Page 3 - DiMaidaetal2013

98 G. Di Maida et al. / Marine Environmental Research 87-88 (2013) 96e102

Fig. 2. Histograms of frequency of shoots age on the three different substrata. The included at fixed factors and location treated as a random
vertical line represents the general mean of shoots age. component orthogonal to substratum. Moreover, if the age of
shoots sampled was different among substrata, it was included as
analyses were made only on meadows sampled in July, to avoid any fixed factor in the models in order to control its confounding. An
confounding effect due to seasonality (Fernández-Torquemada example of the use of the mixed models in the analysis of shoot age
et al., 2008). In particular lengths and width of all leaves in each confounding is provided by Tomasello et al. (2007). For the analysis
shoot were measured. In this way the shoot surface was then of the leaf biometry only three locations (Mondello, Solanto and
calculated. Moreover, the number of leaves without their apex were Trappeto) were considered, while a further location (Favignana)
noted and their percentage was then obtained (coefficient A; was added for the lepidochronological analysis.
Giraud, 1977).
Rhizome elongation, leaf length and shoot surface were modeled
2.2. Statistical analysis through a Linear Mixed Model assuming a normal distribution of
the response variables, as suggested by ShapiroeWilk test out-
Possible differences in growth performance, leaf biometry and comes. On the other hand, leaf production and shoot density
shoot density, among different substrata were tested using GLMMs showed non-normal distributions (ShapiroeWilk Test), thus the
and LMMs (Generalized and Linear Mixed Models). Generalized Linear Mixed Model was applied (Diggle, 1988;
Fahrmeier and Tutz, 1994). The application of GLMM does not need
Shoots were sampled within larger units represented by the any transformation of variables non-Normally distributed, thus
locations. Plants belonging to the same location may thus be maintaining them in the natural scale, which represents an ideal
correlated. Mixed Models allow remarkable statistical gains of condition in order to make easier the interpretation of results
precision in estimation and power in testing taking into account the (Bolker et al., 2009; Lovison et al., 2011). In order to obtain identi-
autocorrelation of shoots within location (Tomasello et al., 2007; Di fiable parameters, results were referred to the intercept, a baseline
Carlo et al., 2011; Lovison et al., 2011). The selection model process category which, in our case, was the rocky substratum. Finally, dif-
performed by Akaike Information Criterion for clustered data (AIC; ferences in frequencies distribution of leaves having lost their apex
Azari et al., 2006) led us to choose models with substratum among substrata were checked by non-parametric chi-square test.

3. Results

Overall, 175 orthotropic shoots, for a total of 1341 annual
rhizome segments, were analyzed using the lepidochronological
approach.

A preliminary exploratory analysis showed that the grand mean
of shoot age was 7.6 years, with evident heterogeneity across
different substrata varying from 1 to 38 years (Fig. 2). More spe-
cifically, shoots sampled on matte have a similar mean value to the
grand mean, while those sampled on a sandy or rocky substratum
show mean values above and below the central position
respectively.

3.1. Growth performance

Vertical growth of plants growing on rock was on average
8.2 Æ 0.7 mm/year/shoot (intercept), which resulted statistically
lower than growth estimated on sand and matte, with differences
of 6.0 Æ 2.7 and 2.4 Æ 0.9 mm/year/shoot respectively (P < 0.001)
(Table 1). The LMM used to model growth performance indicated

Table 1

Results from the best LMM and GLMM fit for the variables analyzed. For fixed effects in each variable the intercept coefficient (SE in bracket) represents the mean value
estimated on rock; the coefficients for sand and matte represent their deviation from rock; while the coefficient of shoot age is the expected variation for every year of aging.
Random effects, expressed as standard deviation, are variance components reflecting differences of fixed effects among locations (StdDev <1 Â 10À3 were set to zero). Variance
components not significant show no fixed effects variations among locations.

Effect Rhizome elongation Leaf production Shoot surface Leaf length Leaf width Shoot density
(mm/year/shoot) (n/year/shoot) (cm2/shoot) (cm) (cm) (n. shoots/m2)

Coefficient P Coefficient P Coefficient P Coefficient P Coefficient P Coefficient P

Fixed effects

Rock (Intercept) 8.22 (0.68) *** 8.27 (0.43) *** 243.88 (13.82) *** 56.34 (2.36) *** 0.93 (0.04) *** 222.27 (15.83) ***

Sand þ6.04 (2.69) * À0.21 (0.59) n.s. þ45.22 (19.02) * þ15.93 (3.28) *** À0.04 (0.05) n.s. þ100.16 (78.02) n.s.

Matte þ2.37 (0.85) ** À0.30 (0.54) n.s. þ113.57 (20.73) *** þ17.49 (2.93) *** þ0.04 (0.05) n.s. þ33.74 (45.65) n.s.

Shoot age (year) À0.45 (0.05) *** À0.04 (0.04) n.s. À3.68 (1.78) * À0.42 (0.31) n.s. 0.00 (0.00) n.s. e e

Random effects (StdDev)

Rock 0.97 *** 0.23 n.s. 0 n.s. 0 n.s. 0.07 n.s. 27.62 ***
0.49 0.01 0 0.04 53.44
Sand 5.06 0.20 19.19 0 0.06 86.84
GLMM LMM LMM LMM GLMM
Matte 0.72

Model LMM

Significance codes: ***P < 0.001; **P < 0.01; *P < 0.05; n.s. P > 0.05.