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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

1

*

Juan A. Delgado

2

Demetrio Rodríguez-Félix

1

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

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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

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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

x

are age-

specific survival probabilities from birth to age

class x (l

x

= p

0

p

l

p

2

... 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

0

, was 0.71; this is the square

of p

3

= 0.84, as suggested by Barlow (1986).

p

1

and p

2

were linearly interpolated from those

two values (p

0

and p

3

); survival rates for age

classes 4 to 20 were considered constant (0.84).

Annual parturition rates at-age x, m

x

,

were 0.9 for age classes ≥ 6, while m

4

was

considered as 1/2 of m

6

, and m

5

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.

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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

x

, 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

l

t

= N

t+1

/N

t

(Nur, 1987) where N

t

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

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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.