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CSIRO PUBLISHING
Marine and Freshwater Research, 2007, 58, 54–66 www.publish.csiro.au/journals/mfr
Maturity and growth characteristics of a commercially
exploited stingray, Dasyatis dipterura
Wade D. Smith
A,C
, Gregor M. Cailliet
A
and Everardo Mariano Melendez
B
A
Moss Landing Marine Laboratories, Pacific Shark Research Center, 8272 Moss Landing Road,
Moss Landing, CA 95039, USA.
B
Universidad Autonóma de Baja California Sur, La Paz, BCS 23080, Mexico.
C
Corresponding author. Email: wsmith@mlml.calstate.edu
Abstract. Maturity and growth characteristics were estimated for Dasyatis dipterura from western Mexico, where it is
a common component of artisanal elasmobranch fisheries. Median disc width at maturity was estimated as 57.3 cm for
females (n =126) and 46.5 cm for males (n =55) respectively. Age estimates were obtained from 304 fishery-derived
specimens (169 female, 135 male). An annual pattern of band-pair deposition was validated through modified centrum
edge and marginal increment analyses. Gompertz, polynomial and von Bertalanffy growth models were fit to disc width
and weight-at-age data. Resulting models were evaluated based on biological rationale, standard error of model estimates,
and Akaike’s information criteria. Growth characteristics differed significantly between females and males. Maximum
age estimates were 28 years for females and 19 years for males. Three-parameter von Bertalanffy growth models of disc
width-at-age data generated the most appropriate fits and produced relatively low estimates of instantaneous growth rates
for females (DW
∞
=92.4 cm, k =0.05, t
0
=−7.61, DW
0
=31.4 cm) and males (DW
∞
=62.2 cm, k =0.10, t
0
=−6.80,
DW
0
=31.3 cm). These values are the lowest reported for myliobatiform stingrays and indicate slow growth rates in
comparison with elasmobranchs in general.
Additional keywords: Dasyatidae, fisheries management, growth models, marginal increment analysis, Mexico, model
selection, Myliobatiformes.
Introduction
The diamond stingray, Dasyatis dipterura (Jordan & Gilbert,
1880), is a broadly distributed eastern Pacific species that attains
disc widths of at least 97 cm and weights to 51 kg (Feder et al.
1974). It has been reported from British Columbia, Canada to
Chile, including theGalápagosandHawaiianIslands (Hart 1973;
Nishida and Nakaya 1990; Lamilla et al. 1995), but most com-
monly ranges from southern California to Peru. D. dipterura
is often inappropriately cited as its junior synonym, D. brevis
(Nelson et al. 2004).
Dasyatis dipterura is common in the shallow, inshore waters
of western Mexico. In the Gulf of California, it was found to be
the second most abundant benthic species taken in exploratory
trawl surveys (Flores et al. 1995). Similar surveys conducted in
the Bahía Magdalena lagoon complex also indicated that this
stingray is one of the primary elements of the soft-bottom dem-
ersal fish assemblage (Mathews and Druck-González 1975).
During the past two decades, multi-species batoid fisheries
have expanded throughout these regions (Márquez-Farías 2002;
Bizzarro et al. in press). Concern over increased shark and
ray catches prompted a moratorium on the issuance of elasmo-
branch fishing permits in 1993, but no other regulations have
been implemented.Although species-specific landings informa-
tion is scarce, D. dipterura has been identified as a primary
component of the artisanal elasmobranch landings in western
Mexico and is likely to be commonly taken as by-catch in trawl
fisheries throughout the region (Villavicencio Garayzar 1995;
Márquez-Farías 2002).
Elasmobranchs typically exhibit life-history characteristics
that include relatively slow growth, late ages of maturity,
low birth rates, long gestation periods and decreased natural
mortality rates over their relatively long life spans (Holden
1973; Stevens et al. 2000). These life-history strategies ren-
der the group especially vulnerable to fisheries exploitation.
Species-specific models of growth, in particular, are essential
for assessing the productivity and resilience of fish populations
to commercial exploitation and provide a basis for estimating
additional life-history parameters including natural mortality
and longevity (e.g. Stearns 1992; Haddon 2001). However, anal-
yses of elasmobranch growth patterns and rates are problematic,
in part because the calcified structures most commonly used
to derive age estimates (vertebral centra) may not provide con-
sistently reliable records of growth (see Cailliet and Goldman
2004). Therefore, the suitability of elasmobranch vertebrae, or
other calcified parts, as ageing structures should be routinely
assessed on a species-specific basis.
Life-history information published on D. dipterura is
restricted to estimates of male size at maturity (Mathews and
Druck-González 1975). If D. dipterura also exhibits the low
fecundity, slow growth, long life span and late age of maturity
© CSIRO 2007 10.1071/MF06083 1323-1650/07/010054
Maturity, age and growth of Dasyatis dipterura Marine and Freshwater Research 55
associated with many other elasmobranchs, depletion or collapse
of targeted populations is possible. An improved understanding
of the life history and population dynamics of D. dipterura is
essential for formulating effective management strategies for
exploited populations. Thus, the objectives of this study were to
determine the fecundity, age and size at maturity, growth char-
acteristics, and longevity of the commercially exploited stingray
D. dipterura from the Bahía Magdalena lagoon complex, B.C.S.
Mexico. We consider and evaluate multiple growth functions in
an effort to determine the most appropriate growth model for
this species.
Materials and methods
Sample collection
Artisanal fishery landings from the Bahía Magdalena lagoon
complex (∼24.46–24.47
◦
N – 111.73
◦
W) were surveyed during
1998–2001 (Fig. 1). Sampling was primarily conducted during
the summer months of June and August, which coincided with
the peak batoid fishing effort within the lagoon complex, but
additional surveys were completed during October (2001) and
Fig. 1. Location of the Bahía Magdalena lagoon complex, Baja California
Sur, México and sampling locations. Numbered symbols signify sampling
locations, the primary study site (6) is distinguished by a triangle. 1, Puerto
Adolfo Lopez Mateo; 2, Puerto San Carlos; 3, San Buteo; 4, Puerto Can-
cún; 5, El Cayuco; 6, Puerto Viejo; 7, Puerto Chale; 8, El Datíl; 9, Loma
Amarilla.
December (1999). The majority of specimens was obtained from
the directed batoid fishery at Puerto Viejo along Bahía Almejas.
Specimens were sexed and disc width (DW) measured to the
nearest centimeter. Weight was determined to the nearest 0.1 kg
using spring scales for all specimens ≤25 kg.
Size at maturity and fecundity
Reproductive condition was assessed to estimate fecundity and
size/age at maturity. Specimens were assigned a binomial matu-
rity status of 0 (immature) or 1 (mature) following measurement
and macroscopic examination of reproductive tracts. Criteria for
maturity were modified after Martin and Cailliet (1988a) and
Snelson et al. (1988). Females were assessed as mature if vitel-
logenic ova >1 cm diameter were present in the left ovary (right
ovaries and uteri are typically non-functional within the family
Dasyatidae) and uteri were well developed with trophonemata
present. Gravid females were recorded as mature and the number
and DW of embryos were recorded. Males were considered to be
mature if the claspers were well calcified, easily rotated, clasper
tips could be expanded, the vas deferens was highly coiled and
the testes were enlarged and lobed.The presence of seminal fluid,
although noted, was not considered to be a primary indicator of
maturity (Pratt 1979).
Median DW-at-maturity (DW
50
) was estimated by fitting a
logistic model to binomial maturity data (Mollet et al. 2000).
Data were binned into 1-cm DW size classes and females and
males were analysed separately. The following form of the logis-
tic equation was fitted using least-squares non-linear regression
and SigmaPlot graphical software (version 8.0, SPSS Inc., 2002
[www.spss.com/, verified December 2006]):
Y =
1
(1 +e
−(a+bx)
)
where Y = maturity status and x =disc width in centimeters.
DW
50
was calculated from the fitted equation as −a/b (Mollet
et al. 2000). Age at maturity was estimated by relating DW
50
for
females and males to the corresponding DW-at-age estimates.
Age estimation
Vertebral samples were removed from the region posterior to the
cranium above the abdominal cavity. To assess banding con-
sistency among vertebral centra, samples collected from the
anterior vertebral region were compared with centra from a
posterior region (above the pelvic girdle) of the same vertebral
column from a subset of specimens. An archived collection of
vertebral samples collected from the Puerto Viejo fishery during
1992 and 1998 was provided by the Laborotorío de los Elasmo-
branqíos at the Universidad Autonóma de Baja California Sur in
La Paz, Mexico for use in this study. All samples were stored in
70% isopropyl alcohol until processed for ageing.
Vertebral centra were separated, manually cleaned and air-
dried. Centrum diameter was measured with dial calipers and
the relationship between DW and vertebral centrum diameter
was examined to determine if vertebrae were an appropriate age-
ing structure for this species (Casselman 1983). To account for
non-concentric growth of vertebral centra, mean centrum diam-
eter (MCD) was calculated from whole centra of each specimen
56 Marine and Freshwater Research W. D. Smith et al.
based on measurements of centrum height and width (near-
est 0.1 mm). Analysis of covariance (ANCOVA) was applied
to compare potential sex-specific differences between MCD
and DW. Because no significant difference in DW (cm) and
MCD (mm) was detected between female and male stingrays,
these data were combined (n =345) (ANCOVA, F =0.833,
P =0.362) to generate the following positive linear relationship:
DW =9.0075 +6.4505 ×MCD (r
2
=0.92).
Vertebrae were embedded in polyester resin and sectioned to
∼0.3 mm using paired diamond blades on a low-speed jeweller’s
saw (Buehler, Evanston, IL, USA). Thin sections were affixed to
glass slides, successively polished with 800- and 1200-grit wet
sandpaper and viewed under transmitted light with a binocular
microscope. Preliminary analyses revealed that unstained, thin-
sectioned centra best distinguished banding patterns among all
vertebral size classes. Centrum faces were brushed with mineral
oil before viewing.
Optically distinct alternating bands were readily distin-
guished within the centra of all free-living specimens (Fig. 2).
Pre-birth banding was not evident within the centra of near-term
embryos. Thus, age 0 was identified as the first translucent band
encountered distal to the focus following an angle change in the
intermedialia that was determined to be the birth mark. Discrete,
alternating opaque and translucent bands were evident within the
corpus calcareum and age estimates were made by enumerating
band pairs (one translucent and one opaque band) in this region.
If a translucent band was determined to be forming on the outer
centrum edge, the age estimate was assigned as the number of
completely formed band pairs plus 0.5 (e.g. 2.5 years).
All vertebrae were prepared and examined by the senior
author. Age estimates were based on four independent counts
of each sample. If agreement was not achieved between at least
two counts after four reads, the sample was excluded from analy-
sis. The clarity and readability of each sample was assessed on a
qualitative scale of 1–5 in a manner modified from Officer et al.
BM
BP
1mm
BM
BP
Fig. 2. Sagittal thin section of a Dasyatis dipterura vertebral centrum
estimated to be 2 years in age. BM, birth mark; BP, band pair – consisting
of one translucent and one opaque band.
(1996), in which samples rated as 1 produced clear, unambigu-
ous band counts and samples from which band counts could
not be reliably obtained were categorised as 5. Final age esti-
mates were based only from samples that received clarity grades
of 1–4.
Reproducibility and precision of resulting age estimates
was assessed using several techniques. The index of aver-
age percentage error (IAPE) and coefficient of variation (CV)
were calculated (Beamish and Fournier 1981; Chang 1982).
Percentage agreement, based on consensus counts and their
corresponding maximum differences, was determined as an
additional measure of precision and to assess sources of count
variation. Perfect agreement and agreement plus or minus 0.5,
1, 2, 3, and 4 or more years were summed overall and calcu-
lated for 5-cm DW size classes following Cailliet and Goldman
(2004).
Consistency of the banding pattern throughout the vertebral
column was evaluated from 30 paired samples collected from
anterior and posterior regions of the column. Centra from both
regions were aged non-consecutively and independently without
knowledge of the centrum location. A paired-sample t-test was
applied to examine the hypothesis that banding patterns were
uniform within monospondylous vertebrae.
Edge and marginal increment analysis
The temporal periodicity of band deposition within vertebral
centra was assessed using two complementary semi-direct meth-
ods of validation (Morales-Nin and Panfili 2002). A common
method of edge analysis (e.g. Yudin and Cailliet 1990) was
modified to include four distinct edge classes based on opti-
cal qualities and the extent of band deposition: narrow opaque
(O1), broad opaque (O2), narrow translucent (T1), and broad
translucent (T2). A narrow band was defined as having a width
that is less than 50% of the previously fully-formed like band
and broad bands on the centrum edge were distinguished as hav-
ing a width that was equal to or greater than half of the previous
like band width.Additionally, mean monthly marginal increment
ratios (MIRs) were used as quantitative assessments (marginal
increment analysis) of band deposition following Conrath et al.
(2002): MIR =MW /PBW, where MW is the margin width or
width of the outer-most forming band and PBW is the width
of the penultimate band pair. Age-0 specimens were excluded
from analysisbecause no completely formed bands were present.
Potential differencesamong mean MIRs werecompared between
months of capture with a non-parametric Kruskal–Wallis test by
ranks (see Simpfendorfer et al. 2000). Dunn’s (1964) compari-
son of group rank sums for unequal sample sizes was applied to
detect which months accounted for any significant differences
indicated by the Kruskal–Wallis test.
Growth models
Mean growth parameters for D. dipterura were calculated
from individual DWs and weight-at-age estimates using
non-linear least-squares techniques. Size-at-age estimates
were fit to five growth models: three-parameter von Berta-
lanffy; modified two-parameter von Bertalanffy; weight-based
von Bertalanffy; Gompertz; and a polynomial function. A
Maturity, age and growth of Dasyatis dipterura Marine and Freshwater Research 57
three-parameter von Bertalanffy growth function (VBGF) was
calculated following Beverton and Holt (1957) as:
DW
t
= DW
∞
(1 −e
−k(t−t
0
)
),
where DW
t
is the mean disc width at age t, DW
∞
is the theoret-
ical average asymptotic disc width, k is the growth coefficient
that describes the average rate at which DW
∞
is attained, t is
the estimated age and t
0
is the hypothetical age at 0 DW. Pre-
dicted size at birth (DW
0
) wascalculated to provide an additional
biological measure by which models could be evaluated (Cailliet
et al. 2006). Growth characteristics of female and male stingrays
were examined to determine if these parameters were equiva-
lent between sexes using analysis of residual sums of squares
(ARSS) (Chen et al. 1992). Results of three-parameter VBGFs
were assessed using ARSS to establish a basis for model devel-
opment. A modification of the VBGF using two-parameters was
also calculated that anchors the model with a known or estimated
size at birth (von Bertalanffy 1960):
DW
t
= DW
∞
−(DW
∞
−DW
0
)(e
(−k+t)
),
where DW
0
is the observed size at birth and the remaining
parameters are as previously defined. Because published esti-
mates of size at birth were unavailable for D. dipterura, mean
DW at birth, as calculated from regressions of MCD, was incor-
porated as DW
0
in two-parameter VBGFs. A weight-based form
of the VBGF was also applied after Fabens (1965) and Ricker
(1979):
w
t
= W
∞
(1 −e
−k(t−t
0
)
)
3
,
where w
t
and W
∞
represent weight-at-age and theoretical
asymptotic weight and the other parameters are as described
above. Predicted weight at birth (W
0
) was calculated following
Ricker (1979).A form of the Gompertz equation was fitted using
DW as well as weight-at-age data following Ricker (1979):
w
t
= W
∞
e
−ke
−gt
,
where w
t
and W
∞
are as defined for the weight based VBGF, k
is a constant such that kg is the instantaneous growth rate when
t =0 and w
t
=W
0
, g is the instantaneous growth rate, and t is
the estimated age. DW-at-age data were substituted for weight
variables to obtain size-at-age models based on the Gompertz
growth function (Ricker 1975). Predicted sizes at birth (DW
0
and W
0
) were also determined from this equation.
An alternative to asymptotic growth models was also fitted to
DW and weight-at-age data using the following three-parameter
polynomial function:
DW
t
/w
t
= a +b ∗t + c ∗t
2
,
where DW
t
and w
t
are as previously defined and a, b, and
c are constants. Polynomial functions have been suggested to
have mathematical advantages to the VBGF (Knight 1968; Roff
1980).
Resultant growth models were assessed based on biology, sta-
tistical fit, and convenience (Moreau 1987). Goodness-of-fit was
determined from standard error of the model estimates (s.e.e.)
(e.g. Cailliet et al. 1992).Additionally,Akaike’s information cri-
terion (AIC) (see Burnham and Anderson 2002) was applied to
rank growth models in terms of their ability to produce the most
parsimonious explanation of observed DW and weight-at-age
data. A form of AIC modified for non-linear least-squares mod-
els was calculated following Burnham and Anderson (2002).
Differences in absolute AIC values (
i
) between all candidate
models and the one that resulted in the minimumAIC value were
calculated as a basis for presenting and ranking growth models,
where
i
greater than 10 have essentially no support and may
be omitted from consideration (Burnham and Anderson 2002).
Longevity
In addition to reporting the maximum observed age in this study,
longevity (ω) was estimated for females and males separately
using three methods.The sizes at which 95% (5(ln 2)/k) and 99%
(7(ln 2)/k)ofDW
∞
are attained were determined as a measure of
ω following Ricker (1979) and Fabens (1965), respectively. Tay-
lor’s (1958) method of estimating life span as the time required
to attain 95% of L
∞
(or DW
∞
) was calculated as:
t
0
+
log
e
(1 −0.95)
k
,
where parameters for the Ricker, Fabens, and Taylor formulas
were obtained from the results of the three-parameter VBGF.
Results
Size at maturity and fecundity
Reproductive observations were based on the direct assessments
of 126 female and 55 male D. dipterura. Females attained matu-
rity at greater sizes than males (Fig. 3). DW
50
was estimated as
57.3 cm for females and 46.5 cm for males. All females greater
than 58-cm DW were determined to be mature. A female of
Fig. 3. Relationship between maturity status and disc width for Dasyatis
dipterura females (n =126) and males (n =54). Grey drop lines indicate
respective median sizes at maturity.
58 Marine and Freshwater Research W. D. Smith et al.
58-cm DW was the largest immature specimen and the smallest
mature female measured 57-cm DW. All males greater than 50-
cm DW were classified as mature. The smallest observed mature
male examined was 47-cm DW and the largest immature male
was 50-cm DW. Seminal fluid was readily expelled from mature
males during August 1998 and 1999, but was not detected during
June, October, or December.
Gravid females were infrequently encountered among the
artisanal fishery landings at Puerto Viejo. Eight gravid females
were observed during August 1999. No gravid females were
observed during August of 1998, but four specimens with char-
acteristics equivalent to post partum conditions were noted.
Observed fecundity ranged from 1 to 3 embryos.
Age estimation
Vertebral centra from 339 specimens (191 females, 148 males)
were processed for ageing.A birth mark was measured and iden-
tified in all samples within 2.2 mm of the focus. Based on the
measurements of 157 centrum images and the linear relation-
ship between MCD and DW, mean DW at birth was estimated
to be 21.3 cm (±1.6 cm s.d.). However, considerable variation
among size at birth was indicated by these extrapolations, rang-
ing from 19 to 28-cm DW.The smallest specimens collected were
25.8-cm DW.
Band counts of paired samples collected from anterior and
posterior regions of monospondylous vertebral centra indicate
a consistent pattern of band pair deposition throughout the ver-
tebral column (Fig. 4). Perfect agreement was achieved in 57%
(n =17)of the estimates from these vertebral regions and percent
agreement ±0.5–1.0 was 73% (n =22). No significant differ-
ence was detected between mean band-pair counts from anterior
and posterior vertebral regions (t
0.05(2),29
=2.045, t =0.68).
Clarity ratings assigned to samples during each round of
age estimates indicated that the readability of banding patterns
within D. dipterura centra was variable and not explicit. The
majority of thin-sectioned centra received a clarity grade of 3
Anterior band count
04812162024
Posterior band count
0
4
8
12
16
20
24
Fig. 4. Pair-wise plot of age estimates from centra collected from anterior
and posterior locations (n =30). Female and male specimens combined. The
45
◦
diagonal line represents 1 : 1 agreement.
(84.4%, n =286), suggesting that two band counts could fre-
quently be interpreted from the samples. No centra were ranked
as unambiguous and exceptional in clarity (grade 1). A total
of 4.1% (n =14) was noted to be unambiguous with reduced
clarity (grade 2), 10.0% (n =34) possessed indefinite band-
ing patterns in one or more locations (grade 4), and 1.4%
(n =5) were discarded because of extremely poor clarity or
damage.
Age estimates of D. dipterura were complicated by diverse
patterns of band deposition observed within the vertebral cen-
tra. Agreement was not achieved among 10.4% (n =35) of the
remaining vertebrae aged in this study following four reads
because of vague or irregular banding patterns. Irregularpatterns
observed within this species included discontinuous, joined,
split, narrow, and crowded or clustered bands. Precision esti-
mates were 9.85% (IAPE) and 13.18% (CV). Overall percent
agreement (±0) was 8.9% from each of the four rounds of
age estimates (Table 1). The percent agreement that differed
based only on disparity of edge type classification (±0.05) was
27.6%, thus cumulative agreement ±0–0.05 years was 36.5%.
Agreement within a maximum of ±1 year was achieved for
73.0% of the centra examined. Agreement of band counts was
most variable among the 40.1–45.0 and 45.1–50-cm DW size
classes.
Edge and marginal increment analysis
Seasonal trends in the type and extent of band development were
detected using centrum edge analysis (Fig. 5). Edge analysis was
conducted on 205 thin-sectioned samples that were determined
to have unambiguous edge types. The proportion and class of
edge types varied among all months examined (February, March,
May, June, August, October, and December). Translucent cen-
trum edges were observed during the winter and spring months
(December–June).Narrow translucent edges (T1) wereobserved
only in December, February, and March. The proportion of cen-
tra with broad translucent edges (T2) decreased from May to
June. During August and October, all samples were determined
to have opaque edges. Broad opaque edges (O2) were the only
type detected during the month of October. Monthly centrum
edge characteristics suggest that a single band pair, comprised of
one translucent and one opaque band, is formed within vertebral
centra each year.
Variation of mean MIRs was also seasonal, closely follow-
ing the trends exhibited by centrum edge analysis (Fig. 5).
Mean MIRs were calculated from 139 D. dipterura centra col-
lected during four non-consecutive years. Lowest monthly mean
MIRs among pooled samples occurred in February, with a peak
in December. Kruskal–Wallis analysis of ranks indicated that
mean MIRs varied significantly among months (H =19.59,
df =6, P =0.003). The mean MIRs of October and Febru-
ary (q
0.05,7
=3.038, Q =3.377) and December and February
(q
0.05,7
=3.038, Q =3.408) were identified as the sources of
significant difference among months. Maximum and minimum
MIRs suggest that band formation is initiated during or shortly
after December (translucent) and May (opaque). Marginal incre-
ment analysis confirmed the annual deposition of a single band
pair within the vertebrae of D. dipterura.
Maturity, age and growth of Dasyatis dipterura Marine and Freshwater Research 59
Table 1. Percentage agreement (PA) between the consensus band-pair count and age estimate with the greatest assigned difference for each sample
in relation to 5cm disc width (DW) size classes
The sample size of each PA calculation is indicated within parentheses. PAs are presented for no difference among rounds (± 0) and ±0.5, 1, 2, 3 and 4 or
more estimated years. Overall and cumulative percentage agreements are summarised for each category
DW (cm) n PA ±0(n)PA±0.5 (n)PA±1(n)PA±2(n)PA±3(n)PA≥4(n)
25.1–30.0 4 0 100.0 (4) 0 0 0 0
30.1–35.0 18 16.7 (3) 50.0 (9) 33.3 (6) 0 0 0
35.1–40.0 40 15.0 (6) 32.5 (13) 42.5 (17) 7.5 (3) 2.5 (1) 0
40.1–45.0 40 5.0 (2) 17.5 (7) 35.0 (14) 37.5 (15) 0 2.5 (1)
45.1–50.0 51 3.9 (2) 1.9 (1) 39.2 (20) 23.5 (12) 4.0 (1) 5.9 (3)
50.1–55.0 54 16.7 (9) 38.9 (21) 20.4 (11) 16.7 (9) 7.7 (2) 5.6 (3)
55.1–60.0 25 8.0 (2) 28.0 (7) 52.0 (13) 4.0 (1) 0 8.0 (2)
60.1–65.0 25 4.0 (1) 28.0 (7) 48.0 (12) 12.0 (3) 4.0 (1) 4.0 (1)
65.1–70.0 26 7.7 (2) 27.0 (7) 38.5 (10) 15.4 (4) 7.7 (2) 3.8 (1)
70.1–75.0 13 0 38.5 (5) 46.2 (6) 15.4 (2) 0 0
75.1–80.0 6 0 16.7 (1) 33.3 (2) 16.7 (1) 33.3 (2) 0
80.1–85.0 2 0 100.0 (2) 0 0 0 0
n 304 27 84 111 50 21 11
PA 8.9 27.6 36.5 16.4 6.9 3.6
Cum. PA 8.9 36.5 73.0 89.5 96.4 100.0
Jan.
(12) (19)
T1 T2 O1 O2
(11) (18) (55) (9) (15)
Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.
Centrum edge type percent frequency
0
20
40
60
80
100
Mean MIR
0.0
0.2
0.4
0.6
0.8
1.0
1
1
10
4
9
3
12
13
37
42
14
9
13
24
13
n =
Fig. 5. Monthly variation in centrum edge type (n =205) and mean
monthlymarginalincrement ratios (MIR) ±1 standard error (n =139) deter-
mined from pooled sexes and size classes. Values within the histogram
represent the number of samples included in monthly centrum edge analy-
ses. Sample sizes incorporated into MIR analysis are listed in parentheses
below the x-axis. T1, narrow translucent edge; T2, broad translucent edge;
O1, narrow opaque edge; O2, broad opaque edge.
Growth models
In total, age estimates from 304 out of 344 D. dipterura verte-
bral samples were incorporated into DW-based growth models.
The largest female in the study measured 83-cm DW and was
estimated to be 25 years of age. A maximum age of 28 was esti-
mated for a 76-cm DW female. The largest (60-cm DW) male
produced a band count of 19 years. Both female and male sam-
ples included age 0 specimens. Growth characteristics differed
significantly between the sexes (ARSS, F =11.73, P<0.0001).
Female and male DW and weight-at-age data were therefore
analysed separately for all models.
Estimates of DW
∞
resulting from three-parameter VBGF
models were greater than those obtained from the two-parameter
form for both females and males (Table 2). The two-parameter
VBGF produced estimates of DW
∞
that were less than the max-
imum sizes of both sexes that were collected during this study.
Size at birth (DW
0
) estimates using the three-parameter VBGF
are notably greater than the estimates based on direct vertebral
measurements (mean =21.3-cm DW).
Female D. dipterura grow at slower rates and mature at later
ages than males. This sexually dimorphic growth pattern was
revealed by both two and three-parameter forms of the VBGF
and was further supported by ARSS (Table 2). However, growth
rates of juvenile females and males were similar. Estimates of
median age at maturity based on the three-parameter VBGF and
DW
50
corresponded to ages of 8–11 years among females and
5–8 years among males.
Growth parameters estimated using DW-based Gompertz
models fell between those predicted by two and three-parameter
VBGFs (Table 2). Predictions of DW
∞
were similar to, but
slightly greater than the maximum sizes observed in this study.
However, DW
0
estimates are greater than those previously cal-
culated usingVBGFs and nearly 10 cm greater than the probable
mean DW at birth. The magnitude of differences in growth
coefficients (k/g) between the sexes was equivalent between
Gompertz and VBGF three-parameter models. Weight-based
Gompertz models predicted smaller weight-at-age estimates for
females and males than weregenerated from theVBGF (Table2).
The VBGF predicted greater W
∞
values and W
0
estimates more
similar to weights obtained from the smallest free-living spec-
imens than were generated using the Gompertz model. Both
weight-based growth models predicted male W
∞
values that
were less than the maximum observed (60-cm DW, 11.4 kg) in
this study.
Measures of model performance applied in this study, AIC
differences and SEE, provided similar levels of support to the
60 Marine and Freshwater Research W. D. Smith et al.
Table 2. Growth parameter estimates, standard error (s.e.), and overall measures of fit from disc width and weight-based models of female and
male Dasyatis dipterura age data
VBGF, von Bertalanffy growth function;AIC, Akaike’s information criterion; s.e.e., standard error of the model estimates; n, sample size. Size at birth (DW
0
)
was anchored at 21.3-cm DW for both females and males in the two-parameter VBGF models. AIC values are based on absolute differences between models
(
i
), where a value of 0 indicates the ‘best’ model
Growth model Parameter Female Male
Estimate s.e. AIC (
i
) s.e.e. n Estimate s.e. AIC (
i
) s.e.e. n
2-Parameter VBGF DW
∞
(cm) 74.49 1.41 35.74 4.70 169 52.58 0.75 25.67 3.77 135
(DW based) k (year
−1
) 0.12 0.01 – – – 0.30 0.02 – – –
3-Parameter VBGF DW
∞
(cm) 92.40 5.02 0 3.65 169 62.18 3.27 0 2.99 135
(DW based) DW
0
(cm) 31.40 – – – – 31.30 – – – –
k (year
−1
) 0.05 0.01 – – – 0.10 0.02 – – –
t
0
(year) −7.61 0.79 – – – −6.80 1.10 – – –
Gompertz DW
∞
(cm) 84.63 2.95 1.48 3.68 169 60.28 2.54 0.50 3.00 135
(DW based) DW
0
(cm) 32.33 – – – – 31.73 – – – –
g (year
−1
) 0.09 0.01 – – – 0.14 0.02 – – –
t
0
(year) 0.96 0.03 – – – 0.64 0.03 – – –
Polynomial y
0
32.23 0.74 1.15 3.67 169 32.18 0.74 1.05 3.01 135
(DW based) a 2.92 0.14 – – – 2.57 0.20 – – –
b −0.05 0.01 – – – −0.07 0.01 – – –
3-Parameter VBGF W
∞
(kg) 35.28 4.78 0.53 1.85 128 10.80 1.21 0.31 1.03 77
(weight based) W
0
(kg) 0.77 – – – – 0.78 – – – –
k (year
−1
) 0.07 0.01 – – – 0.15 0.03 – – –
t
0
(year) −6.67 1.14 – – – −4.15 1.02 – – –
Gompertz W
∞
(kg) 30.05 3.01 1.41 1.87 128 10.27 0.96 0 1.03 77
(weight based) W
0
(kg) 1.81 – – – – 1.22 – – – –
g (year
−1
) 0.10 0.01 – – – 0.19 0.03 – – –
t
0
2.81 0.11 – – – 2.13 0.16 – – –
Polynomial y
0
0.77 0.42 0 1.84 128 0.78 0.31 0.50 1.04 77
(weight based) a 0.97 0.09 – – – 0.89 0.09 – – –
b −0.001 0.004 – – – −0.02 0.01 – – –
Age (years)
105015202530
Disc width (cm)
20
30
40
50
60
70
80
90
Female (n 169)
Male (n 128)
Fig. 6. Three-parameter von Bertalanffy growth function fits to female
and male Dasyatis dipterura disc width-at-age estimates.
candidate models (Table2).Two-parameterVBGF models which
incorporated the estimated size at birth were not determined to
be appropriate descriptors of DW-at-age data for D. dipterura.
The traditional three-parameter VBGF produced the best sta-
tistical fit to DW-at-age data for females and males (Fig. 6).
The polynomial and Gompertz functions provided the best fit
Table 3. Longevity (ω) estimates (years) for Dasyatis dipterura based
on maximum observed ages and three theoretical methods
Method Female Male
ωω
Maximum estimated 28 19
Ricker (95% DW
∞
) 63.5 33.6
Fabens (99% DW
∞
) 88.9 47.1
Taylor (95% DW
∞
) 47.3 22.3
to female and male weight-at-age estimates, respectively. How-
ever, all three-parameter growth functions applied in this study
represent the observed size-at-age data well.
Longevity
A wide range of ω estimates was calculated from three-parameter
VBGF values determined for females and males (Table 3).
All theoretical ω estimates produced values that are consider-
ably greater than the maximum observed ages. Taylor’s (1958)
method of estimation generated the lowest maximum age esti-
mates. Potential maximum ages approaching 90 years are pre-
dicted when ω is considered to represent 99% of DW
∞
. All
estimates indicated that females attain greater ages than males.
Maturity, age and growth of Dasyatis dipterura Marine and Freshwater Research 61
Discussion
Size at maturity and fecundity
Aspects of the reproductive biology of D. dipterura from the
Bahía Magdalena lagoon complex were previously examined
by several researchers. Mathews and Druck-González (1975)
reported the onset of male maturity to occur at ∼47–48-cm
DW and that the majority were mature by 51-cm DW based
on clasper length–DW relationships. These estimates of male
maturity correspond well with those observed during this inves-
tigation. Based on an examination of 31 female specimens,
Villavicencio Garayzar (1995) noted that D. dipterura ≥65-cm
DW contained oocytes of ∼1–2 cm diameter. Other indicators
of reproductive condition were not assessed. We found females
of 57-cm DW to often be mature and those at and above this size
frequently possessed oocytes greater than 1 cm diameter.
Female D. dipterura mature later and grow to larger sizes
than males. Such variation between the sexes is common among
dasyatid stingrays. Female size at maturity is reported as 10 cm
greater for D. imbricatus (Devadoss, 1978), 30 cm greater than
that of males for D. longa (Villavicencio Garayzar et al. 1994),
and 13 cm greater for D. sayi (Snelson et al. 1989).
Fecundity is typically low and notoriously difficult to esti-
mate among myliobatiform rays. Because of stress from capture
and elevation of the specimen from the water, embryos are com-
monly aborted (Struhsaker 1969; Snelson et al. 1988). Gravid
D. dipterura were not an exception to this tendency. When
present, embryos were often expelled upon removal from gill-
nets. Observed fecundity of D. dipterura closely approximates
that of the smaller bodied stingray, D. sabina, and its larger
eastern Pacific congener D. longa, which are estimated to pro-
duce 1–4 offspring annually (Snelson et al. 1988; Villavicencio
Garayzar et al. 1994). However, considering the difficulty in
accurately determining litter size, it is possible that maximum
fecundity of D. dipterura is slightly underestimated.
Age estimation
The inherent variability of band deposition within an ageing
structure and subjectivity associated with interpreting banding
patterns influence the accuracy and precision of age estima-
tion and resulting growth models. The clarity and readability
of banding patterns within the vertebral centra of D. dipterura
were complicated by irregular or discontinuous bands. Structural
discontinuities and low clarity of samples constrained repeata-
bility of estimates and contributed to an overall IAPE of 9.85%.
However, this value is artificially inflated in comparison to other
studies because counts of band pairs in this study were estimated
to the nearest 0.5 years and thus incorporated a greater potential
for error. When precision estimates based on the number of com-
pleted bands (whole values) are considered in this study, overall
IAPE decreases to 8.4%. Similar levels of precision have been
reported for age estimates derived from thin-sectioned vertebrae
among relatively long-lived elasmobranchs including; sandbar
(Carcharhinus plumbeus; Sminkey and Musick 1995) and bull
sharks (Galeocerdo cuvier; Wintner and Dudley 2000).
Vertebrae that had been stored in alcohol for extended peri-
ods were frequently cloudy in appearance and generally more
difficult to read. Of the 92 samples used in this study that had
been collected and stored in alcohol since 1992, 24% of the sam-
ples were discarded as a result of inconsistent reads. In contrast,
only 5% of the samples collected between 1998 and 2000 were
discarded because of a lack of agreement. These latter samples
were stored in alcohol for no longer than six months before being
cleaned and stored dry in vials. Wintner and Cliff (1996) and
Wintner et al. (2002) also noted a reduction in contrast between
growth bands among vertebrae that had been stored in alcohol.
Because long-term storage of elasmobranch vertebrae in alcohol
may severely reduce sample clarity and precision of age esti-
mates, we suggest that ageing structures should be stored frozen
or dry whenever possible.
Edge and marginal increment analysis
Significant differences among pooled monthly mean MIRs indi-
cate that a single band pair is formed annually within the
vertebrae of D. dipterura.This evidence for seasonal band depo-
sition validates the assumption that one band pair is equivalent
to a year for growth models of this species. The pattern of band
deposition observed for D. dipterura agrees with the findings
of Cowley (1997), who concluded that one distinct opaque and
translucent band was formed annually in captive D. chrysonota.
Although commonly employed as a semi-direct validation
method, marginal increment analysis has often been applied
inappropriately and may be of low resolution (Campana 2001).
Validation should ideally be applied to all ages and marginal
increment analyses should be restricted to a single age or size
class at a time (Beamish and McFarlane 1983; Cailliet et al.
2006). Variability of seasonal band deposition patterns may be
obscured by pooling age classes.An observed periodicity of band
deposition that is assumed as valid may not reflect the growth
patterns among all age classes as a result of differences in rel-
ative growth rates, particularly among older classes. Although
low number of samples available from each month restricted the
assessment of age or size-specific marginal increment analyses
in this study, a subsequent assessment of general size classes
supported the trends observed from pooled data alone (Smith
2005). The application of Dunn’s (1964) test on ranks provided
a constructive quantitative assessment of the timing and varia-
tion of band formation that had not previously been applied to
marginal increment data.
The modified technique of centrum edge analysispresented in
this study (see alsoTanaka et al. 1978) provided valuable, corrob-
orative evidence of annual band-pair formation in D. dipterura.
Edge analyses among elasmobranch ageing studies have pri-
marily identified only the type of band forming on the outer
edge of the ageing structure on the basis of optical qualities
(i.e. opaque or translucent bands) (e.g. Yudin and Cailliet 1990;
Wintner et al. 2002). Consideration of the relative width of both
opaque and translucent bands in relation to time of capture may
provide details that would otherwise be undetected through MIR
analysis alone. For example, although the December MIR is the
greatest mean value calculated in the study, it is also associated
with the largest standard error (Fig. 6). Centrum edge analy-
sis from December indicates that both opaque and translucent
margins were present on the edges of vertebrae collected from
this month that the translucent bands were of the narrowest type
(T1) and had not been observed within the sampled population
62 Marine and Freshwater Research W. D. Smith et al.
for several months. Thus, it may be inferred that the standard
error associated with the mean MIR from December (or May)
does not simply result from broad variation in marginal widths
present in the population, but that a shift in the depositional
pattern of band formation may be occurring at this time.
Growth models
Frequently, only a single model is considered in studies of
age and growth although alternative functions may provide
better descriptions of these characteristics (e.g. Moreau 1987;
Cailliet et al. 2006). AIC and SEE results indicated similar lev-
els of support to the growth models considered in this study.
The three-parameter VBGFs based on DW-at-age data produced
the most biologically realistic, best statistical descriptions, and
most practical growth parameters for D. dipterura. Estimates of
DW
∞
from this model were greater than the maximum sizes
included this study, but fell within the range of the maximum
size reported for the species. Evidence of the VBGF’s limited
ability to reflect early growth (Gamito 1998) was observed in
this study, producing DW
0
estimates that were notably greater
than those observed in the field or estimated from vertebral birth
marks. Age 0 D. dipterura were rarely encountered within arti-
sanal fishery landings and the limited number of small specimens
likely contributed to the elevated estimates of DW
0
. However,
the VBGF that incorporated a fixed size at birth (21.3-cm DW)
produced unreasonable fits to the DW-at-age data.
Alternatives to three-parameter VBGFs have been demon-
strated to produce more suitable models of growth in several
studies of elasmobranchs. Gompertz growth functions were
found to provide the best explanations of growth for cownose
rays (Rhinoptera bonasus, Neer and Thompson 2005) and cap-
tive pelagic stingrays (Pteroplatytrygon (Dasyatis) violacea,
Mollet et al. 2002). Carlson and Baremore (2005) developed and
evaluated several growth models for spinner sharks, Carcharhi-
nus brevipinna, and concluded that a logistic form provided
the best overall fit. Polynomial function fits had not previously
been applied in studies of elasmobranch age and growth, but
were generally appropriate and similar in fit to the asymp-
totic three-parameter Gompertz and VBGF models. Despite
preferable mathematical properties associated with polynomial
functions (Knight 1968; Roff 1980), the resulting parameters
cannot be directly evaluated biologically, limiting their broader
application.
The comparatively lower number of data points and lack of
weight information for specimens in excess of 25 kg because of
equipment limitations reduced the explanatory value of weight-
based models in this study. However, the volumetric measure
encompassed by bodyweight data may incorporate greater detail
and thus provide enhanced resolution of growth characteristics.
This potential may prove to be particularly beneficial for growth
descriptions of dorso-ventrally flattened batoids in particular
and warrants more frequent consideration. It should be noted
that DW and weight-based models cannot be directly compared
or evaluated using AIC or SEE alone since these models are
based on different parameters and scales. In addition to the con-
sideration of available biological information, an examination of
standardized residuals would provide a direct method of compar-
ing and selecting growth models that incorporate these differing
estimators of size-at-age (e.g. Glantz and Slinker 2001).
Longevity
The maximum age directly estimated from a population may
not provide an adequate measure of species longevity (Beukema
1989). However, theoretical estimates of longevity derived from
k in this study generated strikingly divergent values of the age at
which 95% of DW
∞
is attained in D. dipterura. The estimates
following Ricker (1979) and Fabens (1965) produced longevities
that are more than double the maximum age observed from verte-
bral counts. Longevities of more than 60 years seem improbable
for D. dipterura and the estimate of 47 years following Taylor
(1958) may provide the most reasonable theoretical prediction
of longevity in this study.
Comparison with other studies
Although elasmobranchs are generally considered to possess
slow growth rates, estimates of growth coefficients (k) encom-
pass a broad range of values (Musick 1999; Cailliet and Goldman
2004). Branstetter (1990) delineated growth rates among sharks
as slow if k is determined to be <0.1 year
−1
and relatively fast
if k>0.1 year
−1
. On this basis, D. dipterura can be consid-
ered as a slow growing elasmobranch. Growth rates of females
and males are similar initially but diverge significantly as matu-
rity is approached. Differential growth rates, maximum sizes,
and longevities are commonly observed among female and male
myliobatiform stingrays (Smith and Merriner 1987; White et al.
2002).
Growth rates estimated for female D. dipterura using the
three-parameter VBGF are the lowest reported for any myliobat-
iform stingray (Table 4). The growth parameters derived from
this study are most comparable to those of the similarly sized
stingray, D. chrysonata (Cowley 1997). Annual growth rates
among the smaller bodied urolophid stingrays are more than
double those of D. dipterura. The bat ray, Myliobatis californica,
also attains similar maximum ages and greater maximum disc
widths but grows at a faster rate (Martin and Cailliet 1988b).The
maximum ages estimated for D. dipterura represent the greatest
longevities observed within the order.
The growth coefficients estimated for D. dipterura approxi-
mate those obtained for several other elasmobranchs. Oviparous
batoids including Dipturus batis (k =0.057; DuBuit 1972),
D. pullopunctata (k =0.05; Walmsley-Hart et al. 1999), and
Leucoraja ocellata (k =0.059; Sulikowski et al. 2003) exhibit
annual rate constants that are comparable to D. dipterura.
However, growth rates of most skates studied to date are
in excess of 0.10 year
−1
(Cailliet and Goldman 2004). Sev-
eral large, long-lived sharks including Carcharhinus plumbeus
(k =0.059; Sminkey and Musick 1995) and Carcharodon car-
charias (k =0.059; Cailliet et al. 1985) also display growth rates
that are relatively similar to the diamond stingray.
Comparisons and interpretations of growth coefficients
between species are restricted by sample sizes, size ranges
incorporated into the study, ageing methodology, validation of
band periodicity, and model fitting techniques (Cailliet and
Goldman 2004). With this in mind, k may still provide a practical,
albeit generalized, characterisation of fundamental life history
traits that may be linked to fecundity, longevity, and size or age
at maturity (Adams 1980; Stearns 1992). The growth charac-
teristics determined in this study indicate that D. dipterura is
Maturity, age and growth of Dasyatis dipterura Marine and Freshwater Research 63
Table 4. Comparison of ageing methods, maturity, age and select growth parameters (k, DW
∞
) among myliobatiform stingrays
All growth data are based on fits of three-parameter von Bertalanffy growth functions. DW
50
, median disc width at maturity; 1st Mat., earliest observed size at maturity; SS, sagital thin-section; NA, not
applicable; NR, not reported; W, whole vertebrae; S, stained; VS, vertical half-section; O, oil-cleared; X, x-radiography
Species Location of study Sex Method n Maximum age k DW
∞
DW
50
1st Mat. Source
(years) (year
−1
) (cm) (cm) (cm)
Dasyatis chrysonota SE South Africa Female SS 165 14 0.070 91.3 NR 50.0 Cowley (1997)
Male SS 105 9 0.175 53.2 NR 40.0
Dasyatis dipterura W Central Mexico Female SS 169 28 0.055 92.4 57.0 57.0 This study
Male SS 135 19 0.103 62.2 46.8 47.0
Myliobatis californica SW USA Female VS, O 104 23 0.100 158.7 88.1 NR Martin and Cailliet (1988b)
Male VS, X 60 6 0.229 100.4 NR NR
Rhinoptera bonasus E USA Female SS 54 10 0.119 125.0 NR 87.0 Smith and Merriner (1987)
Male SS 61 8 0.126 119.2 NR 80.0
Rhinoptera bonasus SE USA Female SS 121 18 0.075 123.8 65.3 62.3 Neer and Thompson (2005)
Male SS 106 16 0.133 110.2 64.2 63.5
Trygonoptera mucosa SW Australia Female SS 324 >17
a
0.241 30.8 25.3 22.0
b
White et al. (2002)
Male SS 400 >17
a
0.493 26.1 22.2 19.0
b
Trygonoptera personata SW Australia Female SS 352 >15
a
0.143 30.3 22.8 19.0
b
White et al. (2002)
Male SS 303 >9
a
0.203 26.9 22.1 19.0
b
Urolophus lobatus SW Australia Female SS 388 15 0.369 24.9 20.1 NR White et al. (2001)
Male SS 448 13 0.514 21.1 16.3 NR
Urolophus paucimaculatus SE Australia Female SS 113 10 0.21 57.3 NR NR Edwards (1980)
Male SS 99 8 0.45 42.8 NR NR
a
Maximum ages not reported; estimates were inferred from figures and do not exceed 20 years.
b
Estimates of first maturity were based on pooled size classes, 19.0–19.9 cm and 22.0–22.9 cm disc width.
64 Marine and Freshwater Research W. D. Smith et al.
a relatively long-lived, slow growing species. Musick (1999)
reviewed life history characteristics of long-lived marine species
and concluded that those with k coefficients equal to or less
than 0.10 year
−1
are extremely vulnerable to overexploitation.
Because of the conservative growth and reproductive charac-
teristics demonstrated by D. dipterura, it is evident that careful
monitoring and precautionary management strategies should be
employed where this species is targeted or incidentally landed.
Acknowledgements
This study was made possible, in part, by funding provided from the Califor-
nia Sea Grant College System (R/F-29PD), Homeland Foundation, Earl H.
and Ethel M. Myers Oceanographic and Marine Biological Trust, National
Marine Fisheries Service via the National Shark Research Consortium and
Pacific Shark Research Center, PADI Foundation, PADI Project AWARE,
San Francisco State University Student Project Fund, and the Packard Foun-
dation Scholarship. Research was conducted in accordance with and under
the approval of the San Francisco State University Committee for the Pro-
tection of Human and Animal Subjects Protocol #01–038. We thank Joseph
Bizzarro, Ann Beesley, Carolina Downton Hoffmann, Felipe Galván Mag-
aña, Carlos Villavicencio Garayzar, and Moss Landing Marine Laboratories’
small boat operations for assistance and support in the field. Mindy Hall pro-
vided valuablelaboratory assistance. We are gratefulto fishermenthroughout
the Bahía Magdalena lagoon complex for their cooperation in this project,
particularly those of Puerto Viejo who offered patience and unrestricted
access to their landings. We also thank two anonymous reviewers and the
editor for their valuable comments.
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Manuscript received 17 May 2006, accepted 13 October 2006
