M .R. Cunha et al. J. Exp. Mar. Biol. Ecol. 248 2000 207 –223
209
population densities Queiroga, 1990, is located at the upper reaches of Canal de Mira,
2
Ria de Aveiro NW Portugal. Ten corer replicates sampled area510 3 0.01 m were collected at low water of new moon spring tides and the samples were preserved in
formalin. In the study area, the average depth at low water is always lower than 0.5 m and the tidal range varies between 0.2 and 1.0 m at neap and spring tides, respectively.
Stratification of the water column was never observed. Water temperature and salinity were recorded at low and high water early morning and beginning of the afternoon,
respectively near the bottom using a SCT meter YSI model 33. Further details on the sampling methodologies, the seasonal variation of environmental factors and the
macrobenthic community in the studied site are given by Cunha and Moreira 1995.
Incubating females of C . multisetosum were later separated from the remaining fauna
and the developmental stage of the embryos was assessed Cunha et al., 2000a. The size of the females, expressed as head length, was measured to the nearest 1 60 mm in three
replicates and the number of embryos per brood was counted only in those females with an undamaged marsupium. In order to minimise the error resulting from intramarsupial
loss only females carrying embryos in an early developmental stage F females with
1
rounded embryos were considered for the statistical analysis. Further details on the abundance, biomass, production, life history and reproductive biology of C
. mul- tisetosum in the site studied are given by Cunha et al. 2000a,b.
2.2. Statistical analysis The significance of the head length L , temperature T and salinity S as sources of
h
variation in the brood size N of C . multisetosum was first assessed by a simple
e
factorial ANOVA SPSS package. The relation between brood size and each factor was analysed separately and then the coefficients of the general equation were estimated
using a non-linear regression model SPSS package.
3. Results
3.1. Data In Ria de Aveiro, C
. multisetosum breeds throughout the year but in May, July and August only a few incubating females were present in the population Table 1. An
intense recruitment peak occurred during the autumn and a smaller peak in spring Cunha et al., 2000a. The analyses hereafter are based on a sample of 217 F females
1
with undamaged marsupium Table 1. The diameter of the recently laid eggs varied from 0.30 to 0.35 mm regardless of the female size. Brood size varied from nine to 72
global average 29.9 and the head length of incubating females ranged from 0.500 to 1.017 mm. The temporal variation in the average brood size and average head length of
incubating C
. multisetosum females showed disagreeing trends especially in the period from September to November Fig. 1.
The relationship between brood size N and head length L obtained by a
e h
least-squares linear regression GR using the global data set was:
2
N 5 2 21.868 1 64.599L R 5 0.183; n 5 217
GR
e h
210 M
.R. Cunha et al. J. Exp. Mar. Biol. Ecol. 248 2000 207 –223 Table 1
a
˜ Water temperature 8C and salinity psu data over the sampling period in Areao
Date Temperature
Salinity F
F n
inc 1
LW HW
LW HW
16 May 1988 19.0
18.0 0.2
0.5 1
0.0 14 June
20.9 21.2
0.5 3.0
85 96.5
3 12 July
22.0 24.1
0.5 1.0
1 100.0
1 10 Aug
23.5 25.3
0.2 1.8
7 28.6
2 13 Sept
22.5 23.7
1.0 6.5
379 70.4
57 10 Oct
18.0 18.0
1.0 6.5
789 96.5
75 07 Nov
17.5 18.0
0.3 2.0
769 24.3
9 07 Dec
12.0 12.5
0.8 2.0
1726 40.6
13 05 Jan 1989
11.0 12.4
2.2 3.0
456 74.1
26 06 Feb
11.5 12.5
0.7 3.0
650 57.1
25 08 Mar
16.2 17.0
0.7 2.6
643 40.9
2 05 Apr
15.0 14.5
0.5 1.2
206 36.4
4
a
The number of incubating females F , the percentage of females carrying embryos in a early
inc
developmental stage F , and the number n of F females examined for statistical analysis are also indicated
1 1
for each month. LW, low water; HW, high water.
The water temperatures and salinities used in the mathematical analysis were the mean of the low and high water values at each sampling occasion Table 1. The mean
temperature and mean salinity varied from 11.7 to 24.48C and from 0.35 to 3.75, respectively. The head length average for each month did not show a significant
correlation with these environmental factors.
3.1. Factorial ANOVA For the analysis of variance the variables were grouped as follows: three temperature
ranges T –T , in 8C: 10–15, 15–20, 20–25; three salinity ranges S –S : 0.0–1.0,
1 3
1 3
Fig. 1. Trends in brood size and head length average values 6S.E. of incubating females of Corophium multisetosum over the study period.
M .R. Cunha et al. J. Exp. Mar. Biol. Ecol. 248 2000 207 –223
211
1.0–2.5, 2.5–4.0; seven head length classes represented by the marks L –L , in mm:
h1 h7
0.500; 0.583; 0.667; 0.750; 0.833; 0.917; 1.000. The first salinity group 0.0–1.0 and four L groups 0.500; 0.583; 0.667; 1.000
h
were excluded due to insufficient number of replicates. Thus, the analysis was accomplished using 173 females of the original set. The data entered into the factorial
ANOVA are displayed in Fig. 2. The homogeneity of variances was assessed by the Levene test P 50.059, ns. The
results of the factorial ANOVA showed the significance of the three factors Table 2. The interaction between temperature and salinity was also significant indicating that
these two factors may act synergistically. Fig. 2 shows that the largest broods occurred in the 15–208C group at both salinity
ranges as well as in the higher salinity group 2.5–4.0 for all temperature ranges. The effect of salinity appears to be less important in the low temperature range. The means
for the salinity S vs. S , temperature T vs. T ; T vs. T ; T vs. T and head length
2 3
1 2
1 3
2 3
groups L vs. L ; L
vs. L ; L vs. L were compared using a t-test H :
m 5m
h4 h5
h4 h6
h5 h6
1 2
that showed significant differences P ,0.001 for all cases. 3.2. Empirical model
The aim of the model is to obtain a simple line N 5 a 1 bL in which the slope b
e h
and the y intercept a are a function of salinity and or temperature. The relationship between temperature and brood size was expressed using a quadratic
model that simulates the observed effect: larger brood size for intermediate temperatures
Fig. 2. Brood size of Corophium multisetosum: average values 1S.E. of subgroups for different ranges of salinity psu, temperature 8C and head length class 4: 0.750; 5: 0.833; 6: 0.917 mm.
212 M
.R. Cunha et al. J. Exp. Mar. Biol. Ecol. 248 2000 207 –223 Table 2
a
Factorial ANOVA for the brood size of Corophium multisetosum Source of variation
SS df
MS F
Significance Main effects
17 893.63 5
3578.73 45.708
,0.001 L
7185.09 2
3592.55 45.88
,0.001
h
T 8188.10
2 4094.05
52.29 ,0.001
S 2520.44
1 2520.44
32.19 ,0.001
2-Way interactions 2276.06
8 284.51
3.63 0.001
ns
L 3T 617.66
4 154.42
1.97 0.101
h ns
L 3S 123.71
2 61.85
0.79 0.456
h
T 3S 978.68
2 489.34
6.25 0.002
ns
3-Way interactions 370.71
4 92.68
1.18 0.320
ns
L 3T 3S 370.71
4 92.68
1.18 0.320
h
Explained 20 540.40
17 1208.26
15.43 ,0.001
Residual 12 135.80
155 78.30
Total 32 676.20
172 189.98
a
The factors are the head length L , in mm, three groups, temperature T, in 8C, three groups and salinity
h
S, in psu, two groups. ns, non significant values.
and smaller brood size for higher or lower values. For simplicity, a first order equation was used to express the relation between brood size and salinity, though the results
suggest that salinities below 0.5 may inhibit breeding and an S-curve provides a better adjustment to the observed data, especially at low salinities.
From the several models fitted to the data the following were selected: 1. The slope is a function of temperature and salinity; the y intercept is a constant:
2
N 5 a 1 b 1 b S 1 b T 1 b T L M
e 1
2 3
h 1
2. The slope is a function of temperature and salinity; the y intercept is a function of salinity:
2
N 5 a 1 a S 1 b 1 b S 1 b T 1 b T L M
e 1
1 2
3 h
2
3. Both the slope and the y intercept are functions of temperature and salinity:
2 2
N 5 a 1 a S 1 a T 1 a T 1 b 1 b S 1 b T 1 b T L M
e 1
2 3
1 2
3 h
3
The coefficients of the three equations are presented in Table 3. The simplest model M explains 63.4 of the observed variation in the brood size of Corophium
1 2
multisetosum. The value of R is slightly higher for the other two models, but it seems that the inclusion of temperature for the estimation of the y intercept M is not very
3
informative; it does not improve the quantity of explained variation and complicates the equation.
Fig. 3 illustrates the variation of the brood size in relation to the head length and temperature at three different salinity values according to model 2. The model predicts
an optimal temperature around 188C and very low fecundity at low salinity values.
M .R. Cunha et al. J. Exp. Mar. Biol. Ecol. 248 2000 207 –223
213 Table 3
Coefficients for the non-linear regression of Eqs. M , M , and M
1 2
3
Coefficients Model 1
Model 2 Model 3
a 229.512
22.940 221.224
a –
28.027 29.348
1
a –
– 2.316
2
a –
– 20.057
3
b 252.073
289.431 267.130
b 8.253
18.171 19.776
1
b 12.370
12.904 10.088
2
b 20.353
20.368 20.300
3 2
R 0.634
0.637 0.637
According to the model, for a salinity value of 0.5 breeding is improbable N ,10
e
outside the optimal temperature range 15–208C. Model 2 will be used to compare the predicted and observed brood size.
3.3. Comparisons between predicted and observed brood size The difference between the predicted and observed brood size, expressed as
percentage of the observed value, was less than 20 in 119 cases and less than 50 in 191 cases from a total of 217. Fig. 4 shows the scatterplot of the observed brood size
against predicted values. The highest deviations observed N 2Predicted N never
e e
exceeded the value of 25 e.g. for the observed N of 67, 59, 72 and 72 in October and
e
46 in March, the corresponding predicted values were 42.4, 35.8, 49.5, 51.4 and 24.4. The observed values N vs. L were plotted separately for each month and a
e h
regression line least squares was estimated for each data subset. The graphical comparison of the lines obtained by the Eqs. M and GR illustrates the better fit of
2
M to the data Fig. 5 especially when low fecundity occurred e.g. December, January
2
Fig. 3. Predicted brood size by the model M according to head length and temperature at three different
2
salinity values S, psu.
214 M
.R. Cunha et al. J. Exp. Mar. Biol. Ecol. 248 2000 207 –223
Fig. 4. Observed and predicted brood size by Eq. M of Corophium multisetosum n 5217.
2
and February. Fig. 6 shows the variation in fecundity throughout the 1-year period as described by model 2 M for the mean values of temperature and salinity recorded
2
each month. Predicted fecundity was moderately high in June then decreased to a minimum in August, when low salinity was coupled with high temperature It rose
sharply in September, reached a maximum in October T 518; S 53.8, then decreased again until December and maintained moderate values thereafter. This pattern corre-
sponds to the observed variation. However, an obvious inconsistency occurred in May: the predicted fecundity varied between 9 and 25 0.5,L ,1.0 mm, but only one
h
incubating female with damaged marsupium was actually collected.
4. Discussion
