

adults and thus to the effect of bycatch mortal-

ity in RV. For other cetaceans it was found that

l is more sensitive to survival of adults than

calves (Young & Keith, 2011). Due to a lagged

response because of the age structure, the

recovery is not immediate; it takes three years

(2019 to 2022) for the population to change

from strong negative to a slight positive trend.

It is unfortunate that there are no abundance

estimates of vaquita for the years 2019 to 2021

to include in the present work. Because of

the continued totoaba poaching at least dur-

ing 2019 (Aceves-Bueno, Read, & Cisneros-

Mata, 2020), it is likely that the population

is smaller now.

Historically, gillnets have produced con-

stant vaquita mortality (Vidal, 1995) which

urged the elimination of totoaba poaching.

From the late 1980s through the 1990s, 30-40

vaquitas died annually in totoaba gillnets (Sil-

ber, 1990; Vidal, 1993), a high rate relative

to the population size (Taylor & Gerrodette,

1993). For a population having between 300

and 500 vaquitas, incidental deaths in totoaba

nets were 5-10 % per year (Villa, 1993). From

1992-2009 bycatch represented 10.78 % of the

population and rose to 21.11 % from 2010-

2013 based on numbers in Urrutia-Osorio et

al. (2015). This increased bycatch mortality

596

Revista de Biología Tropical, ISSN: 2215-2075 Vol. 69(2): 588-600, April-June 2021 (Published Apr. 26, 2021)

coincides with intensified totoaba poaching

over the past decade (Cisneros-Mata, 2020).

There have been unsubstantiated argu-

ments for a negative effect on the vaquita

population of less Colorado river water into

the upper gulf of California (see Flessa et al.,

2019). What has not been discarded is the

obvious: vaquitas perish in gillnets. Hence, we

conclude the same as the vast majority of previ-

ous studies: more fishing nets in upper Gulf of

California resulted in higher incidental mortal-

ity of vaquitas. Moreover, bycatch in totoaba

gillnets has an overwhelming negative effect

(Morzaria-Luna, Ainsworth, Kaplan, Levin, &

Fulton, 2013).

Variability in mitochondrial DNA is relat-

ed to effective genetic population size N

and

vaquita lacks such variability. N

is the mini-

mum size below which the genetic makeup is

randomly affected in the population (Wright,

1931) and is generally lower than total popu-

lation size (Cypriano-Souza, da Silva, Engel,

& Bonatto, 2018). Previous work (Taylor &

Rojas-Bracho, 1999) discarded inbreeding

depression but concern was raised if the popu-

lation remained small. N

for vaquita could be

1/10 (Frankham, 1995), 1/3 (Nunney, 1993)

or 1/2 (Nunney, 1995) of total population.

Thus, an investigation of the genetic pool and

at the current population size of vaquita is

urgently needed.

Extraordinary efforts to assess and save

the vaquita have included aerial and boat

surveys, passive acoustic techniques, and

captive care (Barlow, Fleischer, Forney, &

Maravilla-Chávez, 1993; Taylor & Gerrodette,

1993; Barlow, Gerrodette, & Silber, 1997;

Jaramillo-Legorreta, Rojas-Bracho, & Gerro-

dette, 1999; Jaramillo-Legorreta et al., 2007;

Jaramillo-Legorreta et al., 2019; Rojas-Bracho

et al., 2019). Despite such efforts, results have

been deceptive because no effective actions

have been implemented to eliminate bycatch

mortality (Bobadilla, Álvarez-Borrego, Avi-

la-Foucat, Lara-Valencia, & Espejel, 2011;

Morzaria-Luna et al., 2013). Moreover, unless

poaching of totoaba is completely eliminated

it will be futile to implement any form of use

for this species, including a catch and release

program (see discussion in Cisneros-Mata,

2020). As many studies have previously recom-

mended, serious efforts are needed to eliminate

bycatch mortality of vaquita completely and

promptly, else it will be impossible to recover

this species. Demographically, vaquita seems

viable even at extremely low numbers; its

genetic makeup will be the factor governing

its long-run viability. A recent study (Morin et

al., 2020) is encouraging in this respect since it

concludes that even with current low numbers

the vaquita maintains the genetic diversity of a

healthy population.

Ethical statement: authors declare that

they all agree with this publication and made

significant contributions; that there is no con-

flict of interest of any kind; and that we fol-

lowed all pertinent ethical and legal procedures

and requirements. All financial sources are

fully and clearly stated in the acknowledge-

ments section. A signed document has been

filed in the journal archives.

ACKNOWLEDGMENTS

The authors are indebted to Ere Aceves,

Lorenzo Rojas, Alberto Zirino, Tracey Man-

gin and three anonymous reviewers for com-

ments and criticism to early versions of this

work. MACM and DRF thank CONACYT

for partial financial support; JAD thanks Tec-

nológico Nacional de México for granting a

leave of absence.

RESUMEN

Viabilidad de la población de vaquita marina,

Phocoena sinus (Cetacea: Phocoenidae), amenazada

por la pesca ilegal de Totoaba macdonaldi

(Perciformes: Sciaenidae)

Introducción: Pese a las acciones de conserva-

ción basadas en la ciencia y las políticas recomendadas,

con menos de 20 individuos sobrevivientes, la vaquita

(Phocoena sinus) -endémica del Golfo de California- es

el mamífero marino más amenazado del mundo debido

a su muerte incidental en redes de pesca; una pregunta

597

Revista de Biología Tropical, ISSN: 2215-2075, Vol. 69(2): 588-600, April-June 2021 (Published Apr. 26, 2021)

relevante es si su población se puede recuperar. Objetivo:

Evaluar las expectativas para la vaquita marina durante los

próximos 20 años. Métodos: Identificamos los factores que

afectan a la vaquita marina, construimos tablas de vida,

derivamos parámetros demográficos para diferentes esce-

narios y realizamos un análisis de viabilidad poblacional

utilizando matrices estocásticas de Leslie, estructuradas

por edad. Resultados: La tasa de crecimiento neto de la

vaquita es muy sensible a la supervivencia de los juveniles.

Encontramos que la captura incidental intensiva y conti-

nua en redes de enmalle para la pesca furtiva de totoaba

(Totoaba macdonaldi) durante la última década llevó a la

población de vaquitas a su actual estado crítico. Esto parece

agravarse por la estocasticidad demográfica y un potencial

efecto Allee. Conclusiones: Si la pesca furtiva de totoaba

se elimina de inmediato, demográficamente la vaquita

puede recuperarse; su supervivencia a largo plazo depende-

rá de su incierto estatus genético, aunque los resultados de

un estudio reciente son alentadores en este sentido.

Palabras clave: vaquita; totoaba; estocasticidad demográ-

fica; efecto Allee; análisis de viabilidad poblacional.

REFERENCES

Aceves-Bueno, E., Read, A.J., & Cisneros-Mata, M.Á.

(2020). Illegal fisheries, environmental crime, and the

conservation of marine resources. Conservation Bio-

logy, Online ahead of print. DOI: 10.1111/cobi.13674

Akçakaya, H.R. (2000). Population viability analyses with

demographically and spatially structured models. Eco-

logical Bulletins, 48, 23-38. DOI: 10.2307/20113246

Avila-Forcada, S., Martínez-Cruz, A.L., & Muñoz-Piña,

C. (2012). Conservation of vaquita marina in the

Northern Gulf of California. Marine Policy, 36(3),

613-622. DOI: 10.1016/j.marpol.2011.10.012

Barlow, J. (1986). Factor affecting the recovery of Pho-

coena sinus, the vaquita or Gulf of California Harbor

porpoise. Administrative Report No. LJ 86 37. La

Jolla, USA: U.S. National Marine Fisheries Service.

Barlow, J., Fleischer, L., Forney, K.A., & Maravilla-

Chávez, O. (1993). An experimental aerial survey

for the vaquita (Phocoena sinus) in the northern Gulf

of California. Marine Mammal Science, 9(1), 89-94.

Barlow, J., Gerrodette, T., & Silber, G.K. (1997). First

estimates of vaquita abundance. Marine Mammal

Science, 13(1), 44-58.

Begon, M., Mortimer, M., & Thompson, D.J. (1996).

Population ecology. A unified study of plants and

animals (3rd Ed.). Oxford, United Kingdom: Blac-

kwell Science.

Berec, L., Angulo, E., & Courchamp, F. (2007). Multiple

Allee effects and population management. Trends

in Ecology & Evolution, 22(4), 185-191. DOI:

10.1016/j.tree.2006.12.002

Birch, L.C. (1948). The intrinsic rate of natural increase of

an insect population. The Journal of Animal Ecology,

17(1), 15-26. DOI: 10.2307/1605

Bird, J.P., Martin, R., Akçakaya, H.R., Gilroy, J., Burfield,

I.J., Garnett, S.T., … Butchart, S.H.M. (2020). Gene-

ration lengths of the world’s birds and their implica-

tions for extinction risk. Conservation Biology, 34(5),

1252-1261. DOI: 10.1111/cobi.13486

Bobadilla, M., Álvarez-Borrego, S., Avila-Foucat, S., Lara-

Valencia, F., & Espejel, I. (2011). Evolution of

environmental policy instruments implemented for

the protection of totoaba and the vaquita porpoise

in the Upper Gulf of California. Environmental

Science & Policy, 14(8), 998-1007. DOI: 10.1016/j.

envsci.2011.06.003

Boyce, M.S. (1992). Population viability analysis. Annual

Review of Ecology and Systematics, 23, 481-506.

Camphuysen, K., & Krop, A. (2011). Maternal care, calf-

training and site fidelity in a wild harbour porpoise in

the North Sea. Lutra, 54(2), 123-126.

Caswell, H. (1982). Optimal life histories and the maximi-

zation of reproductive value: A general theorem for

complex life cycles. Ecology, 63(5), 1218-1222. DOI:

10.2307/1938846

Caswell, H. (1989). Matrix population models. Sunderland,

USA: Sinauer Associates.

Cisneros-Mata, M.Á., Botsford, L.W., & Quinn, J.F.

(1997). Projecting viability of Totoaba macdonaldi, a

population with unknown age-dependent variability.

Ecological Applications, 7(3), 968-980.

Cisneros-Mata, M.Á., Montemayor-López, G., &

Román-Rodríguez, M.J. (1995). Life his-

tory and conservation of Totoaba macdonal-

di. Conservation Biology, 9(4), 806-814. DOI:

10.1046/j.1523-1739.1995.09040806.x

Cisneros-Mata, M.Á. (2020). Evaluación de la pobla-

ción de Totoaba macdonaldi. Mexico City, México:

INAPESCA.

Courchamp, F., Clutton-Brock, T., & Grenfell, B. (1999).

Inverse density dependence and the Allee effect.

Trends in Ecology and Evolution, 14(10), 405-410.

DOI: 10.1016/s0169-5347(99)01683-3

Cypriano-Souza, A.L., da Silva, T.F., Engel, M.H., &

Bonatto, S.L. (2018). Effective population size and

the genetic consequences of commercial whaling

on the humpback whales (Megaptera novaean-

gliae) from Southwestern Atlantic Ocean. Gene-

tics and Molecular Biology, 41, 253-262. DOI:

10.1590/1678-4685-gmb-2017-0052

598

Revista de Biología Tropical, ISSN: 2215-2075 Vol. 69(2): 588-600, April-June 2021 (Published Apr. 26, 2021)

D’Agrosa, C., Lennert-Cody, C.E., & Vidal, O. (2000).

Vaquita bycatch in Mexico’s artisanal gillnet fishe-

ries: driving a small population to extinction. Conser-

vation Biology, 14(4), 1110-1119.

Dennis, B. (1989). Allee effects: population growth, critical

density, and the chance of extinction. Natural Resou-

rce Modeling, 3(4), 481-538. DOI: 10.1111/j.1939-

7445.1989.tb00119.x

Fenton, H., Daoust, P.Y., Forzán, M.J., Vanderstichel, R.V.,

Ford, J.K., Spaven, L., … Raverty, S. (2017). Causes

of mortality of harbor porpoises Phocoena phocoena

along the Atlantic and Pacific coasts of Canada.

Diseases of Aquatic Organisms, 122(3), 171-183.

DOI: 10.3354/dao03080

Flessa, K.W., Calderón-Aguilera, L., Cintra-Buenrostro,

C.E., Dettman, D.L., Dietl, G.P., Goodwin, D.H., ...

Zamora-Arroyo, F. (2019). Vaquita face extinction

from bycatch. Comment on Manjarrez-Bringas, N.

et al., Lessons for sustainable development: Marine

mammal conservation policies and its social and

economic effects. Sustainability 2019, 11, 2161-2167.

DOI: 10.3390/su11072161

Frankham, R. (1995). Effective population size/adult popu-

lation size ratios in wildlife: a review. Genetics

Research, 66, 95-107.

Gallucci, V.F., Taylor, I.G., & Erzini, K. (2006). Conserva-

tion and management of exploited shark populations

based on reproductive value. Canadian Journal of

Fisheries and Aquatic Sciences, 63(4), 931-942. DOI:

10.1139/f05-267

García-Gómez, J., & Chávez-Nungaray, E. (2017). Econo-

mic valuation for the socio-environmental protection

of the vaquita porpoise, an endemic species. Región y

Sociedad, 70, 5-29. DOI: 10.22198/rys.2017.70.a818

Gaskin, D.E., Smith, G.J.D., Watson, A.P., Yasui, W.Y., &

Yurick, D.B. (1984). Reproduction in the porpoises

(Phocoenidae): Implications for management. In W.

Perrin, R.L. Brownell Jr., & D.P. DeMaster (Eds.),

Reproduction in whales, dolphins and porpoises (pp.

135-148). La Jolla, USA: Proceedings of the confe-

rence cetacean reproduction: estimating parameters

for stock assessment and management.

Gero, S., Engelhaupt, D., Rendell, L., & Whitehead, H.

(2009). Who Cares? Between-group variation in allo-

parental caregiving in sperm whales. Behavioral Eco-

logy, 20(4), 838-843. DOI: 10.1093/beheco/arp068

Gerrodette, T., Barlow, J., Taylor, B.L., & Silber, G.K.

(1994). First population estimates of the endange-

red porpoise, Phocoena sinus, with implications

for monitoring small populations. Jalisco, México:

International Meeting of the Society for Conservation

Biology and the Association for Tropical Biology.

Ginzburg, L.R., Slobodkin, L.B., Johnson, K., & Bind-

man, A.G. (1982). Quasiextinction probabilities as a

measure of impact on population growth. Risk Analy-

sis, 2(3), 171-181. DOI: 10.1111/j.1539-6924.1982.

tb01379.x

Hill, H.T., Greer, M., Solangi, S.A., & Kuczaj, I.I. (2007).

All mothers are not the same: maternal styles in bott-

lenose dolphins (Tursiops truncatus). International

Journal of Comparative Psychology, 20, 35-54.

Hohn, A.A., Read, A.J., Fernández, S., Vidal, O., & Find-

ley, L.T. (1996). Life history of the vaquita, Phocoena

sinus (Phocoenidae, Cetacea). Journal of Zoolo-

gy, 239, 235-251. DOI: 10.1111/j.1469-7998.1996.

tb05450.x

Jaramillo-Legorreta, A., Cárdenas-Hinojosa, G., Nie-

to-García, E., Rojas-Bracho, L., Thomas, L., Ver

Hoef, J., … Tregenza, N. (2019). Decline towards

extinction of Mexico’s vaquita porpoise (Phocoena

sinus). Royal Society Open Science, 6, 190598. DOI:

10.1098/rsos.190598

Jaramillo-Legorreta, A., Rojas-Bracho, L., Brownell, R.L.,

Read, A.J., Reeves, R.R., Ralls, K., & Taylor, B.L.

(2007). Saving the vaquita: immediate action, not

more data. Conservation Biology, 21(6), 1653-1655.

DOI: 10.1111/j.1523-1739.2007.00825.x

Jaramillo-Legorreta, A., Rojas-Bracho, L., & Gerrodette,

T. (1999). A new abundance estimate for vaquita:

first step for recovery. Marine Mammal Science, 15,

957-973. DOI: 10.1111/j.1748-7692.1999.tb00872.x

Kesselring, T., Viquerat, S., Brehm, R., & Siebert, U.

(2017). Coming of age: Do female harbour porpoi-

ses (Phocoena phocoena) from the North Sea and

Baltic Sea have sufficient time to reproduce in a

human influenced environment? PLoS ONE, 12(10),

e0186951. DOI: 10.1371/journal.pone.0186951

Kokko, H., & Ebenhard, T. (1996). Measuring the stren-

gth of demographic stochasticity. Journal of Theo-

retical Biology, 183(2), 169-178. DOI: 10.1006/

jtbi.1996.0210

Koopman, H.N., & Zahorodny, Z.P. (2008). Life history

constrains biochemical development in the highly

specialized odontocete echolocation system. Proce-

edings of the Royal Society B: Biological Sciences,

275(1649), 2327-2334. DOI: 10.1098/rspb.2008.0457

Lamberson, R.H., Noon, B.R., Voss, C., & McKelvey, K.S.

(1994). Reserve design for territorial species: the

effects of patch size and spacing on the variability of

Northern Spotted owl. Conservation Biology, 8(1),

185-195.

Lande, R. (1993). Risks of population extinction from

demographic and environmental stochasticity and

random catastrophes. The American Naturalist, 142,

911-927.

599

Revista de Biología Tropical, ISSN: 2215-2075, Vol. 69(2): 588-600, April-June 2021 (Published Apr. 26, 2021)

Lande, R. (1998). Demographic stochasticity and Allee

effect on a scale with isotropic noise. Oikos, 83(2),

353-358. DOI: 10.2307/3546849

Lavín, M.F., & Sánchez, S. (1999). On how the Colorado

River affected the hydrography of the upper Gulf of

California. Continental Shelf Research, 19, 1545-

1560. DOI: 10.1016/S0278-4343(99)00030-8

Lee, A.M., Seather, B.E., & Engen, S. (2011). Demo-

graphic stochasticity, Allee effects, and extinction:

The influence of mating system and sex ratio.

The American Naturalist, 177(3), 301-313. DOI:

10.1086/658344

Legendre, S.J., Clobert, J., Moller, A.P., & Sorci, G. (1999).

Demographic stochasticity and social mating system

in the process of extinction of small populations:

the case of passerines introduced in New Zealand.

The American Naturalist, 153(5), 449-453 DOI:

10.1086/303195

Lockyer, C. (2013). Harbour porpoises (Phocoena pho-

coena) in the North Atlantic: Biological parameters.

NAMMCO Scientific Publications, 5, 71-89. DOI:

10.7557/3.2740

Mann, J., & Smuts, B.B. (1998). Natal attraction: alloma-

ternal care and mother–infant separations in wild

bottlenose dolphins. Animal Behaviour, 55(5), 1097-

1113. DOI: 10.1006/anbe.1997.0637

McNamara, J.M., & Harding, K.C. (2004). Measure-

ment error and estimates of population extinc-

tion risk. Ecology Letters, 7(1), 16-20. DOI:

10.1046/j.1461-0248.2003.00550.x

Miller, D., Morgan, B.J.T., Ridout, M.S., Carey, P.D., &

Rothery, P. (2011). Methods for exact perturbation

analysis. Methods in Ecology and Evolution, 2, 283-

288. DOI: 10.1111/j.2041-210X.2010.00074.x

Moloney, C.L., Cooper, J., Ryan, P.G., & Siegfried, W.R.

(1994). Use of a population model to assess the

impact of longline fishing on wandering albatross

Diomedea exulanus populations. Biological Conser-

vation, 70, 195-203.

Montalvo, T.L., & Ortuño, G. (2017). Una inversión de

1,200 mdp no ha servido para rescatar a la vaquita

marina. Retrieved from https://www.animalpolitico.

com/2017/04/vaquita-marina-inversion-proteccion

Morin, P.A, Archer, F.I., Avila, C.D., Balacco, J.R.,

Bukhman, Y.V., Chow, W., … Jarvis, E.D. (2020).

Reference genome and demographic history of

the most endangered marine mammal, the vaqui-

ta. Molecular Ecology Resources, 0, 1-13. DOI:

10.1111/1755-0998.13284

Morzaria-Luna, H.N., Ainsworth, C.H., Kaplan, I.C.,

Levin, P.S., & Fulton, E.A. (2013). Indirect effects

of conservation policies on the coupled human-

natural ecosystem of the upper Gulf of California.

PLoS ONE, 8(5), e64085. DOI: 10.1371/journal.

pone.0064085

Norris, K.S., & McFarland, W.N. (1958). A new harbour

porpoise of the genus Phocoena from the Gulf of

California. Journal of Mammalogy, 39, 22-39.

Nunney, L. (1993). The influence of mating system and

overlapping generations on effective population size.

Evolution, 47(5), 1329-1341. DOI: 10.1111/j.1558-

5646.1993.tb02158.x

Nunney, L. (1995). Measuring the ratio of effective

population size to adult numbers using genetic and

ecological data. Evolution, 49(2), 389-392. DOI:

10.2307/2410351

Nur, N. (1987). Population growth rate and the measure-

ment of fitness: A critical reflection. Oikos, 48(3),

338-341. DOI: 10.2307/3565523

O’Grady, J.J., Reed, D.H., Brook, B.W., & Frankham, R.

(2008). Extinction risk scales better to generations

than to years. Animal Conservation, 11(5), 442-451.

DOI: 10.1111/j.1469-1795.2008.00201.x

Pielou, E.E. (1977). Mathematical Ecology. New York,

USA: John Wiley and Sons.

Rodríguez-Quiroz, G., Aragón-Noriega, E.A., Valenzuela-

Quiñónez, W., & Esparza-Leal, H.M. (2010). Artisa-

nal fisheries in the conservation zones of the Upper

Gulf of California. Revista de Biología Marina y

Oceanografía, 45(1), 89-98.

Rojas-Bracho, L., Gulland, F.M.D., Smith, C.R., Taylor,

B., Wells, R.S., Thomas, P. … Walker, S. (2019). A

field effort to capture critically endangered vaquitas

Phocoena sinus for protection from entanglement in

illegal gillnets. Endangered Species Research, 38,

11-27. DOI: 10.3354/esr00931

Rojas-Bracho, L., Reeves, R.R., & Jaramillo-Legorre-

ta, A. (2006). Conservation of the vaquita Pho-

coena sinus. Mammal Review, 36(3), 179-216. DOI:

10.1111/j.1365-2907.2006.00088.x

Rojas-Bracho, L., & Reeves, R.R. (2013). Vaquitas and

gillnets: Mexico’s ultimate cetacean conservation

challenge. Endangered Species Research, 21, 77-87.

DOI: 10.3354/esr00501

Rojas-Bracho, L., & Taylor, B.L. (1999). Risk factors

affecting the vaquita (Phocoena sinus). Marine Mam-

mal Science, 15(4), 974-989. DOI: 10.1111/j.1748-

7692.1999.tb00873.x

Rosel, P.E., & Rojas-Bracho, L. (1999). Mitochondrial

DNA variation in the critically endangered vaqui-

ta Phocoena sinus Norris and Macfarland, 1958.

Marine Mammal Science, 15(4), 990-1003. DOI:

10.1111/j.1748-7692.1999.tb00874.x

600

Revista de Biología Tropical, ISSN: 2215-2075 Vol. 69(2): 588-600, April-June 2021 (Published Apr. 26, 2021)

Schaffer, W.M. (1981). On reproductive value and fitness.

Ecology, 62(6), 1683-1685. DOI: 10.2307/1941523

Silber, G.K. (1990). Occurrence and distribution of the

vaquita Phocoena sinus in the Northern Gulf of

California. United States Fish Bulletin, 88, 339-346.

Stephens, P.A., Sutherland, W.J., & Freckleton, R.P.

(1999). What Is the Allee Effect? Oikos, 87(1), 185-

190. DOI: 10.2307/3547011

Taylor, B.L., Wells, R.S., Olson, P.A., Brownell, R.L.,

Gulland, F.M.D., Read, A.J., … Rojas-Bracho, L.

(2019). Likely annual calving in the vaquita, Pho-

coena sinus: A new hope? Marine Mammal Science,

35(4), 1603-1612. DOI: 10.1111/mms.12595

Taylor, B.L., & Gerrodette, T. (1993). The uses of statistical

power in conservation biology: the vaquita and Nor-

thern spotted owl. Conservation Biology, 7(3), 489-

500. DOI: 10.1046/j.1523-1739.1993.07030489.x

Taylor, B.L., & Rojas-Bracho, L. (1999). Examining the

risk of inbreeding depression in a naturally rare ceta-

cean, the vaquita (Phocoena sinus). Marine Mammal

Science, 15(4), 1004-1028. DOI: 10.1111/j.1748-

7692.1999.tb00875.x

Thomas, L., Jaramillo-Legorreta, A., Cárdenas-Hinojosa,

G., Nieto-García, E., Rojas-Bracho, L., Ver Hoef,

J.M., … Tregenza, N. (2017). Last call: Passive

acoustic monitoring shows continued rapid decline

of critically endangered vaquita. The Journal of the

Acoustical Society of America, 142(5), EL512-EL517.

Urrutia-Osorio, M.F., Jaramillo-Legorreta, A.M., Rojas-

Bracho, L., & Sosa-Nishizaki, O. (2015). Analysis

of the artisanal fisheries of San Felipe, Mexico: Esti-

mating incidental mortality of the vaquita (Phocoena

sinus). Journal of Marine Animals and Their Ecology,

8(1), 26-35.

Vidal, O. (1993). Aquatic mammal conservation in Latin

America: problems and perspectives. Conservation

Biology, 7(4), 788-795.

Vidal, O. (1995). Population biology and incidental mor-

tality of the vaquita, Phocoena sinus. Report of the

International Whaling Commission (Special Issue),

16, 247-272.

Villa, B. (1993). Recovery plan for the vaquita, Phocoena

sinus. Mexico City, México: Universidad Nacional

Autónoma de México.

Wright, S. (1931). Evolution in Mendelian populations.

Genetics, 16(3), 97-159.

Young, K.E., & Keith, E.O. (2011). A comparative analysis

of cetacean vital rates using matrix population mode-

ling analysis of cetacean vital rates. International

Journal of Applied Science and Technology, 1(6),

261-277.