Environmental Engineering Reference
In-Depth Information
initial size Leporati et al., (2007), which in turn is highly variable both within and between
broods. High coefficients of variation (>20%) in initial weight have been observed in several
octopod species (
Octopus bimaculoides
, Forsythe & Van Heukelem, (1987);
Octopus diguetti
,
DeRusha
et al
.
, (1989);
Octopus ocellatus
, Segawa & Nomoto, (2002). Intra-brood variation,
however, could not be related to either the mother´s weight or day of hatching Briceño-
Jacques et al
.
, (2010). Results suggest that growth rate does not depend on initial size in
O.
maya
Briceño et al., (2010), but small differences in size during early life can be amplified
and accumulated in time Vigliola & Meekan, (2009). This means that inter-individual
variation in initial size has to be considered in experimental designs and data analyses
aimed at understanding cephalopod growth.
Octopus maya
is endemic to the Yucatan Peninsula Voss & Solis Ramirez, (1966), and its
culture has received considerable attention Martinez
et al
.
, (2011); Uriarte
et al
.
, (2011). This
species provides an interesting biological model to test hypotheses on heterogeneity in
growth amongst cultured siblings, and serves to illustrate problems that arise in growth
analysis and possible solutions to them.
Juveniles of
O. maya
from a single female were used. The eggs were held at 28°C (± 1°C) in
an artificial incubator (without maternal care) until hatching. The weight of a total of 84
juveniles, that hatched over the course of 8 d, was recorded 24 h after hatching (W
1
± 0.01g),
and then again on days 15, 45, 75 and 105. Octopuses were housed individually in 300 ml
containers connected to a recirculation system in which water temperature was kept
constant at 27 ± 1
o
C. Octopuses were fed live adult brine shrimp (
Artemia salina
) and pieces
of blue crab (
Callinectes sapidus
) meat
ad libitum
. Overall mortality (at day 105) was 60.7%.
To obtain a curve of weight gain as a function of time, a linear model was adjusted to the
relationship between the natural logarithm of W
1
, W
15
, W
45
, W
75
, and W
105
weights of all
individuals and their corresponding ages:
Y
ij
= α + β
1
X
i
+ e
ij
Previous regression analysis, graphic representations of the data were explored to (i)
identify extreme points (point graphs); (ii) assess normality (histograms and percentile
graphs); and (iii) verify linear relationships
X-Y
graphs; Zuur et al
.
, (2007). The regression
was fitted with a generalized least square (GLS) procedure through restricted maximum
likelihood (REML) and incorporated correlation and variance structures, using GLMM to
ensure that homocedasticity and independence requisites were met (Fig. 9). Models
featuring optimal correlation and variance structures were selected by considering values of
the Akaike information criterion (AIC) and hypothesis tests based on
F
and likelihood ratio
(L ratio) values. Once the significance of regression parameters were established through
F
,
L ratio and
t
-tests, the model was validated by visual inspection of residuals Montgomery &
Peck, (1992). We used the parameter
δ
as an estimator of the tendency of weight variances to
increase with age.
Regression parameters differed significantly from 0 (Table 5). Interdependence of data over
time (because we weighed animals repeatedly) resulted in a cyclic residual pattern, so we
incorporated an autocorrelation structure (spherical spatial structure) in the random-effects
term of the model (ε
i
). Following Pinheiro & Bates, (2000), we kept this structure in the
model, because (i) AIC values indicated that using it improved the model (AIC = 319.45),
Search WWH ::
Custom Search