Shoot Biomass Assessments of the Marine Phanerogam <i>Zostera marina</i> for Two Methods of Data Gathering

doi:10.4236/ajps.2012.311186

Paper Menu >>

Journal Menu >>

American Journal of Plant Sciences, 2012, 3, 1541-1545

http://dx.doi.org/10.4236/ajps.2012.311186 Published Online November 2012 (http://www.SciRP.org/journal/ajps)

1541

Shoot Biomass Assessments of the Marine Phanerogam

Zostera marina for Two Methods of Data Gathering

Elena Solana-Arellano*, Héctor Echavarría-Heras, Victoria Díaz-Castañeda, Olga Flores-Uzeta

Marine Ecology Department, Ensenada Scientific and Higher Education Center, Baja California, México.

Email: *[email protected]

Received August 8th, 2012; revised September 16th, 2012; accepted October 10th, 2012

ABSTRACT

In order to compare to data gathering methods for shoot biomass assessments of Zostera marina, we compare two al-

lometric models each one representing a data gathering method, one at leaf level and the other in aggregated form. The

first allometric model presented leaf dry weight in terms of leaf length as .wl





 The second model is expressed as a

several-variables version of the allometric Equation (1) dry weight of each leaf in a given shoot can be considered to be

a random variable therefore shoot biomass ws can be represented in the form 1.







 Both models presented

similar determination coefficients values of 0.85 and 0.87 respectively. We found no significant differences between

parameters



(p = 0.11) and



(p = 0.50) fitted for each model, showing that both equations conduced to the same

result. Moreover, both fitted models presented high Concordance Correlation Coefficients of reproducibility (ˆ



) (0.92

and 0.91). We concluded that for shoot weight assessments if larger samples and faster data processing is required then

should model of Equation (2) be used. On the other hand, we proposed model of Equation (1) if data at leaf level is

required for other endeavors.

Keywords: Allometric Models; Aggregated Data; Leaf Dry Weight; Shoot Dry Weight

1. Introduction

Because of the valuable services that Zostera marina

meadows provide to shallow coastal ecosystems, [1-6]

accurate measurements of biomass or productivity of this

eelgrass are important for the study and modeling of such

environments. Since shoot biomass is the basic unit to

study production in the eelgrass Z. marina, many at-

tempts have been made to model biomass in terms of

other shoot characteristics as leaf length and width [7,8].

On the other hand, shoot biomass assessments for Z. ma-

rina are reported in a variety of methodologies, some at a

leaf level [7-11], and some in aggregated way [12,14].

Although aggregated data are sometimes easy and faster

to obtain, measurements cannot be used to fit models and

make comparisons with other data sets.

The importance of modeling seagrasses in terms of

other variables has been pointed out by several authors

[7,9,11,15-17]. One of the main features of modeling is

to calibrate non-destructive methods, that is, once the

goodness of fit of a particular model is tested to data, the

model can be used to predict the pertinent dependent

variable from one or several independent variables that

are obtained in a non-destructively way. In this paper we

prove that we can obtain robust allometric parameters

even if the data are collected at leaf level or an aggre-

gated form.

2. Materials and Methods

2.1. Data and Related Calculations

The data used for this study were collected from January

to December 2001 in a Z. marina meadow in Punta

Banda Estuary, located 23 km. south of Ensenada, Baja

California, Mexico at 31˚43'N-46'N and 116˚N37'W-

40'W. For a detailed description of the site see [10].

Since has been proven that for Zostera marina allometric

parameters are time invariant [8,10,18] we believe that a

hole year cycle is sufficient to compare the two methods.

At each sampling time t, using the Kentula and McIntire

method [19], approximately 20 shoots were marked bi-

weekly. Only complete leaves were used for the analysis.

Since Zostera marina present a ribbon like architecture

leaf length was measured from the tip to the ligula [see

[20]), width was measure at halfway of the length, this

measure of width has been proven to be the best repre-

sentative proxy of leaf width [20], dry weigh was also

*Corresponding author.

Shoot Biomass Assessments of the Marine Phanerogam Zostera marina for Two Methods of Data Gathering

1542

determined using standard methodology. For this study

only leaf length and dry weight were analyzed. Data

were then tested at a single leaf bases and in an aggre-

gated form and results were statistically compared. We

also calculated the Lin [21] Concorance Correlation Co-

efficient of reproducibility (ˆ



) for predicted and ob-

served values in each fitted model.

2.2. Formal Methods

Some authors ([7,8,10,11,15] among others), have proven

that leaf dry weight can be consistently represented al-

lometrically in terms of leaf length and/or leaf width or

area. They considered the allometric basic model

,wl





 (1)

were w and l represent the dry weight and length of a

single leaf respectively and



and



are parameters

to be fitted. That means that leaf dry weight can be rep-

resented in terms of leaf length.

On the other hand, when individual leaf dry weight is

not available and dry weight data is represented in an

aggregated form, that is, weight is obtained at a shoot

level, we cannot fit Equation (1). Nevertheless, the dry

weight of each leaf in a given shoot can be considered to

be a random variable and can thus be expressed as sev-

eral-variables version of the allometric Equation (1)

therefore shoot biomass

w can be represented in the

form



wll











 







(2)

where k denotes the length of the kth leaf and ns stands

for the number of leaves in the shoot under consideration.

Models of Equations (1) and (2) where fitted using stan-

dard nonlinear regression methods.

3. Results

For the whole annual cycle, we recovered 128 shoots

with 393 complete leaves. Table 1 shows basic statistic

for leaf length (l), dry weight (w) and shoot dry weight

w showing high variability on all of these variables.

Equation (1) was fitted at leaf level data with a deter-

mination coefficient of 0.85 and fitted parameters α =

1.19 ± 0.045 and β = 0.00002 ± 0.000008. Figure 1

shows predicted versus observed values of this fit. Sub-

sequently the Lin [19] Concordance correlation coeffi-

cient of reproducibility (ˆ



) was performed between ob-

served and predicted values for the fit of Equation (1)

finding a value of 0.92. Similarly, for measurements of

weights at a shoot level, the several-variable version of

Equation (1), (Equation (2)) was fitted using nonlinear

Table 1. basic statistics for leaf length, weight and shoot

weight.

Mean Min. Max. Std. Dev.

Length 188.09 4 517 124.7

Leaf dry weight0.015 0.0001 0.06 0.01

Shoot dry weight0.046 0.005 0.39 0.03

Figure 1. Leaf dry weight in terms of leaf length fitted by

Equation (1).

multiple regression finding a determination coefficient

and values for α = 1.17 ± 0.051 and β =

0.00003 ± 0.000009. The estimation errors for both fit-

tings were 0.00003 and 0.0002 respectively.

20.87R

The corresponding plot of predicted versus observed

values is shown in Figure 2. The Concordance correla-

tion coefficient of reproduciblity was of ˆ0.91



.

Residuals shown Normality and homoscesticity, al-

though dispersion apparently is bigger for residuals of

the fitting of Equation (1) (see Figure 3).

Since Equations (1) and (2) were both fitted using least

square method parameters, they are distributed normally

therefore we performed a t test between parameters find-

ing no significant differences between parameters with a

p-value of 0.11 for



and 0.50 for



. This demon-

strates that the fitted parameters in Equations (1) and (2)

are statistically the same with a 0.95 confidence level.

Moreover, using the Akaike information criterion (AIC)

[22] the AIC for Equation (1) is the minimum between

both fits with a value of −3660 and the AIC for the fitting

of Equation (2) the AIC = −1156.35 therefore since this

is less than 4 times the minimum (3.1) we have consider-

able support to consider it a good model for inference

purposes. Moreover using parameters found in Equations

(1) and (2) we projected mean shoot weight per month,

Figure 4 shows the comparison with observed values.

Shoot Biomass Assessments of the Marine Phanerogam Zostera marina for Two Methods of Data Gathering 1543

Figure 2. Predicted versus observed values of the fitting of

Equation (2) to shoot dry weight in terms lengths of leaves

in a shoot.

(a)

(b)

Figure 3. Distribution of residual of respective fittings (a)

allometric Equation (1); (b) Equation (2), which is a multi-

variate version of Equation (1).

(a)

(b)

Figure 4. Observed (dashed lines) and projected (continu-

ous lines) mean shoot weight per month. (a) By means of

allometric Equation (1) this is, at a leaf level (b) Using the

multivariate Equation (2), this is at a shoot level.

Residuals showed normality and homoscesticity, al-

though dispersion apparently is bigger for residuals of

the fitting of Equation (1) (see Figure 3).

4. Discussion

Body size affects the structure and functioning at all lev-

els of biological organization from individuals, popula-

tions, communities and ecosystems [23]. Related to body

size, is the allometry term used first by Huxley (1932 in

[23]) to describe the study of the relationship between

body size and other variables. The importance of al-

lometric relationships to describe and predict production/

biomass of seagrass communities have been used by

several authors [7-11,15]. Moreover, [24] present a com-

plete discussion on how application of allometric laws

prediction could benefit our understanding of estuaries

and coastal ecology. However, for Z. marina, sampling

Shoot Biomass Assessments of the Marine Phanerogam Zostera marina for Two Methods of Data Gathering

1544

and processing sufficient data to test a robust statistical

method, could be an extremely time consuming endeavor.

For that reason some authors use aggregated data or data

at a shoot level instead of data at a leaf level (non-ag-

gregated) to test differences of some measurements in

time and space [13]. Moreover, data gathering for eel-

grass assessments methods could be time consuming and

destructive. For example at a leaf level, each leaf in a

shoot should be counted, measured (length and width)

and weighted implying a enormous time of sample proc-

essing and for biomass (for example) a bigger error in

weighting each leaf separately.

On the other hand, aggregated data, could be easier to

obtain and present less error, but could not be used in

some models that require individual measurements, as

Equation (1).

We have demonstrated in this work, that for biomass

assessments a several-variables version of the allometric

Equation (1), Equation (2) where leaf dry weights are

aggregated at a shoot level gives the same results as the

assessments found for the fitting of Equation (1). We

found that parameters fitted for both models were statis-

tically the same with p = 0.11 for



and p = 0.50 for



The determination coefficients for both fittings were

also statistically the same (p > 0.05). Moreover Lin [19]

Concordance Correlation Coefficient of reproducibility

(ˆ



) attained exactly the same value for both fits (0.92),

and The AIC shows that both models deserve considera-

tion for statistical inference. Figure 4 shows that pro-

jected values of mean shoot biomass per month are al-

most identical and in a good correspondence with ob-

served values, therefore we consider that Equations (1)

and (2) can be used indistinctly for shoot biomass as-

sessments. Nevertheless, the fitting of Equation (1) gives

us the advantages of a smaller estimation error, but with

the disadvantage of bigger time consuming in data proc-

essing. Whereas in the fitting of Equation (2) processing

data is much less time consuming but have a slight

higher estimation error and a better disposition of residu-

als. Moreover, since the time of processing material in

aggregated form is much less time consuming, bigger

samples can be taken if necessary. In any case, regardless

of the type of data (aggregated or non-aggregated), the

allometric relationship between leaf or shoot dry weight

and leaf length is consistent for Zostera marina. In con-

clusion, for shoot weight assessments, we proposed

model of Equation (2) for large samples and faster data

processing and model of Equation (1) if data at leaf level

is required for other endeavors.

5. Acknowledgements

The authors thank Jose Maria Dominguez and Francisco

Ponce for the art work.

REFERENCES

[1] F. T. Short and C. A. Short, “The Seagrass Filter: Purifi-

cation of Coastal Water,” In: V. S. Kennedy, Ed., The

Estuary as a Filter, Academic Press, Orlando, 1984, pp.

395-413.

[2] G. W. Thayer, W. J. Kenworthy and M. S. Fonseca, “The

Ecology of Eelgrass Meadows of the Atlantic Coast: A

Community Profile,” US Fish and Wildlife Service Divi-

sion of Biological Services, FWS/OBS-84/02, No. 147,

1984.

[3] L. G. Ward, W. M. Kemp and W. R. Boynton, “The In-

fluence of Waves and Seagrass Communities on Sus-

pended Particulates in an Estuarine Embayment,” Journal

of Marine Geology, Vol. 59, No. 1-4, 1984, pp. 85-103.

doi:10.1016/0025-3227(84)90089-6

[4] M. S. Fonseca and J. S. Fisher, “A Comparison of Can-

opy Friction and Sediment Movement between Four Spe-

cies of Seagrass with Reference to Their Ecology and

Restoration,” Marine Ecology Progress Series, Vol. 29,

1986, pp. 15-22. doi:10.3354/meps029015

[5] T. P. Williams, J. M. Bubb and J. N. Lester, “Metal Ac-

cumulation within Salt Marsh Environment: A Review,”

Marine Pollution Bulletin, Vol. 28, No. 5, 1994, pp. 277-

290. doi:10.1016/0025-326X(94)90152-X

[6] K. L. Heck, K. W. Able, C. T. Roman and M. P. Fahay,

“Composition, Abundance, Biomass and Production of

Macrofauna in a New England Estuary: Comparison

among Eelgrass Meadows and Other Nursery Habitats,”

Estuaries, Vol. 18, No. 2, 1995, pp. 379-389.

doi:10.2307/1352320

[7] S. P. Hamburg and P. S. Homann, “Utilization of Growth

Parameters of Eelgrass, Zostera marina, for Productivity

Estimates under Laboratory and in Situ Conditions,” Ma-

rine Biology, Vol. 93, No. 2, 1986, pp. 299-303.

doi:10.1007/BF00508267

[8] E. Solana-Arellano, D. J. Brobon-Gonzalez and H. A.

Echavarria-Heras, “A General Allometric Model for Blade

Production in Zostera marina L.,” Bulletin of Southern

California Academy of Sciences, Vol. 97, 1998, pp. 39-

48.

[9] C. M. Duarte, “Temporal Biomass Variability and Pro-

duction/Biomass Relationships of Seagrass Communi-

ties,” Marine Ecology Progress Series, Vol. 51, 1989, pp.

269-276. doi:10.3354/meps051269

[10] H. Echavarria-Heras, K. S. Lee, E. Solana-Arellano and E.

Franco-Vizcaíno, “Formal Analysis and Evaluation of

Allometric Methods for Estimating Above-Ground Bio-

mass of Eelgrass,” Annals of Applied Biology, Vol. 159,

No. 3, 2011, pp. 503-515.

doi:10.1111/j.1744-7348.2011.00511.x

[11] E. Solana-Arellano, S. E. Ibarra-Obando and H. A. Echa-

varria-Heras, “Calibración de un Modelo Alométrico para

Evaluar la Producción Foliar de Zostera marina L.,”

Hidrobiológica, Vol. 1, 1991, pp. 41-44.

[12] K. Aioi, “Seasonal Change in the Standing Crop of Eel-

grass Zostera marina L. in Odawa Bay, Central Japan,”

Aquatic Botany, Vol. 8, 1980, pp. 343-354.

doi:10.1016/0304-3770(80)90064-9

Shoot Biomass Assessments of the Marine Phanerogam Zostera marina for Two Methods of Data Gathering

1545

[13] K.-S. Lee, S. R. Park and J.-B. Kim, “Production Dy-

namics of the Eelgrass, Zostera marina in Two Bay Sys-

tems on the South Coast of the Korean Peninsula,” Ma-

rine Biology, Vol. 147, No. 5, 2005. pp. 1091-1108.

doi:10.1007/s00227-005-0011-8

[14] W.-T. Li, J.-H. Kima, J.-I. Parka and K.-S. Lee, “Assess-

ing Establishment Success of Zostera marina Transplants

through Measurements of Shoot Morphology and Growth,”

Estuarine, Coastal and Shelf Science, Vol. 88, No. 3.

2010, pp. 377-384. doi:10.1016/j.ecss.2010.04.017

[15] C. M. Duarte, “Allometric Scaling of Seagrass Form and

Productivity,” Marine Ecology Progress Series, Vol. 77,

1991, pp. 289-300. doi:10.3354/meps077289

[16] M. E. Solana-Arellano, H. A. Echavarria-Heras and S. E.

Ibarra-Obando, “Leaf Size Dynamics for Zostera marina

L. in San Quintin Bay, Mexico: A Theoretical Study,”

Estuarine Coastal and Shelf Sciences, Vol. 44, No. 3,

1997, pp. 351-359. doi:10.1006/ecss.1996.0115

[17] T. M. Greve and D. Krause-Jensen, “Predictive Model-

ling of Eelgrass (Zostera marina) Depth Limits,” Marine

Biology, Vol. 146, No. 5, 2005, pp. 849-858.

doi:10.1007/s00227-004-1498-0

[18] H. Echavarria-Heras, E. Solana-Arellano and E. Franco-

Vizcaíno, “An Allometric Method for the Projection of

Eelgrass Leaf Biomass Production Rates,” Mathematical

Biosciences, Vol. 223, No. 1, 2010, pp. 58-65.

doi:10.1016/j.mbs.2009.10.008

[19] M. E. Kentula and C. D. McIntire, “The Autoecology and

Production Dynamics of Eelgrass (Zostera marina L.) in

Netarts Bay, Oregon,” Estuaries, Vol. 9, No. 3, 1986, pp.

188-199. doi:10.2307/1352130

[20] H. Echavarria-Heras, E. Solana-Arellano, C. Leal-Ramirez

and E. Franco-Vizcaíno, “The Length-Times-Width Proxy

for Leaf Área of Eelgrass: Criteria for Evaluating the

Representativeness of Leaf-Width Measurements,” Aqua-

tic Consertation: Marine and Freshwater Ecosystems,

Vol. 21, No. 7, 2011, pp. 604-613.

doi:10.1002/aqc.1219

[21] L. I.-K. Lin, “A Concordance Correlation Coefficient to

Evaluate Reproducibility,” Biometrics, Vol. 45, No. 1,

1989, pp. 255-268. doi:10.2307/2532051

[22] H. Akaike, “An New Look at the Statistical Model Identi-

fication,” IEEE Transactions on Autimatic Control, Vol.

19, No. 6, 1974, pp. 716-723.

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnu

mber=1100705&contentType=Journals+%26+Magazines

&queryText%3DAn+New+Look+at+the+Statistical+Mod

el+Identification

[23] K. J. Anderson-Teixeira, Van M. Savage, A. P. Allen and

J. F. Gillooly, “Allometry and Metabolic Scaling in:

Ecology,” Encyclopedia of Life Sciences (ELS), John

Willey & Sons Ltd., Chichester, 2009.

doi:10.1002/978047001592.a0021222.

[24] L. A. Harris, C. M. Duarte and S. W. Nixon, “Allometric

Laws and Prediction in Estuarine and Coastal Ecology,”

Estuaries and Coasts, Vol. 29, No. 2, 2006, pp. 340-344.

doi:10.1007/BF02782002